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https://www.physicsforums.com/threads/ac-direction-change-how-does-electricity-flow.815478/
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# AC direction change - how does electricity flow?
Tags:
1. May 24, 2015
### matilda
If drift velocity of electrons changes in AC, how does electricity flow through a circuit to then lose potential energy to the devices in the circuit?
Also considering the change in direction, does that mean that the live wire and neutral wire also switch roles in AC mains? I am very confused about this.
2. May 24, 2015
### theodoros.mihos
A wire is something like a line with charge carriers and all rest world with no carriers. This is like an 1D world for electric field, even wire may have complex shape. The energy that these field carriers transfer to a positive charge q on the wire:
$$dW = dF\,dx = -E\,q\,dx$$
that mean the electric field give energy to q for all period, because E and dx change direction together.
Confusion comes for using DC terms to solve AC circuits but devices work differntial on AC or DC voltage. i.e. a capacitor has infinity resistance on DC and 1/ωC on AC, and this "resistance" differs to Ohmic resistance nature.
3. May 24, 2015
### Staff: Mentor
You will find elecricity much easier to understand if you forget about drift velocity and analogies to massive particle kinetic and potential energies.
Imagine a person holding the ends of a rope wrapped around a remote pulley. He moves the rope back and forth, causing the axle of the pulley to heat because of friction. The person is transmitting energy to a remote location in a manner analogous to AC electricity. But the molecules in the rope are not drifting at all, nor are their kinetic or potential energies important.
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https://www.studypug.com/sg/statistics/normal-distribution-and-z-score/z-scores-and-random-continuous-variables
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# Z-scores and random continuous variables
### Z-scores and random continuous variables
#### Lessons
• Introduction
a)
b)
• 1.
Translating Normal Distribution to Standard Normal Distribution
The heights of a population of women are normally distributed. The mean height is 164 cm with a standard deviation of 8 cm. What is the probability of a randomly selected woman who is shorter than 169 cm in this population?
• 2.
The age at which a group of children first started talking is normally distributed. The data set has a mean of 18 months and a standard deviation of 2.3 months. What is the percentage of this group of children who first started talking between 15 and 24 months?
• 3.
Finding Raw Data from Z-Scores
An environmental group did a survey on how much water a population consumed when taking shower and bath. It was found that the amount of water consumption is normally distributed with a mean value of 65 liters and a standard deviation of 4.3 liters. What is the amount of water that separates the least 90% from the most 10%?
• 4.
A school wanted to find out the physical fitness of its students. All students were asked to run for 400 meters on the track as fast as they could, and their finishing times were recorded. The distribution of the finishing times is normal. The mean finishing time is 75 seconds and the standard deviation is 5.5 seconds. What is the finishing time that represents the slowest 85% of students?
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http://math.stackexchange.com/users/24451/bravo?tab=questions
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# Bravo
less info
reputation
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bio website location London, United Kingdom age 26 member for 2 years, 1 month seen 12 hours ago profile views 297
Garam masala.
# 37 Questions
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### Number of possible crosswords
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### A problem in stochastic optimisation
jun 1 '12 at 9:38 Bravo 1,654
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### Sampled or discretised Gaussian Random Variables
mar 15 '12 at 9:13 Bravo 1,654
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### How to interpret positive eigenvector of $A$ in $\frac{dx}{dt}=Ax$?
feb 27 at 19:04 Bravo 1,654
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### Non-zero solutions to $B(p+p^2+p^3+\ldots)=Ap$
jan 15 at 17:17 Bravo 1,654
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### Proof of corollary of Farkas' lemma
oct 19 at 17:10 Bravo 1,654
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https://math.stackexchange.com/questions/3435599/given-a-function-f-check-if-it-is-lebesgue-integrable
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# Given a function f, check, if it is Lebesgue integrable.
I'm not sure if my attempt is fruitful or not. The exercise is as follows:
Given the function $$f: [0,1] \rightarrow \mathbb{R} \cup \{\infty\}$$, $$~f(x) := \frac{1}{\sqrt(x)}$$, $$x \neq 0$$ and $$f(x) := \infty$$, $$~x = 0$$.
Check if f is Lebesgue-integrable.
My assumption is, that $$f$$ is not integrable (although it is measurable). The reason is, that for $$x \rightarrow 0$$ the convergence rate of f towards the y-axis is not fast enough.
($$\textbf{Question 1:}$$ Is there a way to put my very rough and possibly wrong estimation into more mathematical terms?)
Since f(x) $$\geq 0$$ for each $$x\in [0,1]$$, I want to show, that there exists a measurable simple function $$s,$$ $$0\le s\le f$$, such that sup{$$\int_{_{[0,1]}}s ~d\lambda$$ : $$s$$ integrable } $$=\infty$$.
($$\textbf{Question 2:}$$ Is it enough to show this?)
Let $$I_k := [\frac{1}{k+1},\frac{1}{k}]$$ and $$s_n := \sum_{k=1}^n \sqrt{k} ~~\chi_{_{I_k}}$$. Then for each $$n\in \mathbb{N}$$ the inequality $$0 \leq s_n \leq f(x)$$ holds.
To make this a little bit shorter: In the following I would show, that the inequality $$\int_{_{[0,1]}}s_{2n} ~d\lambda - \int_{_{[0,1]}}s_n ~d\lambda \geq \frac{1}{2}$$ holds. Next I'd conclude, that the growing sequence $$\{ \int_{_{[0,1]}}s_n ~d\lambda \}_{n\in \mathbb{N}}$$ converges to $$\infty$$, such that the supremum of this sequence would be $$\infty$$.
• This $f$ is Lebesgue integrable. The value at a single point $x=0$ is irrelevant.
– RRL
Nov 14 '19 at 17:50
Since Lebesgue and Riemann integrals coincide on bounded intervals where the function is Riemann integrable and using the monotone convergence theorem,
$$\int_{(0,1]} x^{-1/2} = \lim_{n \to \infty} \int_{(0,1]}x^{-1/2}\chi_{[1/n,1]}= \lim_{n \to \infty}\int_{1/n}^1 x^{-1/2} \, dx = 2 - \lim_{n \to \infty}\frac{2}{\sqrt{n}} = 2$$
Along the lines of your attempt, we can also consider the sequence of simple functions,
$$\phi_n(x) = \sum_{k=1}^{2^{n}}(k2^{-n})^{-1/2}\chi_{[(k-1)2^{-n}, k{2^{-n}}]}(x)$$
Again applying the MCT we have
$$\int_{(0,1]}x^{-1/2}=\lim_{n \to \infty}\int_{(0,1]}\phi_n= \lim_{n \to \infty}\sum_{k=1}^{2^{n}}(k2^{-n})^{-1/2}\lambda([(k-1)2^{-n},k{2^{-n}}])\\= \lim_{n \to \infty}\frac1{\sqrt{2^n}}\sum_{k=1}^{2^n}\frac1{\sqrt{k}}= \lim_{n \to \infty}\frac1{\sqrt{n}}\sum_{k=1}^{n}\frac1{\sqrt{k}}=2.$$
• Recall that MCT states if $f_n$ is a montonically increasing sequence of measurable functions and $\int_A f_n$ is bounded for all $n$, then $f_n$ converges a.e to an integrable function $f$ such that $\int_A f_n \to \int_A f$.
– RRL
Nov 14 '19 at 17:58
• I see my mistake. Naively I was under the impression that the given function behaves similarly to $\frac{1}{x}$ for $x\in (0,1]$, for which the Lebesgue integral does not exist. In a sense, the "rate of asymptotic convergence" of such functions seems to play a role or better: The uniform continuity, which of course has a connection to the existence of the Riemann integral of unbounded functions. Please correct me if I'm wrong. Thanks for your help! Nov 14 '19 at 22:21
• @JtSpKg: You're welcome. Yes there is a connection to improper Riemann integrals of unbounded functions. If a nonnegative function is improperly Riemann integrable then it is Lebesgue integrable.
– RRL
Nov 14 '19 at 23:48
• One more question. Why does the sum run to $2^{-n}$? Shouldn’t it be $2^n$ instead? Nov 15 '19 at 8:47
• Yes it should be $2^n$. Will edit.
– RRL
Nov 15 '19 at 16:32
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https://cris.bgu.ac.il/en/publications/demand-aware-network-designs-of-bounded-degree-5
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# Demand-aware network designs of bounded degree
Chen Avin, Kaushik Mondal, Stefan Schmid
Research output: Contribution to journalArticlepeer-review
3 Scopus citations
## Abstract
Traditionally, networks such as datacenter interconnects are designed to optimize worst-case performance under arbitrary traffic patterns. Such network designs can however be far from optimal when considering the actual workloads and traffic patterns which they serve. This insight led to the development of demand-aware datacenter interconnects which can be reconfigured depending on the workload. Motivated by these trends, this paper initiates the algorithmic study of demand-aware networks, and in particular the design of bounded-degree networks. The inputs to the network design problem are a discrete communication request distribution, D, defined over communicating pairs from the node set V, and a bound, Δ, on the maximum degree. In turn, our objective is to design an (undirected) demand-aware network N= (V, E) of bounded-degree Δ, which provides short routing paths between frequently communicating nodes distributed across N. In particular, the designed network should minimize the expected path length on N (with respect to D), which is a basic measure of the efficiency of the network. We derive a general lower bound based on the entropy of the communication pattern D, and present asymptotically optimal demand-aware network design algorithms for important distribution families, such as sparse distributions and distributions of locally bounded doubling dimensions.
Original language English 311-325 15 Distributed Computing 33 3-4 https://doi.org/10.1007/s00446-019-00351-5 Published - 1 Jun 2020
## ASJC Scopus subject areas
• Theoretical Computer Science
• Hardware and Architecture
• Computer Networks and Communications
• Computational Theory and Mathematics
## Fingerprint
Dive into the research topics of 'Demand-aware network designs of bounded degree'. Together they form a unique fingerprint.
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https://www.physicsforums.com/threads/universal-gravitation-10-determine-the-rate.614922/
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# Universal gravitation 10- Determine the rate
1. Jun 18, 2012
### dani123
1. The problem statement, all variables and given/known data
As the Earth revolves around the sun, if not only travels a certain distance every second, it also causes an imaginary line between the Earth and the sun to pass through a certain area every second. During one complete trip around the sun, the total area would be approximately equal to ∏R2. The time it would take to do this would be the period, T. Determine the rate at which the area is swept by an imaginary line joining the sun and the Earth as the Earth orbits the sun. Use the Earth's period of 365 days and the mean orbital radius of 1.50x1011.
2. Relevant equations
I have made a list of equations that are relevant for this entire module on universal gravitation. So although there are many of them does not mean that they all apply in this circumstance. The ones relevant to this question will be placed in bold.
Kepler's 3rd law: (Ta/Tb)2=(Ra/Rb)3
motion of planets must conform to circular motion equation: Fc=4∏2mR/T2
From Kepler's 3rd law: R3/T2=K or T2=R3/K
Gravitational force of attraction between the sun and its orbiting planets: F=(4∏2Ks)*m/R2=Gmsm/R2
Gravitational force of attraction between the Earth and its orbiting satelittes: F=(4∏2Ke)m/R2=Gmem/R2
Newton's Universal Law of Gravitation: F=Gm1m2/d2
value of universal gravitation constant is: G=6.67x10-11N*m2/kg2
weight of object on or near Earth: weight=Fg=mog, where g=9.8 N/kg
Fg=Gmome/Re2
g=Gme/(Re)2
determine the mass of the Earth: me=g(Re)2/G
speed of satellite as it orbits the Earth: v=√GMe/R, where R=Re+h
period of the Earth-orbiting satellite: T=2∏√R3/GMe
Field strength in units N/kg: g=F/m
Determine mass of planet when given orbital period and mean orbital radius: Mp=4∏2Rp3/GTp2
3. The attempt at a solution
I highlighted the above equation because I think I am supposed to use this equation for this problem. But I honestly don't understand what this question is actually looking for, so if someone could let me know where I should even begin it would be greatly appreciated! Thank you so much in advance!
2. Jun 18, 2012
### tiny-tim
hi dani123!
sorry, but all the equations you have listed are irrelevant
this is just geometry …
you're given the values of R and T, and you're asked to find the area per time
start with an easy case … what is the area after time T?
Similar Discussions: Universal gravitation 10- Determine the rate
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http://math.stackexchange.com/questions/105378/prove-lim-x-to-infty-sum-1-infty-fracx21n2x2-sum-1-inf
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Prove: $\lim _{x \to \infty}\sum_{1}^{\infty}\frac{x^2}{1+n^2x^2}=\sum_{1}^{\infty}\frac{1}{n^2}$
I want to ask you if can it be so simple to prove that $\lim _{x \to \infty}\sum_{1}^{\infty}\frac{x^2}{1+n^2x^2}=\sum_{1}^{\infty}\frac{1}{n^2}$ by divide the numerator and denominator with $x^2$ and that's it?
If it this simple indeed you can write a comment and I'll delete the question after I'll read it, or perhaps I'm missing something important (and I should involve power series).
Thanks!
-
I think it is not enough. For any $x$, the sum with the $x$ stuff is certainly less than $\sum 1/n^2$. But we need to show that for $x$ large, the sum is very little less. So I would take the difference between $1/n^2$ and the same term with the $x$ stuff, and show that for $x$ large the sum of these differences is small. Details should not take too long! I don't see as simple an argument using power series. – André Nicolas Feb 3 '12 at 18:52
I suggest you check math.stackexchange.com/questions/105487/… – Pedro Tamaroff Feb 4 '12 at 0:47
It is always very tempting to want to interchange the series limit and the limit on $x$, but we have to resist the temptation! It is very important to consider uniform convergence (which is one of the main properties that makes power series so very awesome). – Aru Ray Feb 4 '12 at 2:32
Use $$\frac{1}{n^2} \frac{x^2}{1+x^2} \leqslant \frac{1}{n^2} \frac{x^2}{x^2 + n^{-2}} < \frac{1}{n^2}$$ Thus $$\frac{x^2}{1+x^2} \sum_{n=1}^\infty \frac{1}{n^2} \leqslant \sum_{n=1}^\infty \frac{x^2}{n^2+x^2} < \sum_{n=1}^\infty \frac{1}{n^2}$$ Both upper and the lower bounds have the same limit as $x \to \infty$.
$\lim_{x \to \infty} \sum_{n=1}^\infty f_n(x) = \sum_{n=1}^\infty \lim_{x \to \infty} f_n(x)$, even when both sides converge. It is true for dominated convergence (if there is some convergent series $\sum_{n=1}^\infty b_n$ with $|f_n(x)| \le b_n$ for all $n$ and $x$) and monotone convergence (if $f_n(x)$ is positive, and increasing as a function of $x$). This example satisfies both conditions.
$$\sum \left( \frac{1}{n^2} - \frac{x^2}{1+n^2x^2} \right) = \sum \frac{ 1}{n^2(1+n^2 x^2) } \leq \frac{1}{x^2} \sum \frac{1}{n^4} \to 0.$$
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https://space.stackexchange.com/questions/25417/applying-secondary-orbital-perturbation-effects
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# Applying secondary orbital perturbation effects
I read about secondary effects which influence on orbit propagation like solar radiation, moon, etc. (https://en.wikipedia.org/wiki/Orbit_modeling). First I calculate position vector Rpqw to object (artificial satellite) using 6 orbit elements with following formulas:
u = v + ω
r = a*(1-e*e)/(1+e*cos(v))
p = r * cos(v)
q = r * sin(v)
w = 0.0
RotationMatrix = R3(-Ω)R1(-i)R3(- ω)
Rijk = RotationMatrix * Rpqw
Where:
U – latitude argument
r – distance to object
Rijk – coordinates of object in 3D space in ECI coordinate system (a.k.a. IJK - axis)
a - semimajor axis
i - inclination
Ω - right ascension of the ascending node
ω - argument of perigee
v - true anomaly
I want to know when I must apply effects like solar radiation pressure or atmospheric drag and others, after I calculate Rijk or during the process? And does the applying order matter?
• +1 I'd never heard of Gauss' Planetary Equations before, but they seem quite useful! Great answer. – uhoh Feb 16 '18 at 23:28
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https://rd.springer.com/chapter/10.1007%2F978-3-030-05057-3_35
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• Xin Long
• Jigang Wu
• Long Chen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11336)
## Abstract
Multiple access mobile edge computing is an emerging technique to bring computation resources close to end mobile users. By deploying edge servers at WiFi access points or cellular base stations, the computation capabilities of mobile users can be extended. Existing works mostly assume the remote cloud server can be viewed as a special edge server or the edge servers are willing to cooperate, which is not practical. In this work, we propose an edge-cloud cooperative architecture where edge servers can rent for the remote cloud servers to expedite the computation of tasks from mobile users. With this architecture, the computation offloading problem is modeled as a mixed integer programming with delay constraints, which is NP-hard. The objective is to minimize the total energy consumption of mobile devices. We propose a greedy algorithm with approximation radio of $$(1+\varepsilon )$$ as well as a simulated annealing algorithm to effectively solve the problem. Extensive simulation results demonstrate that, the proposed greedy algorithm can achieve the same application completing time budget performance of the Brute Force optional algorithm with only 31% extra energy cost.
## Keywords
Mobile edge computing Cooperate Greedy algorithm Remote cloud Task dependency
## Notes
### Acknowledgment
This work was supported by the National Natural Science Foundation of China under Grant Nos. 61702115 and 61672171, Natural Science Foundation of Guangdong, China under Grant No. 2018B030311007, and Major R&D Project of Educational Commission of Guangdong under Grant No. 2016KZDXM052. This work was also supported by China Postdoctoral Science Foundation Fund under Grant No. 2017M622632. The corresponding author is Jigang Wu ([email protected]).
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Chen, L., Wu, J., Zhou, G., Ma, L.: QUICK: QoS-guaranteed efficient cloudlet placement in wireless metropolitan area networks. J. Supercomput. 74, 1–23 (2018).
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Chen, M.H., Dong, M., Liang, B.: Joint offloading decision and resource allocation for mobile cloud with computing access point. In: IEEE International Conference on Acoustics, Speech and Signal Processing, pp. 3516–3520 (2016)Google Scholar
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Chen, M.H., Liang, B., Dong, M.: Joint offloading and resource allocation for computation and communication in mobile cloud with computing access point. In: INFOCOM 2017 IEEE Conference on Computer Communications, pp. 1–9. IEEE (2017)Google Scholar
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Ding, L., Melodia, T., Batalama, S.N., Matyjas, J.D.: Distributed routing, relay selection, and spectrum allocation in cognitive and cooperative ad hoc networks. In: Sensor Mesh and Ad Hoc Communications and Networks, pp. 1–9 (2010)Google Scholar
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Dinh, T.Q., Tang, J., La, Q.D., Quek, T.Q.S.: Offloading in mobile edge computing: task allocation and computational frequency scaling. IEEE Trans. Commun. 65(8), 3571–3584 (2017)Google Scholar
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Guo, S., Xiao, B., Yang, Y., Yang, Y.: Energy-efficient dynamic offloading and resource scheduling in mobile cloud computing. In: IEEE INFOCOM 2016 the IEEE International Conference on Computer Communications, pp. 1–9 (2016)Google Scholar
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Hu, Y.C., Patel, M., Sabella, D., Sprecher, N., Young, V.: Mobile edge computing. A key technology towards 5G. ETSI White Paper 11(11), 1–16 (2015)Google Scholar
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Kao, Y.H., Krishnamachari, B., Ra, M.R., Fan, B.: Hermes: Latency optimal task assignment for resource-constrained mobile computing. In: IEEE Conference on Computer Communications (ICC), pp. 1894–1902 (2015)Google Scholar
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Lyu, X., Tian, H., Ni, W., Zhang, Y., Zhang, P., Liu, R.P.: Energy-efficient admission of delay-sensitive tasks for mobile edge computing. IEEE Trans. Commun. 66, 2603–2616 (2018).
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Park, C.B., Park, B.S., Uhm, H.J., Choi, H., Kim, H.S.: IEEE 802.15.4 based service configuration mechanism for smartphone. IEEE Trans. Consum. Electr. 56(3), 2004–2010 (2010).
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Rao, L., Liu, X., Ilic, M.D., Liu, J.: Distributed coordination of internet data centers under multiregional electricity markets. Proc. IEEE 100(1, SI), 269–282 (2012).
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http://uncyclopedia.wikia.com/wiki/Uncyclopedia:VFH/Complete_list_of_applications_of_trigonometry_in_today's_society
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# Uncyclopedia:VFH/Complete list of applications of trigonometry in today's society
## Complete list of applications of trigonometry in today's society (history, logs) (feature) (remove)
Score: 10 readers looking for applicable meaning in their life. Nominated by: 16:54, 26 April 2010 For: 10 Nom+For. Because I absolutely hate lists. 16:54, 26 April 2010 For. A list that ends with only two items is a happy list indeed. mAttlobster. (hello) 20:11, April 26, 2010 (UTC) It's okay. TKFUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUCK 10:00, April 27, 2010 (UTC) For. Because you can't spell "sign" without "sin." Genius! Striker2117 23:31, April 27, 2010 (UTC) $For!$ Because anyone can tell you that suspension bridges are made possible by magic and magic alone. —The preceding unsigned comment was added by Happytimes (talk • contribs) For. The end entirely, completely summarized my feelings about math in general. I approve. —Pelozurian (talk) 03:37, 1 May 2010 (UTC) For! Noooo, don't undermine our suspension bridges. Love, 03:57, May 3, 2010 (UTC) For. per above. Mn-z 15:13, May 3, 2010 (UTC) For. After some thought, feature this shit, I hate math! -- GUN WotM RotM FBotM VFH SK Maj. ΥΣΣ 00:54 EST 6 May, 2010 For. Because Maths is plural. --Sog1970 15:14, May 6, 2010 (UTC) Against: 0 No against votes Comments Comment. Jumps around like a kangeroo...can't decide on this. RomArtus*Imperator ® (Orate) 21:29, May 2, 2010 (UTC)
VFH
Click to feature this article Always check the feature queue first. Note: the queue slot won't be properly filled until the {{FA}} code (with correct date) is on the article.Just follow the instructions if you're unsure.
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https://link.springer.com/article/10.1007/s11192-011-0454-2?error=cookies_not_supported&code=43f543bb-e6e1-4e3f-9b8b-4b1121f49ff1
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# Assessing the value of patent portfolios: an international country comparison
## Abstract
Patent counts have been extensionally used to measure the innovative capacities of countries. However, since economic values of patents may differ, simple patent counts may give misleading rankings, if the patents of one country are on average more valuable than those of another. In the literature several methods have been proposed, which shall adjust for these differences. However, often these do not possess a solid economic micro-foundation and therefore are often ad-hoc and arbitrary procedures. In this paper, we intend to present an adjustment method that is based on the analysis of renewal decisions. The method builds on the theoretical model used in Schankerman and Pakes (1986) and Besson (2008) but goes beyond both approaches in that it recovers the important long tail of the value distribution. It also transfers Besson’s (2008) econometric methodology (applicable to the organisational structures of the US Patent and Trademark Office) also to the European Patent Office which is necessary, since each application here may split up into several national patent documents. The analysis is performed for 22 countries. Exemplarily, we find that in the cohort of 1986 patent applications, Danish patents are about 60% more valuable than the average patent. German patents are a bit below average. Japanese patents are of least value. In the cohort of 1996, Danish patents lose some of their lead but are still more valuable than the average. While German are a bit above average, Japanese patents even fall further behind (possibly due to the economic downturn in since the mid of 1990ies).
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## Notes
1. 1.
The most important difference is that his formulae depend on a hard to measure rate of depreciation rate. This actually occurs also in formulae 3 and 5, but it drops out, when we focus on the patent value instead on the return rate.
2. 2.
There is probably no use in employing more recent data, because the majority of patents expire after 13–14 years (see Table 2). Moving closer to the present will therefore result in a severe increase of the share of censored patent values.
3. 3.
Note that Bessen focuses on the initial return rate. But since this is a somewhat fuzzy concept, we prefer rather to make assumption about the patent value.
4. 4.
Note, however, one subtlety. We do not impose a fixed censoring limit (for example the observed initial return rate is censored, if it takes a value y), but we allow patents to have different censoring values. This more general statement is necessary, because the total renewal costs and thus the according patent values differ by patent office.
5. 5.
This number should roughly correspond to the number of patents that were finally granted, because the number of patents that were granted by the EPO but never appeared at European Patent office should be low.
6. 6.
The latest ISI high-tech list (Legler and Frietsch 2007) provides a classification of both sectors (based on NACE) and goods (based on SITC) according to their technology-intensiveness. Based on the SITC goods classification a concordance to the International Patent Classification (IPC) can be constructed. This concordance table contains 35 particularly technology-intensive fields. The dummies used on this study are fractionalised, which results from the fact that each patent can have several IPC classifications. Suppose for example that a patent has two classification in high-tech-field 1 (HT1), one classification in high-tech-field 2 (HT2) and one classification in a field that does not belong to the ISI high-tech list (LOWTECH), the fractionalised dummy for HT1 would be 0.5, for HT2 it would be 0.25 and for LOWTECH 0.25. The sum over all dummies is therefore unity.
7. 7.
This number is quite large, because the Inpadoc family does not only contain patent documents at different national offices referring to the same invention but also different patents that somehow belong together, e.g., when patents are split up later on in the patenting process.
8. 8.
If we do that by country, e.g., for France, then μ and $$\sigma_{x\beta }^{2}$$ are replaced with the corresponding mean and variance in the subsample of French patents.
9. 9.
We should note, however, that using the value adjustment factors to reweight simple patent counts is retrospective, in that they extrapolate structures from the past: they critically depend on both the explanatory variables x as well as the estimated coefficients β. Therefore, whenever either the distribution of the explanatory variables in one country changes (e.g. French patents may be cited more frequently) or the structure of the regression model expressed by the coefficients changes, then the value adjustment factor needs to be re-estimated. In any case, looking at Table 3 tells us that coefficients appear to not to change excessively. Thus, it seems not too critical to extrapolate them to the present. More likely is that changes in the distributions of the explaining variables account for differences in the value adjustment factor. If we, for example, would like to deduce the VAF for patents with priority year 2005, we could take the coefficients from the regression model corresponding to the data from 1996. We would then use them to derive predicted values for 2005. With these at hand, we again use Eq. 2 to derive value adjustment factor. This procedure clearly implies the constancy of coefficients but it allows for changes in the distributions of the explaining factors. In any case, we cannot exclude the existence of a structural change after 1996. It is well known that this is the time of the patent-surge, which might have induced more severe changes in the regression model. However, this remains to be seen when more recent data becomes available.
## References
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4. Blind, K., Edler, J., Frietsch, R., & Schmoch, U. (2006). Motives to patent empirical evidence from Germany. Research, 35, 655–672.
5. Davison, A. C., & Hinkley, D. V. (1997). Bootstrap methods and their application. Cambridge: Cambridge University Press.
6. De la Potterie, B. V., & van Zeebroeck, N. (2008). A brief history of space and time: The scope-year index as a patent value indicator based on families and renewals. Scientometrics, 75, 319–338.
7. Eaton, J., Kortum, S., Lerner, J. (2004). International patenting and the European patent office: A quantitative assessment. Patents, innovation and economic performance: OECD conference proceedings (pp. 27–52), Paris.
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9. Gambardella, A., Harhoff, D., & Verspagen, B. (2008). The value of European patents. European Management Review, 5, 69–84.
10. Grimpe, C., Hussinger, K. (2008). Building and blocking the two faces of technology acquisition, ZEW-discussion paper, no. 08-042. Mannheim: Centre for European Economic Research.
11. Grönqvist, C. (2009). The private value of patents by patent characteristics evidence from Finland. Journal of Technology Transfer, 34, 159–168.
12. Grupp, H., Legler, H., Jungmittag, A., Schmoch, U. (2000). Hochtechnologie 2000. Neudefinition der Hochtechnologie für die Berichterstattung zur technologischen Leistungsfähigkeit. Deutschlands: Karlsruhe/Hannover Fraunhofer ISI.
13. Hall, B. W., Jaffe, A., & Trajtenberg, M. (2005). Market value and patent citations. The Rand Journal of Economics, 36, 16–38.
14. Harhoff, D., Narin, F., Scherer, F. M., & Vopel, K. (1999). Citation frequency and the value of patented inventions. Review of Economics and Statistics, 81, 511–515.
15. Harhoff, D., Scherer, F. M., & Vopel, K. (2003). Citations, family size, opposition and the value of patent rights. Research Policy, 32, 1343–1363.
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20. Merges, R. P. (1999). As many as six impossible patents before breakfast property rights for business concepts and patent system reform. Berkeley Technology Law Journal, 14, 577–616.
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## Acknowledgments
Financial project support of the German Expert Commission Research and Innovation for the work underlying this article is kindly acknowledged. Helpful comments on an earlier version of this article from the 10th EPO-PATSTAT Conference in Vienna are also acknowledged. I am grateful to Nicolai Mallig for the help that he provided on collecting the necessary patent data from the PATSTAT database. Lastly, I would also like to thank an anonymous referee for his valuable suggestions that helped to improve the article.
## Author information
Authors
### Corresponding author
Correspondence to Torben Schubert.
## Appendix
### Appendix
Define $$\bar{r}_{j}$$ to be the initial return rate associated with a specific patent. The return rate can basically measure any return, no matter if they accrue from selling a protected product or blocking a competitor. Assume that the (non-discounted) return rate at a future point in time τ > 0 can be calculated by $$\overline{{r_{j} }} \cdot \text{e}^{ - d\tau }$$, where d ≥ 0 is a deprecation rate. That is we assume that returns resulting from a patent are exponentially damped. Suppose that there are discrete points in time t i , i = 1, 2,…K, where the owner of a patent has to decide, whether he wants to renew. Denote by PV j the total value of patent j and by PV i,j the return that is attributable to the period [t i , t i+1], that is between any two dates, where renewal decisions are necessary. Letting r m be the internal rate of return (possibly but not necessarily equal to observable interest rates), then we can calculate the net present value of a patent accruing to the period [t i , t i+1] as follows:
\begin{aligned} PV_{j,i} &= \int\limits_{{\tau = t_{i}}}^{{t_{i + 1} }} {\overline{{r_{j} }} {e}^{{ - \left( {r^{m} + d}\right)\tau }} d\tau }\\ &= \overline{{r_{j} }} \left({\int\limits_{\tau = 0}^{\infty } {{e}^{{ - \left( {r^{m} + d}\right)\tau }} } d\tau - \int\limits_{{\tau = t_{i + 1} }}^{\infty} {{e}^{{ - \left( {r^{m} + d} \right)\tau }} } d\tau -\int\limits_{\tau = 0}^{{t_{i} }} {{e}^{{ - \left( {r^{m} + d}\right)\tau }} } d\tau } \right)\\ &= \overline{{r_{j} }}\left( {\int\limits_{\tau = 0}^{\infty } {{e}^{{ - \left( {r^{m} +d} \right)\tau }} } d\tau - \int\limits_{{\tau = t_{i + 1}}}^{\infty } {{e}^{{ - \left( {r^{m} + d} \right)\tau }} } d\tau -\int\limits_{\tau = 0}^{\infty } {{e}^{{ - \left( {r^{m} + d}\right)\tau }} } d\tau + \int\limits_{{\tau = t_{i} }}^{\infty }{{e}^{{ - \left( {r^{m} + d} \right)\tau }} } d\tau } \right)\\&= \overline{{r_{j} }} \left( {\int\limits_{{\tau = t_{i}}}^{\infty } {{e}^{{ - \left( {r^{m} + d} \right)\tau }} } d\tau -\int\limits_{{\tau = t_{i + 1} }}^{\infty } {{e}^{{ - \left({r^{m} + d} \right)\tau }} } d\tau } \right)\\ &=\overline{{r_{j} }} \left( {\frac{{{e}^{{ - r^{m} t_{i} }} -{e}^{{ - r^{m} t_{i + 1} }} }}{{r^{m} + d}}} \right)\\\end{aligned}
(3)
Because the returns are steadily decreasing in time (by assumption) and the renewal fees are steadily increasing (as a matter of fact), a patent is renewed, if and only if $$PV_{j,i} \ge c_{i} \text{e}^{{ - r^{m} t_{i} }}$$, where c i is the renewal fees to be paid in period i.
Now, suppose a patent is renewed in time t * but not in the next period, we trivially have $$PV_{j,i^{*} } \ge c_{i^{*} } \text{e}^{{ - r^{m} t_{j,i^{*}} }}$$ and $$PV_{j,i^{*} + 1} \le c_{i^{*} + 1} \text{e}^{{ - r^{m} t_{j,i^{*} + 1} }}$$. Therefore, if the periods t i and t i+1 are close together, then both PV j,i* and PV j,i*+1 do not differ by much, and we do not lose much in replacing both conditions by the following relationship:
$$PV_{j,i^{*} } \approx c_{i^{*} } \text{e}^{{ - r^{m} t_{j,i^{*} } }}$$
(4)
Using 3 and 4, setting t 1 = 0 and solving for the initial return rate yields
$$\overline{{r_{j} }} = \left\{ {\begin{array}{*{20}c} {\left( {c_{1} \frac{{r^{m} + d}}{{1 - \text{e}^{{ - r^{m} t_{2} }} }}} \right)} & {lapsed} & {after} & {t_{1} } \\ {\left( {c_{2} \text{e}^{{ - r^{m} t_{2} }} \frac{{r^{m} + d}}{{\text{e}^{{ - r^{m} t_{2} }} - \text{e}^{{ - r^{m} t_{3} }} }}} \right)} & {lapsed} & {after} & {t_{2} } \\ \ldots & \ldots & \ldots & \ldots \\ {\left( {c_{K} \text{e}^{{ - r^{m} t_{K} }} \frac{{r^{m} + d}}{{\text{e}^{{ - r^{m} t_{K} }} - \text{e}^{{ - r^{m} t_{K + 1} }} }}} \right)} & {lapsed} & {after} & {t_{K} } \\ \end{array} } \right.$$
(5)
Plugging Eq. 5 into Eq. 3 yields Eq. 1 in Chapter 3.
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Schubert, T. Assessing the value of patent portfolios: an international country comparison. Scientometrics 88, 787 (2011). https://doi.org/10.1007/s11192-011-0454-2
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• Value
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https://www.aimsciences.org/article/doi/10.3934/mbe.2007.4.355
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American Institute of Mathematical Sciences
2007, 4(2): 355-368. doi: 10.3934/mbe.2007.4.355
Delay differential equations via the matrix lambert w function and bifurcation analysis: application to machine tool chatter
1 Department of Mechanical Engineering, University of Michigan, 2350 Hayward Street, Ann Arbor, MI 48109-2125, United States, United States 2 Department of Mathematics, University of Michigan, 525 East University, Ann Arbor, MI 48109-1109, United States
Received September 2006 Revised October 2006 Published February 2007
In a turning process modeled using delay differential equations (DDEs), we investigate the stability of the regenerative machine tool chatter problem. An approach using the matrix Lambert W function for the analytical solution to systems of delay differential equations is applied to this problem and compared with the result obtained using a bifurcation analysis. The Lambert W function, known to be useful for solving scalar first-order DDEs, has recently been extended to a matrix Lambert W function approach to solve systems of DDEs. The essential advantages of the matrix Lambert W approach are not only the similarity to the concept of the state transition matrix in linear ordinary differential equations, enabling its use for general classes of linear delay differential equations, but also the observation that we need only the principal branch among an infinite number of roots to determine the stability of a system of DDEs. The bifurcation method combined with Sturm sequences provides an algorithm for determining the stability of DDEs without restrictive geometric analysis. With this approach, one can obtain the critical values of delay, which determine the stability of a system and hence the preferred operating spindle speed without chatter. We apply both the matrix Lambert W function and the bifurcation analysis approach to the problem of chatter stability in turning, and compare the results obtained to existing methods. The two new approaches show excellent accuracy and certain other advantages, when compared to traditional graphical, computational and approximate methods.
Citation: Sun Yi, Patrick W. Nelson, A. Galip Ulsoy. Delay differential equations via the matrix lambert w function and bifurcation analysis: application to machine tool chatter. Mathematical Biosciences & Engineering, 2007, 4 (2) : 355-368. doi: 10.3934/mbe.2007.4.355
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2017 Impact Factor: 1.23
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https://guzintamath.com/TechPosts/longdiv/longdiv.html
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# Long Division with "Exploding Dots"
If you are a math teacher and you haven't yet seen James Tanton's "Exploding Dots" presentations, I encourage you to dive in. I've cloned a version like the one below to use in the latest release of the Long Division lesson app.
0
0
0
0
0
In this version, I just let users circle their own groups, rather than handling this with code in some way (click the pencil icon to draw, and again to go back to dot manipulation). You can erase your groupings with the windshield wiper button, and you can clear the dots with the trash can button. Here's more of what you can do above:
• Click on an empty part of any column to insert a +1 dot (positive dot), right click on an empty part of a column to insert a –1 dot (negative dot), and double click on a dot or tod to remove it entirely from the division model.
• Click the "explode" button in the bottom right corner to create an explosion in a column, which, in the 1 ← 10 machine removes 10 dots (not tods) in a column and places a dot in the column to the left.
• Right click on a dot (or tod) in a column to "unexplode" it, which removes it from that column and inserts 10 of its kind in the column to the right.
So, for example, to model the subtraction 248 – 169, you can click on the appropriate columns to generate the number 248 with positive dots. Then, right click to insert "tods" in the columns representing –169. You can use the model to add 248 and –169 (the same as the subtraction 248 – 169). You will wind up with something like the model shown at the right:
You can simply be done here and read off the appropriate interpretation of the difference: 100 + –20 + –1. Or, as Tanton says, to make the answer more appropriate "for society," you can "unexplode" a positive dot in the hundreds column, giving you 0 hundreds 8 tens and –1 ones and then "unexplode" a positive tens dot to give you, finally, 0 hundreds, 7 tens, and 9 ones, or 79.
A division example is shown at the right. Here we see that 248 ÷ 11 = 22 (2 groups of 11 tens and 2 groups of 11 ones) with 6 (ones) left over, or 248 = 22 × 11 + 6.
What I find tremendously cool about this model is that, having played with it a lot, I find myself doing some forward thinking with the dividend. That is, I find that the model has me wondering what numbers I can divide into the dividend, rather than what the quotient to any particular problem is. So, I'll plop a number into the model and look for any divisor that will give me easy divisions (divisibility) or think about how I can slightly fudge the model (insert a positive-negative pair in a group, for example) to get cleaner divisions. All of this, for me, quickly transfers to just numbers, so it seems at least plausible that once a student is expert with the model, they don't have to live there. This goes for all the basic operations.
As Tanton goes on to explain in his presentations, the same model can be used for polynomial long division. So, for example, when I search for polynomial long division, the first example I get is $\mathtt{2x^3 + 7x^2 + 2x + 9 \div 2x + 3}$ And one way to model that division is shown at the right. This time, from right to left, our columns represent 1s, $$\mathtt{x}$$s, $$\mathtt{x^2}$$s, $$\mathtt{x^3}$$s, and $$\mathtt{x^4}$$s. Interpreting the quotient, we see that it is $$\mathtt{x^2 + 2x – 2}$$ with 15 left over. (You have to be careful with the 1 ← 10 machine above, though, when representing polynomial long division. Explosions and unexplosions are too difficult to represent on the model, since we don't know what x is (we just know, for example, that there are $$\mathtt{x}$$ $$\mathtt{x}$$'s in $$\mathtt{x^2}$$). But the machine will let you do it anyway, because it's not built for algebraic polynomial long division.
What Curriculum Innovation Looks Like
When I hear the word "innovation" in education, something like the thinking that went into creating Exploding Dots is what I secretly wish everyone meant by the word all the time. The best part of that thinking in this case, for me, is how division is represented. It's fairly straightforward to see how the circling works when we're creating groups of 11. But why should I be able to circle 2 $$\mathtt{x^3}$$ dots along with 3 $$\mathtt{x^2}$$ dots to represent dividing by $$\mathtt{2x + 3}$$? The full answer to that question involves some factoring, but it connects the model with division all the way from elementary to high school. That's pretty powerful. $\mathtt{10(10 + 1) = 100 + 10\,\,}$ $\mathtt{x^2(2x + 3) = 2x^3 + 3x^2}$
I see smaller versions of this kind of innovation occasionally in math ed, and my current opinion is that it's these kinds of small improvements that, over time, create real improvements in student learning: better explanations that allow more students to access and then follow through with the content, allow students to retain the information for longer, or allow students to make deeper connections to later material.
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http://cvgmt.sns.it/paper/1703/
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# Existence of minimizers for spectral problems
created by pratelli on 01 Dec 2011
modified on 16 Feb 2015
[BibTeX]
Published Paper
Inserted: 1 dec 2011
Last Updated: 16 feb 2015
Journal: J. Math. Pures Appl.
Year: 2013
Abstract:
In this paper we show that any increasing functional of the first $k$ eigenvalues of the Dirichlet Laplacian admits a (quasi-)open minimizer among the subsets of ${\mathbb R}^N$ of unit measure. In particular, there exists such a minimizer which is bounded, where the bound depends on $k$ and $N$, but not on the functional. In the meantime, we show that the ratio $\lambda_k(\Omega)/\lambda_1(\Omega)$ is uniformly bounded for sets $\Omega\in{\mathbb R}^N$.
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https://ftp.aimsciences.org/article/doi/10.3934/cpaa.2006.5.813
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Advanced Search
Article Contents
Article Contents
On the uniqueness of ground state solutions of a semilinear equation containing a weighted Laplacian
• We consider the problem of uniqueness of radial ground state solutions to
(P) $\qquad\qquad\qquad -\Delta u=K(|x|)f(u),\quad x\in \mathbb R^n.$
Here $K$ is a positive $C^1$ function defined in $\mathbb R^+$ and $f\in C[0,\infty)$ has one zero at $u_0>0$, is non positive and not identically 0 in $(0,u_0)$, and it is locally lipschitz, positive and satisfies some superlinear growth assumption in $(u_0,\infty)$.
Mathematics Subject Classification: 37C45.
Citation:
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https://wordpandit.com/algebra-quadratic-equations-test-5/
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Select Page
• This is an assessment test.
• To draw maximum benefit, study the concepts for the topic concerned.
• Kindly take the tests in this series with a pre-defined schedule.
Congratulations - you have completed Algebra: Quadratic Equations Test-5. You scored %%SCORE%% out of %%TOTAL%%. You correct answer percentage: %%PERCENTAGE%% . Your performance has been rated as %%RATING%%
Question 1
The product of the present ages of Sarita and Gauri is 320. Eight years from now, Sarita's age will be three times the age of Gauri. What was the age of Sarita when Gauri was born?
A 40 yr B 32 yr C 48 yr D 36 yr
Question 1 Explanation:
Let the age of Sarita be s years and Gauri be g years.
sg=320,
s+8=3(g+8)
s+8=3g+24
=>s-3g=16,sg=320
Solving the equation we can get ,
g=8 and s=40
Thus the age of Sarita when Gauri was born is 40-8=32 years.
Question 2
In a class, the number of girls is one less than the number of the boys. If the product of the number of boys and that of girls is 272, then the number of girls in the class is
A 15 B 14 C 16 D 17
Question 2 Explanation:
Let the number of girls be g and the number of boys be b.
g=b-1
gb=272
Solving the equation or by using options we can find that
g=16 and b=17.
Correct options is (c).
Question 3
If you subtract Rs.1 from the money Bholu has, take its reciprocal, then add it to the square of the money and subtract the money Bholu has, you get two rupees more than the reciprocal of money after subtracting 1 from it. Find the money Bholu has.
A Rs.7 B Rs.5 C Rs.10 D None of these
Question 3 Explanation:
Let the amount with Bholu be Rs. b.
$\begin{array}{l}\frac{1}{b-1}+{{b}^{2}}-b=2+\frac{1}{b-1}\\=>b(b-1)=2\\=>b=2\end{array}$
Question 4
A class decided to have a party for their class at a total cost of Rs.720. Four students decided to stay out of the party. To meet the expenses the remaining students have to increase their share by Rs.9. What is the original cost per student?
A Rs.18, B Rs.24 C Rs.36 D Rs.20
Question 4 Explanation:
Let the number of students = s and the amount paid by each be r.
sr=720
and (s-4)(y+9)=720
Solving the two equations,
s=20 and r=36.
Thus the original cost per student is Rs. 36.
The correct option is (c).
Question 5
$\displaystyle Given\,\,\,\,\frac{\left( \sqrt{x+4}+\sqrt{x-10} \right)}{\sqrt{x+4}-\sqrt{x-10}}=\frac{5}{2},$
The value of x is
A 1 B 331/5 C 263/20 D 17/21
Question 5 Explanation:
$\displaystyle Given\,\,\,\,\frac{\left( \sqrt{x+4}+\sqrt{x-10} \right)}{\sqrt{x+4}-\sqrt{x-10}}=\frac{5}{2},$
$\begin{array}{l}\frac{\left( \sqrt{x+4}+\sqrt{x-10} \right)}{\sqrt{x+4}-\sqrt{x-10}}=\frac{5}{2},\\=>2\left( \sqrt{x+4}+\sqrt{x-10} \right)=5\left( \sqrt{x+4}-\sqrt{x-10} \right)\\=>2\sqrt{x+4}+2\sqrt{x-10}=5\sqrt{x+4}-5\sqrt{x-10}\\=>7\sqrt{x-10}=3\sqrt{x+4}\\=>49(x-10)=9(x+4)\\=>49x-490=9x+36\\=>40x=526\\=>x=\frac{526}{40}=\frac{263}{20}\end{array}$
Once you are finished, click the button below. Any items you have not completed will be marked incorrect.
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https://archive.softwareheritage.org/browse/origin/content/?branch=refs/tags/R-3.0.2&origin_url=https://github.com/cran/statnet&path=man/statnet-package.Rd
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##### https://github.com/cran/statnet
Tip revision: 8b432c0
statnet-package.Rd
\name{statnet-package}
\alias{statnet-package}
\docType{package}
\title{
A Suite of Packages for the Statistical Modeling of Network Data
}
\description{
\pkg{statnet} is a suite of software packages for statistical network analysis.
The packages implement recent advances in network modeling based on
exponential-family random graph models (ERGM), as well as latent space
models and more traditional network methods. The components of the package
provide a comprehensive framework for ERGM-based network modeling: tools for
model estimation, for model evaluation, for model-based network simulation, and
Markov chain Monte Carlo (MCMC) algorithm. The coding is optimized for speed
and robustness.
}
\details{
\pkg{statnet} packages are written in a combination of \R and
\code{C} It is usually used interactively from within the \R graphical
user interface via a command line. it can also be used in
non-interactive (or batch'') mode to allow longer or multiple tasks
to be processed without user interaction. The suite of packages are
available on the Comprehensive \R Archive Network (CRAN) at
\url{http://www.r-project.org/} and also on the \pkg{statnet} project
website at \url{http://statnet.org/}
The \pkg{statnet} suite of packages has the following components:
\itemize{
\item \pkg{ergm} is a collection of functions to fit, simulate from,
plot and evaluate exponential random graph models. The main
functions within the \pkg{ergm} package are
\code{\link[ergm]{ergm}}, a function to fit linear exponential
random graph models in which the probability of a graph is dependent
upon a vector of graph statistics specified by the user;
\code{simulate}, a function to simulate random graphs using an ERGM;
and \code{\link[ergm]{gof}}, a function to evaluate the goodness of
fit of an ERGM to the data. \pkg{ergm} contains many other functions
as well.
\item \pkg{tergm} is a collection of extentions to \pkg{ergm}
enabling it to fit models for dynamic networks.
\item \pkg{ergm.count} is an extension to \pkg{ergm} enabling it to
fit models for networks whose relations are counts.
\item \pkg{ergm.userterms} provides a template for implementing new
ERGM terms.
\item \pkg{sna} is a set of tools for traditional social network
analysis.
\item \pkg{degreenet} is a package for the statistical modeling of
degree distributions of networks. It includes power-law models such
as the Yule and Waring, as well as a range of alternative models
that have been proposed in the literature.
\item \pkg{latentnet} is a package to fit and evaluate latent position
and cluster models for statistical networks The probability of a tie
is expressed as a function of distances between these nodes in a
latent space as well as functions of observed dyadic level
covariates.
%% \item \pkg{netperm}: A package for permutation Models for relational
%% data. It provides simulation and inference tools for exponential
%% families of permutation models on relational structures.
\item \pkg{networksis} is a package to simulate bipartite graphs
with fixed marginals through sequential importance sampling.
\item \pkg{relevent} is a package providing tools to fit relational
event models.
\item \pkg{network} is a package to create, store, modify and plot
the data in network objects. The \code{\link[network]{network}}
object class, defined in the \pkg{network} package, can represent a
range of relational data types and it supports arbitrary vertex /
edge /graph attributes. Data stored as
\code{\link[network]{network}} objects can then be analyzed using
all of the component packages in the \pkg{statnet} suite.
\item \pkg{networkDynamic} extends \pkg{network} with functionality
class.
}
In addition, the following packages are available from the author:
\itemize{ \item \pkg{rSonia}: provides a set of methods to facilitate
exporting data and parameter settings and launching SoNIA (Social
Network Image Animator). SoNIA facilitates interactive browsing of
dynamic network data and exporting animations as a QuickTime movies.
}
\pkg{statnet} is a metapackage, depending on all of the above
packages, so that they can be installed together.
Each of these components is described in detail in the references
loads them all. Each package has associated help files and internal
documentation that is supported by the information on the Statnet
Project website (\url{http://statnet.org/}). A tutorial, support
mailing list, references and links to further resources are provided
there.
When publishing results obtained using this package the original
authors are to be cited as described in
package that you use.
We have invested a lot of time and effort in creating the
\code{statnet} suite of packages for use by other researchers.
lease cite it in all papers where it is used.
}
\author{
Mark S. Handcock \email{[email protected]},\cr
David R. Hunter \email{[email protected]},\cr
Carter T. Butts \email{[email protected]},\cr
Steven M. Goodreau \email{[email protected]},\cr
Pavel N. Krivitsky \email{[email protected]}, and\cr
Martina Morris \email{[email protected]}
Maintainer: Pavel N. Krivitsky \email{[email protected]}
}
\references{
{\pkg{networksis}: Simulate bipartite graphs with fixed
marginals through sequential importance sampling}.
Statnet Project, Seattle, WA.
Version 1, \url{http://statnet.org}.
Bender-deMoll S, Morris M, Moody J (2008).
{Prototype Packages for Managing and Animating Longitudinal
Network Data: \pkg{dynamicnetwork} and \pkg{rSoNIA}.}
{Journal of Statistical Software}, {24} (7).
\url{http://www.jstatsoft.org/v24/i07/}.
Besag, J., 1974, Spatial interaction and the statistical analysis
of lattice systems (with discussion), Journal of the Royal Statistical
Society, B, 36, 192-236.
Butts CT (2006).
{\pkg{netperm}: Permutation Models for Relational Data}.
Version 0.2, \url{http://erzuli.ss.uci.edu/R.stuff}.
Butts CT (2007).
{\pkg{sna}: Tools for Social Network Analysis}.
Version 1.5, \url{http://erzuli.ss.uci.edu/R.stuff}.
Butts CT (2008).
{\pkg{network}: {A} Package for Managing Relational Data in \R.}
{Journal of Statistical Software}, {24} (2).
\url{http://www.jstatsoft.org/v24/i02/}.
Butts CT, with help~from David~Hunter, Handcock MS (2007).
{\pkg{network}: Classes for Relational Data}.
Version 1.3, \url{http://erzuli.ss.uci.edu/R.stuff}.
Frank, O., and Strauss, D.(1986). Markov graphs. Journal of the American
Statistical Association, 81, 832-842.
Goodreau SM, Handcock MS, Hunter DR, Butts CT, Morris M (2008a).
{A \pkg{statnet} Tutorial.}
{Journal of Statistical Software}, {24} (8).
\url{http://www.jstatsoft.org/v24/i08/}.
Goodreau SM, Kitts J, Morris M (2008{{b}}).
{Birds of a Feather, or Friend of a Friend? Using Exponential
Random Graph Models to Investigate Adolescent Social Networks.}
{Demography}, {45}, in press.
Handcock, M. S. (2003)
\emph{Assessing Degeneracy in Statistical Models of Social Networks},
Working Paper \#39,
Center for Statistics and the Social Sciences,
University of Washington.
\url{www.csss.washington.edu/Papers/wp39.pdf}
Handcock MS (2003{{b}}).
{\pkg{degreenet}: Models for Skewed Count Distributions Relevant
to Networks}.
Statnet Project, Seattle, WA.
Version 1. Project homepage at \url{http://statnet.org},
URL: \url{http://CRAN.R-project.org/package=degreenet}.
Handcock MS, Hunter DR, Butts CT, Goodreau SM, Morris M (2003{{a}}).
{\pkg{ergm}: {A} Package to Fit, Simulate and Diagnose
Exponential-Family Models for Networks}.
Statnet Project, Seattle, WA.
Version 2. Project homepage at \url{http://statnet.org},
URL: \url{http://CRAN.R-project.org/package=ergm}.
Handcock MS, Hunter DR, Butts CT, Goodreau SM, Morris M (2003{{b}}).
{\pkg{statnet}: Software tools for the Statistical Modeling of
Network Data}.
Statnet Project, Seattle, WA.
Version 2. Project homepage at \url{http://statnet.org},
URL: \url{http://CRAN.R-project.org/package=statnet}.
Hunter, D. R. and Handcock, M. S. (2006)
\emph{Inference in curved exponential family models for networks},
Journal of Computational and Graphical Statistics.
Hunter DR, Handcock MS, Butts CT, Goodreau SM, Morris M (2008{{b}}).
{\pkg{ergm}: {A} Package to Fit, Simulate and Diagnose
Exponential-Family Models for Networks.}
{Journal of Statistical Software}, {24}(3).
\url{http://www.jstatsoft.org/v24/i03/}.
Krivitsky PN (2012). Exponential-Family Random Graph Models for Valued
Networks. \emph{Electronic Journal of Statistics}, 2012, 6,
1100-1128. \href{http://dx.doi.org/10.1214/12-EJS696}{\code{doi:10.1214/12-EJS696}}
Krivitsky PN, Handcock MS (2008).
Fitting Latent Cluster Models for Social Networks with \pkg{latentnet}.
{Journal of Statistical Software}, {24}(5).
\url{http://www.jstatsoft.org/v24/i05/}.
Krivitsky PN, Handcock MS (2007).
{\pkg{latentnet}: Latent position and cluster models for
statistical networks}.
Seattle, WA.
Version 2. Project homepage at \url{http://statnet.org},
URL: \url{http://CRAN.R-project.org/package=latentnet}.
Morris M, Handcock MS, Hunter DR (2008).
{Specification of Exponential-Family Random Graph Models:
Terms and Computational Aspects.}
{Journal of Statistical Software}, {24}(4).
\url{http://www.jstatsoft.org/v24/i04/}.
Strauss, D., and Ikeda, M.(1990). Pseudolikelihood estimation for social
networks. Journal of the American Statistical Association, 85, 204-212.
}
\keyword{ package }
\keyword{ models }
|
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|
https://research.metastate.dev/juvix-compiling-juvix-to-michelson/
|
## 1 Compiling Juvix to Michelson
Juvix Is a dependently typed programming language inspired by Idris, F★, and Coq. Juvix is designed as a smart contract verification and execution language, where efficient compilation is key, as otherwise any inefficient compilation to the primitives of a virtual machine on a decentralised blockchain will result in extra funds spent in order to execute any given program (for more background on smart contract language design, see The Why of Juvix).
Juvix targets Tezos through its primitive script known as Michelson. Michelson is a peculiar language in that it is a typed stack based language in the lineage of Forth and Kitten. However, unlike these languages, Michelson lacks primitives to make standalone named functions.
Before going forward, we will need to gain some intuition on how stack based languages operate.
### 1.1 Intuition on Stack Based Languages
In a stack based language, function arguments are not named, instead arguments are taken off of the execution stack, and functions return their result to this same stack.
The first example we shall look at is the square function
: square dup * ;
• : means define a new word, in this case square.
• ; signals the end of the definition.
• the dup function takes the item on top of the stack then duplicates it.
• * multiplication operator, as one expects.
We shall now trace the execution of the above program with 3.
3 square
• Step 1
• Reading: 3
• Stack: [ 3 ]
• Step 2
• Reading: Square: dup.
• Stack: [ 3 3 ]
• Step 3
• Reading: Square: *.
• Stack: [ 9 ]
What is interesting about this program is that every time we need to use a variable more than once, we need to call dup before consuming it. Thus stack based languages have similarities to Linear Logic. This detail will be expanded upon in the next section.
Other important functions to keep in mind for stack machines are the stack shuffling operations
1. swap ∷ [ 2 3 ] ⟶ [ 3 2 ]
2. rot ∷ [ 2 3 4 ] ⟶ [ 3 4 2 ]
Michelson in particular has functions which can take other functions. The important one to remember is dip n which protects the top n-1 items of the stack while executing on the nth item and below.
With this out of the way, we can finally talk about how to compile effectively to Michelson.
### 1.2 Optimizations to Consider
Any standard language compiling to a stack machine must consider how to effectively translate their variable semantics into efficient stack shuffling. Since every operation in Michelson has a cost, doing this efficiently is imperative.
#### 1.2.1 Optimizations Relating to Efficient Stack Placement
1. Minimizing the number of dups
An illustrative example is the following
let f x = x
Since Michelson lambdas have a high cost and it is quite limited in the forms it accepts, we opt to beta expand most lambdas away. Juvix is in a unique position due to part of our type theory known as Quantitative Type Theory (QTT), which tracks the usage of all variables. Under a normal compiler pipeline this would mean that most structures can avoid being in garbage collection, however for Michelson this means we can eliminate a single dup and dig drop. Thus, if were to compile the application of f within some nested computation where the x is stored five slots back in stack, then without QTT or some notion of linearity then the expansion would look like the following.
5 dug dup 6 dig
Indeed, there would be no way of knowing that it's safe to completely move away. However, if we were to consider Quantitative Type Theory, with x only being used once then we can always safely write
5 dug
2. Placement of variables after lookup
A more generic optimization is looking up a variable from the environment, which effectively caches the value on the stack until it is consumed.
Let us consider the function f below where the usage of x is 3. Let us consider the application where x is 5 slots away.
let f = x * x
Then the generated code would be.
5 dug dup 6 dig dup *
Thus we can see that we did not have to do another dug dig combo, but instead dup the current variable.
This technique relies on propagating usages effectively, as we have to know whether to dup a value or just move it to be consumed. As currently implemented, there is one restriction that will make this behavior less optimal than it should be. These inefficiencies will be discussed in the next section.
#### 1.2.2 Optimizations Relating to Curry Semantics
For those unfamiliar with currying, in an ML family language, functions only take a single argument.
f a b c = times (a + b + c)
g = f 2 3
h = g 5 6
l = f 2 3 5 6
j = f 2 3 4
Although it may look like each function takes multiple arguments, notice how this example works. f explicitly takes 3 arguments up front (named a b and c), but in reality takes a fourth unarmed argument. As application goes we show sending in 2 arguments to f twice, showing that you can partially apply f and get back a new function that takes two more arguments, where h finally makes it whole. We also can see that we can send in more arguments than there are names for and also the exact number of arguments. When compiling down to a language without curry semantics, it's quite important to get this optimization right.
1. Push enter and eval apply
Historically there have been two techniques in literature for making currying fast. Strict languages like ML and Lisps opted to go for a technique called eval/apply, while traditionally lazy languages like Haskell went for push/enter. However, both lazy languages and strict languages found that push/enter is more complex than eval/apply.
With that said, for Michelson we have opted for a hybrid approach.
The rationale for this mix is the following:
1. Michelson has no concept of a heap
The paper linked under, lazy languages, above, demonstrates that both push/enter and eval/apply operates under an abstract machine with three components. These components are the code, the stack, and the heap. For Michelson, we clearly have the code and the stack (the code is the expression being compiled, and the stack is the result stack). The heap however has to be simulated with the stack. The heap is responsible for the quick storage of all variables and closures used in any expression. Since all we have is a stack, these variables must be stored there, which means that if we have to retrieve a variable that is further back, one has to pay gas for this retrieval.
2. Michelson is a stack machine with lambda
• Another deciding factor, is that Michelson is a stack machine, specifically with an inefficient lambda operation. This operation is inefficient in that all Michelson functions take a single argument, they can't for example consume multiple items off the stack. To simulate multiple arguments, one has to tuple them up before sending it in, then un-tuple them once in the lambda. To get a good intuition on the matter, let us consider a lambda taking n arguments:
• Before we construct the Michelson lambda, we must tuple them all. This costs n-1 pairs
• Inside the lambda we constructed we have to un-pair the argument to use the n arguments. This is not as simple as calling un-pair n-1 times.
• Instead we have to write
dup; car; dip { cdr .... }
• the car gets the first element of the pair, and cdr get the rest of the pair. We have to call dip, as we want the car as is, but to move past it to unpair the other elements.
This process goes on for another n-2 times.
As we can see, the cost of lambda has a high fixed cost, so in our compilation we make sure to build up no intermediate lambdas and inline and beta expand as aggressively as possible, leaving those that another Michelson primitive (such as map) requires one.
In our actual implementation when we come across an exact application: we just inline it immediately (this corresponds to exact in eval/apply). If we come across a partially applied function, we name the arguments on the stack for future reference, and push a virtual (thus it has no cost to lookup!) closure on the stack that can be later fully applied. For over application, we note the arguments which can't be named, we generate names from them and carry them over as extra arguments to the result of the applied function.
With these optimizations, curry semantics for Juvix poses no overhead for generating Michelson.
#### 1.2.3 Various Other Optimizations
1. Lambda Removal
As discussed above, Lambdas are expensive, so we do beta reduction and inlining aggressively to avoid them. This beta reduction does not move the values on the stack at all, instead just naming them for when they are actually used.
Beta reduction in Michelson turn out to be safe due to the limitations of what can be expressed in Michelson. Firstly, Michelson doesn't allow for custom types, instead providing their own data structures. So we currently can't send in any recursive structures, such as a list. Secondly, Michelson lacks functions and the typing to support converting recursive functions into CPS style (Michelson only has first-order typing). Thus all simple tail recursive functions will have to be translated into a Michelson loop before being sent into the backend.
2. Virtual stack
This was also discussed above, we will just note items stored on the virtual stack that is not stored on the Michelson stack:
1. Partially-applied functions
2. Constants
Specifically, these are propagated even through primitive functions if all the arguments are constants!
### 1.3 Limitations of our Current Compiler Pipeline
Currently our compiler is under the phase of rapid development, so many of the phases are quite immature. Namely, we lack a normalization step for our Core intermediate representation (IR). We plan on adding an Administrative Normal Form (ANF) transformation soon that would open up many optimizations while generalizing the Michelson backend logic (we would get constant propagation, and a proper generalized eval/apply model).
Below we shall list known optimizations that can easily happen given a proper ANF form.
#### 1.3.1 Improvements from Normalization
1. More Effective usage movement
Currently, when we move a variable forward, we move all usages except 1 forward with it unless the variable only has one usage left. This means, we always keep behind a copy of the variable behind.
Let us see the example we used before.
let f = x * x
Let us suppose x, like before, is five positions back, however now consider the usage of x being used twice and thrice.
Twice:
5 dug dup 6 dig 6 dug *
thrice (as before):
5 dug dup 6 dig dup *
As we can see, if we only use x twice we pay a cost of digging five again to move the copy over. The first x we moved over has a usage one where we are going to use it right away, so this usage is saved. Thus the only free x is the one six stack positions away!
A smarter plan would be to just move all the usages up, and if any usages are left over after using them, move them right before the consumption point.
So to illustrate, consider the same example from above:
Twice:
5 dug dup *
Thrice (as before):
5 dug dup dup 3 dip *
Notice this is much more efficient, as we don't have to go six positions back immediately, and when we do have to leave a copy behind it is only the minimum number three slots away.
However this optimization is not safe currently. Consider the example below:
f a (x + y) b
If we were to do this technique with x and y having extra usages, then moving them back would cause b to no longer be an argument, instead replacing it with themselves!
Once ANF form is up, the computation will instead be like this
let xy0 = x + y in
f a xy0 b
where every function takes primitives, so these moves would have happened before, thus allowing this optimization to take place.
2. Another benefit of ANF is that with the extension of join points, we can effectively fuse (merge) independent loops into a single loop when they are composed together. This optimization will only show on operations through numbers sadly, as recursive structures in Michelson that are not primitive are not permitted.
### 1.4 Final Thoughts
Overall, Juvix's Michelson backend is efficient while allowing for high level idioms. The costs for currying are gone with the usage of smart and well studied techniques. Usage tracking and inference allows for the programmers to write code without worrying about calling dup or drop by hand. Further, our aggressive inlining of lambdas allow abstractions used for readability of code to have no performance penalties. Many more optimizations are coming that should allow for even faster generated Michelson. In future articles, there will be example smart contracts written in Juvix, in order to showcase that Juvix' Michelson backend can not only make your smart contracts on Tezos faster, but also safer.
Written by Jeremy Ornelas, core developer and researcher at Metastate.
Image Credits: Water Bears from Encyclopedia of Life.
Metastate has ceased its activities on the 31st of January 2021. The team members have joined a new company and working on a new project. If you're interested in programming language theory, functional programming, type theory, formal verification, or compiler engineering positions, check out the open positions at Heliax.
|
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|
https://planetmath.org/1121TheAlgebraicStructureOfDedekindReals
|
11.2.1 The algebraic structure of Dedekind reals
The construction of the algebraic and order-theoretic structure of Dedekind reals proceeds as usual in intuitionistic logic. Rather than dwelling on details we point out the differences between the classical and intuitionistic setup. Writing $L_{x}$ and $U_{x}$ for the lower and upper cut of a real number $x:\mathbb{R}_{\mathsf{d}}$, we define addition as
$\displaystyle L_{x+y}(q)$ $\displaystyle:\!\!\equiv\exists(r,s:\mathbb{Q}).\,L_{x}(r)\land L_{y}(s)\land q% =r+s,$ $\displaystyle U_{x+y}(q)$ $\displaystyle:\!\!\equiv\exists(r,s:\mathbb{Q}).\,U_{x}(r)\land U_{y}(s)\land q% =r+s,$
$\displaystyle L_{-x}(q)$ $\displaystyle:\!\!\equiv\exists(r:\mathbb{Q}).\,U_{x}(r)\land q=-r,$ $\displaystyle U_{-x}(q)$ $\displaystyle:\!\!\equiv\exists(r:\mathbb{Q}).\,L_{x}(r)\land q=-r.$
With these operations $(\mathbb{R}_{\mathsf{d}},0,{+},{-})$ is an abelian group. Multiplication is a bit more cumbersome:
$\displaystyle L_{x\cdot y}(q)$ \displaystyle:\!\!\equiv\begin{aligned} \displaystyle\exists(a,b,c,d:\mathbb{Q% }).&\displaystyle L_{x}(a)\land U_{x}(b)\land L_{y}(c)\land U_{y}(d)\land\\ &\displaystyle\qquad q<\min(a\cdot c,a\cdot d,b\cdot c,b\cdot d),\end{aligned} $\displaystyle U_{x\cdot y}(q)$ \displaystyle:\!\!\equiv\begin{aligned} \displaystyle\exists(a,b,c,d:\mathbb{Q% }).&\displaystyle L_{x}(a)\land U_{x}(b)\land L_{y}(c)\land U_{y}(d)\land\\ &\displaystyle\qquad\max(a\cdot c,a\cdot d,b\cdot c,b\cdot d)
These formulas are related to multiplication of intervals in interval arithmetic, where intervals $[a,b]$ and $[c,d]$ with rational endpoints multiply to the interval
$[a,b]\cdot[c,d]=[\min(ac,ad,bc,bd),\max(ac,ad,bc,bd)].$
For instance, the formula for the lower cut can be read as saying that $q when there are intervals $[a,b]$ and $[c,d]$ containing $x$ and $y$, respectively, such that $q$ is to the left of $[a,b]\cdot[c,d]$. It is generally useful to think of an interval $[a,b]$ such that $L_{x}(a)$ and $U_{x}(b)$ as an approximation of $x$, see \autorefex:RD-interval-arithmetic.
We now have a commutative ring with unit $(\mathbb{R}_{\mathsf{d}},0,1,{+},{-},{\cdot})$. To treat multiplicative inverses, we must first introduce order. Define $\leq$ and $<$ as
$\displaystyle(x\leq y)$ $\displaystyle\ :\!\!\equiv\ \forall(q:\mathbb{Q}).\,L_{x}(q)\Rightarrow L_{y}(% q),$ $\displaystyle(x $\displaystyle\ :\!\!\equiv\ \exists(q:\mathbb{Q}).\,U_{x}(q)\land L_{y}(q).$
Lemma 11.2.1.
For all $x:\mathbb{R}_{\mathsf{d}}$ and $q:\mathbb{Q}$, $L_{x}(q)\Leftrightarrow(q and $U_{x}(q)\Leftrightarrow(x.
Proof.
If $L_{x}(q)$ then by roundedness there merely is $r>q$ such that $L_{x}(r)$, and since $U_{q}(r)$ it follows that $q. Conversely, if $q then there is $r:\mathbb{Q}$ such that $U_{q}(r)$ and $L_{x}(r)$, hence $L_{x}(q)$ because $L_{x}$ is a lower set. The other half of the proof is symmetric. ∎
The relation $\leq$ is a partial order, and $<$ is transitive and irreflexive. Linearity
$(x
is valid if we assume excluded middle, but without it we get weak linearity
$(x (11.2.2)
At first sight it might not be clear what (11.2.2) has to do with linear order. But if we take $x\equiv u-\epsilon$ and $y\equiv u+\epsilon$ for $\epsilon>0$, then we get
$(u-\epsilon
This is linearity “up to a small numerical error”, i.e., since it is unreasonable to expect that we can actually compute with infinite precision, we should not be surprised that we can decide $<$ only up to whatever finite precision we have computed.
To see that (11.2.2) holds, suppose $x. Then there merely exists $q:\mathbb{Q}$ such that $U_{x}(q)$ and $L_{y}(q)$. By roundedness there merely exist $r,s:\mathbb{Q}$ such that $r, $U_{x}(r)$ and $L_{y}(s)$. Then, by locatedness $L_{z}(r)$ or $U_{z}(s)$. In the first case we get $x and in the second $z.
Classically, multiplicative inverses exist for all numbers which are different from zero. However, without excluded middle, a stronger condition is required. Say that $x,y:\mathbb{R}_{\mathsf{d}}$ are apart from each other, written $x\mathrel{\#}y$, when $(x:
$(x\mathrel{\#}y):\!\!\equiv(x
If $x\mathrel{\#}y$, then $\lnot(x=y)$. The converse is true if we assume excluded middle, but is not provable constructively. Indeed, if $\lnot(x=y)$ implies $x\mathrel{\#}y$, then a little bit of excluded middle follows; see \autorefex:reals-apart-neq-MP.
Theorem 11.2.3.
A real is invertible if, and only if, it is apart from $0$.
Remark 11.2.4.
We observe that a real is invertible if, and only if, it is merely invertible. Indeed, the same is true in any ring, since a ring is a set, and multiplicative inverses are unique if they exist. See the discussion following \autorefcor:UC.
Proof.
Suppose $x\cdot y=1$. Then there merely exist $a,b,c,d:\mathbb{Q}$ such that $a, $c and $0<\min(ac,ad,bc,bd)$. From $0 and $0 it follows that $a$, $b$, and $c$ are either all positive or all negative. Hence either $0 or $x, so that $x\mathrel{\#}0$.
Conversely, if $x\mathrel{\#}0$ then
$\displaystyle L_{x^{-1}}(q)$ $\displaystyle:\!\!\equiv\exists(r:\mathbb{Q}).\,U_{x}(r)\land((0 $\displaystyle U_{x^{-1}}(q)$ $\displaystyle:\!\!\equiv\exists(r:\mathbb{Q}).\,L_{x}(r)\land((01)% \lor(r<0\land 1>qr))$
defines the desired inverse. Indeed, $L_{x^{-1}}$ and $U_{x^{-1}}$ are inhabited because $x\mathrel{\#}0$. ∎
The archimedean principle can be stated in several ways. We find it most illuminating in the form which says that $\mathbb{Q}$ is dense in $\mathbb{R}_{\mathsf{d}}$.
Theorem 11.2.5 (Archimedean principle for $\mathbb{R}_{\mathsf{d}}$).
For all $x,y:\mathbb{R}_{\mathsf{d}}$ if $x then there merely exists $q:\mathbb{Q}$ such that $x.
Proof.
By definition of $<$. ∎
Before tackling completeness of Dedekind reals, let us state precisely what algebraic structure they possess. In the following definition we are not aiming at a minimal axiomatization, but rather at a useful amount of structure and properties.
Definition 11.2.6.
An ordered field is a set $F$ together with constants $0$, $1$, operations $+$, $-$, $\cdot$, $\min$, $\max$, and mere relations $\leq$, $<$, $\mathrel{\#}$ such that:
1. 1.
$(F,0,1,{+},{-},{\cdot})$ is a commutative ring with unit;
2. 2.
$x:F$ is invertible if, and only if, $x\mathrel{\#}0$;
3. 3.
$(F,{\leq},{\min},{\max})$ is a lattice;
4. 4.
the strict order $<$ is transitive, irreflexive, and weakly linear ($x);
5. 5.
apartness $\mathrel{\#}$ is irreflexive, symmetric and cotransitive ($x\mathrel{\#}y\Rightarrow x\mathrel{\#}z\lor y\mathrel{\#}z$);
6. 6.
for all $x,y,z:F$:
$\displaystyle x\leq y$ $\displaystyle\Leftrightarrow\lnot(y $\displaystyle x $\displaystyle\Rightarrow x $\displaystyle x\mathrel{\#}y$ $\displaystyle\Leftrightarrow(x $\displaystyle x\leq y $\displaystyle\Rightarrow x $\displaystyle x\leq y$ $\displaystyle\Leftrightarrow x+z\leq y+z,$ $\displaystyle x\leq y\land 0\leq z$ $\displaystyle\Rightarrow xz\leq yz,$ $\displaystyle x $\displaystyle\Leftrightarrow x+z $\displaystyle 0 $\displaystyle\Leftrightarrow xz $\displaystyle 0 $\displaystyle\Rightarrow 0 $\displaystyle 0$ $\displaystyle<1.$
Every such field has a canonical embedding $\mathbb{Q}\to F$. An ordered field is when for all $x,y:F$, if $x then there merely exists $q:\mathbb{Q}$ such that $x.
Theorem 11.2.7.
The Dedekind reals form an ordered archimedean field.
Proof.
We omit the proof in the hope that what we have demonstrated so far makes the theorem plausible. ∎
Title 11.2.1 The algebraic structure of Dedekind reals \metatable
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https://www.physicsforums.com/threads/distance-to-concave-mirror.112882/
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# Distance To Concave Mirror
1. Mar 3, 2006
### ccflyer
Hey eveyone,
I have a concave mirror and an object x distance away from the mirror. I am wondering if anyone knows where you measure from in order to determine how far away the object is from the mirror. Is it from the object to the center of the concave mirror?
Thanks,
ccflyer
2. Mar 3, 2006
### Staff: Mentor
Yes, the "object distance" is the distance along the mirror axis from the object to the vertex of the mirror (the center of the concave surface).
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https://www.georgiainjurylawyersblog.net/cmv-law-the-georgia-cdl-manual/
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COVID-19 Notice: We are providing FREE consultations via in office, phone or video conferencing for your convenience.
# CMV Law: The Georgia CDL Manual
Combination Vehicles, Tankers, Hazardous Materials, and School Buses
While less uncommon than those involving 18-wheelers, cases involving combination vehicles with more than one trailer, tankers, or school buses do arise. These vehicles are often heavier and longer than a typical vehicle, and in the case of tankers, frequently contain hazardous materials, i.e., gasoline. Sections 6-10 address some of the more significant considerations involved in operating these types of vehicles, such as the “crack the whip” effect of a vehicle with a trailer (more pronounced in multi-trailer combinations) (See Sections 6.1.2, 7.1.2) and techniques for avoiding accidents and injuries. (See e.g., Sections 9.7.4, 10.1, 10.2). Again, useful diagrams are given to illustrate many aspects of combination vehicle problems, such as jackknifing. (Section 6.1.5, Figure 6.2)
Sections 6 and 7 include step-by-step instruction on the proper procedures for coupling and uncoupling various combinations. (See Sections 6.4 and 7.2). The Manual also makes the point that two and three-trailer combinations become increasingly subject to instability and overturn. (Section 7.1) Section 7 also details additional air brake checks needed when pulling multiple trailers. (Section 7.4).
Section 8 deals with tankers and notes that such vehicles routinely have a higher center of gravity than other CMVs due to the positioning of the tank and the danger of “surge,” i.e., when a liquid in a partially-full tank moves in reaction to a vehicle maneuver such as rapid deceleration. (Section 8.2.1, 8.2.2).
Although hazardous materials are beyond the scope of this book, they are addressed in considerable detail in Section 9 of the Manual. Note that a special endorsement to the CDL is required in order to transport hazardous materials. (See 49 CFR § 383.83(a),(b)(4); see also 49 CFR 383.121 “Requirements for hazardous materials endorsement”). Additional training is required for transporting certain loads, such as flammable gas or radioactive materials. (See 49 CFR 383.119 “Requirements for tank vehicle endorsement”, 383.121 “Requirements for hazardous materials endorsement”, 397.1-397.19). If you are dealing with a case involving hazardous materials, expert guidance is likely necessary.
School buses, addressed in Section 10 of the Manual, also require specialized knowledge on the part of the driver. For example, knowledge of use of an inside mirror is tested. (See Section 10.1.6). School bus stop, loading, and drop-off procedures are also subject to testing. (See Section 10.2). If counsel is representing a client in an incident that occurred during a school bus stop, it may not be just the other motorist who was at fault. The driver of the school bus should be examined regarding compliance with stopping procedures as well.
Pre-Trip Inspection, Basis Vehicle Control Skills, Test, and On-Road Driving
Section 11 of the Manual outlines the pre-trip inspection procedure that a CDL candidate must follow. The candidate must be able to physically perform the test under the scrutiny of the examiner, identify each part inspected, and tell the examiner the purpose of each component of the test. This may be used as a template for driver deposition in an appropriate case. Certainly not every aspect of the test is relevant in a given case, but judiciously placing the truly relevant inquiries within a wider field of questions pertaining to pre-trip inspection should not be difficult. The components tested are extensive and the particular version of the test administered is selected at a random. Therefore, in practice, a test of the depth described in the Manual is rarely if ever conducted.
The basic vehicle control skills test, also known as the off-road test, is covered in Section 12. Failure to pass the skills test terminates the licensing exam. (See Section 12.1) Testing is conducted on straight line backing, (See Section 12.1.1) offset back/right and left, (See Section 12.2.2, 12.2.3) parallel parking (conventional and driver side), (See Section 12.2.4, 12.2.5) and alley docking. (See Section 12.2.6) These tests are designed to be conducted in a controlled environment before the driver is taken on the road for the on-road test.
The on-road test is the final component of the CDL process, and is covered in Section 13 of the Manual. It requires a candidate driving with an examiner to demonstrate safe operation of a CMV over the course of a test route. It is the equivalent of the “check ride” that a prospective pilot must pass before he can fly with a passenger. The test involves negotiation of turns, (See Section 13.1.1) intersections, (See Section 13.1.2) urban/rural straight driving, (See Section 13.1.3) lane changes, (See Section 13.1.4) expressway operation, (See Section 13.1.5) starting and stopping, (See Section 13.1.6) curves, (See Section 13.1.7) railroad crossing, (See Section 13.1.8) brake usage, (See Section 13.1.13) lane usage, (See Section 13.1.14)bridge/overpass/sign recognition,(See Section 13.1.9) steering, (See Section 13.1.15)traffic checks, (See Section 13.1.16) and turn signal usage (See Section 13.1.17). A driver who fails to properly operate a CMV and causes a crash should be asked whether he passed that element of the road test at issue in a given case. Again, the wide spectrum of tested areas may furnish a template for the deposition examination of a driver or defense expert.
Posted in:
Updated:
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https://planetmath.org/convergenceofriemannzetaseries
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# convergence of Riemann zeta series
The series
$\displaystyle\sum_{n=1}^{\infty}\frac{1}{n^{s}}$ (1)
converges absolutely for all $s$ with real part greater than 1.
Proof. Let $s=\sigma+it$ where $\sigma$ and $t$ are real numbers and $\sigma>1$. Then
$\left|\frac{1}{n^{s}}\right|=\frac{1}{|e^{s\log{n}}|}=\frac{1}{e^{\sigma\log{n% }}}=\frac{1}{n^{\sigma}}.$
Since the series $\sum_{n=1}^{\infty}\frac{1}{n^{\sigma}}$ converges, by the $p$-test (http://planetmath.org/PTest), for $\sigma>1$, we conclude that the series (1) is absolutely convergent in the half-plane $\sigma>1$.
Title convergence of Riemann zeta series ConvergenceOfRiemannZetaSeries 2015-08-22 13:15:14 2015-08-22 13:15:14 pahio (2872) pahio (2872) 8 pahio (2872) Definition msc 11M06 msc 30A99 ModulusOfComplexNumber ComplexExponentialFunction
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https://seriouscephalopod.wordpress.com/2017/11/11/mathing-the-goethe-barometer/
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# Mathing the Goethe Barometer
In my home when I grew up there used to hang a weird glass fixture above the stair leading to the basement. It was always half full with water but I never really paid it much attention. At some point I asked what it was for and got some cryptic answer from my mom that it was for predicting whether it would rain. Ignoring something which was obviously magic I never did figure out how it worked until much later learning about mercury barometers in high school at least the principle became clear.
That thing which used to hang above the stairway was a so called Goethe Barometer. Now for a long time I had maintained an image in my mind that the bulbous shape of the device was mostly for aesthetic purposes or to store excess fluid to limit the effect of evaporation and while those are probably part of the reason they’re not the most interesting one.
In thinking about this design we should think of it as a variation of a U-shaped tube with one end capped. One can imagine calibrating the device by originally having the tube be open at both ends at which point the surface level in both columns are level, and this is retained when one end of the tube is capped so long as the enclosing process doesn’t compress the volume.. If the atmospheric pressure then decreases a difference in pressure between the trapped gas pocket at one end and the atmosphere is established and the water level at the open is raised as it is pushed up by this difference in pressure. Pascals law tells us the difference in pressure between the trapped gas and the atmosphere is related to the height difference of the two levels according to
$p' - p= \rho g h$
Thus such a device can be used as a form of barometer. One of the problems though is that it’s difficult to extract absolute pressure information from the system. Ideally we’d like to be able to derive the pressure difference relative to the pressure when the barometer was closed but unfortunately the pressure in the trapped volume is not constant as a water level change can only occur if the volume of the enclosed gas changes which necessitates a change in it’s pressure .
Thus while qualitative information about whether the pressure is higher or lower than the pressure at sealing can be gathered, the relation isn’t straight forward.
What we’ll do now is to try to arrive at a formula relating the height difference in an ideal barometer and see if we can gather some insights as to why the Goethe barometer looks the way it does in the process. We’ll use this diagram for the principal quantities during calibration and after a pressure change.
We have two kinds of relations from which to mathematically extract the quantities., geometric and physical.
Geometric constrains. Under the condition that the liquid is in-compressible constrains exist relating the height changes.
$A_1 h_1 = A_2 h_2$ (The volume of the liquid is constant)
$h = h_1 + h_2$
Physical contraints We neglect temperature variations, capillary forces, vapor pressure and other presumably secondary phenomena and assume the principal physics are Pascals law and the pressure in the trapped gas being governed by the ideal gas law.
$p_0 V_0 = p_1(V_0 + A_1 h_1)$ (Ideal gas law)
$p_1 - p = \rho g h$ (Pascals law)
Solution: Out goal will be to relate exterior pressure, $p$ to the height difference $h$. From the geometric constraints we get
$h = h_1 + h_2 = \cfrac{A_2}{A_1}h_2 + h_2 = \left (1 + \cfrac{A_2}{A_1} \right )h_1$
$p_1 = p_0 \cfrac{V_0}{V_0 + A_1 h_1} = \cfrac{p_0}{1 + \cfrac{A_1}{V_0}h_1} = \cfrac{p_0}{1 + \cfrac{A_1}{V_0 \left (1 + \cfrac{A_2}{A_1}\right )}h}$
$p = \cfrac{p_0}{1 + \cfrac{A_1}{V_0 \left (1 + \cfrac{A_2}{A_1}\right )}h} - \rho g h$
Now let us think about what characterizes the Goethe Barometer, the fact that the back containing the trapped gas is so much wider than the tubular part open to the air. Eyeballing it $A_2 / A_1 < 0.02$ so in the grand scheme of things it can be neglected which besides implying $h \approx h_2$ and $h_1 \approx 0$ also simplifies the expression
$\boxed{p = \cfrac{p_0}{1 + \cfrac{A_1}{V_0}h} - \rho g h} \quad (A_2/A_1 \approx 0)$
In effect one will have to include the volume of the trapped gas as $A_1 / V_0$ is the same order of magnitude as $h$ in the real case with normal open air pressure variations, and this equation doesn’t simplify further. Also if the surface bordering the trapped gas changes in area as it moves vertically this equation fails and you need to compute directly using the volume changes instead of going via the areas.
One could imagine using a very very large $V_0$ in which case the trapped gas volume would remain close to original pressure.
$p_2 = p_0 - \rho g h_2$
Finally, since many classrooms often contain a genuine U-tube where the area of the two openings are the same I’ll write down the equation for that case
$\boxed{p = \cfrac{p_0}{1 + \cfrac{h}{2h_0}} - \rho g h} \quad (A_2/A_1 = 1)$
Okay, I think that’s all for now though the model could use some developement principally with respect to temperature corrections, both at equilibrium and changes induced by the work involved in compressing or expanding the gas.
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http://math.stackexchange.com/questions/105711/given-two-polynomials-f-and-p-find-a-matrix-which-has-f-as-its-characteri
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# Given two polynomials $f$ and $p$, find a matrix which has $f$ as its characteristic polynomial and $p$ as its minimal polynomial.
I am self-studying the book Linear Algebra from Hoffman and Kunze. The authors make the following comment in the page 196. (Second edition)
If $f=(x-c_{1})^{d_{1}}\cdots(x-c_{k})^{d_{k}}$, $c_{1},...,c_{k}$ distinct, $d_{i}\geq 1$ and $p=(x-c_{1})^{r_{1}}\cdots(x-c_{k})^{r_{k}}$, $1\leq r_{j}\leq d_{j}$. We can find an $n\times n$ matrix which has $f$ as its characteristic polynomial and $p$ as its minimal polynomial. We shall not prove this now.
How do we prove this theorem?
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Dear spohreis: I would start by observing that we can assume $k=1,c_1=0$. – Pierre-Yves Gaillard Feb 4 '12 at 18:00
Hint: Jordan's canonical form. – Yuval Filmus Feb 4 '12 at 18:28
The simplest way to do it is with the Jordan canonical form, as Yuval notes. The important facts:
1. The characteristic polynomial of an upper triangular matrix is just $$\prod_{i=1}^n (t-d_{ii})$$ where $d_{ii}$ are the diagonal entries.
2. The minimal polynomial of a block diagonal matrix is the gcd of the minimal polynomials of the blocks of the matrix.
3. The minimal polynomial of a Jordan block associated to $\lambda$ of size $k\times k$ is $(t-\lambda)^k$.
The three facts above are fairly easy to establish. That will tell you how to construct a matrix with the desired properties.
You can also use the rational canonical form by using companion matrices instead. Then you would replace 1 above with
The characteristic polynomial of a block diagonal matrix is the product of the characteristic polynomials of the blocks.
and 3 with
The characteristic and minimal polynomials of the companion matrix of $p(x)$ are both \$p(x).
-
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https://forum.math.toronto.edu/index.php?PHPSESSID=mseudlilqgak7j1s97lg38os10&topic=1149.msg4026
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### Author Topic: Q7-T0501 (Read 1481 times)
#### Victor Ivrii
• Elder Member
• Posts: 2563
• Karma: 0
##### Q7-T0501
« on: March 30, 2018, 12:22:31 PM »
a. Determine all critical points of the given system of equations.
b. Find the corresponding linear system near each critical point.
c. Find the eigenvalues of each linear system. What conclusions can you then draw about the nonlinear system?
d. Draw a phase portrait of the nonlinear system to confirm your conclusions, or to extend them in those cases where the linear system does not provide definite information about the nonlinear system.
\left\{\begin{aligned} &\frac{dx}{dt} = 1 - y\\ &\frac{dy}{dt} = x^2 - y^2 \end{aligned}\right.
#### Darren Zhang
• Full Member
• Posts: 22
• Karma: 13
##### Re: Q7-T0501
« Reply #1 on: March 30, 2018, 01:13:14 PM »
(a) The critical points are solutions of the equations,$1-y = 0$, $(x-y)(x+y) = 0$
The first equation requires that y= 1 . Based on the second equation, x =1/-1. Hence the critical points are (-1,1) and (1,1).
(b,c) $F(x,y) = 1-y$ and $G(x,y) = x^2-y^2$. The Jacobian matrix of the vector field is $$J = \begin{pmatrix} 0 & -1 \\ 2x & 2y \end{pmatrix}$$
At the critical point $(-1,1)$, the coefficient matrix of the linearized system is $$J(-1,1) = \begin{pmatrix} 0 & -1 \\ -2 & -2 \end{pmatrix}$$
with eigenvalues $r_1 = -1-\sqrt{3}$ and $r_2 = -1+\sqrt{3}$ . The eigenvalues are real, with opposite sign. Hence the critical point is a saddle, which is unstable. At the equilibrium point (1,1), the coefficient matrix of the linearized system is $$J = \begin{pmatrix} 0 & -1 \\ 2 & -2 \end{pmatrix}$$ with complex conjugate eigenvalues $r_1 = -1+i$, $r_2 = -1-i$. The critical point is stable spiral, which is asymptotically stable.
Attached is the part(d)
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https://nift.now.sh/docs/types/std::char.html
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type: std::char
[contents]
#### Syntax
The syntax for std::char definitions is:
f++:
std::char definitions
std::char(definitions)
:=(std::char, definitions)
n++:
@std::char definitions
@std::char(definitions)
@:=(std::char, definitions)
Note: If you are using the first syntax for variable definitions and want to have more code and/or text following on the same line then simply end the definition with ';'.
#### Description
The std::char type is used for character values.
Note: ExprTk does not have direct access to variables of type std::char, if you want the convenience and efficiency of direct access then use char.
Note: If you need to define thousands of variables then := is faster, plus it has useful error messages for unrecognised types.
#### Options
The following options are available for std::char definitions:
option description
const definition of a constant
layer="x" define variable at layer x
private definition of a private
scope+="x" add x to scopes variable can be accessed from
option description
#### f++ example
Examples of std::char being defined with f++:
std::char a='i', b='j'
std::char(x, y, z)
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https://www.cureus.com/articles/10187-evolution-of-technique-in-endoscopic-transsphenoidal-surgery-for-pituitary-adenoma-a-single-institution-experience-from-220-procedures
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"Never doubt that a small group of thoughtful, committed citizens can change the world. Indeed, it is the only thing that ever has."
Original article
peer-reviewed
## Evolution of Technique in Endoscopic Transsphenoidal Surgery for Pituitary Adenoma: A Single Institution Experience from 220 Procedures
### Abstract
#### Introduction
Endoscopic transsphenoidal surgery (ETSS) for pituitary adenoma (PA) has been a recent shift from the traditional microscopic technique. Although some literature demonstrated superiority of ETSS over the microscopic method and some evaluated mono- vs. binostril access within the ETSS, none had explored the potential influence of dedicated instrument, as this procedure had evolved, on patients’ outcomes when compared to traditional microscopic tools.
#### Objective
To investigate our own clinical and radiographic outcomes of ETSS for PA with its technical evolution over time as well as a significance of, having vs. lacking, the special endoscopic tools.
#### Methods
Included patients underwent ETSS for PA performed by the first author (AH). Prospectively recorded patients’ data concerning pre-, intra- and postoperative clinical and radiographic assessments were subject to analysis. The three groups of differently evolving ETSS techniques, beginning with mononostril (MN) to binostril ETSS with standard microsurgical instruments (BN1) and, lastly, binostril ETSS with specially-designed endoscopic tools (BN2), were examined for their impact on the intra- and, short- and long-term, postoperative results. Also, the survival after ETSS for PA, as defined by the need for reintervention in each technical group, was appraised.
#### Results
From January 2006 to 2012, there were 47, 101 and 72 ETSS, from 183 patients, in the MN, BN1 and BN2 cohorts, respectively. Significant preoperative findings were greater proportion of patients with prior surgery (p=0.01) and tumors with parasellar extension (p=0.02) in the binostril (BN1&2) than the MN group. Substantially shorter operative time and less amount of blood loss were evident as our technique had evolved (p<0.001). Despite higher incidence, and more advanced grades, of cerebrospinal fluid leakage in the binostril groups (p < 0.001), the requirement for post-ETSS surgical repair was less than the mononostril cohort (p=0.04). At six-month follow-up (n=214), quantitative radiographic outcome analysis was markedly superior in BN2. Consequently, long-term result was better in this latest technical group. Important negative risk factors, from multivariate Cox regression analysis, were prior surgery, Knosp grade, and firm tumor while BN1, BN2 and percentages of anteroposterior dimension PA removal had positive effect on longer survival.
#### Conclusion
The evolution of technique for ETSS for PA from MN to BN2 has shown its efficacy by improving intra- and postoperative outcomes in our study cohorts. Based on our results, not only that a neurosurgeon, wishing to start performing ETSS, should enroll in a formal fellowship training but he/she should also utilize advanced endoscopic tools, as we have proved its superior results in dealing with PA.
### Introduction
Transsphenoidal surgery (TSS) for pituitary adenoma (PA) has been performed in many centers around the globe for several decades with recent emergence of endoscopic TSS (ETSS). This novel technique has been shown to be as effective as, if not more than, the traditional transseptal microscopic TSS (mTSS) [1-11]. Therefore, it is not surprising to witness a recent shift from mTSS to ETSS [12]. Despite abundant publications for ETSS, few had studied comparative results between mono- vs. binostril access [13, 14]. Moreover, none had examined the effects of, having vs lacking, dedicated tools on patient’s outcomes. We report our own experience of ETSS with specific attention to the evolution of technique starting from mononostril to binostrils, both of which utilized standard microsurgical tools, and, finally, binostrils with advanced, endoscopic-designed, instruments. The primary objective was to investigate the effect, amongst different techniques, of the special equipment whether they resulted in dissimilar need-for-reintervention of PA. The secondary goal was to evaluate, both short- and long-term, clinical and radiographic outcomes of each distinctive technique of ETSS
### Materials & Methods
The operating neurosurgeon (Ake Hansasuta, M.D.) has been particularly interested in pituitary surgery though he had no formal endoscopic endonasal skull base fellowship training. Transitioning from mTSS, after attending several didactic and cadaveric dissection courses, the first ETSS was performed at the Faculty of Medicine Ramathibodi Hospital in January 2006. Since the beginning of our ETSS, prospectively collected information from each case was recorded. The details of pre-, intra-, and postoperative data gathering and outcome evaluation are described below. With approval from the institutional review committee, retrospective analysis of the ETSS records was conducted. Patients who underwent ETSS, with confirmed pathology of pituitary adenoma or its apoplexy, performed by AH were included in this study. Aside from PAs with first-time ETSS, residual tumors were sorted into, based on their radiographic progression, with or without growth.
#### Preoperative and long-term postoperative assessments
Visual Function
With chief complaint of visual disturbance, each patient was examined for visual acuity (VA) by Snellen chart as well as visual field (VF) by automated Humphrey perimetry. After ETSS, visual function was evaluated using the same technique at six months. At this point, each patient’s postoperative visual (VA&VF) outcome was compared with preoperative value and was classified as improved, stable or worsened. For post-ETSS patients in need for urgent reoperation within 24 hours due to rapidly worsening vision, their ophthalmologic data were recorded at the time of reoperation. However, for patients with rapidly declining level of consciousness from postoperative apoplexy, without a possibility to obtain accurate visual function, their data were excluded from our ophthalmologic outcome assessment. Opthalmoplegia, if present before or after surgery, was documented.
Pituitary Hormone Function
After clinical suggestion of non-functioning or functioning PA, routine preoperative serum level of pituitary hormones including growth hormone (GH), age-specific insulin-like growth factor-1 (IGF-1), 8 AM cortisol, prolactin (PRL), thyroid stimulating hormone (TSH), free triiodothyronine (T3), free thyroxine (T4), testosterone, estradiol and gonadotropins, were obtained in every patient. Evidence of abnormally elevated hormone production before ETSS and standard criteria of functioning adenomas’ remission, i.e. GH [15], cortisol and ACTH [16], TSH [17] and PRL [18], were used for diagnosis and verification for postoperative hormonal cure. Diabetes insipidus (DI) after surgery was diagnosed by evidence of polyuria (urine output > 250 milliliter (mL) per hour for two consecutive hours), urine specific gravity < 1.005 and rising serum sodium over 145 milliequivalent per liter (mEq/L). Excluding patients with preexisting DI, new post-ETSS temporary DI was categorized by less than three months need for antidiuretic hormone supplement while long-term administration of it was considered permanent DI.
Preoperative imaging was obtained in all cases. Magnetic resonance imaging (MRI) was available for review in 92% of ETSS. On occasions, computed tomography (CT) scan was the only imaging modality before surgery (8%). Each patient’s sphenoid sinus was grouped into either sellar or presellar type. We did not perform ETSS on patients with concha type. In all cases, measured data of maximal diameter for transverse (X), anteroposterior (Y), and vertical (Z) aspects of their preoperative tumors were obtained. After 2008, volumetric measurement software became available allowing uniform calculation of the PA’s volume. If an MRI was obtained from an outside institute, it would be excluded from the postoperative volumetric analysis. Using Knosp et al., the tumor’s extension into parasellar region was graded [19]. Suprasellar extension was classified by the modified Hardy classification [20].
In case of no clinical indication for earlier radiographic study, such as postoperative apoplexy, the first MRI scan was obtained at six months after ETSS. Postoperative measurement of the tumors’ three dimensions (X, Y, Z) and volume were collected in similar fashion as before surgery. These pre- and postoperative dimensional and volumetric values were calculated for percentages of tumor removal (% removal) as below.
$$percentages\, of\, tumor\, removal\, (dimension[X,Y\, or\, Z]\, or\, volume)\,=\tfrac{preoperative\, (X,Y,Z\, or\, volume)-postoperative\, (X,Y,Z\, or\, volume)}{preoperative\, (X,Y,Z\, or\, volume)}x100$$
Patients without volumetric measurement either before or after ETSS were excluded from the % removal assessment by volume.
#### Evolution of surgical technique (Table 1)
The similarities in all groups were perioperative medication, i.e. routine hydrocortisone and antibiotic, and patient’s positioning using skull clamp with three-point rigid fixation. The left shoulder was elevated and supported to facilitate face turn toward the right side where operating surgeons stood. Either the right-sided abdomen or upper thigh was also prepped and draped for possible fat/fascia graft harvest. Antiseptic nasal wash followed by vasoconstrictive agent-soaked cottonoid packing in both nostrils was routinely done. After this point, each group of ETSS was different in its details of surgery.
First, mononostril ETSS technique (MN) was performed from January 2006 to May 2008 (29 months). Apart from utilizing an endoscope instead of microscope for visualization, most equipment was identical to mTSS. Many of them were bayonet neurosurgical instruments. For access, the right nostril was typically chosen unless this corridor was extremely narrow. After placement of a self-retaining nasal speculum, nasal mucosa below and medial to sphenoid ostium was coagulated away by monopolar cautery prior to sphenoidotomy. Contralateral access was gained by further extension of the bony and mucosal removal. Guided by cross-table lateral fluoroscopy, sellar floor was opened with osteotome and rongeur. After dura opening, using ring curettes of different angle and size, tumor resection began at its lower half followed by deeper portion. Subsequent resection of adenoma was carried out superiorly and, lastly, at its anterior part. If cerebrospinal (CSF) leakage was noted, depending on its grading by Eposito et al. [21], use of harvested fat and fascia graft was performed in every ETSS. In addition, for grade 2 and 3, every patient received lumbar drainage for CSF diversion.
In the second group of patients, the binostril ETSS technique utilizing standard mTSS tools (BN1) was employed from June 2008 to November 2010 (30 months). We abandoned the routine use of self-retaining nasal speculum entirely. With the same mTSS instruments, maneuvers for coagulation of nasal mucosa, sphenoidotomy, sellar enlargement and PA resection were unchanged from the MN technical group. Because of the availability of intraoperative stereotactic navigation, cross-table fluoroscopy usage had faded out. Additionally, flowable hemostatic agent was at hand to deal with troublesome hemorrhage. Unlike the mononostril group, if CSF leakage was observed, dura substitute and fibrin glue were applied for small leakage (grade 0 or 1) without lumbar drain placement. For larger defect (grade 2 or 3) or intraventricular entry, multi-layer closure by dura substitute, fat, fascia and fibrin glue were applied as well as lumbar drainage.
For the third and last technique, we performed binostrils ETSS with advanced endoscopic instruments (BN2). This modification of several steps took place from December 2010 until January 2012 (13 months). First, preparation of mucosa for potential use of vascularized nasoseptal flap, instead of burning it away as in MN or BN1, was done in every case. Secondly, specially designed tools, for endoscopic use, were our new acquisitions. Examples of the equipment were such as bipolar cautery for endoscopic work, instead of regular ones, and transnasal low-speed drill, with different angle of cutting and diamond bur, that could reach sella turcica. The low-speed, 12,000 revolutions per minute (RPM), drill enabled ample bone opening. With the ability to remove bone of skull base, i.e. tuberculum sellae, planum sphenoidale or pterygoid plates, effectively, extended ETSS was, for the first time, possible whereas not applicable in the first two groups. Occasionally, a slim, with extra length, ultrasonic aspirator was of paramount when the neurosurgeon came across hard, or firm, consistency PA. These aforementioned tools helped vastly to overcome obstacle that hindered many problematic steps in the MN and BN1 groups. For sellar closure, in addition to multiple layer application as in BN1, vascularized nasoseptal mucosal flap, described by Hadad et al. [22], in high-grade CSF leakage, or entry into third ventricle was utilized. Lumbar drain usage was seldom.
Mononostril ETSS (MN) Binostril ETSS with basic instruments (BN1) Binostril ETSS with advanced instruments (BN2) Period January 2006-May 2008 June 2008-November 2010 December 2010-January 2012 Self-retaining nasal speculum Yes No No Sphenoid and septal mucosa Monopolar cautery to burn away the mucosa Monopolar cautery to burn away the mucosa Preserved for possible vascularized nasoseptal mucosal flap Sphenoid and sellar bone Osteotome and rongeur Osteotome and rongeur Low-speed drill and rongeur Intraoperative imaging guidance Cross-table lateral view fluoroscopy Cross-table lateral view fluoroscopy and, later, intraoperative stereotactic navigation Intraoperative stereotactic navigation Slim and long ultrasonic aspirator (for firm tumor) No No Yes Hemostasis Monopolar, regular bipolar, gelatin sponge, oxidized cellulose polyanhydroglucuronic acid Monopolar, regular bipolar, gelatin sponge, oxidized cellulose polyanhydroglucuronic acid, later, flowable hemostatic agent As in BN1 plus specifically designed bipolar CSF leakage (grade 0 or 1) Fat, fascia Dura substitute, fibrin glue Dura substitute, fibrin glue CSF leakage (grade 2 or 3) Fat, fascia, lumbar drain Fat, fascia, fibrin glue, lumbar drain Fat, fascia, nasoseptal mucosal flap, seldomly lumbar drain
#### Intraoperative and short-term postoperative assessments
For every ETSS, operative time was charted from the start of nasal packing to the conclusion of surgery. The amount of blood loss, tumor consistency as well as surgical complication(s) were documented. After surgery, all patients were admitted to intermediate or intensive care unit for one night, or longer if necessary, with subsequent transfer to regular ward. Patients with low-grade (0 or 1) CSF leakage were kept flat in bed for two days whereas those with higher grades requiring three to four days due to lumbar drainage. The majority of patients in the BN2 group did not have CSF diversion but were kept in bed for the same length of time. Most patients did not have continued CSF leakage after this point. Without clinical evidence of CSF leakage, patients would subsequently be allowed to gradually increase the degree and the amount of time for upright position. If continued CSF leakage was observed during this period, the patient would remain recumbent with a lumbar drain, in the MN and BN1 groups, or without a lumbar drain in the BN2 group. Persistent CSF leakage, despite lumbar drainage, longer than one week prompted repeat TSS for repair whereas transcranial (TC) route was indicated for failure of cessation after the repeat TSS. Apart from persistent CSF leakage, patients with rapidly worsening visual function or level of consciousness from post-ETSS apoplexy would undergo emergency TSS or TC after radiographic confirmation.
Other than CSF leakage and apoplexy, our short-term postoperative complication included adverse events detected during the hospitalization and subsequent discharge within first 30 days after ETSS. Examples of the complications were epistaxis, temporary DI and serious infectious complication.
#### Follow-up and reintervention
After discharge, follow-up appointments with the neurosurgeon (AH) and endocrinologists were scheduled at two weeks, one and three months. At six months after ETSS, evaluation for visual function (VA&VF), endocrinologic and MRI studies were performed by the methods described previously. Also, the comparison between pre- and post-ETSS outcomes were assessed as mentioned earlier. Patients who underwent emergency re-surgery for post-ETSS apoplexy were excluded from the long-term assessments. If there was no requirement for reintervention at the first six-month postoperative visit, serial MRI would be obtained at six month intervals for the first two years and annually thereafter as long as there was no new therapy.
For patients with residual tumor, decision for reintervention was based on various factors as followed. Frequent rationales for reoperation, ETSS or TC, were persistently high level of hormones in functioning adenomas, symptomatic compression of surrounding structure and recurrent growth of residual tumor. Patient’s age, co-morbidities and, in some, preference were also taken into consideration for reoperation. Apart from surgery, patients were given information in regard to their options for non-surgical treatments such as radiotherapy or medical treatment. Some patients elected to watch their residual tumors by periodic MRI surveillance. After reintervention, the patient would be censored from further data record. For those elected to undergo another ETSS, each patient would start as a new case, who had prior surgery, in the same or different ETSS group.
#### Data analysis
Utilizing Stata software version 12.0 (Stata Corp., College Station, TX), pre-, intra- and postoperative parameters together with outcomes comparison amongst stratified MN, BN1 and BN2 groups were executed with unpaired t-test, rank tests, chi-square and Fisher’s exact test as appropriate, assuming statistical independence. To identify risk factors for reintervention, Cox proportional hazard regression models were used for both univariate and multivariate analyses. Kaplan-Meier graphs were computed, arranged by the three technical groups, to assess the reintervention-free survival. P-value of <0.05 was considered statistically significant.
### Results
#### Patient demographics (Table 2)
Between January 2006 and January 2012, two hundreds and fifty-eight consecutive ETSS have been performed at the Faculty of Medicine Ramathibodi Hospital by the, first author, neurosurgeon (AH). Thirty-eight non-PA, such as craniopharyngioma, meningioma, arachnoid cyst, Rathke’s cleft cyst, epidermoid cyst, chordoma, and non-diagnostic specimens, were excluded, leaving 220 operations for review. Among them, 47, 101 and 72 surgeries were in the MN, BN1 and BN2 group, respectively. There were 21 patients who underwent two ETSS and two patients with three ETSS. Cases with prior surgery in the binostril cohorts (40%) were more frequent than in the mononostril group (17%)(p=0.01). Preoperative radiographic studies amongst the cohorts revealed no significant dimensional or volume measurement difference. Nevertheless, higher Knosp grade (3&4) was more frequent in the BN1&2 groups than MN (p=0.02).
#### Intraoperative findings and short-term outcomes (Table 3)
Mononostril ETSS (MN) Binostril ETSS with basic instruments (BN1) Binostril ETSS with advanced instruments (BN2) p-value Operations: no. 47 101 72 Intraoperative findings and complications Operative time(hour): mean(SD) 5.1(1.2) 4.4(1.3) 3.6(0.9) <0.001 Estimated blood loss(mL): median(range) 420(170-1,200) 295(80-1500) 250(70-580) <0.001 Excessive venous bleeding causing premature termination of ETSS: no.(%) 3(6) 0 0 0.004 Firm tumor: no.(%) 1(2) 11(11) 12(17) 0.045 Intraoperative CSF leakage: no.(%) 13(28) 54(54) 46(64) <0.001 CSF leakage grade <0.001 - 0: no.(%) 34(72) 47(46) 26(36) - 1: no.(%) 7(15) 18(18) 9(12) - 2: no.(%) 6(13) 30(30) 23(32) - 3: no.(%) 0 6(6) 14(20) Carotid artery injury: no.(%) 0 1(1) 0 0.553 Postoperative complications (within 30 days) Death: no.(%) 0 1(1) 0 0.553 Postoperative persistent CSF rhinorrhea requiring surgery either TSS or TC: no.(%) 3(21) 4(7) 1(2) 0.04 Temporary diabetes insipidus: no.(%) 4(8) 9(9) 7(10) 0.912 Postoperative apoplexy: no.(%) 0 3(3) 0 0.167 Worsening visual function: no.(%) 0 1(1) 0 0.567 Meningitis: no.(%) 0 1(1) 1(1) 0.733 Septicemia: no.(%) 0 2(2) 0 0.305 Epistaxis: no.(%) 1(2) 2(2) 1(1) 0.944
Significantly shorter operative time and less amount of blood loss, as our ETSS technique had evolved, was remarkable (p<0.001). Compared to no occurrence in the binostril groups, three surgeries (6%) from the MN group came to premature end due to uncontrollable venous bleeding (p=0.004). Firm tumors were more commonly encountered in the latter groups than MN (p=0.045) which could be related to higher incidence of prior surgery in the binostril groups as described earlier. In spite of greater incidence and advanced grades of CSF leakage observed during ETSS in the binostril, especially the BN2, groups (p<0.001), postoperative persistent leakage requiring additional surgery, either TSS or TC, for repair was substantially less (p=0.04). The rest of intraoperative and short-term, 30-day, analyses were not different among groups. There were one carotid artery injury and one death in the BN1 group. The carotid artery event occurred while rongeuring off sellar bone, albeit real-time navigation. With successful intraoperative hemostasis, the patient did not suffer stroke after an endovascular procedure and lived normal life thereafter. One death occurred in another patient who had previously undergone multiple surgeries, both TC and mTSS, and radiotherapy. This patient had recurrent growth of the residual tumor resulting in progressive optic pathway compression. Unable to resect much tumor due to its firm consistency, apoplectic event, causing rapid decline in mental status ensued. Despite successful evacuation of the hemorrhagic transformation and CSF leak repair via TC approach, he, later, deteriorated from fulminant meningitis/ventriculitis. The patient passed away even with broad-spectrum intravenous antibiotics and aggressive resuscitation. Two additional patients, in the BN1 cohort, suffered postoperative apoplexy with declining level of consciousness in one and significantly worsening vision in the other. Both survived after emergency evacuation of hemorrhagic transformation of suprasellar residual tumors via TC. There was no new postoperative ophthalmoplegia from all technical cohorts.
#### Long-term outcomes (Table 4)
Mononostril ETSS (MN) Binostril ETSS with basic instruments (BN1) Binostril ETSS with advanced instruments (BN2) p-value Operations: no. 47 101 72 Lost follow-up: no.(%) 1(2) 3(3) 2(3) 0.957 Follow up time(month): median(range) 96(6-120) 72(6-96) 55(6-69) <0.001 Reintervention: no.(%) 37(80) 71(72) 40(57) 0.02 Functional adenoma cured: no.(%) 3/7(43) 10/24(42) 7/18(38) 0.916 Permanent diabetes insipidus: no.(%) 0 1(1) 1(1) 0.745 Available subjects for postoperative visual assessment n = 32 n = 63 n = 39 Visual acuity improved: no.(%) 28(88) 58(92) 38(97) 0.279 Visual acuity worsen: no.(%) 0 1(2) 0 0.567 Visual field improved: no.(%) 29(90) 56(90) 36(94) 0.719 Available subjects for pre- and postoperative three dimensional measurements n = 46 n = 98 n = 70 Percentages of tumor removal (transverse): median(range) 29(0-100) 36(0-100) 64(0-100) <0.001 Percentages tumor removal (anteroposterior): median(range) 40(0-100) 39(0-100) 62(5-100) <0.001 Percentages of tumor removal (vertical): median(range) 50(0-100) 46(0-100) 69(17-100) <0.001 Available subjects for pre- and postoperative tumor volumetric calculation N/A n = 66 n = 54 Percentages of tumor removal (volume): median(range) N/A 75(5-100) 84(50-100) 0.04 Tumor removal > 80% volume: no(%) N/A 39(59) 41(75) 0.01
With three patients lost to follow-up and other three patients with postoperative apoplexy, 214 cases were available for long-term assessment. The incidence of temporary and permanent DI was not significantly different among the three technical groups. At the first six-month post-ETSS visit, the % removal clearly demonstrated, by X-Y-Z dimensions. Superior PA resection in the BN2 over BN1 and the BN1 over MN group was obvious (p<0.001). Within the binostril groups, from 120 subjects with available volumetric calculation, the BN2 showed better % removal over the BN1 (p=0.04). In addition, the number of cases with > 80% tumor removal was greater in BN2 than BN1 group (p=0.01).
Reintervention-free interval in the BN2, compared with BN1 and MN, group, from Kaplan-Meier survival curve, almost reached statistical significance (p=0.066) for longer reintervention-free duration of BN2 when all follow-up cases were included(Figure 1).
When only first surgery (ETSS) performed at our institute, excluding those with prior TSS or TC, were considered (n=138), the curve also displayed a trend (p=0.077) with BN1 separating itself further from MN, more than the first, all-patient-included, graph (Figure 2).
Upon direct comparison between BN2 and MN group, significant survival, in all cases (p=0.03) and in first-time ETSS (p=0.017), was perceived (Figures 3, 4).
Despite superior radiographic outcomes after binostril ETSS over MN, from 134 cases with preoperative visual complaints, there was only a trend for slightly better visual function. This improvement, however, did not reach statistical significance (p=0.279).
#### Analyses of risk factors for reintervention
Univariate analyses of various risk factors for reintervention revealed that the BN2 group and apoplexy presentation were associated with favorable outcomes. In contrast, prior surgery and its increasing numbers of procedures had adverse impact on survival-free period. Other negative factors were sphenoid sinus with presellar type, Knosp grade and firm tumor. While the preoperative transverse (X) and anteroposterior (Y) dimensions were correlated with poorer outcome but, to our wonder, not the vertical (Z) measurement. Nevertheless, the postoperative % removal by dimensional and volumetric measurements linked with longer reintervention-free duration (Table 5).
Factors Hazard ratio (95%CI*) p-value* Endoscopic transsphenoidal surgery (ETSS) technique Mononostril ETSS (MN) [reference] 1 N/A Binostril ETSS with basic instruments (BN1) 0.92(0.59-1.44) 0.711 Binostril ETSS with advanced instruments (BN2) 0.62(0.38-1.01) 0.046 Preoperative risk factor Age (per year increase) 0.99(0.98-1.01) 0.855 Male vs Female 0.99(0.72-1.37) 0.966 Visual presentation 1.15(0.80-1.63) 0.451 Apoplexy presentation 0.32(0.11-0.89) 0.028 Asymptomatic presentation 1.18(0.76-1.82) 0.459 Prior surgery 1.78(1.30-2.44) <0.001 Number of prior surgery (per number of surgery increase) 1.37(1.11-1.68) 0.003 Preoperative transverse diameter (per cm increase) 1.29(1.05-1.59) 0.015 Preoperative anteroposterior diameter (per cm increase) 1.08(1.07-1.64) 0.010 Preoperative vertical diameter (per cm increase) 1.08(0.93-1.25) 0.306 Preoperative tumor volume (per mL increase) 1.00(0.98-1.03) 0.76 Presellar type 1.47(1.01-2.15) 0.044 Macroadenoma 1.78(0.56-5.67) 0.326 Hardy grade (per grade increase ) 1.13(0.95-1.34) 0.167 Knosp grade (per grade increase) 1.81(1.45-2.25) <0.001 Duration of symptoms (per month increase) 81.4(71.4-91.3) 0.57 Intraoperative risk factor Firm tumor 1.70(1.01-2.84) 0.044 CSF leakage (per grade increase) 0.95(0.82-1.11) 0.541 Operative time (per hour increase) 1.08(0.94-1.24) 0.277 Postoperative risk factor Visual symptom improvement 1.02(0.73-1.42) 0.928 Pathology Non-functioning adenoma [reference] 1 N/A Growth hormone-producing adenoma 1.23(0.73-2.06) 0.439 Other functioning adenoma 0.60(0.29-1.27) 0.182 Extent of tumor removal Percentages of tumor removal (transverse) (per % removal) 0.978(0.972-0.985) <0.001 Percentages of tumor removal (anteroposterior) (per % removal) 0.975(0.969-0.982) <0.001 Percentages of tumor removal (vertical) (per % removal) 0.978(0.971-0.985) <0.001 Percentages of tumor removal (volume) (per % removal; n=120) 0.980(0.968-0.992) <0.001
Further statistical examination, by multivariate analyses, reconfirmed the positive effect of the BN2. Additionally, it also disclosed increased survival power of the BN1 over MN. Prior surgery, Knosp grade and firm tumor were reiterated as being negative factors. Interestingly, the % removal of anteroposterior (Y), not the transverse (X) or vertical (Z), axis also correlated with longer reintervention-free time (Table 6).
Risk factor Hazard ratio (95%CI*) p-value* Mononostril ETSS (MN) [reference] 1 N/A Binostril ETSS with basic instruments (BN1) 0.57(0.36-0.89) 0.013 Binostril ETSS with advanced instruments (BN2) 0.34(0.21-0.56) <0.001 Prior surgery 1.68(1.28-2.39) 0.004 Knosp grade (per grade increase) 1.84(1.48-2.29) <0.001 Firm tumor 1.67(1.03-2.71) 0.036 Percentages of tumor removal (anteroposterior) (per % removal) 0.98(0.97-0.99) <0.001
### Discussion
Endoscopic endonasal skull base surgery, with clear advantages of minimal brain manipulation and superb panoramic view visualization, is here to stay. Published literature reported outcomes of PA surgery comparing between mTSS vs. ETSS with a trend for superior result towards the endoscopic method especially PA with suprasellar extension [1, 4-6, 9]. In addition, mono- vs binostril access had been reviewed and reports of binostril ETSS with slightly better results were described [13, 14]. Considering abundant information with regard to various techniques of ETSS, none had yet explored the influence of, having vs. lacking, sophisticated endoscopic tools on clinical and radiographic outcomes. Therefore, this study aimed to find out if there was relevant impact from advanced endoscopic equipment over standard mTSS tools in pure ETSS for PA.
Similar to previous publications [23, 24], it is undeniable that one immensely influencing factor in this study must have been our own learning curve acquired over time. Its effect was apparent by shorter operative time and less amount of blood loss as the ETSS had evolved. Without a formal fellowship, the neurosurgeon (AH) had gone through a very steep learning curve struggling with a narrow corridor, during MN, to a wider passage, with BN1, both of which without dedicated instrument. Finally, larger opening with more defined tools in the BN2 group facilitated desirable outcomes. Hence, in addition to adequate training, utilization of advanced instruments is of paramount per our clinical and radiographic results. Although the majority of clinical outcomes were not different between MN and BN1 group, greater extent of tumor resection, as shown by three-dimensional (X, Y, Z) % removal, was noted in the binostril access. Regardless of similarity of the survival curve in Kaplan-Meier estimator, there was positive effect on the reintervention-free duration, by multivariate analysis, of the BN1 over the MN group (p=0.013) indicating some impact of binostril technique (Table 6). This is, perhaps, the true logic that larger corridor, together with wider viewing angle, ameliorating deeper reach, evidently by the frequency and higher grades of CSF leakage in the bi- over mononostril approach. After acquisition of advanced tools, even better exposure, with expanded TSS i.e. transtuberculum or transpterygoid, and tumor resection enabled superior outcomes in the BN2 group.
Intraoperatively, firm tumors in the binostril more than the mononostril group were frequently observed. We believed this phenomenon could partly be from greater numbers of cases with prior surgery, thus, more fibrosis within PAs. Ineffective removal of firm tumors by ring curette in MN and BN1 group was overcome by utilizing long and slim ultrasonic aspirator in BN2. Not only more aggressive PA resection in the binostril groups brought about no, or smaller, residual tumor and, consequently, longer survival but also larger defect of CSF leakage. However, with modification of sellar closure method, the need for additional surgical repair for persistent post-ETSS CSF rhinorrhea was, instead, significantly lower. This is, most likely, owing to vascularized nasoseptal mucosal flap utilized in BN2 cohort despite seldom use of lumbar drainage.
Another apparent difficulty in our early ETSS was managing profuse hemorrhage. It was an extreme challenge dealing with intercavernous sinus, or cavernous sinus itself, outpouring via mononostril approach. Controlling high-pressure venous bleeding, more than oozing, typically required at least two, preferably three, hands to accomplish the task. To no wonder, three ETSS in the MN group had to be prematurely aborted due to failure of adequate hemostasis to proceed with the next step of surgery. In contrast, with binostril access yielding wider exposure, hence, better maneuverability, along with handy flowable hemostasis, no ETSS had to be terminated due to the same reason. Although wider viewing angle was provided by the BN1 technique, a lack of specially designed tools could have affected unforgiving complication(s) namely the postoperative apoplexy from huge bulk of remaining PA at the suprasellar space. While the incidence did not reach statistical significance (p=0.167), by having sophisticated equipment, there was no postoperative apoplexy in the BN2 group, probably by maximizing access and ability to reach deeper, consequently, smaller or no residual tumor, than the BN1 group. In addition, much as bayonet neurosurgical instruments allow surgeon to work without the operating hands obstructing the line of sight via microscope for mTSS, this extra angle consumes more space during endoscopic work creating chopstick effect hindering maneuverability. Utilizing these mTSS tools, that was rather cumbersome, could have been one of other influencing factors resulting in less desirable outcomes in MN and BN1 compared to BN2.
At six-month follow up, it was somewhat disappointing that post-ETSS visual improvement did not reach statistical difference in light of obviously better % tumor removal as this technique had evolved. On the opposite, lacking equipment to tackle firm PA, one worsened visual function from postoperative apoplexy occurred in the BN1 group. Although this did not reach statistical significance, no patient in the BN2 cohort suffered such complication when advanced instruments were available. Despite only a trend for longer survival in BN2 by reintervention-free Kaplan-Meier curves (Figure 3), this inclination became more evident when cases with prior surgery were excluded. Further separation of the curves between BN1 and MN was recognized (Figure 4). Logical explanation for this should be the higher % removal in BN2 over BN1, by advanced tools, and BN1 over MN, by larger exposure, that more aggressive PA resection left smaller residual tumor behind. Thus, PA recurrence was delayed. When ETSS techniques were not considered, as in multivariate analysis, risk factors, for worse outcome, were similar to prior literatures, such as prior surgery, Knosp grade and firm tumor [25-27]. Interestingly, besides binostril approaches, another positive factor was the % tumor removal in the anteroposterior dimension. One probable explanation could be the fact that higher proportion of, or total, PA resection obliged reaching deeper (anteroposterior dimension) into the sella and the tumor. This could, in part, coincide with the increased frequency and higher grades of CSF leakage in the bi- over the mononostril group.
Potential drawbacks in this study are as followed. We admit that there certainly existed selection bias for patients undergoing ETSS in mono- vs binostril group. At the beginning of the first cohort (MN), during the transition from mTSS to ETSS, the neurosurgeon (AH) still performed mTSS in selected functioning PAs for better maneuverability hoping for higher chance of cure. If these cases were to undergo mononostril ETSS, its result could have probably been poorer. In contrast, no patient underwent mTSS in during the binostril ETSS period. One other example of significant selection bias was that, in the MN group, we elected not to perform ETSS for PA with intraventricular extension due to the lack of experience. Furthermore, for fear of major complication as much as awareness of limited maneuverability via undersized corridor, these patients in the mononostril group underwent TC instead of ETSS and then became subjects in the binostril approaches for residual tumor afterwards. This could potentially be the important reason why there was no postoperative apoplexy in MN group. After acquiring more experience along with wider access gained by the binostril method, profiting less cumbersome chopstick effect, cases with this level of difficulty (PA with intraventricular extension) underwent ETSS in the BN1 (9%) and BN2 (11%) group. It might be a valid explanation why three patients suffered postoperative apoplexy in the BN1 cohort. Later, with availability of advanced, slim and long, instruments in the BN2 group, allowing ample exposure and, as a consequence, greater extent of PA removal, thus, there was no postoperative apoplexy as earlier discussed. The other selection bias was evident in the higher proportion of cases with previous surgery, presellar type and parasellar extension, in the BN1&2 group. This particular preference was, again, driven by more experience and advanced tools availability.
Apart from those above-mentioned selection bias, our second pitfall could potentially be from some discrepancy between measurements of, and comparison between, different radiographic modalities. Although the preoperative imaging measurements were mostly from MRI, a few cases had only CT scan before ETSS (8%), making comparisons between different pre- vs postoperative dimension (X, Y, Z) data somewhat less accurate. These cases, however, were omitted from the volumetric calculation. While measuring X, Y, Z provided some objective data, nonetheless, not all PA were perfectly circular or elliptical. There were invasive tumors with odd configurations. Therefore, measuring the widest dimensions could not be universally informative. The other drawback is the different criteria for ETSS failure. We used the definition of “reintervention-free” instead of “progression-free” survival unlike many of the previous reports. Some patients, particularly in the BN2 group, underwent additional treatment before tumor exhibited growth. Reintervention was decided even without clinical or radiographic progression (Table 2). As a consequence, based on the Kaplan-Meier survival estimator, one may notice that, at 48-60 months after ETSS, the BN2 cohort’s curve dropped to almost at the same level as MN or BN1 whereas, up to its first 48 months, it was distinctively superior than the basic-instrument cohort. It appeared as though utilizing advanced tools did not yield long-term advantage (Figures 1-4). This was also an occurrence from our recent selection bias, again, for further treatment in asymptomatic patients most of whom had non-functioning PAs. Some of them underwent redo ETSS in the BN2 group despite no or minimal growth. This particular tendency was due to recent acquisition of more advanced equipment i.e. intraoperative MRI [28], transnasal highspeed drill, bipolar sealer, slim&long doppler ultrasound. Owing to the awareness of, given enough time, residual PA could eventually regrow [29, 30]. Thus, with even better equipment as mentioned, we were inclined to offer, preferably young and healthy, patients repeat ETSS. On the contrary, similar patients in the previous (MN and BN1) groups would have just deferred surgical treatment but continued radiographic surveillance until PA growth was perceived.
In spite of the aforementioned selection bias and more negatively-influencing pre- and intraoperative parameters, the binostril ETSS cohorts demonstrated better clinical and radiographic aftermaths. The dedicated tools were pivotal pieces of success in the BN2 group enabling, near-complete or, complete resection, therefore, resulting in desirable short- and long-term outcomes. This evidence-based data put an emphasis on how modern day ETSS for PA should be performed particularly in those with complex tumor and sphenoid sinus anatomy. Nevertheless, the meaningful comparison between mono- vs binostril ETSS ought to be fairly evaluated by randomized controlled trial utilizing same sophisticated instruments by the same, highly experienced, surgeon. Although a prospectively designed study, to explore within ETSS comparing outcomes between with vs. without special equipment, would ideally generate improved class of evidence for this matter, it would be rather unethical considering previous publication’s and our current results.
Lastly, while this research may not alter the practice of neurosurgeons already utilizing advanced tools, our information ought to be somewhat invaluable for those working in under-developed or developing countries with limited budgets. Dedicated endoscopic equipment and disposable items can immensely escalate the overall surgical care cost of patients with PA when compared to mTSS or ETSS using mTSS tools. For a neurosurgeon with interest in ETSS but lacking formal fellowship and advanced endoscopic instrument training, mitigating major complication(s) by selecting good surgical candidates, i.e. simple PA with straightforward sphenoid sinus anatomy, for his/her start of ETSS is strongly advised.
### Conclusions
Success of ETSS for PA demands several factors. It requires not only tremendous surgical skill and experience but also specially-designed instruments in order to achieve the desirable results. This study demonstrated significantly superior intra- and postoperative clinical and radiographic outcomes in the advanced- over the basic-instrument group as well as the bi- over the mononostril group. Any neurosurgeon willing to commence ETSS, particularly without a fellowship training, ought to be fully furnished with advanced tools. Prior surgery, higher Knops grade and firm tumor were, again, associated with poorer outcome of ETSS for PA.
### References
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11. Li A, Liu W, Cao P, Zheng Y, Bu Z, Zhou T: Endoscopic versus microscopic transsphenoidal surgery in the treatment of pituitary adenoma: A Systematic review and meta-analysis. World Neurosurg. 2017, 101:236–246.
12. Rolston JD, Han SJ, Aghi MK: Nationwide shift from microscopic to endoscopic transsphenoidal pituitary surgery. Pituitary. 2016, 19:248–250. 10.1007/s11102-015-0685-y
13. Conrad J, Ayyad A, Wuster C, et al.: Binostril versus mononostril approaches in endoscopic transsphenoidal pituitary surgery: clinical evaluation and cadaver study. J Neurosurg. 2016, 125:334–345. 10.3171/2015.6.JNS142637
14. Wen G, Tang C, Zhong C, et al.: Mononostril versus binostril endoscopic transsphenoidal approach for pituitary adenomas: A Systematic review and meta-Analysis. PLoS One. 2016, 11:0153397. 10.1371/journal.pone.0153397
15. Giustina A, Chanson P, Bronstein MD, et al.: A consensus on criteria for cure of acromegaly. J Clin Endocrinol Metab. 2010, 95:3141–3148. 10.1210/jc.2009-2670
16. Biller BM, Grossman AB, Stewart PM, et al.: Treatment of adrenocorticotropin-dependent Cushing's syndrome: a consensus statement. J Clin Endocrinol Metab. 2008, 93:2454–2462. 10.1210/jc.2007-2734
17. Tjornstrand A, Nystrom HF: Diagnosis of endocrine disease: Diagnostic approach to TSH-producing pituitary adenoma. Eur J Endocrinol. 2017, 177:183–197. 10.1530/EJE-16-1029
18. Mehta GU, Lonser RR: Management of hormone-secreting pituitary adenomas. Neuro Oncol. 2017, 19:762–773. 10.1093/neuonc/now130
19. Knosp E, Steiner E, Kitz K, Matula C: Pituitary adenomas with invasion of the cavernous sinus space: a magnetic resonance imaging classification compared with surgical findings. Neurosurgery. 1993, 33:610–617.
20. Wilson CB: Clinical management of pituitary disorders. Neurosurgical management of large and invasive pituitary tumors. Tindall GT, Collins WF (ed): Raven Press, New York; 1979:335–342.
21. Esposito F, Dusick JR, Fatemi N, Kelly DF: Graded repair of cranial base defects and cerebrospinal fluid leaks in transsphenoidal surgery. Neurosurgery. 2007, 60:295–303. 10.1227/01.NEU.0000255354.64077.66
22. Hadad G, Bassagasteguy L, Carrau RL, Mataza JC, Kassam A, Snyderman CH, Mintz A: A novel reconstructive technique after endoscopic expanded endonasal approaches: vascular pedicle nasoseptal flap. Laryngoscope. 2006, 116:1882–1886. 10.1097/01.mlg.0000234933.37779.e4
23. Leach P, Abou-Zeid AH, Kearney T, Davis J, Trainer PJ, Gnanalingham KK: Endoscopic transsphenoidal pituitary surgery: evidence of an operative learning curve. Neurosurgery. 2010, 67:1205–1212. 10.1227/NEU.0b013e3181ef25c5
24. Shikary T, Andaluz N, Meinzen-Derr J, Edwards C, Theodosopoulos P, Zimmer LA: Operative learning curve after transition to endoscopic transsphenoidal pituitary surgery. World Neurosurg. 2017, 102:608–612.
25. Chohan MO, Levin AM, Singh R, et al.: Three-dimensional volumetric measurements in defining endoscope-guided giant adenoma surgery outcomes. Pituitary. 2016, 19:311–321. 10.1007/s11102-016-0709-2
26. Esquenazi Y, Essayed WI, Singh H, Mauer E, Ahmed M, Christos PJ, Schwartz TH: Endoscopic endonasal versus microscopic transsphenoidal surgery for recurrent and/or residual pituitary adenomas. World Neurosurg. 2017, 101:186–195.
27. Przybylowski CJ, Dallapiazza RF, Williams BJ, et al.: Primary versus revision transsphenoidal resection for nonfunctioning pituitary macroadenomas: matched cohort study. J Neurosurg. 2017, 126:889–896. 10.3171/2016.3.JNS152735
28. Thiabpha A, Hansasuta A: Initial experience with ultra-low-field intraoperative magnetic resonance imaging in endoscopic endonasal transsphenoidal surgery for pituitary adenoma at ramathibodi hospital. J Med Assoc Thailand. 2016, 99:30–38.
29. Dallapiazza RF, Grober Y, Starke RM, Laws ER, Jr., Jane JA, Jr.: Long-term results of endonasal endoscopic transsphenoidal resection of nonfunctioning pituitary macroadenomas. Neurosurgery. 2015, 76:42–52. 10.1227/NEU.0000000000000563
30. Watts AK, Easwaran A, McNeill P, Wang YY, Inder WJ, Caputo C: Younger age is a risk factor for regrowth and recurrence of nonfunctioning pituitary macroadenomas: Results from a single Australian centre. Clin Endocrinol (Oxf). 2017, 87:264–271. 10.1111/cen.13365
Original article
peer-reviewed
### Author Information
###### Ethics Statement and Conflict of Interest Disclosures
Human subjects: Consent was obtained by all participants in this study. Faculty of Medicine Ramathibodi Hospital, Mahidol University ethic review committee clearance issued approval ID 10-55-34. With approval from the institutional review committee, retrospective analysis of the ETSS records was conducted. Animal subjects: All authors have confirmed that this study did not involve animal subjects or tissue. Conflicts of interest: In compliance with the ICMJE uniform disclosure form, all authors declare the following: Payment/services info: All authors have declared that no financial support was received from any organization for the submitted work. Financial relationships: All authors have declared that they have no financial relationships at present or within the previous three years with any organizations that might have an interest in the submitted work. Other relationships: All authors have declared that there are no other relationships or activities that could appear to have influenced the submitted work.
###### Acknowledgements
The authors would like to express our sincere gratitude for major assistance in statistical analysis along with valuable advices from Dr. Panuwat Lertsitichai and Ms. Suraida Aeesoa. In addition, we gratefully thank Dr. Thongchai Bhongmakapat and Dr. Boonsam Roongpuvapaht, our otolaryngologists, for their tremendous patience enduring this lengthy learning process together.
Original article
peer-reviewed
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http://openstudy.com/updates/50e1e9ebe4b0e36e3513dc1d
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## ksaimouli 3 years ago graph this x=-y^2 and x=2-3y^2 Delete Cancel Submit
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1. ksaimouli
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@Luis_Rivera
2. anonymous
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Im thinking if you solve for y it'll make it a little easier to see what you're working with
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5. ksaimouli
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@stgreen how did u get that $y=-\sqrt{x} ,y=\sqrt{\frac{ x-2 }{ -3 }}$
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|dw:1356983182794:dw|
7. anonymous
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both are parabolas.you know how to plot parabolas?? http://www.dummies.com/how-to/content/how-to-graph-a-parabola.html
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is sqrtx a parabola ?lol
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take square on both sides..it'll remove sqtrt and take the form of parabola
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Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.
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https://christopherdanielson.wordpress.com/tag/camping/
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# Tag Archives: camping
## Further adventures in Kindergarten fractions
I took the kids camping this past weekend. Fall along the Mississippi River, mid-70-degree days and 50-degree nights. Pretty much perfect. Having read information about our state park together earlier in the day—including the park’s acreage—Tabitha posed a question.
Tabitha (five and a half): How many acres or miles is our campsite?
Me: It’s only a small fraction of a square mile, but it’s about $\frac{1}{8}$ of an acre.
Tabitha: What’s a fraction?
Me: It’s like when you cut something up. It’s a number bigger than zero, but less than one.
Tabitha: Huh? That doesn’t make any sense!
Me: Well, let’s say you, Griffy and I had three s’mores, and we wanted to share them equally. We would each get one, right?
Tabitha: Yeah.
Me: But what if we only had 2?
Tabitha: Well, then you’d have to cut them in half.
Me: Right. So $\frac{1}{2}$ is a fraction
Tabitha: Oh.
[later]
Tabitha: But what’s the number? You said a fraction was a number bigger than zero, but less than 1.
Me: One-half is more than zero, but less than one.
Tabitha: Half of what?
Me: Half of anything is more than nothing, but less than the whole thing.
Tabitha: But what’s the number? A half isn’t a number!
I have been thinking about the moment when there is a choice to talk math with my kids. I have been trying to understand what I need to know in order to recognize that a choice exists and in order to pursue a mathematical conversation.
Fractions are tough because there really is a lot of specialized knowledge about how people learn them. I have been reading and teaching from the book Extending Children’s Mathematics over the last year or so. The authors make the argument that fair sharing is the best entry point for children’s sense-making about fractions. Not part-whole. Not number line. Fair sharing.
Notice how this plays out in my conversation with Tabitha. I start with part-whole, move to (arguably) number line and she protests that these ideas make no sense.
But as soon as I go with fair sharing, she’s on it. She gets that things sometimes need to be cut up in order to be shared equally.
She also understands—and this is crucial—that halves are meaningless without a referent whole. “Half of what?” is a brilliant and essential question.
So what did I need to know in order to pursue this conversation? I needed to know that there are multiple ways of thinking about fractions, and that fair sharing is going to be helpful for a young child to think about. And that part-whole and number line are going to be dead ends.
Tabitha learns from the conversation that fractions have to do with fair sharing. She doesn’t understand one-eighth—the fraction that initiated the conversation. She doesn’t understand anything more about the size of our campsite, nor about acres, miles or even square miles.
She learns that fractions have to do with sharing. That’s a pretty good Kindergarten-level idea, right there.
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https://trac-hacks.org/ticket/9747
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Opened 6 years ago
Closed 19 months ago
# Add visual calendar elements that span multiple days
Reported by: Owned by: anonymous Steffen Hoffmann normal WikiTicketCalendarMacro normal Gantt mattmgm@… 0.12
### Description
This is a very cool plugin, but I was hoping to tie it into tracjsganttplugin and other plugins, as well as use tickets to indicate e.g., vacations.
To that effect, it would be extremely useful to add a start date as well as the due/finish date and have this visually represented on the calendar.
### comment:1 in reply to: description Changed 6 years ago by Steffen Hoffmann
Keywords: Gantt added Calendar that spans multiple days → Add visual calendar elements that span multiple days
Thanks for your interest in this code.
... To that effect, it would be extremely useful to add a start date as well as the due/finish date and have this visually represented on the calendar.
I see. Please acknowledge, that historically both calendar macros are more aiming at easy wiki docs navigation. The former ticket calendar fork (WikiTicketCalendarMacro) adds links to milestones and tickets. Lately I added some fancy tests with graphically result representation. Your suggestion might be in line - pushing the calendar(s) beyond what they've been ever meant to be and look like before.
Well, the ticket (create)time is already available as an option: rendered in blue, if requested. But there is no graphical connection yet. I've been fighting clutter in the WikiTicketCalendarMacro by adding a "condensed" mode (ticket numbers only). Putting (much) more bars than just due milestones would go into the opposite direction. Do you have a sketch to show the look you envision for this feature?
And beware, that Gantt may look like a simple overlay of a calendar with bars, but technically there is a lot more behind. Because vertical alignment at least within a row (= week) would be a requirement as I guess, rendering just cell-by-cell as we do today won't work anymore. This increases table build calculations by some magnitudes. A rather complex task. Do you have some code to show feasibility of the enhancement, or do you plan to contribute such "real code" (= patches) in the future?
Hint: If you really care, check-out the trunk branch from wikicalendarmacro repository part. This is the only accepted base for ongoing development since I've merged both macros recently.
### comment:2 Changed 19 months ago by Ryan J Ollos
Resolution: → wontfix new → closed
The plugin is deprecated. Feature requests should be directed to WikiCalendarMacro.
### Modify Ticket
Change Properties
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## Journal of the Franklin Institute
### Engineering and Applied Mathematics
Short Title: J. Franklin Inst. Publisher: Elsevier (Pergamon), Oxford ISSN: 0016-0032; 1879-2693/e Online: http://www.sciencedirect.com/science/journal/00160032 Comments: Journal abbreviations vary in sources of the older volumes
Documents Indexed: 6,850 Publications (since 1875) References Indexed: 6,499 Publications with 191,196 References.
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### Authors
59 Park, Juhyun (Jessie) 58 Cao, Jinde 46 Shi, Peng 43 Xu, Shengyuan 41 Ding, Feng 35 Karimi, Hamid Reza 33 Hayat, Tasawar 32 Xia, Yuanqing 31 Jiang, Bin 31 Zhong, Shou-Ming 30 Yang, Guanghong 28 Chen, Wai-Kai 27 Al-saedi, Ahmed Eid Salem 27 Liu, Fei 27 Lu, Junwei 27 Swann, William Francis Gray 27 Zhang, Qingling 26 Mahmoud, Magdi Sadik Mostafa 26 Zhao, Xudong 26 Zhu, Quanxin 25 Ku, Yu-Hsiung 25 Kwon, O. M. 24 Basin, Michael V. 24 Su, Hongye 24 Xia, Jianwei 24 Yue, Dong 23 Huang, Tingwen 23 Tsai, Jason Sheng-Hong 22 Zhang, Zhengqiang 21 Guan, Zhihong 21 Hua, Changchun 21 Liu, Jinliang 21 Shtessel, Yuri B. 21 Zhang, Huaguang 20 Alsaadi, Fuad Eid S. 20 Shi, Kaibo 20 Xiang, Zhengrong 19 Zheng, Wei Xing 19 Zou, Yun 18 Chu, Yuming 18 Sadek, Ibrahim S. 18 Tian, Engang 18 Wang, Zhen 18 Yu, Li 17 Brown, David P. 17 Lu, Renquan 17 Niu, Yugang 17 Pipes, Louis A. 17 Swamy, M. N. S. 17 Wang, Zidong 17 Wu, Zhengguang 17 Zhang, Weihai 17 Zhou, Wuneng 16 Hinamoto, Takao 16 Jia, Yingmin 16 Jiang, Haijun 16 Li, Yongmin 16 Liu, Xinzhi 16 Tzafestas, Spyros G. 16 Yan, Huaicheng 15 Deng, Feiqi 15 Fei, Shumin 15 Hwang, Chyi 15 Shieh, Leang-San 15 Wu, Min 14 Guan, Xinping 14 Haddad, Wassim Michael 14 Kao, Yonggui 14 Li, Junmin 14 Li, Shihua 14 Ma, Yuechao 14 Park, PooGyeon 14 Shen, Hao 14 Yoo, Sung Jin 13 Chen, Guanrong 13 Dauphin-Tanguy, Geneviève 13 Duan, Guangren 13 Fang, Jian’an 13 Fridman, Leonid M. 13 Hu, Cheng 13 Lee, Chien-Hua 13 Li, Xiaodi 13 Liang, Jinling 13 Nguang, Sing Kiong 13 Paraskevopoulos, Paraskevas N. 13 Peng, Chen 13 Trinh, Hieu Minh 13 Wang, Zhanshan 13 Wu, Ligang 13 Xie, Xiangpeng 13 Zong, Guangdeng 12 Boiko, Igor M. 12 Chaparro, Luis F. 12 Chen, Wuhua 12 Gao, Huijun 12 Hsiao, Feng-Hsiag 12 Jiang, Yaolin 12 Ren, Zhang 12 Sun, Yuangong 12 Teo, Kok Lay ...and 9,693 more Authors
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### Fields
4,883 Systems theory; control (93-XX) 602 Information and communication theory, circuits (94-XX) 521 Computer science (68-XX) 387 Ordinary differential equations (34-XX) 374 Operations research, mathematical programming (90-XX) 339 Probability theory and stochastic processes (60-XX) 317 Biology and other natural sciences (92-XX) 289 Numerical analysis (65-XX) 272 Calculus of variations and optimal control; optimization (49-XX) 216 Mechanics of deformable solids (74-XX) 214 Mechanics of particles and systems (70-XX) 159 Statistics (62-XX) 156 Combinatorics (05-XX) 137 Partial differential equations (35-XX) 126 Linear and multilinear algebra; matrix theory (15-XX) 98 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 95 Real functions (26-XX) 82 Dynamical systems and ergodic theory (37-XX) 74 Fluid mechanics (76-XX) 56 Harmonic analysis on Euclidean spaces (42-XX) 56 Optics, electromagnetic theory (78-XX) 47 Approximations and expansions (41-XX) 47 Integral transforms, operational calculus (44-XX) 46 Functions of a complex variable (30-XX) 44 Special functions (33-XX) 43 History and biography (01-XX) 42 Operator theory (47-XX) 35 General and overarching topics; collections (00-XX) 35 Classical thermodynamics, heat transfer (80-XX) 33 Integral equations (45-XX) 21 Difference and functional equations (39-XX) 15 Mathematical logic and foundations (03-XX) 15 Quantum theory (81-XX) 12 Functional analysis (46-XX) 11 Differential geometry (53-XX) 10 Number theory (11-XX) 10 Statistical mechanics, structure of matter (82-XX) 9 Geophysics (86-XX) 8 Potential theory (31-XX) 7 Measure and integration (28-XX) 7 Sequences, series, summability (40-XX) 6 Global analysis, analysis on manifolds (58-XX) 5 Convex and discrete geometry (52-XX) 5 Relativity and gravitational theory (83-XX) 4 General topology (54-XX) 3 Algebraic geometry (14-XX) 3 Several complex variables and analytic spaces (32-XX) 3 Geometry (51-XX) 2 Order, lattices, ordered algebraic structures (06-XX) 2 Field theory and polynomials (12-XX) 2 Category theory; homological algebra (18-XX) 2 Group theory and generalizations (20-XX) 2 Astronomy and astrophysics (85-XX) 1 Abstract harmonic analysis (43-XX)
### Citations contained in zbMATH Open
4,672 Publications have been cited 30,005 times in 16,604 Documents Cited by Year
Auxiliary function-based integral inequalities for quadratic functions and their applications to time-delay systems. Zbl 1395.93450
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Disturbance attenuation properties of time-controlled switched systems. Zbl 1022.93017
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Dissipative dynamical systems: basic input-output and state properties. Zbl 0451.93007
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Stability of stochastic delay neural networks. Zbl 0991.93120
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Walsh operational matrices for fractional calculus and their application to distributed systems. Zbl 0377.42004
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Algebraic system theory: An analyst’s point of view. Zbl 0332.93001
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Chebyshev series approach to system identification, analysis and optimal control. Zbl 0538.93013
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1983
$$p$$th moment exponential stability of impulsive stochastic functional differential equations with Markovian switching. Zbl 1290.93205
Zhu, Quanxin
2014
Existence and global stability analysis of equilibrium of fuzzy cellular neural networks with time delay in the leakage term under impulsive perturbations. Zbl 1241.92006
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2011
A sliding mode approach to $$H_{\infty }$$ synchronization of master-slave time-delay systems with Markovian jumping parameters and nonlinear uncertainties. Zbl 1254.93046
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2012
On the degrees of the vertices of a directed graph. Zbl 0173.26404
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Passivity-based control for uncertain stochastic jumping systems with mode-dependent round-trip time delays. Zbl 1254.93148
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2012
$$H_\infty$$ finite-time control for switched nonlinear discrete-time systems with norm-bounded disturbance. Zbl 1214.93043
Xiang, Weiming; Xiao, Jian
2011
New approach to delay-dependent $$\mathcal H_\infty$$ control for continuous-time Markovian jump systems with time-varying delay and deficient transition descriptions. Zbl 1307.93444
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2015
Two direct Tustin discretization methods for fractional-order differentiator/integrator. Zbl 1051.93031
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2003
Chaos in the fractional order unified system and its synchronization. Zbl 1166.34030
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2008
A Walsh series direct method for solving variational problems. Zbl 0339.49017
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Mixed $$\mathcal H_\infty$$/passive sampled-data synchronization control of complex dynamical networks with distributed coupling delay. Zbl 1355.93113
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2017
The Kumaraswamy Weibull distribution with application to failure data. Zbl 1202.62018
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2010
On gravitational waves. Zbl 0017.09601
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Matrix iterative methods for solving the Sylvester-transpose and periodic Sylvester matrix equations. Zbl 1293.93289
Hajarian, Masoud
2013
Optimal control of linear delay systems via hybrid of block-pulse and Legendre polynomials. Zbl 1070.93028
Marzban, H. R.; Razzaghi, M.
2004
Improved results on stability of linear systems with time-varying delays via Wirtinger-based integral inequality. Zbl 1393.93104
Kwon, O. M.; Park, M. J.; Park, Ju H.; Lee, S. M.; Cha, E. J.
2014
An age dependent epidemic model. Zbl 0305.92010
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Stability analysis of a class of stochastic differential delay equations with nonlinear impulsive effects. Zbl 1207.34104
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2010
Parameter-dependent robust stability for uncertain Markovian jump systems with time delay. Zbl 1227.93126
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2011
Non-fragile finite-time extended dissipative control for a class of uncertain discrete time switched linear systems. Zbl 1395.93280
Xia, Jianwei; Gao, Hui; Liu, Mingxin; Zhuang, Guangming; Zhang, Baoyong
2018
Outer synchronization of partially coupled dynamical networks via pinning impulsive controllers. Zbl 1395.93091
Lu, Jianquan; Ding, Chengdan; Lou, Jungang; Cao, Jinde
2015
Stochastic maximum principle for distributed parameter systems. Zbl 0519.93042
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1983
Observer-based sliding mode control for a class of discrete systems via delta operator approach. Zbl 1202.93066
Yang, Hongjiu; Xia, Yuanqing; Shi, Peng
2010
Exponential synchronization for complex dynamical networks with sampled-data. Zbl 1264.93013
Wu, Zheng-Guang; Park, Ju H.; Su, Hongye; Song, Bo; Chu, Jian
2012
Synchronization of chaotic neural networks with time delay in the leakage term and parametric uncertainties based on sampled-data control. Zbl 1300.93113
Gan, Qintao; Liang, Yuhua
2012
Variational approach to some damped Dirichlet nonlinear impulsive differential equations. Zbl 1228.34048
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2011
The solution of the Bagley-Torvik equation with the generalized Taylor collocation method. Zbl 1188.65107
Çenesiz, Yücel; Keskin, Yıldıray; Kurnaz, Aydın
2010
Control of PDE-ODE cascades with Neumann interconnections. Zbl 1298.93279
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2010
Delay-dependent robust exponential stability of Markovian jumping reaction-diffusion Cohen-Grossberg neural networks with mixed delays. Zbl 1300.93131
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2012
Stability notions and Lyapunov functions for sliding mode control systems. Zbl 1372.93072
Polyakov, Andrey; Fridman, Leonid
2014
New delay-dependent robust stability criteria for uncertain neutral systems with mixed delays. Zbl 1395.93467
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2014
Stochastic stability analysis for discrete-time singular Markov jump systems with time-varying delay and piecewise-constant transition probabilities. Zbl 1264.93267
Wu, Zheng-Guang; Park, Ju H.; Su, Hongye; Chu, Jian
2012
Adaptive second order terminal sliding mode controller for robotic manipulators. Zbl 1372.93065
Mondal, Sanjoy; Mahanta, Chitralekha
2014
Finite-time synchronization of coupled discontinuous neural networks with mixed delays and nonidentical perturbations. Zbl 1395.93354
Yang, Xinsong; Song, Qiang; Liang, Jinling; He, Bin
2015
Stochastic stabilizability and $$H_\infty$$ control for discrete-time jump linear systems with time delay. Zbl 0967.93095
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1999
Delay-dependent stability and dissipativity analysis of generalized neural networks with Markovian jump parameters and two delay components. Zbl 1347.93265
Chen, Guoliang; Xia, Jianwei; Zhuang, Guangming
2016
Network-based passive estimation for switched complex dynamical networks under persistent dwell-time with limited signals. Zbl 1450.93078
Wang, Yudong; Hu, Xiaohui; Shi, Kaibo; Song, Xiaona; Shen, Hao
2020
Synchronization of dynamical networks with nonlinear coupling function under hybrid pinning impulsive controllers. Zbl 1398.93144
Li, Yuanyuan; Lou, Jungang; Wang, Zhen; Alsaadi, Fuad E.
2018
A linear matrix inequality approach to robust fault detection filter design of linear systems with mixed time-varying delays and nonlinear perturbations. Zbl 1201.93033
Karimi, H. R.; Zapateiro, M.; Luo, N.
2010
Adaptive control and synchronization of Lorenz systems. Zbl 1051.93514
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1999
Extended dissipative synchronization for semi-Markov jump complex dynamic networks via memory sampled-data control scheme. Zbl 1450.93082
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2020
Delay-dependent stochastic stability and $$H_{\infty}$$ analysis for time-delay systems with Markovian jumping parameters. Zbl 1040.93068
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2003
A note on stability of neutral delay-differential systems. Zbl 0969.34066
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1999
Robust adaptive sliding mode control for uncertain discrete-time systems with time delay. Zbl 1298.93112
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2010
Dynamical behaviors of discrete-time fuzzy cellular neural networks with variable delays and impulses. Zbl 1167.93369
Song, Qiankun; Cao, Jinde
2008
Constacyclic codes over $$\mathbb F_2 + u\mathbb F_2$$. Zbl 1176.94074
Abualrub, Taher; Siap, Irfan
2009
New results on exact controllability of a class of fractional neutral integro-differential systems with state-dependent delay in Banach spaces. Zbl 1451.93032
Ravichandran, C.; Valliammal, N.; Nieto, Juan Jose
2019
Novel master-slave synchronization criteria of chaotic Lur’e systems with time delays using sampled-data control. Zbl 1367.93357
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2017
Stability and dissipativity analysis of static neural networks with interval time-varying delay. Zbl 1307.93446
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2015
Existence of solutions for nonlinear fractional $$q$$-difference integral equations with two fractional orders and nonlocal four-point boundary conditions. Zbl 1372.45007
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2014
Mixed $$\mathcal H_\infty$$ and passive control for singular Markovian jump systems with time delays. Zbl 1395.93197
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2015
Improved least squares identification algorithm for multivariable Hammerstein systems. Zbl 1395.93287
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2015
Improved stability conditions of time-varying delay systems based on new Lyapunov functionals. Zbl 1393.93097
Lee, Tae H.; Park, Ju H.
2018
Actuator and sensor faults estimation based on proportional integral observer for TS fuzzy model. Zbl 1398.93202
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2017
Decomposition based least squares iterative identification algorithm for multivariate pseudo-linear ARMA systems using the data filtering. Zbl 1355.93190
Ding, Feng; Wang, Feifei; Xu, Ling; Wu, Minghu
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Distributed event-triggered control of discrete-time heterogeneous multi-agent systems. Zbl 1268.93097
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2013
On homogeneity and its application in sliding mode control. Zbl 1372.93054
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Asynchronous dissipative filtering for nonlinear jumping systems subject to fading channels. Zbl 1429.93391
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2020
Discrete Wirtinger-based inequality and its application. Zbl 1395.93448
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2015
Finite-time non-fragile $$l_2-l_\infty$$ control for jumping stochastic systems subject to input constraints via an event-triggered mechanism. Zbl 1398.93107
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2018
A collocation method using Hermite polynomials for approximate solution of pantograph equations. Zbl 1221.65187
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2011
The solution to matrix equation $$AX+X^TC=B$$. Zbl 1171.15015
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2007
Adaptive synchronization for delayed neural networks with stochastic perturbation. Zbl 1169.93350
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2008
A property of the eigenvalues of the symmetric positive definite matrix and the iterative algorithm for coupled Sylvester matrix equations. Zbl 1293.15006
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2014
Stability analysis for neutral Markovian jump systems with partially unknown transition probabilities. Zbl 1300.93180
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On stability and stabilization of singular uncertain Takagi-Sugeno fuzzy systems. Zbl 1395.93459
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2014
Controllability of fractional-order partial neutral functional integrodifferential inclusions with infinite delay. Zbl 1231.93018
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2011
Quadrotor vehicle control via sliding mode controller driven by sliding mode disturbance observer. Zbl 1254.93038
Besnard, Lénaïck; Shtessel, Yuri B.; Landrum, Brian
2012
Taylor series approach to system identification, analysis and optimal control. Zbl 0561.93018
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Stability of Markovian jump systems with generally uncertain transition rates. Zbl 1287.93106
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Effect of leakage time-varying delay on stability of nonlinear differential systems. Zbl 1293.34065
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2013
Output feedback exponential stabilization of uncertain chained systems. Zbl 1119.93057
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A delay distribution based stability analysis and synthesis approach for networked control systems. Zbl 1166.93381
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A switched system approach to $$H_\infty$$ control of networked control systems with time-varying delays. Zbl 1214.93044
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$$H_\infty$$ guaranteed cost control for uncertain Markovian jump systems with mode-dependent distributed delays and input delays. Zbl 1185.93036
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On the applications of Laplace and Sumudu transforms. Zbl 1286.35185
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Reachable set estimation and controller design for distributed delay systems with bounded disturbances. Zbl 1290.93020
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Improved stability criteria for switched positive linear systems with average dwell time switching. Zbl 1364.93693
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Chebyshev polynomial solutions of systems of higher-order linear Fredholm-Volterra integro-differential equations. Zbl 1086.65121
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$$H_\infty$$ control for discrete-time singular Markov jump systems subject to actuator saturation. Zbl 1273.93066
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On the stability of nonlinear systems with leakage delay. Zbl 1166.93367
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2009
A new Legendre wavelet operational matrix of derivative and its applications in solving the singular ordinary differential equations. Zbl 1237.65079
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2011
Switched controller design for stabilization of nonlinear hybrid systems with time-varying delays in state and control. Zbl 1298.93290
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2010
On stability criteria for neural networks with time-varying delay using Wirtinger-based multiple integral inequality. Zbl 1395.93444
Lee, Tae H.; Park, Ju H.; Park, Myeong-Jin; Kwon, Oh-Min; Jung, Ho-Youl
2015
Stochastically asymptotic stability of delayed recurrent neural networks with both Markovian jump parameters and nonlinear disturbances. Zbl 1202.93169
Zhu, Quanxin; Yang, Xinsong; Wang, Hongchu
2010
Stabilization for a coupled PDE-ODE control system. Zbl 1231.93095
Tang, Shuxia; Xie, Chengkang
2011
Adaptive sliding mode tracking control for a flexible air-breathing hypersonic vehicle. Zbl 1254.93044
Hu, Xiaoxiang; Wu, Ligang; Hu, Changhua; Gao, Huijun
2012
Laguerre functions in signal analysis and parameter identification. Zbl 0481.93025
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1982
New robust delay-dependent stability and $$H_{\infty}$$ analysis for uncertain Markovian jump systems with time-varying delays. Zbl 1286.93199
Zhao, Xudong; Zeng, Qingshuang
2010
Stability and stabilization for discrete-time systems with time-varying delays via augmented Lyapunov-Krasovskii functional. Zbl 1269.93089
Kwon, O. M.; Park, M. J.; Park, Ju H.; Lee, S. M.; Cha, E. J.
2013
Synchronization criteria for coupled stochastic neural networks with time-varying delays and leakage delay. Zbl 1254.93012
Park, M. J.; Kwon, O. M.; Park, Ju H.; Lee, S. M.; Cha, E. J.
2012
Controllability of Volterra-Fredholm type systems in Banach spaces. Zbl 1160.93005
Hernández M., Eduardo; O’Regan, Donal
2009
Sampled-data general partial synchronization of Boolean control networks. Zbl 1480.93251
Lin, Lin; Zhong, Jie; Zhu, Shiyong; Lu, Jianquan
2022
Robust stability of switched delayed logical networks with all unstable modes. Zbl 1480.93313
Kong, Xiangshan; Li, Haitao; Lu, Xiaodong
2022
Finite-time state bounding of homogeneous nonlinear positive systems with disturbance. Zbl 1480.93373
Zhu, Xingao; Liu, Shutang; Sun, Yuangong
2022
Stability analysis of positive switched systems based on a $$\Phi$$-dependent average dwell time approach. Zbl 1480.93360
Yu, Qiang; Yuan, Xiaoyan
2022
Analysis of positive fractional-order neutral time-delay systems. Zbl 1480.93207
Huseynov, Ismail T.; Mahmudov, Nazim I.
2022
On the robustness of cyber-physical LPV systems under DoS attacks. Zbl 1481.93028
Pessim, Paulo S. P.; Lacerda, Márcio J.
2022
Co-design of an event-triggered dynamic output feedback controller for discrete-time LPV systems with constraints. Zbl 1481.93076
de Souza, Carla; Tarbouriech, Sophie; Leite, Valter J. S.; Castelan, Eugênio B.
2022
$$\mathcal{H}_\infty$$ control of event-triggered quasi-LPV systems based on an exact discretization approach – a linear matrix inequality approach. Zbl 1481.93029
Campos, Víctor C. S.; Frezzatto, Luciano; Oliveira, Tiago G.; Estrada-Manzo, Víctor; Braga, Márcio F.
2022
Fuzzy quantized sampled-data control for extended dissipative analysis of T-S fuzzy system and its application to WPGSs. Zbl 1458.93148
Cai, Xiao; Wang, Jun; Zhong, Shouming; Shi, Kaibo; Tang, Yiqian
2021
Actuator and sensor fault estimation for discrete-time switched T-S fuzzy systems with time delay. Zbl 1458.93157
Liu, Ying; Wang, Youqing
2021
The impact of hospital resources and environmental perturbations to the dynamics of SIRS model. Zbl 1459.92133
Lan, Guijie; Yuan, Sanling; Song, Baojun
2021
A novel event-triggered strategy for networked switched control systems. Zbl 1455.93117
Gao, Hui; Shi, Kaibo; Zhang, Hongbin
2021
Adaptive event-based tracking control of unmanned marine vehicle systems with DoS attack. Zbl 1458.93141
Ye, Zehua; Zhang, Dan; Wu, Zheng-Guang
2021
Delay-dependent cluster synchronization of time-varying complex dynamical networks with noise via delayed pinning impulsive control. Zbl 1464.93059
Ling, Guang; Liu, Xinzhi; Ge, Ming-Feng; Wu, Yonghong
2021
Simultaneous observer-based fault detection and event-triggered consensus control for multi-agent systems. Zbl 1464.93072
Li, Shanglin; Chen, Yangzhou; Zhan, Jingyuan
2021
Event-triggered consensus control for second-order multi-agent system subject to saturation and time delay. Zbl 1465.93145
Wang, Jinran; Luo, Xiaoyuan; Yan, Jing; Guan, Xinping
2021
Hierarchical gradient- and least squares-based iterative algorithms for input nonlinear output-error systems using the key term separation. Zbl 1465.93040
Ding, Feng; Ma, Hao; Pan, Jian; Yang, Erfu
2021
$$\mathcal{H}_\infty$$ fuzzy state estimation for delayed genetic regulatory networks with random gain fluctuations and reaction-diffusion. Zbl 1472.92116
Sun, Lin; Wang, Jing; Chen, Xiangyong; Shi, Kaibo; Shen, Hao
2021
Global stabilization of linear systems subject to input saturation and time delays. Zbl 1455.93146
Wu, Jiawei; Huang, Ling
2021
Finite-time stability and stabilization results for switched impulsive dynamical systems on time scales. Zbl 1455.93177
Kumar, Vipin; Djemai, Mohamed; Defoort, Michael; Malik, Muslim
2021
Hopf bifurcation and synchronization of a five-dimensional self-exciting homopolar disc dynamo using a new fuzzy disturbance-observer-based terminal sliding mode control. Zbl 1455.93110
Wei, Zhouchao; Yousefpour, Amin; Jahanshahi, Hadi; Erkin Kocamaz, Uǧur; Moroz, Irene
2021
Energy analysis of a class of state-dependent switched systems with all unstable subsystems. Zbl 1455.93156
Chen, Danhong; Peng, Yunfei
2021
Finite-time inter-layer projective synchronization of Caputo fractional-order two-layer networks by sliding mode control. Zbl 1455.93179
Wu, Xifen; Bao, Haibo; Cao, Jinde
2021
New results on reachable sets bounding for delayed positive singular systems with bounded disturbances. Zbl 1455.93010
Huu Sau, Nguyen; Huong, Dinh Cong; Thuan, Mai Viet
2021
On fault detection of discrete-time switched systems via designing time-varying residual generators. Zbl 1455.93093
Li, Jiao; Jia, Fanlin; He, Xiao
2021
Leaderless consensus control of nonlinear multi-agent systems under directed topologies subject to input saturation using adaptive event-triggered mechanism. Zbl 1470.93147
Rehan, Muhammad; Tufail, Muhammad; Ahmed, Shakeel
2021
Abnormal spatio-temporal source estimation for a linear unstable parabolic distributed parameter system: an adaptive PDE observer perspective. Zbl 1458.93118
Feng, Yun; Wang, Yaonan; Wang, Jun-Wei; Li, Han-Xiong
2021
Fault estimation and fault tolerant control for discrete-time nonlinear systems with perturbation by a mixed design scheme. Zbl 1458.93060
Yang, Ximing; Li, Tieshan; Wu, Yue; Wang, Yang; Long, Yue
2021
Implicit higher-order moment matching technique for model reduction of quadratic-bilinear systems. Zbl 1458.93040
Asif, Mian Mohammad Arsalan; Ahmad, Mian Ilyas; Benner, Peter; Feng, Lihong; Stykel, Tatjana
2021
Global Mittag-Leffler consensus for fractional singularly perturbed multi-agent systems with discontinuous inherent dynamics via event-triggered control strategy. Zbl 1458.93228
Zhang, Yuqing; Wu, Huaiqin; Cao, Jinde
2021
Double stochastic resonance induced by varying potential-well depth and width. Zbl 1459.94043
Qiao, Zijian; Liu, Jian; Ma, Xin; Liu, Jinliang
2021
Improved event-triggered control for networked control systems subject to deception attacks. Zbl 1459.93107
Wu, Zhiying; Xiong, Junlin; Xie, Min
2021
Robust visual servoing control for quadrotors landing on a moving target. Zbl 1459.93124
Zhao, Wanbing; Liu, Hao; Wang, Xinlong
2021
Finite-time synchronization for periodic T-S fuzzy master-slave neural networks with distributed delays. Zbl 1459.93162
Liu, Chang; Guo, Yuru; Rao, Hongxia; Lin, Ming; Xu, Yong
2021
Mean-square integral input-to-state stability of nonlinear impulsive semi-Markov jump delay systems. Zbl 1459.93159
Lin, Yu; Zhang, Yu; Bloch, Anthony
2021
Quasi-synchronization of coupled neural networks with reaction-diffusion terms driven by fractional Brownian motion. Zbl 1459.93062
Song, Xiaona; Li, Xingru; Song, Shuai; Zhang, Yijun; Ning, Zhaoke
2021
Secure chaotic communication based on extreme multistability. Zbl 1457.94008
Pisarchik, A. N.; Jaimes-Reátegui, R.; Rodríguez-Flores, C.; García-López, J. H.; Huerta-Cuellar, G.; Martín-Pasquín, F. J.
2021
Global output feedback stabilization for a class of nonlinear systems with multiple uncertainties. Zbl 1459.93147
Sun, Zong-Yao; Zhang, Kai; Chen, Chih-Chiang; Zhao, Qian
2021
Global practical tracking for nonlinear systems with uncertain dead-zone input via output feedback. Zbl 1464.93025
Jia, Xianglei; Xu, Shengyuan; Shi, Xiaocheng; Zhang, Zhengqiang
2021
Privacy-preserving weighted average consensus and optimal attacking strategy for multi-agent networks. Zbl 1464.93073
Wang, Aijuan; Liu, Wanping; Li, Tiehu; Huang, Tingwen
2021
Scaled consensus problem for multi-agent systems with semi-Markov switching topologies: a view from the probability. Zbl 1464.93070
Guo, Xing; Liang, Jinling; Lu, Jianquan
2021
Command filtered adaptive neural network synchronization control of fractional-order chaotic systems subject to unknown dead zones. Zbl 1464.93075
Ha, Shumin; Chen, Liangyun; Liu, Heng
2021
Flexible optimal Kalman filtering in wireless sensor networks with intermittent observations. Zbl 1465.93220
Zhong, Yigen; Liu, Yonggui
2021
Distributed observer-based cooperative guidance with appointed impact time and collision avoidance. Zbl 1471.93111
Li, Guofei; Lü, Jinhu; Zhu, Guoliang; Liu, Kexin
2021
Recursive distributed fusion estimation for nonlinear stochastic systems with event-triggered feedback. Zbl 1471.93178
Li, Li; Fan, Mingyang; Xia, Yuanqing; Zhu, Cui
2021
Fuzzy adaptive output-feedback tracking control for nonlinear strict-feedback systems in prescribed finite time. Zbl 1472.93111
Yuan, Xu; Chen, Bing; Lin, Chong
2021
Finite-time stabilization of fractional-order fuzzy quaternion-valued BAM neural networks via direct quaternion approach. Zbl 1472.93161
Chen, Shenglong; Li, Hong-Li; Kao, Yonggui; Zhang, Long; Hu, Cheng
2021
Multi-sensor Kalman filtering over packet-dropping networks subject to round-robin protocol scheduling. Zbl 1472.93189
Ren, Xiu-Xiu; Yang, Guang-Hong
2021
Observer-based fault estimation for a class of discrete-time switched affine systems: an application to the DC-DC converter. Zbl 1472.93056
Liao, Fang; Zhu, Yanzheng; Zhou, Donghua
2021
Robust gain-scheduling $$\mathcal{H}_\infty$$ control of uncertain continuous-time systems having magnitude- and rate-bounded actuators: an application of full block S-procedure. Zbl 1472.93031
Kucukdemiral, Ibrahim B.; Yazici, Hakan
2021
Positive consensus for multi-agent systems with average dwell time switching. Zbl 1472.93167
Cao, Xiangyang; Li, Yan
2021
From Morse triangular form of ODE control systems to feedback canonical form of DAE control systems. Zbl 1472.93018
Chen, Yahao; Respondek, Witold
2021
Stability analysis of impulsive stochastic delayed differential systems with infinite delay or finite delay and average-delay impulses. Zbl 1472.93194
Xu, Haofeng; Zhu, Quanxin
2021
On the matching equations of kinetic energy shaping in IDA-PBC. Zbl 1472.93077
Harandi, M. Reza J.; Taghirad, Hamid D.
2021
A fuzzy control framework for interconnected nonlinear power networks under TDS attack: estimation and compensation. Zbl 1455.93111
Zhong, Zhixiong; Zhu, Yanzheng; Lin, Chih-Min; Huang, Tao
2021
A cost-effective wireless network migration planning method supporting high-security enabled railway data communication systems. Zbl 1455.93076
Wen, Tao; Ge, Quanbo; Lyu, Xinan; Chen, Lei; Constantinou, Costas; Roberts, Clive; Cai, Baigen
2021
Exponential stabilization of switched linear systems subject to actuator saturation with stabilizable and unstabilizable subsystems. Zbl 1455.93168
Ma, Ruicheng; Zhang, Hongrui; Zhao, Shengzhi
2021
On asymmetric periodic solutions in relay feedback systems. Zbl 1455.93061
Boiko, I. M.; Kuznetsov, N. V.; Mokaev, R. N.; Akimova, E. D.
2021
Optimal actuator switching synthesis of observer-based event-triggered state feedback control for distributed parameter systems. Zbl 1455.93057
Mu, Wenying; Qiu, Fang; Zhuang, Bo; Chen, Ligang
2021
Leader-following consensus control for semi-Markov jump multi-agent systems: an adaptive event-triggered scheme. Zbl 1455.93184
Wang, Huijiao; Xue, Bing; Xue, Anke
2021
Optimal control problem for a general reaction-diffusion tumor-immune system with chemotherapy. Zbl 1455.92071
Dai, Feng; Liu, Bin
2021
LQ preview state feedback with output regulation constraint. Zbl 1455.93063
Hashikura, Kotaro; Jaafar, Jad Musaddiq Bin; Kojima, Akira; Kamal, Md Abdus Samad; Yamada, Kou
2021
Asynchronous $$H_\infty$$ controller design for neutral singular Markov jump systems under dynamic event-triggered schemes. Zbl 1455.93047
Wang, Haotian; Wang, Yanqian; Zhuang, Guangming
2021
Threshold dynamics and pulse control of a stochastic ecosystem with switching parameters. Zbl 1455.92160
Zhang, Hongxia; Liu, Xinzhi; Xu, Wei
2021
$$\boldsymbol{H}_\infty$$ dynamic observer-based fuzzy integral sliding mode control with input magnitude and rate constraints. Zbl 1455.93043
Echreshavi, Zeinab; Shasadeghi, Mokhtar; Asemani, Mohammad Hassan
2021
Pinning synchronization of fractional-order memristor-based neural networks with multiple time-varying delays via static or dynamic coupling. Zbl 1455.93157
Jia, Jia; Zeng, Zhigang; Wang, Fei
2021
On the exponential stabilization of a flexible structure with dynamic delayed boundary conditions via one boundary control only. Zbl 1455.93166
Chentouf, Boumediène; Mansouri, Sabeur
2021
Adaptive fuzzy-based composite anti-disturbance control for a class of switched nonlinear systems with unknown backlash-like hysteresis. Zbl 1467.93199
Xie, Jing; Sun, Ping; Yang, Dong
2021
Disturbance-observer-based formation-containment control for UAVs via distributed adaptive event -triggered mechanisms. Zbl 1467.93226
Wei, Lili; Chen, Mou; Li, Tao
2021
A fast terminal sliding mode control scheme with time-varying sliding mode surfaces. Zbl 1467.93061
Yao, Meibao; Xiao, Xueming; Tian, Yang; Cui, Hutao
2021
Adaptive output feedback fault tolerant control for uncertain nonlinear systems based on actuator switching. Zbl 1467.93183
Sun, Chen; Lin, Yan
2021
Sampled observer-based adaptive decentralized control for strict-feedback interconnected nonlinear systems. Zbl 1467.93173
Guo, Hai-Yu; Zhang, Xiao-Guang
2021
Optimal control of singular Boolean control networks via Ledley solution method. Zbl 1470.93078
Wang, Yuanhua; Guo, Peilian
2021
State estimation for semi-Markovian switching CVNNs with quantization effects and linear fractional uncertainties. Zbl 1470.93154
Li, Qiang; Liang, Jinling; Gong, Weiqiang
2021
Robust mixed-sensitivity $$\mathcal{H}_\infty$$ control of weight on bit in geological drilling process with parameter uncertainty. Zbl 1470.93050
Ma, Sike; Wu, Min; Chen, Luefeng; Lu, Chengda; Cao, Weihua
2021
Practical constrained output feedback formation control of underactuated vehicles via the autonomous dynamic logic guidance. Zbl 1470.93060
Zhang, Guoqing; Zhang, Chenliang; Lang, Lei; Zhang, Weidong
2021
On adequate sets of multi-valued logic. Zbl 07383508
Cheng, Daizhan; Feng, Jun-e; Zhao, Jianli; Fu, Shihua
2021
Exponentially admissibility of neutral singular systems with mixed interval time-varying delays. Zbl 1470.93063
Chen, Wenbin; Xu, Shengyuan; Li, Ze; Li, Yongmin; Zhang, Zhengqiang
2021
$$p$$th Moment exponential stability of switched discrete-time stochastic systems: a multiple Lyapunov functions method. Zbl 1470.93134
Fan, Lina; Zhu, Quanxin
2021
Stabilization of periodic oscillations with transient delayed feedback control. Zbl 1458.93207
Zheng, Yuan-Guang; Zhang, Ying-Ying
2021
Mean-square stability of stochastic system with Markov jump and Lévy noise via adaptive control. Zbl 1458.93262
Li, Mengling; Deng, Feiqi; Zheng, Xiaofeng; Luo, Jinnan
2021
Optimal output regulation for heterogeneous descriptor multi-agent systems. Zbl 1458.93019
Zhang, Liping; Zhang, Guoshan
2021
Finite-time trajectory tracking control for a stratospheric airship with full-state constraint and disturbances. Zbl 1458.93223
Yuan, Jiace; Zhu, Ming; Guo, Xiao; Lou, Wenjie
2021
Pinning synchronization of delayed complex networks under self-triggered control. Zbl 1458.93231
Zhou, Xiaotao; Li, Lulu; Zhao, Xiao-Wen
2021
Robust fault estimation and isolation for a descriptor LPV system with disturbance. Zbl 1458.93243
Chen, Zhengquan; Han, Lu; Hou, Yandong
2021
State estimation for jump Markov nonlinear systems of unknown measurement data covariance. Zbl 1458.93244
Li, Ke; Zhao, Shunyi; Ahn, Choon Ki; Liu, Fei
2021
Extended hybrid control scheme for asynchronous switching. Zbl 1458.93126
Sehatnia, Arman; Hashemzadeh, Farzad; Baradarannia, Mahdi
2021
Stability and stabilization of Markov jump systems with generally uncertain transition rates. Zbl 1458.93260
Guo, Yafeng
2021
Prescribed-time containment control with prescribed performance for uncertain nonlinear multi-agent systems. Zbl 1458.93156
Liu, Dacai; Liu, Zhi; Chen, C. L. Philip; Zhang, Yun
2021
Asynchronous quantized control of Markovian switching Lur’e systems with event-triggered strategy. Zbl 1458.93163
Kang, Wei; Cheng, Jun; Zhou, Xia; Cao, Jinde; Wang, Hailing
2021
Synchronization control of neutral-type neural networks with sampled-data via adaptive event-triggered communication scheme. Zbl 1458.93229
Zhang, He; Ma, Qian; Lu, Junwei; Chu, Yuming; Li, Yongmin
2021
A numerical solution of a class of periodic coupled matrix equations. Zbl 1455.65064
Lv, Lingling; Chen, Jinbo; Zhang, Zhe; Wang, Baowen; Zhang, Lei
2021
Exponential bipartite synchronization of delayed coupled systems over signed graphs with Markovian switching via intermittent control. Zbl 1458.93214
Wang, Mengxin; Guo, Jia; Qin, Sitian; Feng, Jiqiang; Li, Wenxue
2021
Stabilizability of complex complex-valued memristive neural networks using non-fragile sampled-data control. Zbl 1459.93139
Zhang, Ruimei; Zeng, Deqiang; Park, Ju H.; Shi, Kaibo; Liu, Yajuan
2021
Prescribed performance bipartite consensus for nonlinear agents with antagonistic interactions: a PI transformation approach. Zbl 1459.93164
Gkesoulis, Athanasios K.; Psillakis, Haris E.
2021
Expected power bound and stability of two-dimensional digital filters with multiplicative noise in the FMLSS model. Zbl 1459.93103
Wang, Bao; Zhu, Quanxin; Xu, Lei
2021
Event-triggered control for networked control system via an improved integral inequality. Zbl 1459.93105
Hu, Feng; Jiao, Chunting; Chang, Hongbin; Su, Xiaojie; Gu, Yongcheng
2021
Reliable dissipative control for fuzzy singular semi-Markovian jump systems with mode-dependent delays and randomly occuring uncertainties. Zbl 1459.93089
Li, Xin; Mu, Xiaowu; Yang, Zhe
2021
Secure distributed Kalman filter using partially homomorphic encryption. Zbl 1459.93181
Sadeghikhorami, Ladan; Safavi, Ali Akbar
2021
Distributed coordination on state-dependent fuzzy graphs. Zbl 1459.93018
Oyedeji, Mojeed O.; Mahmoud, Magdi S.; Xia, Yuanqing
2021
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### Cited by 19,645 Authors
212 Cao, Jinde 194 Park, Juhyun (Jessie) 170 Zhong, Shou-Ming 104 Shi, Peng 96 Al-saedi, Ahmed Eid Salem 89 Ding, Feng 87 Karimi, Hamid Reza 86 Zhu, Quanxin 79 Xu, Shengyuan 75 Kwon, O. M. 74 Wang, Zhen 71 Zhang, Qingling 68 Cheng, Jun 67 Lam, James 66 Hayat, Tasawar 63 Kao, Yonggui 62 Wang, Zidong 61 Xia, Jianwei 60 Liu, Xinzhi 59 Shi, Kaibo 58 Ma, Yuechao 58 Yang, Guanghong 56 Alsaadi, Fuad Eid S. 56 Li, Xiaodi 54 Sakthivel, Rathinasamy 54 Xiang, Zhengrong 53 Zhao, Xudong 52 Rakkiyappan, Rajan 51 Jiang, Haijun 51 Zhao, Jun 50 Zhang, Huaguang 48 Huang, Tingwen 47 Deng, Feiqi 47 Liu, Fei 46 Jiang, Bin 45 Fei, Shumin 44 Zong, Guangdeng 43 Razzaghi, Mohsen 43 Xia, Yuanqing 41 Ali, M. Syed 41 Wu, Min 41 Wu, Zhengguang 40 Zhou, Wuneng 39 Su, Hongye 39 Wang, Jing 38 Trinh, Hieu Minh 37 Hua, Changchun 37 Zhang, Weihai 37 Zhang, Zhengqiang 36 Băleanu, Dumitru I. 36 Basin, Michael V. 35 Fuhrmann, Paul A. 35 Guan, Zhihong 35 Hu, Cheng 35 Li, Junmin 35 Mahmoud, Magdi Sadik Mostafa 35 Qi, Wenhai 35 Sun, Yuangong 34 Chen, Xiangyong 34 Hwang, Chyi 34 Lu, Jianquan 34 Machado, José António Tenreiro 34 Nguang, Sing Kiong 34 Yue, Dong 34 Zeng, Zhigang 34 Zheng, Wei Xing 33 Ahmad, Bashir 33 Balasubramaniam, Pagavathigounder 33 Li, Tao 33 Liang, Jinling 33 Lu, Junwei 33 Vaidyanathan, Sundarapandian 33 Wu, Yuqiang 33 Zhuang, Guangming 32 Li, Wenxue 32 Sezer, Mehmet 32 Shen, Hao 31 Duan, Guangren 31 Li, Chuandong 31 Sun, Ji Tao 31 Zhu, Hong 30 Anthoni, Selvaraj Marshal 30 Chen, Guanrong 30 Mathiyalagan, Kalidass 30 Wang, Jinrong 30 Zhang, Baoyong 29 Chu, Yuming 29 Jiang, Yaolin 29 Wang, Zhanshan 28 Efimov, Denis V. 28 Kiliçman, Adem 28 Li, Shihua 28 Liu, Jinliang 28 Lu, Renquan 28 Niu, Yugang 28 Park, PooGyeon 27 Jiang, Daqing 27 Mu, Xiaowu 27 Zou, Yun 26 Han, Qinglong ...and 19,545 more Authors
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### Cited in 716 Journals
3,744 Journal of the Franklin Institute 913 Applied Mathematics and Computation 654 International Journal of Systems Science. Principles and Applications of Systems and Integration 623 Automatica 614 International Journal of Control 504 Mathematical Problems in Engineering 496 Nonlinear Dynamics 308 Advances in Difference Equations 294 Nonlinear Analysis. Hybrid Systems 274 International Journal of Systems Science 274 Information Sciences 252 Chaos, Solitons and Fractals 238 Complexity 237 Circuits, Systems, and Signal Processing 235 Systems & Control Letters 218 Abstract and Applied Analysis 185 Asian Journal of Control 181 International Journal of Robust and Nonlinear Control 173 Applied Mathematical Modelling 156 Communications in Nonlinear Science and Numerical Simulation 141 Discrete Dynamics in Nature and Society 136 Neural Networks 136 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 125 European Journal of Control 120 Mathematics and Computers in Simulation 116 Computers & Mathematics with Applications 107 Journal of Mathematical Analysis and Applications 104 Journal of Computational and Applied Mathematics 103 Journal of Optimization Theory and Applications 93 Journal of Systems Science and Complexity 87 Fuzzy Sets and Systems 85 Computational and Applied Mathematics 84 Linear Algebra and its Applications 79 International Journal of Adaptive Control and Signal Processing 75 International Journal of Computer Mathematics 70 Applied Mathematics Letters 64 Journal of Control Science and Engineering 61 Journal of Applied Mathematics 61 Journal of Applied Mathematics and Computing 59 Mathematical Methods in the Applied Sciences 58 Discrete Mathematics 58 Optimal Control Applications & Methods 52 International Journal of Control, I. Series 51 Physica A 50 Journal of Vibration and Control 48 AIMS Mathematics 47 SIAM Journal on Control and Optimization 46 Acta Mechanica 44 Journal of Inequalities and Applications 44 Nonlinear Analysis. Modelling and Control 42 Nonlinear Analysis. Real World Applications 41 Multidimensional Systems and Signal Processing 40 Computer Methods in Applied Mechanics and Engineering 40 International Journal of Applied Mathematics and Computer Science 40 International Journal of Biomathematics 39 Mathematical and Computer Modelling 37 Kybernetika 37 International Journal of Applied and Computational Mathematics 36 Chaos 35 Boundary Value Problems 34 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 33 Discrete and Continuous Dynamical Systems. Series B 32 Automation and Remote Control 29 Discrete and Continuous Dynamical Systems. Series S 28 Mathematical Biosciences 27 Applied Numerical Mathematics 27 Fractional Calculus & Applied Analysis 27 Physical Review, II. Series 26 Applicable Analysis 26 Discrete Applied Mathematics 26 Journal of Mathematical Physics 26 Soft Computing 26 International Journal of Nonlinear Sciences and Numerical Simulation 25 Theoretical Computer Science 25 Mathematical and Computer Modelling of Dynamical Systems 25 Journal of Mathematics 24 International Journal of General Systems 24 Journal of Computational Physics 24 Journal of Difference Equations and Applications 24 Multibody System Dynamics 24 Journal of Applied Analysis and Computation 23 Journal of Nonlinear Science and Applications 22 MCSS. Mathematics of Control, Signals, and Systems 22 Advances in Mathematical Physics 21 Mathematical Biosciences and Engineering 21 Journal of Control Theory and Applications 20 Stochastic Analysis and Applications 20 Numerical Algorithms 20 Fractals 19 European Journal of Operational Research 19 Journal of Mathematical Chemistry 19 Journal of Function Spaces 18 ZAMP. Zeitschrift für angewandte Mathematik und Physik 18 Acta Applicandae Mathematicae 18 Journal of the Egyptian Mathematical Society 18 Differential Equations and Dynamical Systems 18 Arabian Journal for Science and Engineering 17 Journal of Differential Equations 17 Mathematical Systems Theory 17 Signal Processing ...and 616 more Journals
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### Cited in 63 Fields
10,853 Systems theory; control (93-XX) 2,909 Ordinary differential equations (34-XX) 1,413 Biology and other natural sciences (92-XX) 1,272 Numerical analysis (65-XX) 1,138 Probability theory and stochastic processes (60-XX) 882 Computer science (68-XX) 855 Information and communication theory, circuits (94-XX) 770 Operations research, mathematical programming (90-XX) 735 Partial differential equations (35-XX) 676 Calculus of variations and optimal control; optimization (49-XX) 591 Dynamical systems and ergodic theory (37-XX) 503 Mechanics of deformable solids (74-XX) 478 Mechanics of particles and systems (70-XX) 450 Real functions (26-XX) 409 Linear and multilinear algebra; matrix theory (15-XX) 371 Combinatorics (05-XX) 286 Integral equations (45-XX) 275 Statistics (62-XX) 251 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 244 Operator theory (47-XX) 233 Harmonic analysis on Euclidean spaces (42-XX) 217 Special functions (33-XX) 211 Fluid mechanics (76-XX) 194 Integral transforms, operational calculus (44-XX) 176 Difference and functional equations (39-XX) 125 Approximations and expansions (41-XX) 116 Functions of a complex variable (30-XX) 105 Number theory (11-XX) 99 Classical thermodynamics, heat transfer (80-XX) 85 Statistical mechanics, structure of matter (82-XX) 81 Relativity and gravitational theory (83-XX) 67 Quantum theory (81-XX) 63 Global analysis, analysis on manifolds (58-XX) 58 Functional analysis (46-XX) 51 Optics, electromagnetic theory (78-XX) 39 Mathematical logic and foundations (03-XX) 39 Differential geometry (53-XX) 33 History and biography (01-XX) 32 Measure and integration (28-XX) 27 General and overarching topics; collections (00-XX) 24 Sequences, series, summability (40-XX) 22 Geophysics (86-XX) 21 Commutative algebra (13-XX) 18 Convex and discrete geometry (52-XX) 17 Algebraic geometry (14-XX) 15 Field theory and polynomials (12-XX) 14 Order, lattices, ordered algebraic structures (06-XX) 13 General topology (54-XX) 10 Nonassociative rings and algebras (17-XX) 10 Topological groups, Lie groups (22-XX) 9 Group theory and generalizations (20-XX) 9 Several complex variables and analytic spaces (32-XX) 9 Abstract harmonic analysis (43-XX) 9 Geometry (51-XX) 8 Associative rings and algebras (16-XX) 8 Astronomy and astrophysics (85-XX) 6 Potential theory (31-XX) 6 Manifolds and cell complexes (57-XX) 6 Mathematics education (97-XX) 4 Category theory; homological algebra (18-XX) 3 General algebraic systems (08-XX) 1 $$K$$-theory (19-XX) 1 Algebraic topology (55-XX)
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https://jyx.jyu.fi/handle/123456789/57452?show=full
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dc.contributor.author ALICE Collaboration dc.date.accessioned 2018-03-28T05:52:54Z dc.date.available 2018-03-28T05:52:54Z dc.date.issued 2018 dc.identifier.citation ALICE Collaboration. (2018). D-Meson Azimuthal Anisotropy in Midcentral Pb-Pb Collisions at √sNN = 5.02 TeV. Physical Review Letters, 120(10), Article 102301. https://doi.org/10.1103/PhysRevLett.120.102301 dc.identifier.other CONVID_27973293 dc.identifier.other TUTKAID_77198 dc.identifier.uri https://jyx.jyu.fi/handle/123456789/57452 dc.description.abstract The azimuthal anisotropy coefficient v 2 of prompt D 0 , D + , D * + , and D + s mesons was measured in midcentral (30%–50% centrality class) Pb-Pb collisions at a center-of-mass energy per nucleon pair √ s N N = 5.02 TeV , with the ALICE detector at the LHC. The D mesons were reconstructed via their hadronic decays at midrapidity, | y | < 0.8 , in the transverse momentum interval 1 < p T < 24 GeV / c . The measured D -meson v 2 has similar values as that of charged pions. The D + s v 2 , measured for the first time, is found to be compatible with that of nonstrange D mesons. The measurements are compared with theoretical calculations of charm-quark transport in a hydrodynamically expanding medium and have the potential to constrain medium parameters. dc.language.iso eng dc.publisher American Physical Society dc.relation.ispartofseries Physical Review Letters dc.subject.other heavy-ion collisions dc.subject.other D mesons dc.subject.other anisotropy dc.title D-Meson Azimuthal Anisotropy in Midcentral Pb-Pb Collisions at √sNN = 5.02 TeV dc.type article dc.identifier.urn URN:NBN:fi:jyu-201803271861 dc.contributor.laitos Fysiikan laitos fi dc.contributor.laitos Department of Physics en dc.type.uri http://purl.org/eprint/type/JournalArticle dc.date.updated 2018-03-27T12:16:47Z dc.description.reviewstatus peerReviewed dc.relation.issn 0031-9007 dc.relation.numberinseries 10 dc.relation.volume 120 dc.type.version publishedVersion dc.rights.copyright © 2018 CERN, for the ALICE Collaboration. This is an open access article distributed under the terms of the Creative Commons License. dc.rights.accesslevel openAccess fi dc.subject.yso hiukkasfysiikka jyx.subject.uri http://www.yso.fi/onto/yso/p15576 dc.rights.url https://creativecommons.org/licenses/by/4.0/ dc.relation.doi 10.1103/PhysRevLett.120.102301
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Except where otherwise noted, this item's license is described as © 2018 CERN, for the ALICE Collaboration. This is an open access article distributed under the terms of the Creative Commons License.
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https://forum.allaboutcircuits.com/threads/pwm-circuit-help-24v-house-lighting-system-450w-max-leds.120447/
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# PWM circuit help, 24v house lighting system 450w max LED's
#### Evanguy
Joined Dec 21, 2014
81
I'm making a pwm circuit for leds at 450watts max, i have a few questions and I'm very open for suggestion
in my house i plan to make all my own power for the lights we use, I'm trying to get off the grid but i want to step into this. currently 100% if my heat and hot water are from wood that i cut off my own wood lot,
so a little about the system in planning, the house has a total of 14 rooms, and i wish to run 25watts per room, with 3 rooms getting 50 watts
i bought 450, 1w led's http://www.ebay.ca/itm/50pcs-Brand-...hash=item2c85751197:m:mA9ClcekVcDeTh--R1Ag-ww
I'm a machinist by trade, so I'm going to make aluminum fixtures to mount the leds on to hold them and to control heat also they will be slightly dishes
so the leds are directed in different directions
using 16/2 cl2 stranded wire with a 24 volt system, no more then 25w per line, longest run (1 direction) is 30 feet,
Ill be alright on the wiring of the modules and the switches and my fathers been an electrician for 40 years now so I've been around all that stuff, but I'm new to this type of electronics
i want to build a PWM controller and i wish to be able to pwm the whole system
so I'm thinking
battery bank at 24v
24v into into pwm controller
24v pwm fed into a fuse box as the "mains"
from the fuse box send out 14 lines to each room with switches and led modules in the rooms
plan to do some testing with the leds and figure how many per fixture
most times i hope to have only the lights on we need so I'm thinking probably not more then 150 watts(high end of things) at any given time but i do have 450 leds so its possible it can be that much power
I have made up three drawings mostly compiled of things on found on line, still missing a few parts, you will notice the "T" parts missing and a few resistor values missing, as I'm still undecided on them or have figured them out yet
and input on those parts would be nice, but with poking around and reading data sheets ill be able to get them
im unsure of witch circuit would be ideal for my situation, it will be on and running 24/7, i plan to build at least 2 so have backup's in case needed
#### #12
Joined Nov 30, 2010
18,217
300-350 ma, 3.2V to 3.4V
Light Emitting Diodes are not light bulbs and they are not resistors, they are diodes. As a diode, they will allow all the current you have, and they will smoke. Therefore, every LED must have current limiting. That is usually done with a resistor, and that resistor has to get rid of all the voltage in excess of the LED voltage. The point is, providing 24 volts to the LEDs means you have to use up 20.7 volts in the resistor. That is a big (86%) waste of power.
You would be much better off providing 5 volts to the LEDs and using up 1.7 volts in the current limiting resistor. About 5.6 ohms@1 watt should do the trick. That way you would waste 1/3 of your total power in the resistors.
Another way to do this is to put a bunch of LEDs in series and use one resistor for several LEDs. Six LEDs in series will use up about 19.2 volts to 20.4 volts. Use up the other part of the 24 volts with a resistor of size 15 ohms @ 3 watts. This cuts your waste heat to about 18%.
See where I'm going here?
While I'm at it, those push-pull output stages aren't necessary at the frequency you're using. You can slow the oscillator down to maybe 50 HZ and not see the blinking. At that speed, a simple resistor on the mosfet gate can drag it to the "off" condition with time to spare.
#### Evanguy
Joined Dec 21, 2014
81
well i guess i could have added more info then i did. also yes sorry i know they are not light bulbs, they are a diode that happens to also give off visible light in the process of doing their job
sorry, ill be putting these in series and parallel, i was thinking of using 7 leds per fixture and 3 fixtures per room and then feeding them 22.4v and using the appropriate resistor to limit current to amount needed.
i want to run them at 24v so i can get away with 16/2 wire as non of this will be in wall, i want to hide it under base boards and keep it discrete as possible, dropping it down through the floor at the base of the door case into my unfinished basement.
if I'm using 7 leds per fixture, 3 fixtures per room, i was going to run the 7leds in series and the 3 fixtures in parallel and feeding about 24v 1amp per room. I'm going to limit the current on the fixtures them selves or just after the switch. and this pwm is a global thing within my house so in the day all lights can be ran at 65% duty cycle or so, and any other time never more then 90% duty cycle (controlling the pwm is a later task for now its a pot)
i do see where you are going and i like it a lot, i was headed there and forgot to inform you i was on my way.
"While I'm at it, those push-pull output stages aren't necessary at the frequency you're using. You can slow the oscillator down to maybe 50 HZ and not see the blinking. At that speed, a simple resistor on the mosfet gate can drag it to the "off" condition with time to spare."
^^ thanks for this, this is exactly what i was wondering, so i can use drawing 1 then, thanks, i had thought so and that was the first circuit i drew up after i looked more into pwm controllers i noticed there could be a lot more going on then my simple drawing, but i see why, its for the speeds, that are far greater then anything i need.
also "C2" is the trigger so adjusting that will change the frequency, or do you think this already low enough to work with the resistor feeding into the mosfet?
#### John P
Joined Oct 14, 2008
1,872
Actually it's very common not to run large LEDs with a resistor in series, but instead to use an electronic constant-current circuit with an inductor. That design is much more efficient, which you need to be concerned about if your input power is limited. You can buy little boards to do the job for not much cash on eBay--I've done it.
http://www.ebay.ca/itm/1-pcs-6-10x1...470280?hash=item2ed06f9948:g:U64AAOxyTMdTO6pP
However, I suggest that you didn't get the right components. Those LEDs you have will get very hot, and it'll be a hassle to build heat sinks for so many of them. I think you'd have done better to get the "star" type, where they come pre-mounted to a circuit board which has a metal core, and which can be easily screwed down to a flat surface.
http://www.ebay.ca/itm/1W-3W-High-P...hash=item21040e72f7:m:mtnGxNiwP4t_jmTWW970UGw
Reactions: #12
#### #12
Joined Nov 30, 2010
18,217
JohnP has a better idea. I didn't go there because I can't design a circuit that will do what he says. Fortunately, they already exist in a retail version.
You are still missing some information. IF your seven LEDs all turn out to need 3.4 volts each, 22.4 volts won't turn them on and there is no voltage left for the resistor to work with. The constant current driver from JohnP eliminates that problem because it mostly doesn't care if you are exact about about the voltage you can provide. It will slap the LEDs with whatever voltage they need to accept 350 ma.
I did catch the part about you being able to make heat sinks. You have parts in hand? Examine them to find out if you will need an insulation layer between them and the aluminum.
C2 doesn't have anything to do with the mosfet. It's a timing capacitor. Right now, you seem to be running at 350 Hz. That will work just fine, or you could slow it all down with a bigger capacitor. Then again, the constant current drivers might be adjustable and the whole PWM thing becomes redundant. The design isn't finished. You still have more to discover.
#### ronv
Joined Nov 12, 2008
3,770
well i guess i could have added more info then i did. also yes sorry i know they are not light bulbs, they are a diode that happens to also give off visible light in the process of doing their job
sorry, ill be putting these in series and parallel, i was thinking of using 7 leds per fixture and 3 fixtures per room and then feeding them 22.4v and using the appropriate resistor to limit current to amount needed.
i want to run them at 24v so i can get away with 16/2 wire as non of this will be in wall, i want to hide it under base boards and keep it discrete as possible, dropping it down through the floor at the base of the door case into my unfinished basement.
if I'm using 7 leds per fixture, 3 fixtures per room, i was going to run the 7leds in series and the 3 fixtures in parallel and feeding about 24v 1amp per room. I'm going to limit the current on the fixtures them selves or just after the switch. and this pwm is a global thing within my house so in the day all lights can be ran at 65% duty cycle or so, and any other time never more then 90% duty cycle (controlling the pwm is a later task for now its a pot)
i do see where you are going and i like it a lot, i was headed there and forgot to inform you i was on my way.
"While I'm at it, those push-pull output stages aren't necessary at the frequency you're using. You can slow the oscillator down to maybe 50 HZ and not see the blinking. At that speed, a simple resistor on the mosfet gate can drag it to the "off" condition with time to spare."
^^ thanks for this, this is exactly what i was wondering, so i can use drawing 1 then, thanks, i had thought so and that was the first circuit i drew up after i looked more into pwm controllers i noticed there could be a lot more going on then my simple drawing, but i see why, its for the speeds, that are far greater then anything i need.
also "C2" is the trigger so adjusting that will change the frequency, or do you think this already low enough to work with the resistor feeding into the mosfet?
I think you have a basic problem with the LEDs.
They need a pretty good heatsink. There is a little pad on the bottom of them that needs to be soldered to a heatsink. This is almost impossible to do by hand without melting the plastic of the LED.
#### Sensacell
Joined Jun 19, 2012
2,722
If your whole plan is about using your limited electrical energy with high efficiency, it's essential to use a switch-mode LED driver to drive your LED's, using a resistor is terribly inefficient, especially for a single diode at 24 V.
Rolling your own LED lights is a ton of work when you consider the driver electronics and heat-sink requirements.
I would consider using an integrated DC-DC constant-current regulator "puck" as per the attached file.
You would be able to run several LED's from one puck, in a series connection - with high efficiency.
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#### Evanguy
Joined Dec 21, 2014
81
John P, Yes i see exactly what your saying, i probably should have looked into this more, but i did have to start some where lol
also about the leds, i seen the star ones, but didnt get them because ill make my own heat sinks that work for all the leds in each fixture
also on the water jet at work, i could get quite a few of those heat sinks cut out, and then i can change the thickness if my heat sinks dont work as planed, Thanks for the links its opened up a few more options
#12, i see what you mean about the voltage being at 22.4 and no voltage left for the resistors to work, i havent even considered that at all, i love learning, thanks. and no i dont have parts in hand yet they are in the mail as of 2 days ago. but ill look into them and see, if they dont need the layer i was planning on using thermal paste to attach them to the heat sink, but also little wire holders to hold the led down,
and the only reason i was talking about the cap and the mosfet was because you said i cant go to high of frequency with the simple resistor into the mosfet and the cap sets the frequency i figured so i asked if its going to set the frequency to under the amount i should stay under without a push pull setup. you answered that, Thanks.
Ronv, i believe it will be a lot of work, i hope to get one fixture a day done once i get all the parts here, and instead of soldering them i was going to use a wire clamp to hold them down and also thermal paste under them, much like a cpu is held down in a PC
Sensacell, now we are getting somewhere, thanks and i did plan on running them in series, 24v into 1 led isnt the plan, i believe the work load will be huge, i would like to get this finished within a few months kinda of thing.
and in that link you sent me there are ones that will work with 1000ma, so i could use one per room after the light switch powering all the leds per room. also i see pwm input i could run another single wire for that control..
thanks guys your helping a lot and making me learn, i like.
#### Evanguy
Joined Dec 21, 2014
81
Ok, so ive changed around what i plan to do. i now plan on using local(on each led fixture) STCS1 chip circuits for constant 1300ma.
Now ill be using 16/3 wire so i can send pwm along with the power for each circuits pwm input.
Ill have a new circuit drawing up tonight i hope. it also coveres the whole system.
Battery->Fuse->switch->scts1->leds
24-12v buck converter->555pwm circuit->scts1 chip
I also feel i should put a 100uh inductor in series with the leds but im unsure of where and if it will effect pwm
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#### #12
Joined Nov 30, 2010
18,217
A 555 PWM circuit doesn't care if you have enough microhenries. That's a triac you're thinking of.
#### tcmtech
Joined Nov 4, 2013
2,867
I don't get the whole endeavor and concept here.
I've been buying Zilotek LED lights for $3.48 a pair that are one of the best 60 watt bulb equivalent LED light I have seen yet. They put out 800 lumens at 8 watts input which to be honest there isn't a DIY person here that will touch that price and create a equivilant end product. If it was me and I wanted to cut my electrical usage down I would not be messing around with a whole house custom lighting system with wires running wire where just for lighting I would be putting all my available AE generated power into a basic grid tie system (Store bought unit or pirate GTI build) and be using it to shave the overall utility power consumption down. Thread Starter #### Evanguy Joined Dec 21, 2014 81 I see what you are saying. and it makes sence to me and others. but i would like to get off the grid totally over time. also this would be a fun project, not worries about saving money or time and more wanting to build a system that works for me. the entire house needs new wiring. its 60 years old and here is a crazy mess of wires from people adding and changing things i have a 100amp main and there is 30 breakers all being used. the system is a mess Since i bought the house i totaly redid all the plumbing and now im pickjng away at the electrical. There are mice and squirrls in the attic with all my current wiring and its a little scary. so i want to do the lighting at 24v and rewire all the plugs for 120v bit send them intonthe basement instead of attic. and over time wire the plugs to inverters and aslo run them off my own power. This is nothjng to do with cost. i dont care if it costs me twics as much really. and even if i cant make my power for cheaper then i can buy it, atleast it helps in my quest for self sistainibilty i also grow/hunt about 80% of our total food. #### tcmtech Joined Nov 4, 2013 2,867 I can follow the want to be more self sufficient. Years ago I built my own boiler systems in order to cut my winter heating costs down to near nothing. I've also played with wind power off and on for years as well. It started out all fun but believe me manual operation of a half assed designs got old fast so it eventually got redesigned into all integrated systems that work with my existing electrical power and heating systems so that there was no where near the manual work and time involved in using any of it. Believe me if you really intend to go self sufficient put the time and money into integrating it into your modern already in use systems so that it works with the common off the shelf plug and play AC powered components you already have and use. You will appreciate the upfront work and planning of doing so later! Believe me since everything we use is designed to work around our common 120/240 VAC 60 hz power designing a totally independant electrical system for a limited application is a waste of time and money. Been there done that and it got old. If you have AE based electrical power generation you are better off tieing it into your existing AC systems over setting it up as a independent sub systems. Especially if you are intending to use it in more than just one specific dedicated location. #### mcgyvr Joined Oct 15, 2009 5,394 I was going to recommend the LDD's.. Glad someone already did they are excellent for "high power LEDs" vs resistors and ensure a fixed current even with varying forward voltages... and they are cheap enough to not have to roll your own. Put all the LDDs in your "control room" and run the outputs to each LED fixture.. Then you can supply multiple LDDs with the same 5V PWM signal and have the option of splitting it at anytime by simply adding more 5V PWM "controllers". Today you might want all lights dimmed the same.. Tomorrow you may want to set the "mood" in certain rooms vs others.. Having multiple 5V PWM "controllers" would allow that.. And then get crazy and have the ability to dim from your smartphone. Thread Starter #### Evanguy Joined Dec 21, 2014 81 Mcgyvr, Thanks. i now do plan on running the led drivers in the "control room". good idea. and I've seen the LLD-H but I'm going to need 1300ma for 24w, the 1000ma one could work if i rearranged my led strings but i would lose a few led's. so i plan on using stcs1 drivers, they also cost very little. Here is the system im planning, realistically it will be 360w total 15x24W ,max (if all rooms on at once and pwm at off) only the switch, inductor and leds will be located outside of the control room im going to build 15 stcs1 drivers, 1 pwm driver (for now, may also add an arduino in the mix), 15 led fixtures, at this stage it may be driven with a 120vac-24vdc transformer (just spent any extra money i had on our new to us, wood fire oven and stove and chimney for it, to get rid of the electric ones) or i may build it and wait until i cant get a used bank of batteries out of a forklift type rig before setting it up. its going to be a while building all the circuits ill bet, also my drawing is missing 1 led in series with the 4 strings Edit, i feel i should add some back info on this because i get what Tcmtech is saying. but im also different then most people, we use durning the winter months about 800kwh, summer is alot less. we are changing out the stove and oven for wood powered. we dont have a microwave, or a tv, my wife has hand mixers for cooking, we dry our clothes on the close line (inside winter, outside summer) we do use a washing machine though, all the heat and hot water we make via wood burning (outside boiler for summer) right now the only things that are pluged in/running all the time are; oven/stove(soon gone), clothes washer, fridge/freezer combo , well pump , 2x cell phone chargers , small radio and this computer im on(10"netbook), modem and a lamp in my bedroom. ohh also all the lights in the house, 14 rooms. we live the simplest lives we can lol, we have animals and a small farm on the go, also a large wood lot, one the house is paid off (10 more years) i plan to retire (42yrs) and just try and "live off the land" as they say, sell firewood(225$ a cord here) and snowblow (with tractor) drive ways for any income needed, also sell farmed stuff, money isnt a concern in my life
i already run my shop off a generator (welder(s), mill, lathe, lights the whole shop needs to be "started up"
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#### mcgyvr
Joined Oct 15, 2009
5,394
I will NEVER recommend LEDs in parallel without current limiting on each series string..
They WON'T share equally..
#### Evanguy
Joined Dec 21, 2014
81
ohhh, i see what your getting at, you mean one string may not play nice in the sharing game. so along with the constant current driver i should also have a resistor in series with each string of leds to set current equally between the three string?
#### mcgyvr
Joined Oct 15, 2009
5,394
ohhh, i see what your getting at, you mean one string may not play nice in the sharing game. so along with the constant current driver i should also have a resistor in series with each string of leds to set current equally between the three string?
Personally I would use a higher voltage to avoid parallel strings altogether..
Or "current mirrors" can be incorporated..
Or more "drivers"
Or different LEDs..
#### Evanguy
Joined Dec 21, 2014
81
Ive looked up current mirrors, they look good and ill poke around with them a bit more. but i see what your saying about more "drivers" and using 1 string per driver. if i did that and stepped the voltage to 36v i could run ten leds per driver.
Thanks for the help so far. i have more to look into and think about.
Also the leds i bought they are 1w ~100lm
the three watt ones were only ~220 lm.
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http://genkuroki.web.fc2.com/MathJax/LivePreviewMathJax-jquery.html
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# Live Preview of MathJax Type Setting
## Input
Examples: $\varphi_i$, $\dfrac12$, $\sum_{n=1}^\infty x^n$, etc
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https://mast.queensu.ca/~mingo/seminar/winter_2014.html
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# Seminar on Free Probability and Random Matrices Winter 2014
## Organizers: J. Mingo and S. Belinschi <!-- document.write("(Last Modified: "+document.lastModified+")") //--> Schedule for Current Term
Tuesday, April 1, 4:30 - 6:00, Jeff 319
Josué Vázquez-Becerra (Queen's)
Asymptotically liberating sequences of random unitary matrices, Part II
In these lecture series, we will discuss a recent paper by Greg W. Anderson and Brendan Farrell which exhibits some systems of random unitary matrices that, when used for conjugation, lead to freeness.
Thursday, March 20, 4:30 - 6:00, Jeff 319
Ruiming Zhang (Northwest A & F University, Yangling)
On Complete Asymptotic Expansions of Certain $q$-Special Functions
According to Paul Turán special functions are defined as useful mathematical functions. Clearly, the mathematical functions $e^{az}$ and $\Gamma(z)$ are fundamental special functions. In mathematics a function $f(q,z)$ is an $q$-analogue of $g(z)$ means that $g(z)$ could be obtained as $q\to1$ limit of $f(q,z)$ under suitable scalings. A special function may have many interesting $q$-analogues, for example, $q$-special functions $e_{q}(z),$ $E_{q}(z)$ $A_{q}(z)$ and $\mathcal{E}_{q}(\cos\alpha,\cos\beta;t)$ are all $q$-analogues of $e^{az}$. $q$-analogues of classical special functions have many important applications in mathematics and physics. The Euler's $q$-exponential function $E_{q}(-z) = (z;q)_{\infty} = \prod_{k=0}^{\infty} \left(1-zq^{k} \right), \quad q \in (0,1), z \in \mathbb{C}$ is an $q$-analogue of $e^{-z}$ and Jackson's $q$-gamma function $\Gamma_{q}(z) = \frac{(q;q)_{\infty}} {(q^{z};q)_{\infty}} (1-q)^{1-z} \quad q \in (0,1), z \in \mathbb{C}$ is an $q$-analogue of $\Gamma(z)$. These two $q$-functions are the cornerstones of the theory of basic hypergeometric series (a.k.a $q$-series). In this talk we present a derivation for the complete asymptotic expansions of $(z;q)_{\infty}$ and $\Gamma_{q}(z)$ via an Mellin transform. These asymptotic formulas are valid throughout the entire complex plane, uniformly on compact subsets. The formula for $(z;q)_{\infty}$ suggests that the modular properties of Dedekind eta function is a consequence of vanishing of odd Bernoulli numbers.
Tuesday, March 18, 4:30 - 6:00, Jeff 319
Josue Vázquez Becerra (Queen's)
Asymptotically liberating sequences of random unitary matrices Part I: Functions of the χχ-class.
In these lecture series, we will discuss a recent paper by Greg W. Anderson and Brendan Farrell which exhibits some systems of random unitary matrices that, when used for conjugation, lead to freeness. Specifically, in this lecture we will introduce the functions of the χχ-class and present some of their properties related to sequences of complex matrices.
Tuesday, March 11, 4:30 - 6:00, Jeff 319
Hao-Wei Huang (Queen's)
Regularization properties of free convolutions with $\boxplus$-infinitely divisible measures II
We will continue discussing the regularity properties of the free additive convolution. Specifically, a probability measure $\mu$ on $\mathbb{R}$ is said to have the property (H) if the density of $\mu\boxplus\nu$ is positive and analytic everywhere on $\mathbb{R}$ for any probability measure $\nu$ on $\mathbb{R}$. We will provide necessary and sufficient conditions on $\mu$ so that $\mu$ has the property (H) when it is $\boxplus$-infinitely divisible. We will also give some examples which have the property (H).
Thursday, March 6, 4:30 - 6:00, Jeff 319
Benoît Collins (Ottawa)
Numerical range for random matrices
We review the notion of numerical range, and show that it behaves in an almost deterministic way for very general examples of random matrix models. By passing, we obtain norm estimates for DT-random matrix models introduced by Dykema and Haagerup. Joint work with Sasha Litvak, Karol Zyckowski, Piotr Gawron.
Tuesday, February 25, 4:30 - 6:00, Jeff 319
Hao-Wei Huang (Queen's)
Regularization properties of free convolutions with $\boxplus$-infinitely divisible measures
Let $\mu$ and $\nu$ be probability measures on $\mathbb{R}$. We will discuss some regularization properties of free additive convolution $\mu\boxplus\nu$, where $\mu$ is $\boxplus$-infinitely divisible. More precisely, we will provide necessary and sufficient conditions on $\mu$ so that for any $\nu$ the density of $\mu\boxplus\nu$ is positive and analytic everywhere on $\mathbb{R}$. We will also give necessary and sufficient conditions so that the density is analytic at points at which the density vanishes. This is a joint work with Jiun-Chau Wang.
Tuesday, February 11, 4:30 - 6:00, Jeff 319
Jerry Gu (Queen's)
Bi-freeness and left-right cumulant functionals in free probability, III
We will first finish the proof from last week, then we will briefly discuss a new concept in free probability, called bi-freeness, which was introduced by D. Voiculescu last year. On a free product of Hilbert spaces with specified unit vector, there are two actions of the operators of the initial spaces, corresponding to a left and to a right tensorial factorization, respectively. The notion of bi-free independence (or bi-freeness) arises when algebras of left-operators and algebras of right-operators on the free product space are considered at the same time.
Tuesday, February 4, 4:30 - 6:00, Jeff 319
Jerry Gu (Queen's)
Joint moments of left-right canonical operators on full Fock space, II
We will continue from last week and give an alternative description for the special'' set of partitions that was introduced last time. The definition arises from the concept of a double-ended queue used in theoretical computer science which, in a certain way, describes the joint action of the left-right canonical operators on full Fock space. If time permits, we will prove the main theorem stated last week.
Tuesday, January 28, 4:30 - 6:00, Jeff 319
Jerry Gu (Queen's)
Joint moments of left-right canonical operators on full Fock space
Let $\mathcal{T}$ be the full Fock space over $\mathbb{C}^d$ and consider a $(2d)$-tuple $A_1, \dots, A_d, B_1, \dots, B_d$ of canonical operators on $\mathcal{T}$, where $A_1, \dots, A_d$ act on the left and $B_1, \dots, B_d$ act on the right. The joint moments of the $(2d)$-tuple can be computed using the family of $(l, r)$-cumulant functionals, which enlarges the family of free cumulant functionals. Moreover, let $f$ and $g$ be the joint $R$-transforms of $(A_1, \dots, A_d)$ and $(B_1, \dots, B_d)$ with respect to the vacuum-state defined on $\mathcal{B}(\mathcal{T})$, then it turns out that every joint moment of the combined $(2d)$-tuple can be written in a canonical way as a sum of products of coefficients of $f$ and $g$ combined. This talk is based on a recent paper by M. Mastnak and A. Nica.
Tuesday, January 21, 4:30 - 6:00, Jeff 319
Mario Diaz (Queen's)
Noncommutative functions, the Taylor-Taylor formula and applications, II Some Analytical Aspects
This series of lectures, which are divided in three parts, are based on the paper of Verbovetskyi and Vinnikov "Foundations of Noncommutative Function Theory".
Tuesday, January 14, 4:30 - 6:00, Jeff 319
Mario Diaz (Queen's)
Noncommutative functions, the Taylor-Taylor formula and applications
This series of lectures, which are divided in three parts, are based on the paper of Verbovetskyi and Vinnikov "Foundations of Noncommutative Function Theory". Part I: Taylor-Taylor (TT) Formula Part II: Some Analytical Aspects Part III: Application Part I. In this part we will introduce the noncommutative functions and their difference-differential operator. Motivated by the latter, we will define the so called higher order noncommutative functions. Finally, we will derive the TT formula, the analogue of the classical Taylor formula in the case of noncommutative functions.
Previous Schedules
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https://www.gradesaver.com/textbooks/math/algebra/algebra-1/chapter-10-radical-expressions-and-equations-10-1-the-pythagorean-theorem-lesson-check-page-602/1
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## Algebra 1
$x=39$
In order to solve this equation, you need to use The Pythagorean Theorem, which is: $a^{2}+b^{2}=c^{2}$ Now when we replace the variables with numbers we get: $36^{2}+15^{2}=x^2$ (In this case, $x$ represents $c$) When you simplify this equation, you get: $1296+225=x^{2}$ When we simplify this further by adding the first two numbers, we get: $1521=x^2$ Finally, we can take the square root of both of these numbers: $\sqrt x^2=\sqrt1521$ Finally, we get our answer: $x=39$
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https://link.springer.com/article/10.1007/s00211-019-01051-9
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Numerische Mathematik
, Volume 142, Issue 3, pp 667–711
# Correcting for unknown errors in sparse high-dimensional function approximation
• Anyi Bao
• Simone Brugiapaglia
Article
## Abstract
We consider sparsity-based techniques for the approximation of high-dimensional functions from random pointwise evaluations. To date, almost all the works published in this field contain some a priori assumptions about the error corrupting the samples that are hard to verify in practice. In this paper, we instead focus on the scenario where the error is unknown. We study the performance of four sparsity-promoting optimization problems: weighted quadratically-constrained basis pursuit, weighted LASSO, weighted square-root LASSO, and weighted LAD-LASSO. From the theoretical perspective, we prove uniform recovery guarantees for these decoders, deriving recipes for the optimal choice of the respective tuning parameters. On the numerical side, we compare them in the pure function approximation case and in applications to uncertainty quantification of ODEs and PDEs with random inputs. Our main conclusion is that the lesser-known square-root LASSO is better suited for high-dimensional approximation than the other procedures in the case of bounded noise, since it avoids (both theoretically and numerically) the need for parameter tuning.
## Mathematics Subject Classification
65D15 41A10 94A20
## Notes
### Acknowledgements
BA, AB and SB acknowledge the Natural Sciences and Engineering Research Council of Canada through Grant 611675 and the Alfred P. Sloan Foundation and the Pacific Institute for the Mathematical Sciences (PIMS) Collaborative Research Group “High-Dimensional Data Analysis”. SB acknowledges the support of the PIMS Post-doctoral Training Center in Stochastics. The authors are grateful to Claire Boyer, John Jakeman, Richard Lockhart, Akil Narayan, and Clayton G. Webster for interesting and fruitful discussions.
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https://si.m.wikipedia.org/wiki/%E0%B6%89%E0%B6%BB%E0%B6%A7%E0%B7%8A%E0%B6%A7%E0%B7%9A_%E0%B7%84%E0%B7%8F_%E0%B6%94%E0%B6%AD%E0%B7%8A%E0%B6%AD%E0%B7%9A_%E0%B7%81%E0%B7%8A%E2%80%8D%E0%B6%BB%E0%B7%92%E0%B6%AD
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# ඉරට්ටේ හා ඔත්තේ ශ්රිත
In mathematics, ඉරට්ටේ ශ්රිත හා ඔත්තේ ශ්රිත are ශ්රිතයs which satisfy particular symmetry relations, with respect to taking additive inverses. They are important in many areas of mathematical analysis, especially the theory of power series and Fourier series. They are named for the parity of the powers of the power functions which satisfy each condition: the function f(x) = xn is an even function if n is an even integer, and it is an odd function if n is an odd integer.
## ඉරට්ටේ ශ්රිත
ƒ(x) = x2 ඉරට්ටේ ශ්රිතයක් සඳහා උදාහරණයකි.
ƒ(x) = x3 ඔත්තේ ශ්රිතයක් සඳහා උදාහරණයකි.
ƒ(x) = x3 + 1 ඔත්තේ හෝ ඉරට්ටේ දෙකම නොවන.
Let f(x) be a real-valued function of a real variable. Then f is even if the following equation holds for all x in the domain of f:
${\displaystyle f(x)=f(-x).\,}$
ජ්යාමිතිකව , ඉරට්ටෙ ශ්රිතයක ප්රස්තාරයසමිමිතික with respect to the y-axis, meaning that its graph remains unchanged after ප්රතිබිම්බය about the y-axis.
ඉරට්ටෙ ශ්රිත සඳහා උදාහරණ ලෙස |x|, x2, x4, cos(x), and cosh(x).
## ඔත්තේ ශ්රිත
Again, let f(x) be a තාත්වික-valued function of a real variable. Then f is odd if the following equation holds for all x in the domain of f:
${\displaystyle -f(x)=f(-x)\,,}$
or
${\displaystyle f(x)+f(-x)=0\,.}$
Geometrically, the graph of an odd function has rotational symmetry with respect to the origin, meaning that its graph remains unchanged after rotation of 180 degrees about the origin.
Examples of odd functions are x, x3, sin(x), sinh(x), and erf(x).
## සමහර තොරතුරු
Note: A function's being odd or even does not imply differentiability, or even continuity. For example, the Dirichlet function is even, but is nowhere continuous. Properties involving Fourier series, Taylor series, derivatives and so on may only be used when they can be assumed to exist.
### මූලික ගුණ
• The only function which is both even and odd is the constant function which is identically zero (i.e., f(x) = 0 for all x).
• The sum of an even and odd function is neither even nor odd, unless one of the functions is identically zero.
• The sum of two even functions is even, and any constant multiple of an even function is even.
• The sum of two odd functions is odd, and any constant multiple of an odd function is odd.
• The product of two even functions is an even function.
• The product of two odd functions is an even function.
• The product of an even function and an odd function is an odd function.
• The quotient of two even functions is an even function.
• The quotient of two odd functions is an even function.
• The quotient of an even function and an odd function is an odd function.
• The derivative of an even function is odd.
• The derivative of an odd function is even.
• The composition of two even functions is even, and the composition of two odd functions is odd.
• The composition of an even function and an odd function is even.
• The composition of any function with an even function is even (but not vice versa).
• The integral of an odd function from −A to +A is zero (where A is finite, and the function has no vertical asymptotes between −A and A).
• The integral of an even function from −A to +A is twice the integral from 0 to +A (where A is finite, and the function has no vertical asymptotes between −A and A).
### ශ්රේණි
• The Maclaurin series of an even function includes only even powers.
• The Maclaurin series of an odd function includes only odd powers.
• The Fourier series of a periodic even function includes only cosine terms.
• The Fourier series of a periodic odd function includes only sine terms.
### වීජීය වියුහය
• Any linear combination of even functions is even, and the even functions form a vector space over the reals. Similarly, any linear combination of odd functions is odd, and the odd functions also form a vector space over the reals. In fact, the vector space of all real-valued functions is the direct sum of the subspaces of even and odd functions. In other words, every function f(x) can be written uniquely as the sum of an even function and an odd function:
${\displaystyle f(x)=f_{\text{even}}(x)+f_{\text{odd}}(x)\,,}$
where
${\displaystyle f_{\text{even}}(x)={\frac {f(x)+f(-x)}{2}}}$
is even and
${\displaystyle f_{\text{odd}}(x)={\frac {f(x)-f(-x)}{2}}}$
is odd.
• The even functions form a commutative algebra over the reals. However, the odd functions do not form an algebra over the reals.
### ප්රසංවාද
In signal processing, harmonic distortion occurs when a sine wave signal is multiplied by a non-linear transfer function. The type of harmonics produced depend on the transfer function:[1]
• When the transfer function is even, the resulting signal will consist of only even harmonics of the input sine wave; ${\displaystyle 2f,4f,6f,\dots \ }$
• When it is odd, the resulting signal will consist of only odd harmonics of the input sine wave; ${\displaystyle 1f,3f,5f,\dots \ }$
• When it is asymmetric, the resulting signal may contain either even or odd harmonics; ${\displaystyle 1f,2f,3f,\dots \ }$
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http://mathoverflow.net/questions/50572/optimally-directing-switches-for-a-random-walk/50588
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# Optimally directing switches for a random walk
If you are sometimes called upon directing a random walk in a directed graph, how should you direct it so as to maximize the probability it goes where you want?
## Formal statement
More specifically, suppose you are given a directed graph $G$ with edge weights, two designated vertices $s$ and $t$, and a subset of the vertices $S$. The edges weights represent the transition probabilities of the random walk, the vertex $s$ the start, the vertex $t$ the target, and the set $S$ the set of switches. You are guaranteed that the weights on the out-edges of any node are non-negative and sum to one, that $t$ is absorbing (i.e., $t$ has one out-edge directed towards itself), and that the out-degree of any vertex in $S$ is exactly two.
A random walk is taken on $G$, starting at $s$. For any given vertex not in $S$, the weight on an out-edge is the probability that the walk will travel in that direction. Every time that the walk reaches a switch (a vertex in $S$), you are allowed to choose which of the two edges the walk will travel along (and you are allowed probabilistic strategies). How should you direct the path if you want to maximize the probability that the walk ends up at your target $t$?
## Questions
I am most interested in this as an algorithmic question. How fast can you find the optimal strategy with respect to the size of the graph? My specific application has about 100 switches among 200 vertices in a fairly sparse graph (say out-degree bounded above by 6).
But we can also ask purely mathematical questions. For example, my intuition says (and I can hand-wave a proof) that there exists an optimal strategy that is deterministic in the sense that it always chooses the same direction for a given switch and this direction does not depend on the initial vertex $s$. Is this actually true?
Also, is there a sense in which the optimal strategy needs to "coordinate" among the switches? That is, is there a local optimum that is not a global optimum?
## Notes
A note on connectivity: we may assume that the graph is sufficiently connected. If not, we can identify all vertices that cannot be reached from the start node, as well as all of those that cannot reach the target node, into a single, absorbing fail state. We may assume the start node is not the fail node.
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Is the number of steps fixed? – fedja Dec 28 '10 at 16:03
Also, can I make two different choices if the switch is reached twice? – fedja Dec 28 '10 at 16:08
No, the walk is infinite. However, note that once the walk reaches an absorbing vertex (such as the target $t$), it stays there. – aorq Dec 28 '10 at 16:10
Yes, you may make a separate choice each time a switch is reached. My intuition says you won't, but I'll be happily surprised if you prove me wrong. – aorq Dec 28 '10 at 16:26
Here's my proof sketch of "determinism". Look at a strategy as a probability distribution on choices, where repeated choices are treated separately. Then, by the usual argument, there is an optimal strategy that is pure (any mixed strategy is a convex combination of pure strategies). Now suppose the walk reaches vertex $v$ at time $a$ and time $b$ and you made different decisions. Why would you do that -- if the decision at $b$ was optimal, then you should make the same decision at $a$. Finally, it shouldn't matter where you start because all that matters is where you are now. – aorq Dec 28 '10 at 16:33
This is the simple stochastic games problem, but for only one player, and there is a polynomial-time algorithm for it based on linear programming, which is described in Anne Condon's paper "On Algorithms for Simple Stochastic Games." Look in this paper for the linear programming algorithm for SSG's with no min vertices. In one of her papers on simple stochastic games, Condon does indeed prove that the setting of the switches is independent of the start node, and that in the optimal strategy, the switch settings never need to change.
-
Edit: apparently I'm linking to a paper that has a different definition of 'switch'
The reachability problem is NP-complete for unweighted directed switch graphs.
Sounds fishy. Go back from $t$ and see from where you can reach it, expanding the set $S$. If you see a switch that can reach into the current version of $S$, just point it there and add it to $S$. Perhaps, the notions of a switch are different or they talk about full connectivity rather than reaching a given vertex. – fedja Dec 28 '10 at 19:44
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http://www.sciencemadness.org/talk/viewthread.php?tid=5839&page=3
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Sciencemadness Discussion Board » Fundamentals » Organic Chemistry » benzyl alcohol oxidation Select A Forum Fundamentals » Chemistry in General » Organic Chemistry » Reagents and Apparatus Acquisition » Beginnings » Miscellaneous » The Wiki Special topics » Technochemistry » Energetic Materials » Biochemistry » Radiochemistry » Computational Models and Techniques » Prepublication Non-chemistry » Forum Matters » Legal and Societal Issues » Detritus » Test Forum
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Author: Subject: benzyl alcohol oxidation
kmno4
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"The acid is the solvent for the alcohol and is in great excess. Everything should be stirred well for several hours (that is probably too long). The dense lower layer is collected and separated with a funnel to remove any of the acid solution. It is then dried with a suitable drying agent and is ready to use for many purposes."
At this conditions - dense lower layer is HCl(aq). I do not know what are "many purposes" but making benzyl cyanide from this crude product was very unsuccessful. Besides, I always wanted to do some quantitative measurements of reaction: benzyl alcohol+ HCl(aq)... And now I am going to do that (If I have time ).
Sorry for starting offtopic.
By Nicodem:
Assuming x = 0.5 as a realistic value we get:
k1/k2 ≈ e^(6.05) ≈ 423
(...)Yet, taking those approximations, the calculation indicates the oxidation of BnOH might even be a few hundred times faster than the oxidation of PhCHO (assuming the same order of reaction).
I agree with it. But look at Table 1 in ACS paper:
BDE(C-H) for ØCH2OH is 79 (or ~84) kcal/mol
BDE(C-H) for ØCHO is 86 kcal/mol
and
"Normalized Second-Order Rate Constant of H-Abstraction from H-Donor Substrates by BTNO" in MeCN:
k<sub>H</sub> for ØCH2OH is 0,94 (1/Ms)
k<sub>H</sub> for ØCHO is 0,8 (1/Ms)
so k<sub>1</sub>/k<sub>2</sub> ≈ 1
Besides there is large acceleration of rate in protic, H-bonding solvent (AcOH) and order is this time reverted: hydrogen is abstracted from aldehyde faster than from alcohole.
[Edited on 27-4-2008 by kmno4]
Nicodem
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Indeed I agree. Assuming the Evans-Polanyi relation for the two reactions to be of a similar value (calculated as equal) is the weakest assumption in my calculations. This factor depends highly on the one electron oxidant used and other conditions and I have no idea how the persulfate influences it. Therefore x=y was the only assumption I could take without using too much imagination.
With some transition metal one electron oxidants even the oxidation of toluene to benzaldehyde most commonly completely stops at PhCHO stage (talking about the numerous and well studied Co/Cu/Mn/etc catalyzed oxidations of toluene with oxygen). Often no PhCOOH can be detected. Considering that the BDE of Bn-H is 89 kcal/mol, thus even more than for PhCO-H, I can't think of anything else but that the E<sub>a</sub> for radical oxidations of PhCHO is commonly quite higher (but obviously not always as demonstrated by the kinetic measurement you cite).
Anyway, those calculations were plain exercise since they can not give a reliable number given the bold assumptions used. It was more about showing the difference in the BDE values of the two substrates and showing how small absolute differences can give rise to huge differences in the kinetics.
Anyway, if anybody has another explanation for the reaction stopping at the PhCHO stage, I would be glad to hear it. Radical oxidations are not something I'm familiar with.
Done.
Attachment: BDE_values_for_BnOH_and_BzH_references.rar (1.2MB)
…there is a human touch of the cultist “believer” in every theorist that he must struggle against as being unworthy of the scientist. Some of the greatest men of science have publicly repudiated a theory which earlier they hotly defended. In this lies their scientific temper, not in the scientific defense of the theory. - Weston La Barre (Ghost Dance, 1972)
Ephoton
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Mood: trying to figure out why I need a dark room retreat when I live in a forest of wattle.
I found a good source of otc benzyl alcohol the other day I would like to share.
concrete floor stripper. usualy around 20 + %
hehe (I am now a hazard to others look out world)
[Edited on 29-4-2008 by Ephoton]
bash-2.05#
evil_lurker
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Take your BzOH, place in diethyl ether with an equivalent of sodium hydroxide and molecular sieves to form sodium benzylate.
React with BnCl ala Williamson ether synthesis to dibenzyl ether (DBE).
Oxidize the DBE with dilute nitric acid catalized with sodium nitrite.
Reported yields as high as 80% based on DBE with the reaction sucessfully scaled up to 1 mole with similar results.
[Edited on 29-4-2008 by evil_lurker]
Not all chemicals are bad. Without chemicals such as hydrogen and oxygen, for example, there would be no way to make water, a vital ingredient in beer.
kmno4
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Offtopically about reaction of benzyl alcohol(=BA) and HCl(aq)(=AC).
On the picture: 5 test-tubes with with mixtures BA and AC, shaken
many times to reach equilibrium or close to it (at least I think so).
Test tube 1: 2g BA/2g AC [ 75 minutes]
Test tube 2: 2g BA/3g AC [ 50 minutes]
Test tube 3: 2g BA/4g AC [ 30 minutes]
Test tube 4: 2g BA/5g AC [ less than 30 minutes]
Test tube 5: 2g BA/6g AC [ less than 30 minutes]
I also made 2g BA/1g AC but this mixture did not split into separate layers ( I waited 8 hours). For the rest of mixtures, time of separating given in [ ].
To estimate degree of conversion BA into benzyl chloride I titrated (twice) remaining water-acid layer.
Results:
Test tube 1: 2g BA/2g AC -------------
Test tube 2: 2g BA/3g AC 44%
Test tube 3: 2g BA/4g AC 52%
Test tube 4: 2g BA/5g AC 67%
Test tube 5: 2g BA/6g AC 73%
Layer from test tube 1 was not investigated, because water+acid was not separated completly from organic layer and it would cause too big errors.
(from 2g BA/1g AC mixture it did not separete at all)
In no case density of organic layer is larger than water layer, as can be seen. To convert alcohol into chloride quantitatively, large excess of acid is needed. Use of CaCl2, ZnCl2 etc..., would be more convenient.
All values given by me are approximations. It would be good if someone could repeat these measurements.
End of offtopic
I have found interesting article about oxidation of benzyl alcohol with persulfate.
Aqueous Media Oxidation of Alcohols with Ammonium Persulfate
Chinese Journal of Chemistry, 2007, 25, 836—838
If someone is interested, link to article: http://mihd.net/egpdyq2
[Edited on 3-5-2008 by kmno4]
Magpie
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Thanks, kmno4, for posting that journal article. I will be trying their method for making n-butyraldehyde soon.
evil_lurker
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Well I think I have me a project for this summer.
1. Partially convert BnOH to BzCl as close to 1:1 ratio within reason. Start by adding the appropriate amount of 37% HCl to the alchol, heat and agitate to 80íC till it reaches equilibrium.
2. Drain water/acd, add in small quantity of NaOH (enough to remove HCl from previous reaction) then add in concentrated NaOH solution with either a tiny bit of triethylamine or tri-n-butylamine to form the ether.
3 Drain NaOH solution, rinse with a little nitric acid to remove alkali, drain again, then add in dilute HN03/NaNO2 catalyst solution and stirr for several hours.
If one used a reaction flask with bottom drain it could damn near be "one pot" with no solvents, use fairly cheap and easy to get reagents, and be completed in 5-6 hours with no need for isolation of intermediate products.
Not all chemicals are bad. Without chemicals such as hydrogen and oxygen, for example, there would be no way to make water, a vital ingredient in beer.
Nicodem
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Kmno4, that was some nice looking and strict scientific experimentation of which I wish we had posted more and more often.
Thanks also for the paper. It is interesting to see that no overoxidation products are detected. But what is most confusing to me is that butanol reacts efficiently already at 30°C, while for the benzylic, allylic and secondary alcohols they used 75-85°C. Looks like a reversed reactivity order of what is expected for a radical oxidation (and the authors don't even bother giving any hypothesis to account for the differences).
Magpie, you better don't use this method as is on a larger scale since it was developed on a 1 mmol scale. Scaling it up by multiplication could get you in troubles of the type you encountered in your latest butanol oxidation trial. In my experience similar mmol reactions (of which Tetrahedron letter and Synthesis abounds) scaled up usually end up in runaways.
Evil_lurker, you might want to first try out that Bn2O oxidation with HNO3/NaNO2 on BnOH itself before wasting time with its etherification.
[Edited on 3/5/2008 by Nicodem]
…there is a human touch of the cultist “believer” in every theorist that he must struggle against as being unworthy of the scientist. Some of the greatest men of science have publicly repudiated a theory which earlier they hotly defended. In this lies their scientific temper, not in the scientific defense of the theory. - Weston La Barre (Ghost Dance, 1972)
evil_lurker
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Quote: Originally posted by Nicodem Evil_lurker, you might want to first try out that Bn2O oxidation with HNO3/NaNO2 on BnOH itself before wasting time with its etherification.
I had considered that... did I miss something in the paper amongst all the tecnical info?
Not all chemicals are bad. Without chemicals such as hydrogen and oxygen, for example, there would be no way to make water, a vital ingredient in beer.
Nicodem
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You forgot that in 15% HNO3 the media is acidic enough to cleave Bn2O to BnOH. You also forgot the context of the article – the authors were looking for an economical use of Bn2O which is a worthless side product in the industrial preparation of BnOH. Cited from the paper:
Quote: During the oxidation of DBE, BnOH is formed and oxidised to BzH.[ref 7] Benzoic acid is formed by oxidation of benzaldehyde. Therefore, with the progress of the reaction the yield of BnOH decreases and that of BzOH increases. Presence of BnOH in the final product may not be a serious problem as it can be recovered from the reaction mixture by fractional distillation and is a value-added product.
In short, the treatment of BnOH with refluxing HNO3 gives BzOH just like when starting with toluene (BnH), but at milder conditions (90°C) you can actually get viable yields of BzH with BzOH being the major side product. The presence of nitrite works in your favor, assumingly as a source of NO2 to start the radical chain reaction.
garage chemist
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KMnO4, the mixtures of benzyl alcohol and conc HCl have to be heated to effect the reaction! Try it again, and this time heat the test tubes in a boiling water bath.
I have very successfully made benzyl chloride many times from conc aqueous HCl and benzyl alcohol. At a certain temperature, the reaction spntaneously takes place and is over in a few minutes, with complete separation of phases. HCl is used in at least threefold excess. No other reagents are added.
Look at Rhodiums methods for benzyl chloride from -alcohol.
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detritus
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Hi,
Really interesting stuff here. But I am not old enough to buy the pure alcohol from any distributors, can anyone help with any info on OTC source of BzOH in the US?
MagicJigPipe
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There's probably no useful OTC source of BnOH (it's Bn not Bz) in the US. You can get it from pharmacies but when I did that it cost me like $18 for 100mL (I think a couple of other places quoted$40 a quart). Definitely not a practical source unless you work with VERY small amounts like Woelen.
"There must be no barriers to freedom of inquiry ... There is no place for dogma in science. The scientist is free, and must be free to ask any question, to doubt any assertion, to seek for any evidence, to correct any errors. ... We know that the only way to avoid error is to detect it and that the only way to detect it is to be free to inquire. And we know that as long as men are free to ask what they must, free to say what they think, free to think what they will, freedom can never be lost, and science can never regress." -J. Robert Oppenheimer
evil_lurker
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www.lemelange.com $45 gallon USP grade (repacked under non USP conditions so it can't be labelled as such due to FDA regs). [Edited on 3-5-2008 by evil_lurker] [Edited on 3-5-2008 by evil_lurker] Not all chemicals are bad. Without chemicals such as hydrogen and oxygen, for example, there would be no way to make water, a vital ingredient in beer. MagicJigPipe International Hazard Posts: 1553 Registered: 19-9-2007 Location: USA Member Is Offline Mood: Suspicious Hey! They used to be$35 a gallon! Or are you including shipping?
"There must be no barriers to freedom of inquiry ... There is no place for dogma in science. The scientist is free, and must be free to ask any question, to doubt any assertion, to seek for any evidence, to correct any errors. ... We know that the only way to avoid error is to detect it and that the only way to detect it is to be free to inquire. And we know that as long as men are free to ask what they must, free to say what they think, free to think what they will, freedom can never be lost, and science can never regress." -J. Robert Oppenheimer
evil_lurker
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They went up on it I reckon. Need to order a gallon or so.
Not all chemicals are bad. Without chemicals such as hydrogen and oxygen, for example, there would be no way to make water, a vital ingredient in beer.
azo
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pitty you don't live in australia i could of given you a gallon i use it for work as a addative solvent.
MagicJigPipe
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Just mail it. Even with shipping it might be cheaper and it's certainly not HAZMAT.
"There must be no barriers to freedom of inquiry ... There is no place for dogma in science. The scientist is free, and must be free to ask any question, to doubt any assertion, to seek for any evidence, to correct any errors. ... We know that the only way to avoid error is to detect it and that the only way to detect it is to be free to inquire. And we know that as long as men are free to ask what they must, free to say what they think, free to think what they will, freedom can never be lost, and science can never regress." -J. Robert Oppenheimer
kmno4
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Mood: No Mood
Quote: Originally posted by garage chemist KMnO4, the mixtures of benzyl alcohol and conc HCl have to be heated to effect the reaction! Try it again, and this time heat the test tubes in a boiling water bath. (...)
I do not say no. My experiments were conducted at room temperature, concentration of HCl(aq) is 35.4%, only to prove
that Fleaker's post says untruth.
Besides, heating of concentrated HCl somehow scares me....
I do not like gaseous HCl
kmno4
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Quote: Originally posted by Nicodem In short, the treatment of BnOH with refluxing HNO3 gives BzOH just like when starting with toluene (BnH), but at milder conditions (90°C) you can actually get viable yields of BzH with BzOH being the major side product. The presence of nitrite works in your favor, assumingly as a source of NO2 to start the radical chain reaction.
Kinetics of Oxidation of Benzyl Alcohol with Dilute Nitric Acid
Ind. Eng. Chem. Res. 2005, 44, 325-333
Attachment: ie0303911.pdf (176kB)
evil_lurker
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Mood: On the wagon again.
Dude, the information that paper contains is sweeet.
If it is indeed true, we may now finally have a viable method for the home manufacture of BnH from BnOH.
Not all chemicals are bad. Without chemicals such as hydrogen and oxygen, for example, there would be no way to make water, a vital ingredient in beer.
MagicJigPipe
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Why would you want to make toluene out of BnOH? What a waste!
"There must be no barriers to freedom of inquiry ... There is no place for dogma in science. The scientist is free, and must be free to ask any question, to doubt any assertion, to seek for any evidence, to correct any errors. ... We know that the only way to avoid error is to detect it and that the only way to detect it is to be free to inquire. And we know that as long as men are free to ask what they must, free to say what they think, free to think what they will, freedom can never be lost, and science can never regress." -J. Robert Oppenheimer
evil_lurker
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Mood: On the wagon again.
Quote: Originally posted by MagicJigPipe Why would you want to make toluene out of BnOH? What a waste!
Ummm did you miss something here?
BnH is benzaldehyde, BnOH is benzyl alcohol.
Not all chemicals are bad. Without chemicals such as hydrogen and oxygen, for example, there would be no way to make water, a vital ingredient in beer.
Nicodem
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I just knew this would happen as it always happens every time abbreviations and acronyms are used on this forum (like the TCCA vs. TCT confusion coming up all the time).
BnH is toluene since Bn stands for benzyl. Benzaldehyde would be BzH since Bz stands for benzoyl. Therefore it would be preferable to simply use PhCHO for benzaldehyde to avoid further confusion among those who are unfamiliar with such organic shorthand conventions as Bz which are rarely used anyway.
MagicJigPipe
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Yes, evil lurker. Abbv. like that are based on a certain structure/moeity and not just an abbv. of a certain word.
Bn = Ph-CH2 Therefore, like Nicodem pointed out, a benzyl group with a hydrogen is toluene. Another example: Ph is C6H5 so benzene would be PhH (I've also seen benzene represented as "Ph" but that is technically incorrect) and phenol is PhOH. I can understand BzH. If that was used I would have realized he was speaking of benzaldehyde.
I just find BzH easier than typing PhCHO.
[Edited on 5-7-2008 by MagicJigPipe]
"There must be no barriers to freedom of inquiry ... There is no place for dogma in science. The scientist is free, and must be free to ask any question, to doubt any assertion, to seek for any evidence, to correct any errors. ... We know that the only way to avoid error is to detect it and that the only way to detect it is to be free to inquire. And we know that as long as men are free to ask what they must, free to say what they think, free to think what they will, freedom can never be lost, and science can never regress." -J. Robert Oppenheimer
Pages: 1 3 5
Sciencemadness Discussion Board » Fundamentals » Organic Chemistry » benzyl alcohol oxidation Select A Forum Fundamentals » Chemistry in General » Organic Chemistry » Reagents and Apparatus Acquisition » Beginnings » Miscellaneous » The Wiki Special topics » Technochemistry » Energetic Materials » Biochemistry » Radiochemistry » Computational Models and Techniques » Prepublication Non-chemistry » Forum Matters » Legal and Societal Issues » Detritus » Test Forum
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|
http://mathhelpforum.com/advanced-algebra/84922-l-t-problem.html
|
# Thread: L.T problem.....
1. ## L.T problem.....
Q:let T from R^3 to R^3 be a linear transformation and I be identity transformation of R^3.If there is a scalar c and a non zero vector x belongs to R^3 s.t T(x)=cx, then rank(T-cI)
A)can'tbe 0
B)can't be 1
C)can't be 2
D)can't be 3
2. Originally Posted by Mathventure
Q:let T from R^3 to R^3 be a linear transformation and I be identity transformation of R^3.If there is a scalar c and a non zero vector x belongs to R^3 s.t T(x)=cx, then rank(T-cI)
A) can'tbe 0
B) can't be 1
C) can't be 2
D) can't be 3
D) is the answer. (the rank-nullity theorem)
|
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|
http://journal.svmo.ru/en/archive/article?id=1601
|
#### Middle Volga Mathematical Society Journal
MSC2010 37D20, 37G70
### Many-dimensional solenoid invariant saddle-type sets
#### E. V. Zhuzhoma1, N. V. Isaenkova2, V. S. Medvedev3
Annotation In the paper we construct some example of smooth diffeomorphism of closed manifold. This diffeomorphism has one-dimensional (in topological sense) basic set with stable invariant manifold of arbitrary nonzero dimension and the unstable invariant manifold of arbitrary dimension not less than two. The basic set has a saddle type, i.e. is neither attractor nor repeller. In addition, it follows from the construction that the diffeomorphism has a positive entropy and is conservative (i.e. its jacobian equals one) in some neighborhood of the one-dimensional solenoidal basic set. The construction represented in this paper allows to construct a diffeomorphism with the properties stated above on the manifold that is diffeomorphic to the prime product of the circle and the sphere of codimension one. discrete dynamical system, basic set, solenoid, separator, topological entropy.
1Evgeny V. Zhuzhoma, Professor of Department of Fundamental Mathematics, National Research University <> (25/12 B. Pecherskaya st., Nizhny Novgorod 603005, Russia), Ph.D. (Physics and Mathematics), ORCID: http://orcid.org/0000-0001-8682-7591, [email protected]
2Nataliya V. Isaenkova, Professor of Department of Mathematics, Computer Science and Information Technology, Nizhny Novgorod Academy of the Ministry of the Interior of the Russian Federation (3 Ankudinovskoye Sh., Nizhny Novgorod 603950, Russia), Ph.D. (Physics and Mathematics), ORCID: http:// orcid.org/0000-0003-4880-3526, [email protected]
3Vyacheslav S. Medvedev, Researcher TAPRADESS laboratory, National Research University <> (25/12 B. Pecherskaya, Nizhny Novgorod 603005, Russia), Ph.D. (Physics and Mathematics), ORCID: http://orcid.org/0000-0001-6369-0000, [email protected]
Citation: E. V. Zhuzhoma, N. V. Isaenkova, V. S. Medvedev, "[Many-dimensional solenoid invariant saddle-type sets]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,20:1 (2018) 23–29 (In Russian)
DOI 10.15507/2079-6900.20.201801.23-29
|
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|
http://www.tomdalling.com/blog/random-stuff/using-git-for-hacky-archive-deduplication/
|
Have you ever wished that tar or zip would deduplicate files when creating an archive? Well here's a hacky solution using git.
How It Works
Git already has deduplication functionality, due to the way it stores files. Internally, files are named using their own checksums, so if two files have the same checksum then only one copy of the file is stored.
So, to make use of this, if you add all the files to a new git repo then it will perform the deduplication. Then, you archive the .git directory of the repo with zip or tar.
When unarchiving, you just do the opposite. Unzip the .git directory inside the destination directory. Run git reset --hard to bring back all the duplicate files. Then, just delete the .git folder.
Git will also do zlib compression if you run git gc --aggressive. Bzip2 compression is better, but why not have both?!
The Results
I took some recent work, which I know contains duplicate files, to test if this would actually work. Here are the results:
39M original
3.5M original.gitar
10M original.tar.bz2
2.7M original.tar.lrz *see update below
The original directory contained 39mb of files. Running tar cjf original.tar.bz2 original, which uses bzip2 compression, compressed the folder to about 25% of it's original size. The git method compressed the folder to about 10% of it's original size. So it does actually work.
Update: lrzip is better
After publishing this article, someone suggested trying lrzip, which I hadn't heard of before. It doesn't do file deduplication per se, but it does a good job of compressing files with large chunks of redundant data – such as a tarball of duplicate files. By default it uses LZMA compression, which seems to be better than bzip2.
Running tar cf original.tar original && lrzip original.tar produces a file named original.tar.lrz with a size of 2.7M, which is a bit better than the git method.
The Script
Update: Sam Gleske has written a more robust script here: http://github.com/sag47/drexel-university/tree/master/bin .
Here is a quick and nasty script called gitar.sh that makes these deduplicated archives. Use gitar.sh myfolder to create the myfolder.gitar archive. Then use gitar.sh myfolder.gitar to recreate the original folder.
Do whatever you want with the script. I've released it under the MIT license just because I don't want to get sued if someone copy/pastes it onto a production server and everything explodes.
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|
http://tex.stackexchange.com/questions/75905/float-placement-at-the-end-of-the-document
|
# float placement at the end of the document [duplicate]
Is there a way I can specify an option to tell TeX to place all of the floats I have in my document at the end of the document? Specifically I am inserting them currently where I will need them eventually but for the working paper phase I would like to have them all just follow the text of my document. Is this possible?
-
## marked as duplicate by tohecz, Torbjørn T., egreg, cmhughes, percusseOct 8 '12 at 21:28
Maybe the `endfloat` package would help. See tex.stackexchange.com/questions/49483/… – egreg Oct 8 '12 at 20:55
|
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|
https://datatracker.ietf.org/doc/draft-irtf-icnrg-flic/
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# File-Like ICN Collections (FLIC) draft-irtf-icnrg-flic-04
Document Type Active Internet-Draft (icnrg RG) , , , 2022-10-24 Internet Research Task Force (IRTF) Experimental Mailing list discussion Active RG Document Unknown (None) I-D Exists (None) (None) (None)
draft-irtf-icnrg-flic-04
ICNRG C. Tschudin
Internet-Draft University of Basel
Intended status: Experimental C.A. Wood
Expires: 27 April 2023 Cloudflare
M.E. Mosko
PARC, Inc.
D. Oran, Ed.
Network Systems Research & Design
24 October 2022
File-Like ICN Collections (FLIC)
draft-irtf-icnrg-flic-04
Abstract
This document describes a simple "index table" data structure and its
associated Information Centric Networking (ICN) data objects for
organizing a set of primitive ICN data objects into a large, File-
Like ICN Collection (FLIC). At the core of this collection is a
_manifest_ which acts as the collection's root node. The manifest
contains an index table with pointers, each pointer being a hash
value pointing to either a final data block or another index table
node.
Status of This Memo
This Internet-Draft is submitted in full conformance with the
provisions of BCP 78 and BCP 79.
Internet-Drafts are working documents of the Internet Engineering
Task Force (IETF). Note that other groups may also distribute
working documents as Internet-Drafts. The list of current Internet-
Drafts is at https://datatracker.ietf.org/drafts/current/.
Internet-Drafts are draft documents valid for a maximum of six months
and may be updated, replaced, or obsoleted by other documents at any
time. It is inappropriate to use Internet-Drafts as reference
material or to cite them other than as "work in progress."
This Internet-Draft will expire on 27 April 2023.
Copyright (c) 2022 IETF Trust and the persons identified as the
Tschudin, et al. Expires 27 April 2023 [Page 1]
Internet-Draft FLIC October 2022
This document is subject to BCP 78 and the IETF Trust's Legal
Provisions Relating to IETF Documents (https://trustee.ietf.org/
license-info) in effect on the date of publication of this document.
and restrictions with respect to this document.
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1. FLIC as an ICN experimental tool . . . . . . . . . . . . 5
1.2. Requirements Language . . . . . . . . . . . . . . . . . . 5
2. Design Overview . . . . . . . . . . . . . . . . . . . . . . . 5
3. FLIC Structure . . . . . . . . . . . . . . . . . . . . . . . 7
3.1. Terminology . . . . . . . . . . . . . . . . . . . . . . . 7
3.2. Locators . . . . . . . . . . . . . . . . . . . . . . . . 8
3.3. Name Constructors . . . . . . . . . . . . . . . . . . . . 9
3.4. Manifest Metadata . . . . . . . . . . . . . . . . . . . . 11
3.5. Pointer Annotations . . . . . . . . . . . . . . . . . . . 12
3.6. Manifest Grammar (ABNF) . . . . . . . . . . . . . . . . . 12
3.7. Manifest Trees . . . . . . . . . . . . . . . . . . . . . 15
3.7.1. Traversal . . . . . . . . . . . . . . . . . . . . . . 15
3.8. Manifest Encryption Modes . . . . . . . . . . . . . . . . 16
3.8.1. AEAD Mode . . . . . . . . . . . . . . . . . . . . . . 17
3.8.2. RSA-OAEP Key Transport Mode . . . . . . . . . . . . . 18
3.9. Protocol Encodings . . . . . . . . . . . . . . . . . . . 20
3.9.1. CCNx Encoding . . . . . . . . . . . . . . . . . . . . 20
3.9.1.1. CCNx Hash Naming Strategy . . . . . . . . . . . . 21
3.9.1.2. CCNx Single Prefix Strategy . . . . . . . . . . . 21
3.9.1.3. CCNx Segmented Prefix Strategy . . . . . . . . . 22
3.9.1.4. CCNx Hybrid Strategy . . . . . . . . . . . . . . 23
3.9.2. NDN Encoding . . . . . . . . . . . . . . . . . . . . 23
3.9.2.1. NDN Hash Naming . . . . . . . . . . . . . . . . . 23
3.9.2.2. NDN Single Prefix . . . . . . . . . . . . . . . . 24
3.9.2.3. NDN Segmented Prefix . . . . . . . . . . . . . . 25
3.9.2.4. NDN Hybrid Schema . . . . . . . . . . . . . . . . 26
3.10. Example Structures . . . . . . . . . . . . . . . . . . . 26
3.10.1. Leaf-only data . . . . . . . . . . . . . . . . . . . 26
3.10.2. Linear . . . . . . . . . . . . . . . . . . . . . . . 27
4. Experimenting with FLIC . . . . . . . . . . . . . . . . . . . 27
5. Usage Examples . . . . . . . . . . . . . . . . . . . . . . . 27
5.1. Locating FLIC leaf and manifest nodes . . . . . . . . . . 27
5.2. Seeking . . . . . . . . . . . . . . . . . . . . . . . . . 28
5.3. Block-level de-duplication . . . . . . . . . . . . . . . 30
5.4. Growing ICN collections . . . . . . . . . . . . . . . . . 30
5.5. Re-publishing a FLIC under a new name . . . . . . . . . . 30
6. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 31
6.1. FLIC Payload Type . . . . . . . . . . . . . . . . . . . . 31
6.2. FLIC Manifest Metadata and Annotation TLVs . . . . . . . 32
Tschudin, et al. Expires 27 April 2023 [Page 2]
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7. Security Considerations . . . . . . . . . . . . . . . . . . . 32
7.1. Integrity and Origin Authentication of FLIC Manifests . . 33
7.2. Confidentiality of Manifest Data . . . . . . . . . . . . 34
7.3. Privacy of names and linkability of access patterns . . . 34
8. References . . . . . . . . . . . . . . . . . . . . . . . . . 34
8.1. Normative References . . . . . . . . . . . . . . . . . . 34
8.2. Informative References . . . . . . . . . . . . . . . . . 35
Appendix A. Building Trees . . . . . . . . . . . . . . . . . . . 37
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 39
1. Introduction
ICN architectures, such as Content-Centric Networking (CCNx)[RFC8569]
and Named Data Networking [NDN], are well suited for static content
distribution. Each piece of (possibly immutable) static content is
assigned a name by its producer. Consumers fetch this content using
said name. Optionally, consumers may specify the full name of
content, which includes its name and a unique (with overwhelming
probability) cryptographic digest of said content.
| Note: The reader is assumed to be familiar with general ICN
| concepts from CCNx or NDN. For general ICN terms, this
| document uses the terminology defined in [RFC7927]. Where more
| specificity is needed, we utilize CCNx [RFC8569] terminology
| where a Content Object is the data structure that holds
| application payload. Terms defined specifically for FLIC are
| enumerated below in Section 3.1.
To enable requests with full names, consumers need a priori knowledge
of content digests. A Manifest, a form of catalog, is a data
structures commonly employed to store and transport this information.
Typically, ICN manifests are signed content objects (data) which
carry a collection of hash digests. As content objects, a manifest
itself may be fetched by full name. A manifest may contain either
hash digests of, or pointers to, either other manifests or content
objects. A collection of manifests and content objects represents a
large piece of application data, e.g., one that cannot otherwise fit
in a single content object. Because a manifest contains a collection
of hashes, it is by definition non-circular because one cannot hash
the manifest before filling it in.
Tschudin, et al. Expires 27 April 2023 [Page 3]
Internet-Draft FLIC October 2022
Structurally, this relationship between manifests and content objects
is reminiscent of the UNIX inode concept with index tables and memory
pointers. In this document, we specify a simple, yet extensible,
manifest data structure called FLIC - _File-Like ICN Collection_.
FLIC is suitable for ICN protocol suites such as CCNx and NDN. We
describe the FLIC design, grammar, and various use cases, e.g.,
ordered fetch, seeking, de-duplication, extension, and variable-sized
encoding. We also include FLIC encoding examples for CCNx and NDN.
The purpose of a manifest is to concisely name, and hence point to,
the constiuent pieces of a larger object. A FLIC manifest does this
by using a _root_ manifest to name and cryptographically sign the
data structure and then use concise lists of hash-based names to
indicate the constituent pieces. This maintains strong security from
a single signature. A Manifest entry gives one enough information to
create an _Interest_ for that entry, so it must specify the name, the
hash digest, and if needed, the locators.
FLIC is a distributed data structure illustrated by the following
picture.
root manifest
.------------------------------------.
| optional name: |
| /icn/name/of/this/flic |
| |
| HashGroup (HG): |
| overall digest, locator, etc. | .------.
| hash-valued data pointer -----------> | data |
| ... | ------' sub manifest
| hash-valued manifest pointer ------. .------------------.
| | --> | ----->
| optional additional HashGroups | | ----->
| | ------------------'
| optional signature |
------------------------------------'
Figure 1: A FLIC manifest and its directed acyclic graph
A key design decision is how one names the root manifest, the
application data, and subsidiary manifests. FLIC uses the concept of
a Name Constructor. The root manifest (in fact, any FLIC manifest)
may include a Name Constructor that instructs a manifest reader how
to properly create Interests for the associated application data and
subsidiary manifests. The Name Constructors allow interest
construction using a well-known, application-independent set of
rules. Some name constructor forms are tailored towards specific ICN
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protocols, such as CCNx or NDN; some are more general and could work
with many protocols. We describe the allowed Name Constructor
methods in Section 3.3. There are also particulars of how to encode
the name schema in a given ICN protocol, which we describe in
Section 3.9.
FLIC has encodings for CCNx (Section 3.9.1) as per RFC 8609 [RFC8609]
and for NDN (Section 3.9.2).
An example implementation in Python may be found at
[FLICImplementation].
1.1. FLIC as an ICN experimental tool
FLIC enables experimentation with how to structure and retrieve large
data objects and collections in ICN. By having a common data
structure applications can rely on, with a common library of code
that can be used to create and parse manifest data structures,
applications using ICN protocols can both avoid unnecessary
reinvention and also have enhanced interoperability. Since the
design attempts to balance simplicity, universality, and
extensibility, there are a number of important experimental goals to
achieve that may wind up in conflict with one another. We provide a
partial list of these experimental issues in Section 4. It is also
important for users of FLIC to understand that some flexibility and
extensions might be removed if use cases do not materialize to
justify their inclusion in an eventual standard.
1.2. Requirements Language
The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
"SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this
document are to be interpreted as described in [RFC2119].
2. Design Overview
The FLIC design adopts the proven UNIX inode concept of direct and
indirect pointers, but without the specific structural forms of
direct versus indirect. FLIC is a collection of pointers, and when
one de-references the pointer it could be an application object or
another FLIC manifest. The pointers in FLIC use hash-based naming of
Content Objects analogous to the function block numbers play in UNIX
inodes.
Because FLIC uses hash-based pointers as names, FLIC graphs are
inherently acyclic. Both CCNx and NDN support hash-based naming,
though the details differ (see Section 3.9.1 and Section 3.9.2).
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The FLIC datastructure is an acyclic digraph of Content Objects. In
this document, our examples are trees, but that is not a requirement.
For example, a de-duplication representation might have a common
object with many 0s and that object could be references from multiple
places in the tree. As another example, there could be a common sub-
collection of objects organized in a Manifest, and that sub-manifest
could be included in multiple places.
In FLIC terms, a direct pointer links to application-level data,
which is a Content Object with application data in the Payload. An
indirect pointer links to a Content Object with a FLIC Manifest in
| Note: A substantial advantage of using hash-based naming is
| that it permits block-level de-duplication of application data
| because two blocks with the same payload will have the same
| hash name.
The FLIC structure that is expected most applications would use
consists of a root manifest with a strong cryptographic signature and
then cryptographically strong (e.g. SHA256 [SHS]) hash names as
pointers to other manifests. The advantage of this structure is that
the single signature in the root manifest covers the entire data
structure no matter how many additional manifests are in the data
structure. Another advantage of this structure is it removes the
need to use chunk (CCNx) or segment (NDN) name components for the
subordinate manifests.
Another usage is to have a signed Root Manifest with a single pointer
to the Top Manifest. The Top Manifest maybe a CCNx Nameless object.
This method allows an intermediary service to respond to client
requests with its own signed Manifest that then points to a small
Root manifest. The client trusts the intermediary's reponse because
of the intermediary's signature, and then trusts the content because
of the Root manifest. In some cases, the intermediary could embed
the Root Manifest (because it is small) and avoid additional round
peer-to-peer sharing protocol [ProjectOrigin].
FLIC supports manifest encryption separate from application payload
encryption (See Section 3.8). It has a flexible encryption envelope
to support various encryption algorithms and key discovery
mechanisms. The byte layout allows for in-place encryption and
decryption.
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A limitation of this approach is that one cannot construct a hash-
based name for a child until one knows the payload of that child. In
practical terms, this means that one must have the complete
application payload available at the time of manifest creation.
FLIC's design allows straightforward applications that just need to
traverse a linear set of related objects to do so simply, but FLIC
has two extensibility mechanisms that allow for more sophisticated
uses: manifest metadata, and pointer annotations. These are
described in Section 3.4 and Section 3.5 respectively.
FLIC goes to considerable lengths to allow creation and parsing by
application-independent library code. Therefore, any options used by
applications in the data structure or encryption capabilities MUST
NOT require applications to have application-specific Manifest
traversal algorithms. This ensures that such application agnostic
libraries can always successfully parse and traverse any FLIC
Manifest by ignoring the optional capabilities.
The reader may find it useful to refer to Section Example Usages
(Section 5) from time to time to see worked out examples.
3. FLIC Structure
3.1. Terminology
Data Object: a CCNx nameless Content Object that usually only has
of the data.
Direct Pointer: borrowed from inode terminology, it is a CCNx link
using a content object hash restriction and a locator name to
point to a Data Object.
Hash Group: KA collection of pointers. A Manifest should have
atleast one Hash Group. A Hash Group may have its own associated
meta data and Name Constructor.
Indirect Pointer: borrowed from inode terminology, it is a CCNx link
using a content object hash restriction and a locator name to
point to a manifest content object.
Internal Manifest: some or all pointers are indirect. The order and
number of each is up to the manifest builder. By convention, all
the direct manifests come first, then the indirect.
Leaf Manifest: all pointers are direct pointers.
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Locator: A routing hint in an Interest used by forwarding to get the
Interest to where it can be matched based on its Name Constructor-
derived name.
Manifest: a CCNx ContentObject with PayloadType 'Manifest' and a
Payload of the encoded manifest. A leaf manifest only has direct
pointers. An internal manifest has a mixture of direct and
indirect pointers.
Manifest Waste: a metric used to measure the amount of waste in a
manifest tree. Waste is the number of unused pointers. For
example, a leaf manifest might be able to hold 40 direct pointers,
but only 30 of them are used, so the waste of this node is 10.
Manifest tree waste is the sum of waste over all manifests in a
tree.
Name Constructor: The specification of how to construct an Interest
for a Manifest entry.
Root Manifest: A signed, named, manifest that points to nameless
manifest nodes. This structure means that the internal tree
structure of internal and leaf manifests have no names and thus
may be located anywhere in a namespace, while the root manifest
has a name to fetch it by.
Top Manifest: One useful manifest structure is to use a Root
manifest that points to a single Internal manifest called the Top
Manifest. The Top manifest the begins the structure used to
organize manifests. It is also possible to elide the two and use
only a root manifest that also serves in the role of the top
manifest.
3.2. Locators
Locators are routing hints used by forwarders to get an Interest to a
node in the network that can resolve the Interest's name. In some
naming conventions, the name might only be a hash-based name so the
Locator is the only available routing information. Locators exist in
both CCNx and NDN, though the specific protocol mechanisms differ. A
FLIC manifest represents locators in the same way for both ICN
protocols inside Name Constructors (Section 3.3), though they are
encoded differently in the underlying protocol. See Section 3.9 for
encoding differences.
A manifest Node may define one or more Locator prefixes that can be
used in the construction of Interests from the pointers in the
manifest. The Locators are inherited when walking a manifest tree,
so they do not need to be defined everywhere. It is RECOMMENDED that
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only the Root manifest contain Locators so that a single operation
can update the locators. One use case when storing application
payloads at different replicas is to replace the Root manifest with a
new one that contains locators for the current replicas.
3.3. Name Constructors
A Manifest may define zero or more name constructors in
NameConstructorDefinitions (NCD) located in the Manifest Node. An
NCD associates a Name Constructor Id (NCID) to a Name Constructor.
The NCID is used in other parts of the Manifest to refer to that
specific definition.
A manifest organizes pointers inside Hash Groups. Each Hash Group
uses an NCID to indicate what Name Constructor to use to fetch the
pointers inside the group.
NCID 0 is the default name constructor. If it is not defined in an
NCD, it is assumed to be a HashNamingConstructor. A Manifest may re-
define the default as needed.
A Manifest MUST use locally unique NCIDs in the NCD.
NCDs and their associated NCIDs are inherited as one traverses a
manifest. That is, a manifest consumer must remember the NCDs as it
traverses manifests. If it encounters a HashGroup that uses an
unknown NCID, the RECOMMENDED action is to report a malformed
manifest to the user.
A Manifest may update an NCID. If a child manifest re-defines an
NCID, the manifest consumer MUST use the new definition from that
point forward under that Manifest branch.
It is RECOMMENDED that only the root or similar top-level manifest
define NCDs and they not be re-defined in subsequent manifests.
We expect that an application constructing a Manifest will take one
of three approaches to name constructors. The advantage of using, or
re-defining, the default name constructor is that any hash groups
that use it do not need to specify an NCID and thus might save some
space.
* A manifest might define (or use) a default name constructor and
mix subsequent Manifest and Data objects under that same
namespace. The manifest only needs to use one Hash Group and can
freely mix Manifest and Data pointers.
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* A manifest might define (or use) a default name constructor for
subsequent Manifests and define a second NCD for the application
data. This places all subsequent manifests under the default
constructor and places all application data under the second NCD.
The Manifest must use at least two Hash Groups.
There are a few options on how to organize the Hash Groups:
(1) Manifest Hash Group followed by Data Hash group,
(2) Data Hash Group followed by Manifest Hash Group,
(3) Intermix multiple manifest and data hash groups for
(4) use a data-on-leaf only approach: the interior manifests
would use the manifest hash group and the leaves would use
the data hash group. Other organizations are possible.
* Define multiple NCDs for subsequent manifests and data, or not use
the default NCD, or use some other organization.
In this specification, we define the following four types of Name
Constructors. Additional name constructor types may be specified in
a subsequent revision of the specification. Here, we informally
define the name constructors. Section 3.6 specifies the encoding of
each name constructor.
Type 0 (Interest-Derived Naming): Use whatever name was used in the
Interest to retrieve this Manifest, less a hash component, and
append the desired hash value.
Type 1 (Data-Derived Naming): Use the Manifest Name, less a hash
component, as the Interest name, and append the desired hash
value.
Type 2 (Prefix List): The NCD specifies a list of 1 or more name
prefixes. The consumer may use any (or all) of those prefixes
with the desired hash appended.
Type 3 (Segmented Naming): As in Type 2, but the consumer MUST track
Segment Numbers. If the Hash Group provides Segment Number
annotations for each pointer, it MUST use those numbers.
Otherwise, the consumer MUST use a 0-based counter that follows
the traversal order.
In Type 0, the consumer uses some name N to fetch a manifest. When
the consumer receives the Manifest back, it begins issuing interests
for the content using the same name N, but with the hash pointers
from the manifest.
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In Type 1, the consumer uses some name N to fetch a manifest. The
consumer receives a manifest back with name M inside the Manifest
Content Object. The consumer then uses the name M plus hash pointers
from the manifest.
In Type 2, the consumer receives a manifest and begins traversing it.
If it visits a Hash Group with a PrefixSchema Name Constructor, then
that Name Constructor provides a list of 1 or more locators to use.
The consumer may use any or all of the provided locators, plus the
hash pointer, to fetch the contents.
In Type 3, if a Hash Group has a SegmentedSchema Name Constructor,
then the consumer uses the same mechanism as Type 2, but with the
addition of a Segment Number in the name. Segmented naming is only
compatible with deterministic traversal orders or if the Manifest
provides Segment Number annotations for each pointer. If the Hash
Group provides hints about other traversal orders, then it must also
provide Segment Number annotations for each prefix.
The FLIC Manifest may be extended by defining TLVs that apply to the
Manifest as a whole, or alternatively, individually to every data
object pointed to by the Manifest. This basic specification does not
or via Vendor TLVs. FLIC uses a Vendor TLV structure identical to
[RFC8609] for vendor-specific annotations that require no
standardization process.
For example, some applications may find it useful to allow
specialized consumers such as _repositories_ (for example
[repository]) or enhanced forwarder caches to pre-place, or
adaptively pre-fetch data in order to improve robustness and/or
what subset of the compound object to fetch and in what order.
| Note: FLICs ability to use separate namespaces for the Manifest
| and the underlying Data allows different encryption keys to be
| used, hence giving a network element like a cache or repository
| access to the Manifest data does not as a side effect reveal
| the contents of the application data itself.
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3.5. Pointer Annotations
FLIC allows each manifest pointer to be annotated with extra data.
Object pointed to without having to first fetch the corresponding
Content Object. This specification defines one such annotation. The
_SizeAnnotation_ specifies the number of application layer octets
covered by the pointer.
An annotation may, for example, give hints about a desirable
traversal order for fetching the data, or an importance/precedence
indication to aid applications that do not require every content
object pointed to in the manifest to be fetched. This can be very
useful for real-time or streaming media applications that can perform
error concealment when rendering the media.
Vendor TLVs. FLIC uses a Vendor TLV structure identical to [RFC8609]
for vendor-specific annotations that require no standardization
process.
3.6. Manifest Grammar (ABNF)
The manifest grammar is mostly, but not entirely independent of the
ICN protocol used to encode and transport it. The TLV encoding
therefore follows the corresponding ICN protocol, so for CCNx FLIC
uses 2 octet length, 2 octet type and for NDN uses the 1/3/5 octet
types and lengths (see [NDNTLV] for details). There are also some
differences in how one structures and resolves links. [RFC8569]
defines HashValue and Link for CCNx encodings. The NDN
ImplicitSha256DigestComponent defines HashValue and NDN Delegation
these differences.
The basic structure of a FLIC manifest comprises a security context,
a node, and an authentication tag. The security context and
authentication tag are not needed if the node is unencrypted. A node
is made up of a set of metadata, the NodeData, that applies to the
entire node, and one or more HashGroups that contain pointers.
The NodeData element defines the namespaces used by the manifest.
There may be multiple namespaces, depending on how one names
subsequent manifests or data objects. Each HashGroup may reference a
single namespace to control how one forms Interests from the
HashGroup. If one is using separate namespaces for manifests and
application data, one needs at least two hash groups. For a manifest
structure of "MMMDDD," (where M means manifest (indirect pointer) and
D means data (direct pointer)) for example, one would have a first
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HashGroup for the child manifests with its namespace and a second
HashGroup for the data pointers with the other namespace. If one
used a structure like "MMMDDDMMM," then one would need three hash
groups.
TYPE = 2OCTET / {1,3,5}OCTET ; As per CCNx or NDN TLV
LENGTH = 2OCTET / {1,3,5}OCTET ; As per CCNx or NDN TLV
Manifest = TYPE LENGTH [SecurityCtx] (EncryptedNode / Node) [AuthTag]
SecurityCtx = TYPE LENGTH AlgorithmCtx
AuthTag = TYPE LENGTH *OCTET ; e.g. AEAD authentication tag
EncryptedNode = TYPE LENGTH *OCTET ; Encrypted Node
Node = TYPE LENGTH [NodeData] 1*HashGroup
NodeData = TYPE LENGTH [SubtreeSize] [SubtreeDigest] [Locators]
0*Vendor 0*NcDef
SubtreeSize = TYPE LENGTH INTEGER
SubtreeDigest = TYPE LENGTH HashValue
NcDef = TYPE LENGTH NcId NcSchema
NcId = TYPE LENGTH INTEGER
NcSchema = InterestDerivedSchema / DataDerivedSchema /
PrefixSchema / SegmentedSchema
InterestDerivedSchema = TYPE LENGTH [ProtocolFlags]
PrefixSchema = TYPE LENGTH Locators [ProtocolFlags]
SegmentedSchema = TYPE LENGTH Locators [ProtocolFlags]
HashValue = TYPE LENGTH *OCTET ; As per ICN Protocol
Link = TYPE LENGTH *OCTET ; As per ICN protocol
ProtocolFlags = TYPE LENGTH *OCTET
; ICN-specific flags, e.g. must be fresh
HashGroup = TYPE LENGTH [GroupData] (Ptrs / AnnotatedPtrs)
Ptrs = TYPE LENGTH *HashValue
AnnotatedPtrs = TYPE LENGTH *PointerBlock
PointerBlock = TYPE LENGTH *Annotation Ptr
Ptr = TYPE LENGTH HashValue
Annotation = SizeAnnotation / Vendor
SizeAnnotation = TYPE LENGTH Integer
Vendor = TYPE LENGTH PEN *OCTET
GroupData = TYPE LENGTH [NcId] [LeafSize] [LeafDigest]
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[SubtreeSize] [SubtreeDigest]
LeafSize = TYPE LENGTH INTEGER
LeafDigest = TYPE LENGTH HashValue
KeyNum = TYPE LENGTH INTEGER
RsaKemCtx = 2 LENGTH RsaKemData
KeyId = TYPE LENGTH HashValue; ID of Key Encryption Key
WrappedKey = TYPE LENGTH 1*OCTET
Figure 2: FLIC Grammar
SecurityCtx: information about how to decrypt an EncryptedNode. The
structure will depend on the specific encryption algorithm.
AlgorithmId: The ID of the encryption method (e.g. preshared key, a
AlgorithmData: The context for the encryption algorithm.
EncryptedNode: An opaque octet string with an optional
authentication tag (i.e. for AEAD authentication tag)
Node: A plain-text manifest node. The structure allows for in-place
encryption/decryption.
SubtreeSize: The size of all application data at and below the Node
or Group
SubtreeDigest: The cryptographic digest of all application data at
and below the Node or Group
Locators: An array of routing hints to find the manifest components
HashGroup: A set of child pointers and associated metadata
Ptrs: A list of one or more Hash Values
GroupData: Metadata that applies to a HashGroup
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LeafSize: Size of all application data immediately under the Group
(i.e. via direct pointers)
LeafDigest: Digest of all application data immediately under the
Group
Ptr: The ContentObjectHash of a child, which may be a data
ContentObject (i.e. with Payload) or another Manifest Node.
3.7. Manifest Trees
3.7.1. Traversal
FLIC manifests use a pre-order traversal. This means they are read
top to bottom, left to right. The algorithms in Figure 3 show the
pre-order forward traversal code and the reverse-order traversal
code, which we use below to construct such a tree. This document
does not mandate how to build trees. Appendix A provides a detailed
example of building inode-like trees.
If using Annotated Pointers, an annotation could influence the
traversal order.
preorder(node)
if (node = null)
return
visit(node)
for (i = 0, i < node.child.length, i++)
preorder(node.child[i])
reverse_preorder(node)
if (node = null)
return
for (i = node.child.length - 1, i >= 0, i-- )
reverse_preorder(node.child[i]) visit(node)
Figure 3: Traversal Pseudocode
In terms of the FLIC grammar, one expands a node into its hash
groups, visiting each hash group in order. In each hash group, one
follows each pointer in order. Figure 4 shows how hash groups inside
a manifest expand like virtual children in the tree. The in-order
traversal is M0, HG1, M1, HG3, D0, D1, D2, HG2, D3, D4.
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M0 ____
| \
HG1 HG2
| \ | \
M1 D2 D3 D4
|
HG3
| \
D0 D1
Figure 4: Node Expansion
Using the example manifest tree shown in Figure 6, the in-order
traversal would be: Root, M0, M1, D0, D1, D2, M2, D3, D4, D5, M3, D6,
D7, D8.
3.8. Manifest Encryption Modes
This document specifies two encryption modes. The first is a
preshared key mode, where the parties are assumed to have the
decryption keys already. It uses AES-GCM or AES-CCM. This is
useful, for example, when using a key agreement protocol such as
CCNxKE [I-D.wood-icnrg-ccnxkeyexchange]. The second is an RSA key
encapsulation mode (RsaKem [RFC5990]), which may be used for group
keying.
Additional modes may be defined in subsequent specifications. We
expect that an RSA KemDem mode and Elliptic Curve mode should be
specified.
All encryption modes use standard encryption algorithms and
specifications. Where appropriate, we adopt the TLS 1.2 standards
for how to use the encryption algorithms. This section specifies how
to encode algorithm parameters or ICN-specific data.
For group key based encryption, we use RsaKem. This specification
only details the pertinent aspects of the encryption. It describes
how a consumer locates the appropriate keys in the ICN namespace. It
does not specify aspects of a key manager which may or may not be
used as part of key distribution and management, nor does it specify
the protocol between a key manager and a publisher. In its simpliest
form, the publisher could be the key manager, in which case there is
no extra protocol needed between the publisher and key manager.
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While the preshared key algorithm is limited in use, the AES
encryption mode described applies to the group key mechanisms too.
The group key mechanism facilitates the distribution of the shared
key without an on-line key agreement protocol like (the expired
draft) CCNxKE [I-D.wood-icnrg-ccnxkeyexchange].
This mechanism uses AES-GEM [AESGCM] or AES-CCM [RFC3310] for
manifest encryption. A publisher creating a SecurityCtx SHOULD use
the mechanisms in [RFC6655] for AES-CCM Nonce generation and
[RFC5288] for AES-GCM Nonce generation.
As these references specify, it is essential that the publisher
creating a Manifest never use a Nonce more than once for the same
key. For keys exchanged via a session protocol, such as CCNx, the
publisher MUST use unique nonces on each Manifest for that session.
If the key is derived via a group key mechanism, the publisher MUST
ensure that the same Nonce is not used more than once for the same
Content Encryption Key.
the key length and algorithm.
The KeyNum identifies a key on the receiver. The key MUST be exactly
of the length specific by the Mode. Many receivers may have the same
key with the same KeyNum.
When a Consumer reads a manifest that specifies a KeyNum, the
consumer SHOULD verify that the Manifest's publisher is an expected
one for the KeyNum's usage. This trust mechanism employed to
ascertain whether the publisher is expected is beyond the scope of
this document, but we provide an outline of one such possible trust
mechanism. When a consumer learns a shared key and KeyNum, it
associates that KeyNum with the publisher ID used in a public key
signature. When the consumer receives a signed manifest (e.g. the
root manifest of a manifest tree), the consumer matches the KeyNum's
publisher with the Manifest's publisher.
Each encrypted manifest node has a full security context (KeyNum,
Nonce, Mode). The AEAD decryption is independent for each manifest
so Manifest objects can be fetched and decrypted in any order. This
design also ensures that if a manifest tree points to the same
subtree repeatedly, such as for deduplication, the decryptions are
all idempotent.
To encrypt a Manifest, the publisher:
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1. Removes any SecurityCtx or AuthTag from the Manifest.
2. Creates a SecurityCtx and adds it to the Manifest.
3. Treats the Manifest TLV through the end of the Node TLV Length as
unencrypted authenticated Header. That includes anything from
the start of the Manifest up to but not including the start of
the Node's body.
4. Treats the body of the Node to the end of the Manifest as
encrypted data.
5. Appends the AEAD AuthTag to the end of the Manifest, increasing
the Manifest's length
6. Changes the TLV type of the Node to EncryptedNode.
To decrypt a Manifest, the consumer:
1. Verifies that the KeyNum exists and the publisher is trusted for
that KeyNum.
2. Saves the AuthTag and removes it from the Manifest, decreasing
the Manifest length.
3. Changes the EncryptedNode type to Node.
4. Treats everything from the Manifest TLV through the end of the
Node Length as unencrypted authenticated Header. That is, all
bytes from the start of the Manifest up to but not including the
start of the Node's body.
5. Treats the body of the Node to the end of the Manifest as
encrypted data.
6. Verifies and decrypts the data using the key and saved AuthTag.
7. If the decryption fails, the consumer SHOULD notify the user and
stop further processing of the manifest.
3.8.2. RSA-OAEP Key Transport Mode
The RSA-OAEP mode uses RSA-OAEP (see RFC8017 Sec 7.1 [RFC8017] and
[RSAKEM]) to encrypt a symmetric key that is used to encrypt the
Manifest. We call this RSA key the Key Encryption Key (KEK) and each
group member has this private key. A separate key distribuiton
system is responsible for distributing the KEK. For our purposes, it
is reasonable to assume that the KEK private key is available at a
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Locator and that group members can decrypt this private key.
The symmetric key MUST be one that is compatible with the AEAD Mode,
i.e. a 128-bit or 256-bit random number. Further, the symmetric key
MUST fit in the OAEP envelope (which will be true for normal-sized
keys).
Any group key protocol and system needed are outside the scope of
this document. We assume there is a Key Manager (KM) and a Publisher
(P) and a set of group members. Through some means, the Publisher
therefore has at its disposal:
* A Content Encryption Key (CEK), i.e. the symmetric key.
* The RSA-OAEP wrapped CEK.
* The KeyId of the KEK used to wrap the CEK.
* The Locator of the KEK, which is shared under some group key
protocol.
This Manifest specification requires that if a group member fetches
the KEK key at Locator it can decrypt the WrappedKey and retrieve the
CEK.
In one example, a publisher could request a key for a group and the
Key Manager could securely communicate (CEK, Wapped_CEK, KeyId,
Locator) back to the publisher. The Key Manager is responsible for
publishing the Locator. In another example, the publisher could be a
group member and have a group private key in which case the publisher
can create their own key encryption key, publish it under the Locator
and proceed. The publisher generates CEK, Wrapped_CEK, KeyId, and a
Locator on its own.
To create the wrapped key using a Key Encryption Key:
1. Obtain the CEK in binary format (e.g. 32 bytes for 256 bits)
2. RSA encrypt the CEK using the KEK public key with OAEP padding,
following RFC8017 Sec 7.1 [RFC8017]. The encryption is not
signed because the root Manifest must have been signed by the
To decrypt the wrapped key using a Key Encryption Key:
1. RSA decrypt the WrappedKey using the KEK private key with OAEP
padding, following RFC8017 Sec 7.1 [RFC8017].
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2. Verify the unwrapped key is a valid length for the AEADMode.
To encrypt a Manifest, the publisher:
1. Acquires the set of (CEK, Wrapped_CEK, KeyId, Locator).
2. Creates a SecurityCtx and adds it to the Manifest. The
3. Encrypts the Manifest as per AEAD Mode using the RSA-OAEP
SecurityCtx and CEK.
To decrypt a Manifest, the consumer:
1. Acquires the KEK from the Key Locator. If the consumer already
has a cached copy of the KeyId in memory, it may use that cached
key.
2. SHOULD verify that it trusts the Manifest publisher to use the
provided key Locator.
3. Decrypts the WrappedKey to get the CEK. If the consumer has
already decrypted the same exact WrappedKey TLV block, it may use
that cached CEK.
per AEAD Mode, ignoring the KeyNum steps.
3.9. Protocol Encodings
3.9.1. CCNx Encoding
In CCNx, application data content objects use a PayloadType of
T_PAYLOADTYPE_DATA. In order to clearly distinguish FLIC Manifests
from application data, a different payload type is required.
Therefore this specification defines a new payload type of
Name = TYPE LENGTH *OCTET ; As per RFC8569
ExpiryTime = TYPE LENGTH *OCTET ; As per RFC8569
Payload : TYPE LENGTH *OCTET ; the serialized Manifest object
Figure 5: CCNx Embedding Grammar
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3.9.1.1. CCNx Hash Naming Strategy
The Hash Naming Strategy uses CCNx nameless content objects. This
means that only the Root Manifest should have a name embedded in the
Content object. All other are CCNx nameless objects. The Manifest
should provide a set of Locators that the client may use to form the
Interests.
It proceeds as follows:
* The Root Manifest content object bound to a name assigned by the
publisher and signed by the publisher. It also may have a set of
Locators used to fetch the remainder of the manifest. The root
manifest has a single HashPointer that points to the Top Manifest.
It may also have cache control directives, such as ExpiryTime.
* The Root Manifest has an NsDef that specifies HashSchema. Its
GroupData uses that NsId. All internal and leaf manifests use the
same GroupData NsId. A Manifest Tree MAY omit the NsDef and NsId
elements and rely on the default being HashSchema.
* The Top Manifest is a nameless CCNx content object. It may have
cache control directies.
* Internal and Leaf manifests are nameless CCNx content objects,
possibly with cache control directives.
* The Data content objects are nameless CCNx content objects,
possibly with cache control directives.
* To form an Interest for a direct or indirect pointer, use a Name
from one of the Locators and put the pointer HashValue into the
ContentObjectHashRestriction.
3.9.1.2. CCNx Single Prefix Strategy
The Single Prefix strategy uses a named Root manifest and then all
other data and sub-manifest objects use the same Name. They are
differentiated only by their hash.
It proceeds as follows:
* The Root Manifest content object has a name used to fetch the
manifest. It is signed by the publisher. It has a single Locator
used to fetch the remainder of the manifest using the commong
Single Prefix name. It has a single HashPointer that points to
the Top Manifest. It may also have cache control directives, such
as ExpiryTime.
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* The Root Manifest has an NsDef that specifies PrefixSchema with
the Locator for the single prefix.
* The Top Manifest has the name SinglePrefixName. It may have cache
control directies. Its GroupData elements must have an NsId that
references the NsDef.
* An Internal or Leaf manifest has the name SinglePrefixName,
possibly with cache control directives. Its GroupData elements
must have an NsId that references the NsDef.
* The Data content objects have the name SinglePrefixName, possibly
with cache control directives.
* To form an Interest for a direct or indirect pointer, use
SinglePrefixName as the Name and put the pointer HashValue into
the ContentObjectHashRestriction.
3.9.1.3. CCNx Segmented Prefix Strategy
The Segmented Prefix schema uses a different name in all Content
Objects and distinguishes them via their ContentObjectHash. Note
that in CCNx, using a SegmentedPrefixSchema means that only the Root
Manifest has a Locator for the Segmented Prefix (minus the segment
number).
| *Optional*: Use AnnotatedPointers to indicate the segment
| number of each hash pointer to avoid needing to infer the
| segment numbers.
It proceeds as follows:
* The Root Manifest content object has a name used to fetch the
manifest. It is signed by the publisher. It has a set of
Locators used to fetch the remainder of the manifest. It has a
single HashPointer that points to the Top Manifest. It may also
have cache control directives, such as ExpiryTime.
* The Root Manifest has an NsDef that specifies SegmentedPrefix and
the SegmentedPrefixSchema element specifies the
SegmentedPrefixName.
* The publisher tracks the chunk number of each content object
within the NsId. Objects are be numbered in their traversal
order. Within each manifest, the name can be constructed from the
SegmentedPrefixName plus a Chunk name component.
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* The Top Manifest has the name SegmentedPrefixName plus chunk
number. It may have cache control directies. It's GroupData
elements must have an NsId that references the NsDef.
* An Internal or Leaf manifest has the name SegmentedPrefixName plus
chunk number, possibly with cache control directives. Its
GroupData elements must have an NsId that references the NsDef.
* The Data content objects have the name SegmentedPrefixName plus
chunk number, possibly with cache control directives.
* To form an Interest for a direct or indirect pointer, use
SegmentedPrefixName plus chunk number as the Name and put the
pointer HashValue into the ContentObjectHashRestriction. A
consumer must track the chunk number in traversal order for each
SegmentedPrefixSchema NsId.
3.9.1.4. CCNx Hybrid Strategy
A manifest may use multiple schemas. For example, the application
payload in data content objects might use SegmentedPrefix while the
manifest content objects might use HashNaming.
The Root Manifest should specify an NsDef with a first NsId (say 1)
as the HashNaming schema and a second NsDef with a second NsId (say
2) as the SegmentedPrefix schema along with the SegmentedPrefixName.
Each manifest (Top, Internal, Leaf) uses two or more HashGroups,
where each HashGroup has only Direct (with the second NsId) or
Indirect (with the first NsId). The number of hash groups will
depend on how the publisher wishes to interleave direct and indirect
pointers.
Manifests and data objects derive their names according to the
application's naming schema.
3.9.2. NDN Encoding
In NDN, all Manifest Data objects use a ContentType of FLIC (1024),
while all application data content objects use a PayloadType of Blob.
3.9.2.1. NDN Hash Naming
In NDN Hash Naming, a Data Object has a 0-length name. This means
that an Interest will only have an ImplicitDigest name component in
it. This method relies on using NDN Forwarding Hints.
It proceeds as follows:
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* The Root Manifest Data has a name used to fetch the manifest. It
is signed by the publisher. It has a set of Locators used to
fetch the remainder of the manifest. It has a single HashPointer
that points to the Top Manifest. It may also have cache control
directives.
* The Root Manifest has an NsDef that specifies HashSchema. Its
GroupData uses that NsId. All internal and leaf manifests use the
same GroupData NsId. A Manifest Tree MAY omit the NsDef and NsId
elements and rely on the default being HashSchema.
* The Top Manifest has a 0-length Name. It may have cache control
directies.
* Internal and Leaf manifests has a 0-length Name, possibly with
cache control directives.
* The application Data use a 0-length name, possibly with cache
control directives.
* To form an Interest for a direct or indirect pointer, the name is
only the Implicit Digest name component derived from a pointer's
HashValue. The ForwardingHints come from the Locators. In NDN,
one may use one or more locators within a single Interest.
3.9.2.2. NDN Single Prefix
In Single Prefix, the Data name is a common prefix used between all
objects in that namespace, without a Segment or other counter. They
are distinguished via the Implicit Digest name component. The FLIC
Locators go in the ForwardingHints.
It proceeds as follows:
* The Root Manifest Data object has a name used to fetch the
manifest. It is signed by the publisher. It has a set of
Locators used to fetch the remainder of the manifest. It has a
single HashPointer that points to the Top Manifest. It may also
have cache control directives.
* The Root Manifest has an NsDef that specifies SinglePrefix and the
SinglePrefixSchema element specifies the SinglePrefixName.
* The Top Manifest has the name SinglePrefixName. It may have cache
control directies. Its GroupData elements must have an NsId that
references the NsDef.
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* An Internal or Leaf manifest has the name SinglePrefixName,
possibly with cache control directives. Its GroupData elements
must have an NsId that references the NsDef.
* The Data content objects have the name SinglePrefixName, possibly
with cache control directives.
* To form an Interest for a direct or indirect pointer, use
SinglePrefixName as the Name and append the pointer's HashValue
into an ImplicitDigest name component. Set the ForwardingHints
from the FLIC locators.
3.9.2.3. NDN Segmented Prefix
In Segmented Prefix, the Data name is a common prefix plus a segment
number, so each manifest or application data object has a unique full
name before the implicit digest. This means the consumer must
maintain a counter for each SegmentedPrefix namespace.
| *Optional*: Use AnnotatedPointers to indicate the segment
| number of each hash pointer to avoid needing to infer the
| segment numbers.
It proceeds as follows:
* The Root Manifest Data object has a name used to fetch the
manifest. It is signed by the publisher. It has a set of
Locators used to fetch the remainder of the manifest. It has a
single HashPointer that points to the Top Manifest. It may also
have cache control directives.
* The Root Manifest has an NsDef that specifies SegmentedPrefix and
the SegmentedPrefixSchema element specifies the
SegmentedPrefixName.
* The publisher tracks the segment number of each Data object within
a SegmentedPrefix NsId. Data is numbered in traversal order.
Within each manifest, the name is constructed from the
SegmentedPrefixName plus a Segment name component.
* The Top Manifest has the name SegmentedPrefixName plus segment
number. It may have cache control directies. Its GroupData
elements must have an NsId that references the NsDef.
* An Internal or Leaf manifest has the name SegmentedPrefixName plus
segment number, possibly with cache control directives. Its
GroupData elements must have an NsId that references the NsDef.
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* The Data content objects have the name SegmentedPrefixName plus
chunk number, possibly with cache control directives.
* To form an Interest for a direct or indirect pointer, use
SegmentedPrefixName plus segment number as the Name and put the
pointer HashValue into the ImplicitDigest name component. A
consumer must track the segment number in traversal order for each
SegmentedPrefixSchema NsId.
3.9.2.4. NDN Hybrid Schema
A manifest may use multiple schemas. For example, the application
payload in data content objects might use SegmentedPrefix while the
manifest content objects might use HashNaming.
The Root Manifest should specify an NsDef with a first NsId (say 1)
as the HashNaming schema and a second NsDef with a second NsId (say
2) as the SegmentedPrefix schema along with the SegmentedPrefixName.
Each manifest (Top, Internal, Leaf) uses two or more HashGroups,
where eash HashGroup has only Direct (with the second NsId) or
Indirect (with the first NsId). The number of hash groups will
depend on how the publisher wishes to interleave direct and indirect
pointers.
Manifests and data objects derive their names according to the
application's naming schema.
3.10. Example Structures
3.10.1. Leaf-only data
Root
|
______ M0 _____
/ | \
M1 M2 M3
/ | \ / | \ / | \
D0 D1 D2 D3 D4 D5 D6 D7 D8
Figure 6: Leaf-only manifest tree
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3.10.2. Linear
Of special interest are "skewed trees" where a pointer to a manifest
may only appear as last pointer of (sub-) manifests. Such a tree
becomes a sequential list of manifests with a maximum of datapointers
per manifest packet. Beside the tree shape we also show this data
structure in form of packet content where D stands for a data pointer
and M is the hash of a manifest packet.
Root -> M0 ----> M1 ----> ...
|->DDDD |->DDDD
4. Experimenting with FLIC
FLIC is expected to enable a number of salient experiments in the use
of ICN protools by applications. These experiments will help not
only to inform the desirable structure of ICN applications but
reflect back to the features included in FLIC to evaluate their
usefulness to those applications. While many interesting design
aspects of FLIC remain to be discovered through experience, a number
of important questions to be answered through experimentation
include:
* use for just files or other collections like directories
* use for particular applications, like streaming media manifests
* utility of pointer annotations to optimize retrieval
* utility of the encryption options for use by repositories and
forwarders
* need for application metadata in manifests
5. Usage Examples
5.1. Locating FLIC leaf and manifest nodes
The names of manifest and data objects are often missing or not
unique, unless using specific naming conventions. In this example,
we show how using manifest locators is used to generate Interests.
Take for example the figure below where the root manifest is named by
hash h0. It has nameless children with hashes with hashes h1 ... hN.
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Objects:
manifest(name=/a/b/c, ptr=h1, ptr=hN) - has hash h0
nameless(data1) - has hash h1
...
nameless(dataN) - has hash hN
Query for the manifest:
interest(name=/a/b/c, implicitDigest=h0)
Figure 7: Data Organization
After obtaining the manifest, the client fetches the contents. In
this first instance, the manifest does not provide any Locators data
structure, so the client must continue using the name it used for the
manifest.
interest(name=/a/b/c, implicitDigest=h1)
...
interest(name=/a/b/c, implicitDigest=hN)
Figure 8: Data Interests
Using the locator metadata entry, this behavior can be changed:
Objects:
manifest(name=/a/b/c,
hashgroup(loc=/x/y/z, ptr=h1)
hashgroup(ptr=h2) - has hash h0
nameless(data1) - has hash h1
nameless(data2) - has hash h2
Queries:
interest(name=/a/b/c, implicitDigest=h0)
interest(name=/x/y/z, implicitDigest=h1)
interest(name=/a/b/c, implicitDigest=h2)
Figure 9: Using Locators
5.2. Seeking
Fast seeking (without having to sequentially fetch all content) works
by skipping over entries for which we know their size. The following
expression shows how to compute the byte offset of the data pointed
at by pointer P_i, call it offset_i. In this formula, let P_i.size
represent the Size value of the _i_-th pointer.
offset_i = \sum_{k=1}^{i-1} > P_k.size.
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With this offset, seeking is done as follows:
Input: seek_pos P, a FLIC manifest with a hash group having N entries
Output: pointer index i and byte offset o, or out-of-range error
Algorithm:
offset = 0
for i in 1..N do
if (P > offset + P_i.size)
return (i, P - offset)
offset += P_i.size
return out-of-range
Figure 10: Seeking Algorithm
Seeking in a BlockHashGroup is different since offsets can be quickly
computed. This is because the size of each pointer P_i except the
last is equal to the SizePerPtr value. For a BlockHashGroup with N
pointers, OverallByteCount D, and SizePerPointer L, the size of P_N
is equal to the following:
D - ((N - 1) * L)
In a BlockHashGroup with k pointers, the size of P_k is equal to:
D - L * (k - 1)
Using these, the seeking algorithm can be thus simplified to the
following:
Input: seek_pos P, a FLIC manifest with a hash group having
OverallByteCount S and SizePerPointer L.
Output: pointer index i and byte offset o, or out-of-range error
Algo:
if (P > S)
return out-of-range
i = floor(P / L)
if (i > N)
return out-of-range # bad FLIC encoding
o = P mod L
return (i, o)
Figure 11: Seeking Algorithm
| *Note*: In both cases, if the pointer at position i is a
| manifest pointer, this algorithm has to be called once more,
| seeking to seek_pos o inside that manifest.
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5.3. Block-level de-duplication
Consider a huge file, e.g. an ISO image of a DVD or program in binary
be patched. In this case, all existing encoded ICN chunks can remain
in the repository while only the chunks for the patch itself is added
to a new manifest data structure, as is shown in the diagram below.
For example, the venti archival file system of Plan9 [venti] uses
this technique.
old_mfst - - > h1 --> oldData1 <-- h1 < - - new_mfst
\ - > h2 --> oldData2 <-- h2 < - - /
\ replace3 <-- h5 < - -/
\- > h3 --> oldData3 /
\ > h4 --> oldData4 <-- h4 < - /
Figure 12: De-duplication
5.4. Growing ICN collections
A log file, for example, grows over time. Instead of having to re-
FLIC the grown file it suffices to construct a new manifest with a
manifest pointer to the old root manifest plus the sequence of data
hash pointers for the new data (or additional sub-manifests if
necessary).
| *Note* that this tree will not be skewed (anymore).
old data < - - - mfst_old <-- h_old - - mfst_new
/
new data1 <-- h_1 - - - - - - - - -/
new data2 /
... /
new dataN <-- h_N - - - - - - - -/
Figure 13: Growing A Collection
5.5. Re-publishing a FLIC under a new name
There are several use cases for republishing a collection under a new
namespace, or having one collection exist under several namespaces:
* It can happen that a publisher's namespace is part of a service
provider's prefix. When switching provider, the publisher may
want to republish the old data under a new name.
* A publishes wishes to distribute its content to several
repositories and would like a result to be delivered from the
repository for consumers who have good connectivity to that
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repository. For example, the publisher /alpha wishes to place
content at /beta and /gamma, but routing only to /alpha would not
send a request to either /beta or /gamma. The operators of of
/beta and /gamma could create a named and signed version of the
root manifest with appropriate keys (or delegate that to /alpha)
so the results are always delivered by the corresponding
repository without having to change the bulk of the manifest tree.
This can easily be achieved with a single nameless root manifest for
the large FLIC plus arbitrarily many per-name manifests (which are
signed by whomever wants to publish this data):
data < - nameless_mfst() <-- h < - mfst(/com/example/east/the/flic)
< - mfst(/com/example/west/old/the/flic)
< - mfst(/internet/archive/flic234)
Figure 14: Relocating A Collection
| Note that the hash computation (of h) only requires reading the
| nameless root manifest, not the entire FLIC.
This example points out the problem of HashGroups having their own
hints which are "hardcoded" deep inside the FLIC but might have
become outdated. We therefore recommend to name FLIC manifests only
at the highest level (where these names have no locator function).
Child nodes in a FLIC manifest should not be named as these names
serve no purpose except retrieving a sub-tree's manifest by name, if
would be required.
6. IANA Considerations
IANA is requested to perform the actions in the following sub-
sections.
| IANA should also note that FLIC uses the definitions of
Register FLIC as a Payload Type in the _CCNx Payload Types_ Registry
referring to the description in Section 3.9.1 as follows:
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+======+====================+================================+
| Type | Name | Reference |
+======+====================+================================+
| TBA | T_PAYLOADTYPE_FLIC | Section 3.9.1 and |
| | | Section 3.6.2.2.1 of [RFC8609] |
+------+--------------------+--------------------------------+
Table 1: FLIC CCNx Payload Type
6.2. FLIC Manifest Metadata and Annotation TLVs
Create the following registry to be titled _FLIC Manifest Metadata
and Annotation TLVs_ Manifest Metadata is described in Section 3.4;
Pointer Annotations are described in Section 3.5. The registration
procedure is *Specification Required*. The Type value is 2 octets.
The range is 0x0000-0xFFFF. Allocate a value for the single
_SizeAnnotation_ TLV.
+======+===================+====================+
| Type | Name | Reference |
+======+===================+====================+
| TBA | T_SIZE_ANNOTATION | Size (Section 3.5) |
+------+-------------------+--------------------+
Table 2: FLIC Manifest Metadata and
Annotation TLVs
7. Security Considerations
TODO Need a discussion on:
* signing and hash chaining security. (*Note: Did I cover this
* republishing under a new namespace. (*Note: need help here - is
this to reinforce that you can re-publish application data by
creating a new root Manifest and signing that, requiring only one
signature to change?*)
* encryption mechanisms. (*Note: did I cover this adequately
below?*)
* encryption key distribution mechanisms.(*Note: not sure what needs
to be said here*)
* discussion of privacy, leaking of linkability information - *could
really use some help here*.
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*Anything else?????*.
7.1. Integrity and Origin Authentication of FLIC Manifests
A FLIC Manifest is used to describe how to form Interests to access
large CCNx or NDN application data. The Manifest is itself either an
individual content object, or a tree of content objects linked
together via the corresponding content hashes. The NDN and CCnx
protocol architectures directly provide both individual object
integrity (using cryptographically strong hashes) and data origin
authentication (using signatures). The protocol specifications,
[NDN] and CCNx [RFC8609] respectively, provide the protocol machinery
and keying to support strong integrity and authentication.
Therefore, FLIC utilizes the existing protocol specifications for
these functions, rather than providing its own. There are a few
subtle differences in the handling of signatures and keys in NDN and
CCNx worth recapitulating here:
* NDN in general adds a signature to every individual data packet
rather than aggregating signatures via some object-level scheme.
When employing FLIC Manifests to multi-packet NDN objects, it is
expected that the individual packet signatures would be elided and
the signture on the Manifest used instead.
* In contrast, CCNx is biased to have primitive objects or pieces
thereof be "nameless" in the sense they are identified only by
their hashes rather than each having a name directly bound to the
content through an individual signature. Therefore, CCNx depends
heavily on FLIC (or an alternative method) to provide the name and
the signed binding of the name to the content described in the
Manifest
A FLIC Manifest therefore gets integrity of its individual pieces
through the existing secure hashing procedures of the underlying
protocols. Origin authentication of the entire Manifest is achieved
through hash chaining and applying a signature *only* to the root
Manifest of a manifest tree. It is important to note that the Name
of the Manifest, which is what the signature is bound to, need not
bear any particular relationship to the names of the application
objects pointed to in the Manifest via Name Constructors. This has a
number of important benefits described in Section 3.3.
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7.2. Confidentiality of Manifest Data
ICN protocol architectures like CCNx and NDN, while providing
integrity and origin authentication as described above, leaves
confidentiality issues entirely in the domain of the ICN application.
Therefore, since FLIC is an application-level construct in both NDN
and CCNx, it is incumbent on this specification for FLIC to provide
the desired confidentiality properties using encryption. One could
leave the specification of Manifest encryption entirely in the hands
of the individual application utilizing FLIC, but this would be
undesirable for a number of reasons:
* The sensitivity of the information in a Manifest may be different
from the sensitivity of the application data it describes. In
some cases, it may not be necessary to encrypt manifests, or to
encrypt them with a different keying scheme from that used for the
application data
* One of the major capabilities enabled by FLIC is to allow
repositories or forwarding caches to operate on Manifests (see in
particular Section 3.4). In order to allow such intermediaries to
interpret manifests without revealing the underlying application
data, separate encryption and keying is necessary
* A strong design goal of FLIC is _universality_ such that it can be
used transparently by many different ICN applications. This
argues that FLIC should have a set of common encryption and keying
capabilities that can be delegated to library code and not have to
be re-worked by each individual application (see Section 2,
Paragraph 11)
Therefore, this specification directly specifies two encryption
encapsulations and associated links to key management, as described
in Section 3.8. As more experience is gained with various use cases,
additional encryption capabilities may be needed and hence we expect
the encryption aspects of this specification to evolve over time.
7.3. Privacy of names and linkability of access patterns
What to say here, if anything?
8. References
8.1. Normative References
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[RFC2119] Bradner, S., "Key words for use in RFCs to Indicate
Requirement Levels", BCP 14, RFC 2119,
DOI 10.17487/RFC2119, March 1997,
<https://www.rfc-editor.org/info/rfc2119>.
[RFC3310] Niemi, A., Arkko, J., and V. Torvinen, "Hypertext Transfer
Protocol (HTTP) Digest Authentication Using Authentication
and Key Agreement (AKA)", RFC 3310, DOI 10.17487/RFC3310,
September 2002, <https://www.rfc-editor.org/info/rfc3310>.
[RFC5116] McGrew, D., "An Interface and Algorithms for Authenticated
Encryption", RFC 5116, DOI 10.17487/RFC5116, January 2008,
<https://www.rfc-editor.org/info/rfc5116>.
[RFC5288] Salowey, J., Choudhury, A., and D. McGrew, "AES Galois
Counter Mode (GCM) Cipher Suites for TLS", RFC 5288,
DOI 10.17487/RFC5288, August 2008,
<https://www.rfc-editor.org/info/rfc5288>.
[RFC5990] Randall, J., Kaliski, B., Brainard, J., and S. Turner,
"Use of the RSA-KEM Key Transport Algorithm in the
Cryptographic Message Syntax (CMS)", RFC 5990,
DOI 10.17487/RFC5990, September 2010,
<https://www.rfc-editor.org/info/rfc5990>.
[RFC6655] McGrew, D. and D. Bailey, "AES-CCM Cipher Suites for
Transport Layer Security (TLS)", RFC 6655,
DOI 10.17487/RFC6655, July 2012,
<https://www.rfc-editor.org/info/rfc6655>.
[RFC8017] Moriarty, K., Ed., Kaliski, B., Jonsson, J., and A. Rusch,
"PKCS #1: RSA Cryptography Specifications Version 2.2",
RFC 8017, DOI 10.17487/RFC8017, November 2016,
<https://www.rfc-editor.org/info/rfc8017>.
[RFC8569] Mosko, M., Solis, I., and C. Wood, "Content-Centric
Networking (CCNx) Semantics", RFC 8569,
DOI 10.17487/RFC8569, July 2019,
<https://www.rfc-editor.org/info/rfc8569>.
[RFC8609] Mosko, M., Solis, I., and C. Wood, "Content-Centric
Networking (CCNx) Messages in TLV Format", RFC 8609,
DOI 10.17487/RFC8609, July 2019,
<https://www.rfc-editor.org/info/rfc8609>.
8.2. Informative References
Tschudin, et al. Expires 27 April 2023 [Page 35]
Internet-Draft FLIC October 2022
[AESGCM] Dworkin, M., "Recommendation for Block Cipher Modes of
Operation: Galois/Counter Mode (GCM) and GMAC", National
Institute of Standards and Technology SP 800-38D, 2007,
<https://doi.org/10.6028/NIST.SP.800-38D>.
[FLICImplementation]
Mosko, M., "FLIC Implementation in Python", various,
<https://github.com/mmosko/ccnpy>.
[I-D.wood-icnrg-ccnxkeyexchange]
Mosko, M., Uzun, E., and A. Christopher Wood, "CCNx Key
Exchange Protocol Version 1.0", Work in Progress,
Internet-Draft, draft-wood-icnrg-ccnxkeyexchange-02, 6
July 2017, <https://www.ietf.org/archive/id/draft-wood-
icnrg-ccnxkeyexchange-02.txt>.
[NDN] "Named Data Networking", various,
<https://named-data.net/project/execsummary/>.
[NDNTLV] "NDN Packet Format Specification.", 2016,
<http://named-data.net/doc/ndn-tlv/>.
[ProjectOrigin]
Mosko, M., "Peer-to-Peer Sharing with CCNx 1.0", 2014,
<https://github.com/PARC/CCNxReports/blob/master/
SelectedTopics/p2pshare.pdf>.
[repository]
"Repo Protocol Specification", Various,
<https://redmine.named-data.net/projects/repo-ng/wiki/
Repo_Protocol_Specification>.
[RFC7927] Kutscher, D., Ed., Eum, S., Pentikousis, K., Psaras, I.,
Corujo, D., Saucez, D., Schmidt, T., and M. Waehlisch,
"Information-Centric Networking (ICN) Research
Challenges", RFC 7927, DOI 10.17487/RFC7927, July 2016,
<https://www.rfc-editor.org/info/rfc7927>.
[RSAKEM] Barker, E., Chen, L., Roginsky, A., Vassilev, A., Davis,
R., and S. Simon, "Recommendation for Pair-Wise Key-
Establishment Using Integer Factorization Cryptography",
National Institute of Standards and Technology SP 800-56B
Rev. 2, 2019, <https://doi.org/10.6028/NIST.SP.800-56Br2>.
[SHS] Technology, N. I. O. S. A., "Secure Hash Standard, United
States of American, National Institute of Science and
Technology, Federal Information Processing Standard (FIPS)
180-4", National Institute of Standards and Technology SP
Tschudin, et al. Expires 27 April 2023 [Page 36]
Internet-Draft FLIC October 2022
180-4, 2012,
<https://csrc.nist.gov/publications/fips/fips180-4/
fips180-4_final.pdf>.
[venti] "Venti: a new approach to archival storage", Bell Labs
Document Archive /sts/doc, 2002,
<http://doc.cat-v.org/plan_9/4th_edition/papers/venti/>.
Appendix A. Building Trees
This appendix describes one method to build trees. It constructs a
pre-order tree in a single pass of the application data, going from
the tail to the beginning. This allows us to work up the right side
of the tree in a single pass, then work down each left branch until
we exhaust the data. Using the reverse-order traversal, we create
the right-most-child manifest, then its parent, then the indirect
pointers of that parent, then the parent's direct pointers,then the
parent of the parent (repeating). This process uses recursion, as it
is the clearest way to show the code. A more optimized approach
could do it in a true single pass.
Because we're building from the bottom up, we use the term 'level' to
be the distance from the right-most child up. Level 0 is the bottom-
most level of the tree, such as where node 7 is:
1
2 3
4 5 6 7
preorder: 1 2 4 5 3 6 7
reverse: 7 6 3 5 4 2 1
The Python-like pseudocode build_tree(data, n, k, m) algorithm
creates a tree of n data objects. The data[] array is an array of
Content Objects that hold application payload; the application data
has already been packetized into n Content Object packets.An interior
manifest node has k direct pointers and m indirect pointers.
Tschudin, et al. Expires 27 April 2023 [Page 37]
Internet-Draft FLIC October 2022
build_tree(data[0..n-1], n, k, m)
# data is an array of Content Objects (Data in NDN) with application payload.
# n is the number of data items
# k is the number of direct pointers per internal node
# m is the number of indirect pointers per internal node
segment = namedtuple('Segment', 'head tail')(0, n)
level = 0
# This bootstraps the process by creating the right most child manifest
# A leaf manifest has no indirect pointers, so k+m are direct pointers
root = leaf_manifest(data, segment, k + m)
# Keep building subtrees until we're out of direct pointers
while not segment.empty():
level += 1
root = bottom_up_preorder(data, segment, level, k, m, root)
return root
bottom_up_preorder(data, segment, level, k, m, right_most_child=None)
manifest = None
if level == 0:
assert right_most_child is None
# build a leaf manifest with only direct pointers
manifest = leaf_manifest(data, segment, k + m)
else:
# If the number of remaining direct pointers will fit
# in a leaf node, make one of those. Otherwise, we need to be
# an interior node
if right_most_child is None and segment.length() <= k + m:
manifest = leaf_manifest(data, segment, k+m)
else:
manifest = interior_manifest(data, segment, level, k, m, right_most_child)
return manifest
leaf_manifest(data, segment, count)
# At most count items, but never go before the head
start = max(segment.head(), segment.tail() - count)
manifest = Manifest(data[start:segment.tail])
segment.tail -= segment.tail() - start
return manifest
Tschudin, et al. Expires 27 April 2023 [Page 38]
Internet-Draft FLIC October 2022
interior_manifest(data, segment, level, k, m, right_most_child)
children = []
if right_most_child is not None:
children.append(right_most_child)
interior_indirect(data, segment, level, k, m, children)
interior_direct(data, segment, level, k, m, children)
manifest = Manifest(children)
return manifest, tail
interior_indirect(data, segment, level, k, m, children)
# Reserve space at the head of the segment for this node's
# direct pointers before descending to children. We want
# the top of the tree packed.
reserve_count = min(k, segment.tail - segment.head)
while len(children) < m and not segment.head == segment.tail:
child = bottom_up_preorder(data, segment, level - 1, k, m)
# prepend
children.insert(0, child)
# Pull back our reservation and put those pointers in our direct children
interior_direct(data, segment, level, k, m, children)
while len(children) < k+m and not segment.head == segment.tail:
pointer = data[segment.tail() - 1]
children.insert(0, pointer)
segment.tail -= 1
Christian Tschudin
University of Basel
Email: [email protected]
Christopher A. Wood
Cloudflare
Email: [email protected]
Marc Mosko
PARC, Inc.
Email: [email protected]
Tschudin, et al. Expires 27 April 2023 [Page 39]
Internet-Draft FLIC October 2022
David Oran (editor)
Network Systems Research & Design
Email: [email protected]
Tschudin, et al. Expires 27 April 2023 [Page 40]
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https://www.tutorialspoint.com/how-i-can-get-a-cartesian-coordinate-system-in-matplotlib
|
How I can get a Cartesian coordinate system in Matplotlib?
MatplotlibPythonData Visualization
To plot a Cartesian coordinate system in matplotlib, we can take the following Steps −
• Initialize a variable (N) with a value.
• Create random data points for x and y.
• Plot the points using scatter method with x and y data points.
• To display the figure, use show() method.
Example
import numpy as np
import matplotlib.pyplot as plt
plt.rcParams["figure.figsize"] = [7.00, 3.50]
plt.rcParams["figure.autolayout"] = True
N = 50
x = np.random.rand(N)
y = np.random.rand(N)
plt.scatter(x, y)
plt.show()
Output
Updated on 15-May-2021 12:34:21
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https://eng.libretexts.org/Bookshelves/Electrical_Engineering/Electronics/Book%3A_Semiconductor_Devices_-_Theory_and_Application_(Fiore)/09%3A_BJT_Class_B_Power_Amplifiers
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# 9: BJT Class B Power Amplifiers
$$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$ $$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$$$\newcommand{\AA}{\unicode[.8,0]{x212B}}$$
Learning Objectives
After completing this chapter, you should be able to:
• Define class B operation.
• Determine AC load lines for class B amplifier stages.
• Determine the compliance, maximum load power, efficiency and required device ratings for class B circuits.
• Discuss the advantages and disadvantages of class B operation versus class A operation.
• Discuss the origin of notch distortion and methods used to mitigate it.
• Explain the operation of a current mirror.
• Explain the operation of a Sziklai pair.
• Explain the operation and use of a $$V_{BE}$$ multiplier.
• Outline the operation of fully complimentary and quasi complimentary output stages utilizing direct coupled driver stages.
• Discuss methods to protect the output devices from overload.
This page titled 9: BJT Class B Power Amplifiers is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by James M. Fiore via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.
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http://math.stackexchange.com/questions/215161/techniques-for-bounding-a-sum
|
# Techniques for bounding a sum
I have a very messy function. It consists sums four levels deep, and the inner-most term is itself quite messy.
$$\sum \sum \sum \sum (\mbox{stuff})$$
I can't find a closed form for this function. However, I don't need an exact closed form; I'm only interested in the asymptotic behavior. One idea I have is to approximate the sum using integrals. Would that work? What are some other techniques I can use to upper and/or lower bound a function when the sum is too messy to get into closed form?
Edit: one of the formulas I'm working with looks like this: $$\sum_{x_1 = 1}^n \sum_{x_2 = 1}^n \sum_{y_1 = 1}^n \sum_{y_2=1}^n \left( n^{-2} \left(\frac{n- y_2 + y_1 - 1}{n}\right)^{x_2 - x_1 - 1} \right)$$
-
I didn't include the formula because I don't want someone to simplify a specific formula for me; I want to know general techniques for asymptotically bounding a sum of sums. – Joe Oct 16 '12 at 21:58
I think it does depend on what is (stuff). There is no simple way to do it, because each of the $\Sigma$ can bring about a lot of complexity, for example, just imagine $\Sigma_{prime}$. – picakhu Oct 16 '12 at 21:59
There's really nothing I can tell you without at least some information about the formula. – Alexander Gruber Oct 16 '12 at 22:01
If stuff is messy, won't the integrals be messy as well? – Hagen von Eitzen Oct 16 '12 at 22:01
@HagenvonEitzen my idea for using integrals came from a simple proof bounding the harmonic series in the coupon collector problem. – Joe Oct 16 '12 at 22:44
For the formula you post, the outer two sums are geometric series and can be summed that way. Then you can combine $y_1-y_2$ to give $2n+1$ terms (one of which is zero) instead of $n^2$ and your problem is linear in $n$ instead of fourth order.
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https://socratic.org/questions/54b376a4581e2a2c8874af57#116769
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Chemistry
Topics
# Question #4af57
Jan 12, 2015
Sodium hydroxide is a strong base, which means it dissociates completely in aqueous solution into ${\text{Na}}^{+}$ and ${\text{OH}}^{-}$ ions.
This tells you that the concentrations of the ${\text{Na}}^{+}$ cations and of the ${\text{OH}}^{-}$ anions will be equal to each other, and to the initial concentration of $\text{NaOH}$.
Since you start with ${10}^{- 5}$ $\text{M}$ $\text{NaOH}$, in aqueous solution you'll end up with
$\left[{\text{Na}}^{+}\right] = {10}^{- 5}$ $\text{M}$ and $\left[{\text{OH}}^{-}\right] = {10}^{- 5}$ $\text{M}$
The equation to use in this case is
$p O H = - \log \left(\left[O {H}^{-}\right]\right) = - \log \left({10}^{- 5}\right) = 5$
This implies a pH of
$p H = 14 - p O H = 14 - 5 = 9$
##### Impact of this question
2097 views around the world
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https://www.shaalaa.com/question-bank-solutions/concept-physical-quantities-measurement-select-correct-alternative-piece-paper-dimensions-15-m-x-20-cm-has-area-30-m2-300-cm2-03-m2-3000-m3_32421
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ICSE Class 7CISCE
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# Select the Correct Alternative a Piece of Paper of Dimensions 1.5 M X 20 Cm Has Area : 30 M2 300 Cm2 0.3 M2 3000 M3 - ICSE Class 7 - Physics
ConceptConcept of Physical Quantities and Measurement
#### Question
Select the correct alternative
A piece of paper of dimensions 1.5 m x 20 cm has area :
1. 30 m2
2. 300 cm2
3. 0.3 m2
4. 3000 m3
#### Solution
0.3 m2
Is there an error in this question or solution?
#### APPEARS IN
Solution Select the Correct Alternative a Piece of Paper of Dimensions 1.5 M X 20 Cm Has Area : 30 M2 300 Cm2 0.3 M2 3000 M3 Concept: Concept of Physical Quantities and Measurement.
S
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https://codegolf.meta.stackexchange.com/questions/18256/popularity-of-questions-based-on-post-time-and-the-most-useless-graph-ever?noredirect=1
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# Popularity of questions, based on post time (and the most useless graph ever)
Back when I was new to Code Golf SE (then PPCG), a lot of my questions didn't do too well, and I didn't have the experience to tell whether they were good challenged or not. As such, I would often blame it on anything I could, like post time.
A few years later, I've started to wonder about whether or not post time affects post popularity. Long story short: it doesn't.
At first, it sounds plausible. If you post during a time when few people are online, such as when major timezones would be asleep, maybe fewer people would answer, vote, or comment, and your question would be buried.
I ran a simple SEDE query on Code Golf (SELECT ViewCount, CreationDate FROM Posts WHERE PostTypeId = 1 or similar), and copied the ~10k results from the downloadable CSV to a JS script (JavaScript, as I found out, is not great at data analysis). I created this badly formatted graph, on a logarithmic scale:
The X axis is time, from 00:00:00 to 23:59:59 (UTC). The Y axis is logarithmic (radix 10), with each longer line (every 5 short lines) being 1.
As you can see by the line of best fit (it looks a little high to me, but IDK), post time has pretty much no affect on popularity. The slope of said line is somewhere in the range of -21 views for each hour later in the day.
Being the nerd that I am, I noticed a seemingly higher density of dots to the right, indicating more posts, so I created another graph, which is oddly sinusoidal in appearance:
The X axis is hours (UTC, floored), and the Y axis is total number of questions, on a linear scale of 0 to 750. This graph is slightly more useful, showing that the highest number of questions are posted between 14:00:00 and 21:00:00 UTC. This is between morning and mid-afternoon in the US, and late afternoon to night in the UK.
I can't seem to find much of a purpose for this information, but do what you want with it. I guess I wasted my time so you don't have to, although it's entirely feasible that I'm the only one boring enough to even think about this (:.
Part two: The relationships between question length, views, and votes
• The line of best fit is being pulled up by the outliers, which are much higher than they seem thanks to the log scale. :) – El'endia Starman Nov 10 '19 at 5:30
• @El'endiaStarman Makes sense, I thought it might have something to do with it – Redwolf Programs Nov 10 '19 at 5:32
• This is great and not at all boring. But I think you should look for features of questions which are correlated with number of votes. How about the number of characters in a question for example? Or the number of \$ signs? – Anush Nov 10 '19 at 7:42
• @Anush I think I'll do that; this was a lot of fun. Thanks for the suggestion! – Redwolf Programs Nov 10 '19 at 14:51
• I can't speak for everyone, but when I browse CGCC for the first time in a day, I check the list of recently posted challenges to see if I've missed anything good. – Jo King Nov 10 '19 at 22:41
• @JoKing That seems to be what most people do, judging by the R squared value of 0.00037 on that line of best fit – Redwolf Programs Nov 11 '19 at 1:55
• @Anush I did some more analysis (post length and views, views/votes): codegolf.meta.stackexchange.com/questions/18262/… – Redwolf Programs Nov 11 '19 at 3:52
• It kinda makes sense: more people are online to see the answer at peak times, but more people are posting answers, so fewer see yours. Interesting that the two factors cancel almost completely. – Dewi Morgan Nov 11 '19 at 17:56
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|
https://codegolf.stackexchange.com/questions/142056/rotate-matrix-rows-according-to-the-row-above/142059
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# Specifications
For this challenge, you will be given a matrix of some sort in any reasonable format for a 2-D array. For each row except the last, in order from top (first) to bottom (last), rotate the row below it by x to either direction (you choose a consistent direction to use) where x is the first element in the current row.
# Reference
A reference implementation in Python can be found here
# Example
Let's walk through an example. Take the following matrix for example:
1 5 8
4 7 2
3 9 6
Let's say we're rotating right. First we rotate [4 7 2] to the right by 1 because the first element of [1 5 8] is 1. Thus, we get [2 4 7] as the second row. The matrix is now like this:
1 5 8
2 4 7
3 9 6
Then, we rotate [3 9 6] to the right by 2 because the first element of the second row is 2. Thus we get:
1 5 8
2 4 7
9 6 3
# Challenge
Implement the above
# Test Cases
Test cases are given as a list of lists in Python style.
Input -> Output
[[6, 7, 10, 1, 10, 7], [7, 3, 7, 8, 9, 2], [6, 8, 3, 9, 3, 1], [6, 3, 8, 6, 4, 1], [7, 5, 2, 9, 7, 2], [2, 10, 9, 9, 7, 9], [8, 8, 10, 10, 8, 4]] -> [[6, 7, 10, 1, 10, 7], [7, 3, 7, 8, 9, 2], [1, 6, 8, 3, 9, 3], [1, 6, 3, 8, 6, 4], [2, 7, 5, 2, 9, 7], [7, 9, 2, 10, 9, 9], [4, 8, 8, 10, 10, 8]]
[[8, 10, 4, 3, 9, 4, 6], [8, 8, 8, 8, 6, 7, 5], [6, 2, 2, 4, 8, 9, 6], [1, 7, 9, 9, 10, 7, 8]] -> [[8, 10, 4, 3, 9, 4, 6], [5, 8, 8, 8, 8, 6, 7], [2, 4, 8, 9, 6, 6, 2], [7, 8, 1, 7, 9, 9, 10]]
[[6, 2, 4, 4, 4], [5, 9, 10, 5, 4], [3, 5, 7, 2, 2], [1, 5, 5, 10, 10], [8, 2, 3, 2, 1], [3, 3, 9, 5, 10], [9, 5, 9, 7, 2]] -> [[6, 2, 4, 4, 4], [4, 5, 9, 10, 5], [5, 7, 2, 2, 3], [1, 5, 5, 10, 10], [1, 8, 2, 3, 2], [10, 3, 3, 9, 5], [9, 5, 9, 7, 2]]
[[3, 6, 3, 7, 4], [8, 8, 1, 5, 8], [7, 5, 1, 9, 4], [3, 9, 10, 8, 6]] -> [[3, 6, 3, 7, 4], [1, 5, 8, 8, 8], [4, 7, 5, 1, 9], [9, 10, 8, 6, 3]]
[[5, 6, 1, 2, 6], [1, 10, 10, 1, 4], [6, 2, 7, 1, 7], [9, 5, 8, 6, 3], [4, 5, 1, 2, 1], [8, 6, 1, 1, 3]] -> [[5, 6, 1, 2, 6], [1, 10, 10, 1, 4], [7, 6, 2, 7, 1], [6, 3, 9, 5, 8], [1, 4, 5, 1, 2], [3, 8, 6, 1, 1]]
[[10, 1, 2], [9, 9, 10], [2, 4, 7]] -> [[10, 1, 2], [10, 9, 9], [7, 2, 4]]
[[4, 5, 6], [6, 9, 4], [9, 3, 2], [3, 5, 9], [5, 5, 3], [9, 1, 4]] -> [[4, 5, 6], [4, 6, 9], [2, 9, 3], [5, 9, 3], [5, 3, 5], [1, 4, 9]]
[[8, 7, 6, 5], [9, 8, 6, 6], [7, 9, 7, 10]] -> [[8, 7, 6, 5], [9, 8, 6, 6], [10, 7, 9, 7]]
[[10, 2, 8, 8, 1], [2, 10, 1, 4, 10], [3, 2, 5, 3, 8], [5, 1, 8, 1, 8], [6, 1, 3, 1, 2], [7, 9, 1, 1, 2]] -> [[10, 2, 8, 8, 1], [2, 10, 1, 4, 10], [3, 8, 3, 2, 5], [8, 1, 8, 5, 1], [3, 1, 2, 6, 1], [1, 1, 2, 7, 9]]
[[9, 1, 3, 2, 7], [3, 8, 10, 3, 3], [8, 10, 7, 9, 5], [8, 1, 4, 9, 9], [6, 8, 4, 10, 10], [4, 7, 6, 2, 2], [8, 5, 3, 7, 6]] -> [[9, 1, 3, 2, 7], [8, 10, 3, 3, 3], [7, 9, 5, 8, 10], [9, 9, 8, 1, 4], [8, 4, 10, 10, 6], [6, 2, 2, 4, 7], [6, 8, 5, 3, 7]]
Generate more testcases here
• we rotate [4 7 2] to the right by 1 ... we get [2 7 4] Wait, what? Shouldn't it be [2 4 7]? Or am I misunderstanding "rotation"? – totallyhuman Sep 7 '17 at 21:58
• For each row except the last Shouldn't that be except the first? – totallyhuman Sep 7 '17 at 22:00
• @icrieverytim rotate the row below it technically this is inconsistent with my title but eh – HyperNeutrino Sep 7 '17 at 22:03
• Are we guaranteed that the matrix is positive integers and that the matrix has at least two rows? – Giuseppe Sep 7 '17 at 22:14
• Since x can be larger than the length of the row below (according to the test cases), what exactly is [2, 5, 8] rotated by 4? The second test case says it's [2, 5, 8] which doesn't make a lot of sense to me... – totallyhuman Sep 7 '17 at 22:20
# Husk, 4 bytes
G(ṙ←
Try it online!
Rotates rows to the left.
### Explanation
G in Husk is scanl (or cumulative reduce from left, as some languages call it). When given a function of type x->x->x (like in this case) it can use as starting value the first element of the list.
( is needed here to combine the following two functions into a single one.
ṙ is "rotate to the left" and takes a number and a list as arguments.
← returns the first element of a list.
# Jelly, 6 5 bytes
ṙ@Ḣð\
Try it online!
Rotates to the left.
Saved a byte thanks to @Jonathan Allan.
## Explanation
ṙ@Ḣð\ Input: array of arrays M
ð\ Cumulative reduce over each array using
ṙ@ Rotate the RHS array using each in the LHS array
• You can dump the € – Jonathan Allan Sep 7 '17 at 22:48
• @JonathanAllan Thanks. Isn't ɓ supposed to work here, as in ṙḢɓ\. – miles Sep 7 '17 at 22:52
• Ah, that actually may require a code change to reduce_cumulative; it would make sense to do so... – Jonathan Allan Sep 7 '17 at 23:00
## C++, 187 149 bytes
• 38 bytes thanks to Karl Napf
Output is done by the reference type parameter The parameter's type have to be a std::vector<std::vector<int>> type
auto r=[](auto&a){for(int i=1,j,v;i<a.size();++i){v=a[i-1][0]%a[i].size();for(j=0;j<v;++j){a[i].insert(a[i].begin(),a[i].back());a[i].pop_back();}}};
Trying to do as #define A a[i] and replacing all occurences of a[i] by A will result with same byte count code
Code to help for the test :
//Shift operator overload
std::ostream& operator<<(std::ostream& os, std::vector<std::vector<int>>& v) {
os << "{\n";
for (auto&a : v) {
os << "\t{ ";
for (auto&b : a) {
os << b << ' ';
}
os << "},\n";
}
return os << "}\n";
}
And in the main function
std::vector<std::vector<int>> t{
{1,5,8},
{4,7,2},
{3,9,6}
};
std::cout << t;
r(t);
std::cout << t;
• You can drop the #include and std::vector<... declarations by using an unnamed generic lambda [](auto&a){...} and demanding the input to be like vector<vector<int>> as I did in my challenges, e.g. codegolf.stackexchange.com/questions/100205/… – Karl Napf Sep 8 '17 at 16:08
# Haskell, 84 59 45 bytes
Shifts to the left (now using Leo's approach):
scanl1(\a r->(drop<>take$a!!0modlength r)r) Try it online! • 59 bytes: Try it online! – Laikoni May 4 '18 at 23:36 • @Laikoni: Damn that's so much nicer and saves a whole lot of bytes, thanks a lot! – ბიმო May 5 '18 at 0:23 # Python 2, 65 bytes l=input();K=0 for i in l:g=-K%len(i);e=i[g:]+i[:g];print e;K=e[0] Try it online! # Python 2, 55 bytes (possibly broken) If this version is found to fail for some test cases, I can assure you the above works. I am currently half-asleep, so feel free to remove this version in case it is invalid by editing. l=input();K=0 for i in l:e=i[-K:]+i[:-K];print e;K=e[0] Try it online! • You need to add modulo somewhere in there. The rotation numbers are sometimes longer than the lengths. – totallyhuman Sep 7 '17 at 22:15 • @icrieverytim I think it's fixed – Mr. Xcoder Sep 7 '17 at 22:17 • ...Actually, the test cases don't reflect that, which is in turn because the reference implementation doesn't use modulo. I'll ask OP whether it's needed. – totallyhuman Sep 7 '17 at 22:19 # 05AB1E, 9 bytes vyNFÁ}=нƒ Try it online! vy # For each row: NFÁ} # Rotate this row N times (initially 0) = # Print without popping н # Get the head ƒ # Assign that to N # Perl 5, 41 + 1 (-a) = 42 bytes push@F,shift@F for 1..$r;say"@F";$r=$F[0]
Try it online!
Rotates to the left. Takes the input as lines of space separated integers.
How?
Remove an element from the left end of the list, put it on the right end as many times as we should rotate ($r). Since $r starts at undef (equivaltent to 0 in this usage), nothing happens to the first line. Output the list. Save the first element of the list in \$r so we can rotate that many times on the next line.
# Pyth, 11 bytes
VQ=ZhJ.>NZJ
Try it here!
# Explanation
• VQ - For each list in the matrix input:
• =Z - Assign Z to the value of the below statement. Its initial value is 0, so that helps us with the first row.
• h - The first element of ...
• J.>NZ - ... The current list, cyclically rotated by Z places, and assigned to a variable J.
• J - Print J.
# R, 77 bytes
function(B){for(i in 2:nrow(B))B[i,]=rep(B[i,],sum(B))[1:ncol(B)+B[i-1,1]]
B}
Try it online!
Rotates rows to the right.
Replicates each row of B sum(B) times (creating a huge vector), then grabs the appropriate values from that replicated vector to put into the correct row.
I also wrote a function in the header that converts from the python matrix format to R matrices.
# APL (Dyalog), 14 bytes
Anonymous tacit prefix function. Takes list of lists as argument and prints rows on separate lines with the numbers in each row separated by single spaces. Rotates left (although the explanation mentions how rotate right).
{⎕←⍺⌽⍨⊃⍵}/0,⍨⌽
Try it online!
⌽ reverse the argument (because reduction is right-to-left)
0,⍨ append a zero (for initial rotation of zero steps)
{}/ reduce by the following anonymous lambda, where ⍺ is the element on the left and ⍵ on the right (the reduction goes right-to-left
⊃ pick the first of the right argument
⍺⌽⍨ rotate the left argument to the left* that many steps
⎕← output to STDOUT with a trailing line-break
* To rotate right, insert a - to the right of ⍨. This will negate the rotation amount.
|
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http://quant.stackexchange.com/questions/3609/how-to-annualize-dividends-paid-at-varying-intervals/3622
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# How to annualize dividends paid at varying intervals?
I am attempting to write a function that will calculate the annualized rate of return for individual dividends made by illiquid investments. These dividends are paid at varying intervals and the illiquid investment does not have an observable market price.
I have looked at using:
[(1 + YTD ROR)1/(#of days/365)] – 1
However, this does not seem valid if this dividend is one of many that have been made this year.
Below are 3 sample cases:
A Investment
$10 / 1 unit 1/31/2011 -$0.11 div / 1 unit - 1.1% ROI - 4.4% annualized ROI
4/30/2011 - $0.08 div / 1 unit - 0.8% ROI - 3.2% annualized ROI 7/31/2011 -$0.10 div / 1 unit - 1.0% ROI - 4% annualized ROI
For investment A the assumption is being made that each dividend paid was being paid on a quarterly basis
B Investment
$10 / 1 unit 1/31/2011 -$0.11 div / 1 unit - 1.1% ROI - 13.2% annualized ROI
2/27/2011 - $0.10 div / 1 unit - 1.0% ROI - 12% annualized ROI 3/30/2011 -$0.10 div / 1 unit - 1.0% ROI - 12% annualized ROI
For investment B the assumption is being made that each dividend paid would be paid monthly.
C Investment
$10 / 1 unit 5/30/2011 -$2.00 / 1 unit - 20% ROI - 48.6% annualized ROI (assuming 365 days in a year)
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|
https://kyushu-u.pure.elsevier.com/en/publications/primary-soot-particle-distributions-in-a-combustion-field-of-4-kw
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# Primary soot particle distributions in a combustion field of 4 kw pulverized coal jet burner measured by time resolved laser induced incandescence (TiRe-LII)
Nozomu Hashimoto, Jun Hayashi, Noriaki Nakatsuka, Kazuki Tainaka, Satoshi Umemoto, Hirofumi Tsuji, Fumiteru Akamatsu, Hiroaki Watanabe, Hisao Makino
Research output: Contribution to journalArticlepeer-review
18 Citations (Scopus)
## Abstract
To develop accurate models for the numerical simulation of coal combustion field, detailed experimental data using laser techniques, which can figure out the basic phenomena in a coal flame, are necessary. In particular, soot is one of the important intermediate substances in a coal flame. This paper is the first paper in the world reporting soot particle size distributions in a coal flame. The spatial distribution of the primary soot particle diameter were measured by the combination of the time-resolved laser induced incandescence (TiRe-LII) method and the thermophoretic sampling (TS) method. The primary soot particle diameter distribution was expressed by the log normal function based on the particle diameter measurement using SEM images obtained from the TS samples. The relative function between the signal decay ratio obtained by TiRe-LII and the primary soot particle diameter was defined based on the log normal function. Using the relative function, the spatial distributions of the primary soot particle diameter with the soot volume fraction were obtained. The results show that the small isolated soot regions instantaneously exist in the entire combustion field. This characteristics is different from spray combustion field. From the ensemble-averaged TiRe-LII images, it was found that the soot volume fraction and the primary soot particle diameter increases with increasing the height above the burner in any radial distance. It was also found that the volumetric ratio of small particles decreases with increasing radial distance at the region close to the burner exit. However, the variation of the soot particle diameter distribution along the radial direction becomes small in the downstream region. This tendency is caused by the turbulent mixing effect. It is expected that the accurate soot formation model will be developed in the near future by using the data reported in this paper.
Original language English JTST0049 Journal of Thermal Science and Technology 11 3 https://doi.org/10.1299/jtst.2016jtst0049 Published - 2016
## All Science Journal Classification (ASJC) codes
• Atomic and Molecular Physics, and Optics
• Materials Science(all)
• Instrumentation
• Engineering (miscellaneous)
## Fingerprint
Dive into the research topics of 'Primary soot particle distributions in a combustion field of 4 kw pulverized coal jet burner measured by time resolved laser induced incandescence (TiRe-LII)'. Together they form a unique fingerprint.
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http://mathhelpforum.com/advanced-algebra/217358-polynomial-rings-gausss-lemma-print.html
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# Polynomial Rings - Gauss's Lemma
Printable View
• April 12th 2013, 10:52 PM
Bernhard
3 Attachment(s)
Polynomial Rings - Gauss's Lemma
I am trying to understand the proof of Gauss's Lemma as given in Dummit and Foote Section 9.3 pages 303-304 (see attached)
On page 304, part way through the proof, D&F write:
"Assume d is not a unit (in R) and write d as a product of irreducibles in R, say $d = p_1p_2 ... p_n$ . Since $p_1$ is irreducible in R, the ideal $(p_1)$ is prime (cf Proposition 12, Section 8.3 - see attached) so by Proposition 2 above (see attached) the ideal $p_1R[x]$ is prime in R[x] and $(R/p_1R)[x]$ is an integral domain. ..."
My problems with the D&F statement above are as follows:
(1) I cannot see why the ideal $(p_1)$ is a prime ideal. Certainly Proposition 12 states that "In a UFD a non-zero element is prime if and only if it is irreducible" so this means $p_1$ is prime since we were given that it was irreducible. But does that make the principal ideal $(p_1)$ a prime ideal? I am not sure! Can anyone show rigorously that $(p_1)$ a prime ideal?
(2) Despite reading Proposition 12 in Section 8.3 I cannot see why the ideal $p_1R[x]$ is prime in R[x] and $(R/p_1R)[x]$ is an integral domain. ...". (Indeed, I am unsure that $p_1R[x]$ is an ideal!) Can anyone show explicitly and rigorously why this is true?
I would really appreciate clarification of the above matters.
Peter
• April 13th 2013, 12:56 AM
Bernhard
Re: Polynomial Rings - Gauss's Lemma
In trying to answer my problem (1) above - I cannot see why the ideal $(p_1)$ is a prime ideal - I was looking at definitions of prime ideals and trying to reason from there.
I just looked up the definition of a prime element in D&F to find the following on page 284:
The non-zero element $p \in R$ is called prime if the ideal (p) generated by p is a prime ideal!
So the answer to my question seems obvious:
$p_1 irreducible \Longrightarrow p_1$ prime $\Longrightarrow (p_1)$ prime ideal
Although this now seems obvious, I would like someone to confirm my reasoning (which as I said now seems blindingly obvious! :-)
Peter
• April 13th 2013, 04:01 AM
rushton
Re: Polynomial Rings - Gauss's Lemma
If we have $f \in K[x]$ for some polynomial ring $K[x]$ then the following are equivalent
1) f is irreducible
2) (f) is prime
3) (f) is maximal
$\\ Proof: (3) \Rightarrow (2) \Rightarrow (1) \Rightarrow (3) \\ \\ (3) \Rightarrow (2) is obvious by definition of maximal and prime ideals. \\ \\ (2) \Rightarrow (1) \\ Suppose f is not irreducible. \\ Then f=g \cdotp h with deg(g),deg(h) < deg(f) . \\ Now we get g,h are not in (f) but g \cdotp h is in (f). \\ This is a contradiction to (f) being a prime ideal. \\ \\ (1) \Rightarrow (3) \\ We do this by showing if J \supset (f) then J contains a unit. \\ Let J be generated by a single element, say g, so J=(g) . \\ If f \in (g) then f = q \cdotp g for some poly q. \\ f is irreducible so either q or g is a unit. \\ Suppose q is a unit. \\ Then g = q^{-1} \cdotp f \Rightarrow g \in (f) \Rightarrow (g)=(f) . \\ This contradicts J \supset (f) . \\ Thus g is a unit.$
• April 13th 2013, 04:08 AM
rushton
Re: Polynomial Rings - Gauss's Lemma
You can't say a polynomial itself is prime (at least to my knowledge).
The idea of a prime ideal as far as I know comes from the ideals of the integers generated by a prime number.
But a prime number and an irreducible polynomial are somewhat related, neither can be factored in their given ring/field.
• April 13th 2013, 04:18 AM
rushton
Re: Polynomial Rings - Gauss's Lemma
Sorry about the piecewise answers but I am doing one part at a time haha.
$p_{1}R[x] is just the ideal (p_{1}) as for an ideal if r \in R and i \in I then r \cdotp i \in I$
• April 13th 2013, 04:38 AM
rushton
Re: Polynomial Rings - Gauss's Lemma
$\\ R/I is an integral domain \Leftrightarrow I is prime. \\ \\ Proof \\ \\ \Rightarrow \\ Given a \cdotp b \in I we need to show a \in I or b \in I. \\ \bar{a} \cdotp \bar{b} = 0 \ \Rightarrow \ \bar{a} = 0 or \bar{b} = 0 \ \Rightarrow a \in I or b \in I. \\ \\ \Leftarrow \\ Given a \cdotp b \in I we must have \bar{a} \cdotp \bar{b} = 0 as I is the kernel of the canonical homomorphism thus \bar{a} = 0 or \bar{b} = 0.$
• April 13th 2013, 04:56 AM
Gusbob
Re: Polynomial Rings - Gauss's Lemma
Quote:
Originally Posted by rushton
The idea of a prime ideal as far as I know comes from the ideals of the integers generated by a prime number.
Not quite. For example, $(2)$ and $(3)$ are not actually prime in the ring of integers $\mathbb{Z}[\sqrt{-5}]$
The idea of a prime ideal comes from attempts to extend the fundamental theorem of arithmetic. In the same way we have unique (up to sign) prime factorisations of integers in rationals, we want to have to have some sort of phenomena in the ring of integers in other fields, particularly imaginary quadratic fields. However, in the ring of integers $\mathbb{Z}[\sqrt{-5}]$ of $\mathbb{Q}[\sqrt{-5}]$, we have $2\cdot 3 =6= (1+\sqrt{-5})(1-\sqrt{-5})$, so factorisation is certainly not unique. However, setting $A=(2,1+\sqrt{-5}), \overline{A}=(2,1-\sqrt{-5}),B=(3,1+\sqrt{-5}),\overline{B}=(3,1-\sqrt{-5})$, we have
$(6)=(2)(3)=(\overline{A}A)(\overline{B}B)=( \overline{A} \overline{B})(AB)=(1-\sqrt{-5})(1+\sqrt{-5})$.
So in this case, $(2)$ and $(3)$ are not actually prime. It can be shown that the prime 'factors' of the ideal generated by 6 are $A,\overline{A},B,\overline{B}$
It turns out that there is unique factorisation of prime ideals in the ring of integers in any imaginary quadratic field.
• April 13th 2013, 05:06 AM
rushton
Re: Polynomial Rings - Gauss's Lemma
Yeah but technically isn't $\mathbb{Z} [ \sqrt{-5}]$ the ring of polynomials with coefficients in $\mathbb{Z}$ adjoining $\sqrt{-5}$? So it wouldnt actually be the field of integers?
• April 13th 2013, 05:37 AM
Gusbob
Re: Polynomial Rings - Gauss's Lemma
Quote:
Originally Posted by rushton
Yeah but technically isn't $\mathbb{Z} [ \sqrt{-5}]$ the ring of polynomials with coefficients in $\mathbb{Z}$ adjoining $\sqrt{-5}$? So it wouldnt actually be the field of integers?
$\mathbb{Z} [ \sqrt{-5}]$ is the ring of algebraic integers in the field $\mathbb{Q} [ \sqrt{-5}]$.
• April 13th 2013, 05:45 AM
rushton
Re: Polynomial Rings - Gauss's Lemma
Ah I get what you mean now, yeah your totally right.
field of integers .......lol
• April 13th 2013, 06:09 PM
Bernhard
Re: Polynomial Rings - Gauss's Lemma
Thanks Rushton
You write:
"You can't say a polynomial itself is prime (at least to my knowledge).
The idea of a prime ideal as far as I know comes from the ideals of the integers generated by a prime number.
But a prime number and an irreducible polynomial are somewhat related, neither can be factored in their given ring/field. "
Dummit and Foote on page 284 give the following definitions of irreducible and prime for integral domains.
-------------------------------------------------------------------------------------------------------------------------------
"Definition Let R be an integral domain.
(1) Suppose $r \in R$ is non-zero and not a unit. Then r is called irreducible in R if whenever r = ab with $a, b \in R$ at least one of a or b must be a unit in R. Otherwise r is said to be reducible.
(2) The non-zero element $p \in R$ is called prime in R if the ideal (p) generated by p is a prime ideal. In other words, a non-zero element p is a prime if it is not a unit and whenever p|ab for any $a,b \in R$, then either p|a or p|b."
--------------------------------------------------------------------------------------------------------------------------------
So where a ring of polynomials is an integral domain we have a definition of prime and irreducible elements (polynomials). Do you agree? What do you think?
Mind you most algebra books I have referenced just talk about irreducible polynomials - so maybe for polynomials (for some reason) irreducible and prime are the same thing? Can someone clarify this point?
Another point is that I am unsure why D&F restrict these definitions to an integral domain thus leaving the terms undefined for general rings that are not integral domains. Can someone clarify?
Yet another problem I have with the above definitions by D&F is the following: D&F write: "In other words, a non-zero element p is a prime if it is not a unit and whenever p|ab for any $a,b \in R$, then either p|a or p|b." - How does this follow from (p) being a prime ideal.
Peter
Note: D&F's definition of prime ideal is on page 255 and is as follows:
Definition: Assume R is commutative. An ideal P is called a prime ideal if $P \ne R$ and whenever the product of two elements $a,b \in R$ is an element of P, then at least on of a and b is an element of P.
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http://nd.ics.org.ru/authors_nd/detail/413098-aik_kurdoglyan
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0
2013
Impact Factor
# Aik Kurdoglyan
ul. Milchakova 8a, Rostov-on-Don, 344090 Russia
Southern Federal University
## Publications:
Kurakin L. G., Kurdoglyan A. V. Semi-Invariant Form of Equilibrium Stability Criteria for Systems with One Cosymmetry 2019, Vol. 15, no. 4, pp. 525-531 Abstract The systems of differential equations with one cosymmetry are considered [1]. The ordinary object for such systems is a one-dimensional continuous family of equilibria. The stability spectrum changes along this family, but it necessarily contains zero. We consider the nondegeneracy condition, thus the boundary equilibria separate the family on linearly stable and instable areas. The stability of the boundary equilibria depends on nonlinear terms of the system. The stability problem for the systems with one cosymmetry is studied in [2]. The general problem is to apply the stability criteria one needs to compute coefficients of the model system. It is especially difficult if the system has a large dimension, while a number of critical variables may be small. A method for calculating coefficients is proposed in [3]. In this work the expressions for the known stability criteria are proposed in a form convenient for calculation. The explicit formulas of the coefficients of the model system are given in semi-invariant form. They are expressed using the generalized eigenvectors of the linear matrix and its conjugate matrix. Keywords: stability, critical case, neutral manifold, cosymmetry, semi-invariant form Citation: Kurakin L. G., Kurdoglyan A. V., Semi-Invariant Form of Equilibrium Stability Criteria for Systems with One Cosymmetry, Rus. J. Nonlin. Dyn., 2019, Vol. 15, no. 4, pp. 525-531 DOI:10.20537/nd190411
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http://math.stackexchange.com/questions/13396/find-an-unbiased-estimate-for-%ce%bbs-poisson-distribution
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# Find an unbiased estimate for λs (Poisson distribution)
So I have this problem to solve...
Let X denote the number of paint defects found in a square yard section of a car body painted by a robot.
These data are obtained: 8, 5, 0, 10, 0, 3, 1, 12, 2, 7, 9, 6
Assume that X has a Poisson distribution with parameter λs.
a) Find an unbiased estimate for λs.
b) Find an unbiased estimate for the average number of flaws per square yard.
c) Find an unbiased estimate for the average number of flaws per square foot.
I have no idea where to begin. I mean, how do I even find ANY unbiased estimate? The textbook is worthless imo and I can't find any good readings on the web either... please help.
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The Wikipedia page en.wikipedia.org/wiki/Poisson_distribution#Parameter_estimation has a simple formula for an unbiased estimation of $\lambda$. It is even the one you might guess. – Ross Millikan Dec 7 '10 at 17:17
@Ross no, that's not it. I need an unbiased estimate, not maximum likelihood. 2 separate things (according to my textbook at least). – Mickel Dec 7 '10 at 17:48
It claims this is an unbiased estimator, with a short justification. – Ross Millikan Dec 7 '10 at 18:02
For any distribution with mean $\theta$ ($\theta = \lambda s$ in your example), the sample average is an unbiased estimator for $\theta$: $E(\bar X_n) = \theta$. – Shai Covo Dec 7 '10 at 19:30
Also, what's the difference between a) and b)? Maybe "Assume that X has a Poisson distribution with parameter $\lambda$" (rather than $\lambda s$)? – Shai Covo Dec 7 '10 at 19:43
In a somewhat more general setting, let $A(R)$ denote the area of region $R$. If the number of flaws found on region $R$ follows a Poisson distribution, then the mean is proportional to $A(R)$. That is, if $X(R)$ denotes the number of flaws found on region $R$, then $X(R)$ is Poisson distributed with mean $\lambda A(R)$, for some fixed $\lambda > 0$. Now, if $X_1,\ldots,X_n$ are i.i.d. Poisson$(\lambda)$ rv's (corresponding to the number of flaws found on a unit-area region, say square yard), then $\frac{1}{n}\sum\nolimits_{i = 1}^n {X_i }$ is an unbiased estimator for $\lambda$, and in turn, $\frac{1}{n}\sum\nolimits_{i = 1}^n {A(R) X_i }$ is an unbiased estimator for $\lambda A(R) = {\rm E}[X(R)]$. So, in order to estimate ${\rm E}[X(R)]$, it suffices to estimate $\lambda$ (and then just multiply by $A(R)$).
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http://mathhelpforum.com/geometry/202415-ellipses-word-problem-print.html
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# Ellipses word problem
• Aug 21st 2012, 01:39 PM
Greymalkin
1 Attachment(s)
Ellipses word problem
Attachment 24569
Problem above, from what I understand you are to find the vertical distance to an edge that is 6 feet from a vertex.
I'm trying to triangulate from the focus distances to the point to create an equation I can equate.
Using distance from the focus(c= $\sqrt{(25^2-14^2)}=20.71$
Setting the center at the origin, the distance from 2 foci = $2(\sqrt{20.71^2+14^2}=50$
Therefore the point 6 feet from the vertex, which is 19 ft from the origin, and is 39.71ft from the last focus, is equated by: $50-(39.71^2+b^2=c^2)$
This is where my approach halts, is my approach wrong? Or is there something I am just not seeing?
Edit answer is ~9.1
• Aug 21st 2012, 05:23 PM
GJA
Re: Ellipses word problem
Hi, Greymalkin.
I think your approach is good, nice work! I think a small hint will get things going in the right direction.
Since you're taking the origin to sit "in the middle" so-to-speak, we know that $x$ and $y$ must satisfy the equation
$\frac{x^{2}}{(25)^{2}}+\frac{y^{2}}{(14)^{2}}=1,$
where 25 is the major radius of the ellipse, and 14 is the minor radius. What you determined in your work was that the $x$ coordinate of the point we're interested is $x=-19$. Our goal is to know what the height $y$ is at this point; to determine this we can use the ellipse equation above since we know what $x$ is at the point of interest.
Does this help? Let me know if anything is unclear.
Good luck!
Edit: I was thinking of the bank on the left of the picture, that's why I have $x=-19$ above, but if you wanted to consider the right bank you could use $x=19$. It's all academic because we're going to square things in the equation of the ellipse anyways!
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http://math.stackexchange.com/questions/32433/are-calculus-and-real-analysis-the-same-thing
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# Are calculus and real analysis the same thing?
1. I guess this may seem stupid, but how calculus and real analysis are different from and related to each other?
I tend to think they are the same because all I know is that the objects of both are real-valued functions defined on $\mathbb{R}^n$, and their topics are continuity, differentiation and integration of such functions. Isn't it?
2. But there is also $\lambda$-calculus, about which I honestly don't quite know. Does it belong to calculus? If not, why is it called *-calculus?
3. I have heard at the undergraduate course level, some people mentioned the topics in linear algebra as calculus. Is that correct?
Thanks and regards!
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λ-calculus is something completely different: see en.wikipedia.org/wiki/Lambda_calculus – lhf Apr 12 '11 at 1:45
I would say "calculus is to analysis as arithmetic is to number theory", including real and complex analysis under that umbrella. – Alex Becker Apr 12 '11 at 1:47
The term "calculus" can be used generally to mean something like "manipulation". The subject in math that we call calculus today was previously more well known by a longer name "calculus of infinitesimals", so named because at the time of its development, it was thought of as exactly that, the science of manipulating infinitesimally small numbers. It's in this sense that $\lambda$-calculus is named: it deals with the manipulation of "lambdas". See: en.wikipedia.org/wiki/Calculus_%28disambiguation%29 – matt Apr 12 '11 at 1:49
I think "calculus" in general means "to calculate". So, with this in mind, calculus uses the results of analysis to calculate things. Analysis is all the theory behind calculus. – Matt Gregory Apr 12 '11 at 2:00
@matt: thanks! I have heard that at the undergraduate course level, some people refer to topics in linear algebra as calculus. Is that correct? – Tim Apr 12 '11 at 2:05
1. A first approximation is that real analysis is the rigorous version of calculus. You might think about the distinction as follows: engineers use calculus, but pure mathematicians use real analysis. The term "real analysis" also includes topics not of interest to engineers but of interest to pure mathematicians.
2. As is mentioned in the comments, this refers to a different meaning of the word "calculus," which simply means "a method of calculation."
3. This is imprecise. Linear algebra is essential to the study of multivariable calculus, but I wouldn't call it a calculus topic in and of itself. People who say this probably mean that it is a calculus-level topic.
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we had courses analysis 1 and analysis 2 but the books had titles like Calculus. However these books were total 2000 pages too complex that any textbook for calculus i seen seemed childish too simple . So now i understand ,that books are analysis books. – Parhs Mar 3 '12 at 2:15
@Parhs: What books? – Tim Mar 3 '12 at 2:28
They are written in greek. I was wrong , the total pages are 2800 (2 theory and some problems and examples and 2 other only problems.) It uses literature from apostol,ayoub,birkhoff,comtet,ciang and lots of other[80 total].But they are extreemly hard to read. Even the most difficult textbook for calculus is easy compared to them.And they are given at engineering school – Parhs Mar 3 '12 at 2:54
In Eastern Europe (Poland, Russia) there is no difference between calculus and analysis (there is mathematical analysis of function of real/complex variable/s).
In my opinion this distinction is typical for Western countries to make the following difference:
• calculus relies mainly on conducting "calculations" (algebraic transformations applied to function, derivation of theorems/concepts by methods of elementary mathematics, computations applied to specific problem)
• analysis relies mainly on conducting "analysis" of properties of functions (derivation of theorems, proving theorems)
However, still this distinction is unnecessary:
• (the most important) issues of "calculus" and "analysis" are very often linked together so that distinction is impossible (e.g. consideration of concept of limit in calculus due to Cauchy or Heine is actually the same as in analysis)
• it makes artificial ambiguity in perception of mathematical analysis
• it isolates common sense approach obtained from elementary mathematics and disables straightforward transition from elementary mathematics to higher mathematics
• issues of "calculus" and "analysis" treated together enables acquisition of deeper understanding of subject by making extension from methods gained from elementary mathematics.
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Sorry, but you must be confusing Anglo-Saxon countries and Western Europe. In France, there is no such thing as "calculus", and I suspect it's true for most of continental Europe. – Jean-Claude Arbaut Aug 26 '14 at 15:19
No such thing as "calculus" in Italy too. – LtWorf Jan 31 at 9:38
As I understand the terms, calculus is just differentiation and integration, whereas real analysis also includes such topics as the definition of a real number, infinite series, and continuity. But perhaps I am out of date.
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https://socratic.org/questions/if-an-object-is-dropped-how-fast-will-it-be-moving-after-4s
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Physics
Topics
If an object is dropped, how fast will it be moving after 4s?
Apr 16, 2016
$39.2 \frac{m}{s}$
Explanation:
If an object is dropped, the major force acting on it is gravity. We mostly ignore smaller variables like air resistance. The acceleration of gravity downwards is about $9.8 m {s}^{-} 2$.
Acceleration is how much velocity ($\frac{m}{s}$) changes by the second, so the units for acceleration are $\frac{\frac{m}{s}}{s}$ or $\frac{m}{s} ^ 2$, which is also written mathematically as $m {s}^{-} 2$.
If we have four seconds of movement, then multiply that by the acceleration and it will give you the velocity.
$9.8 \frac{m}{s} ^ 2 \cdot 4 s = 39.2 \frac{m \cdot s}{s} ^ 2 = 39.2 \frac{m}{s}$
Impact of this question
199 views around the world
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https://earthscience.stackexchange.com/questions/2755/how-is-carbon-distributed-among-the-atmosphere-the-oceans-the-biomass-and-the?noredirect=1
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# How is carbon distributed among the atmosphere, the oceans, the biomass and the unburnt fossil fuels?
In relation to my other question about carbon cycle and climate change, i would like to know some estimates of the carbon distribution among the atmosphere, the oceans, the biomass and the unburnt fossil fuels.
Here are more specific parts of this question.
1. How much carbon is there on Earth?
2. How much carbon is there in the atmosphere (in the form of CO2 and other gases)?
3. How much carbon is there in the oceans in the form of CO2 and gases?
4. How much carbon is there currently in the biomass?
5. How much carbon is there left in the form of fossil fuels?
If possible, i would also like to know how this distribution has changed, for example, over the last 100 years (in particular, how much carbon from the fossil fuels has been burnt over the last 100 years).
• I highly suggest you take a look at the presentations here: globalcarbonproject.org/carbonbudget/14/hl-compact.htm – farrenthorpe Nov 9 '14 at 17:29
• I assume this question is at least somewhat related to anthropogenic global warming. If so, other forms of carbon, especially methane, are also pretty relevant. – naught101 Nov 11 '14 at 1:24
• @naught101, thanks, i should have not restricted the question to CO and CO2 only, maybe i will edit it. It is not exactly about global warming, it is about carbon distribution in form, place and time. – Alexey Nov 11 '14 at 8:14
• There is an interesting movie made by NASA that shows how CO2 in the atmosphere spreads across Earth. However, it only covers 2 years (May 2005-June 2007). – THelper Dec 4 '14 at 10:55
1.How much carbon is there on Earth?
Taken as whole, the Earth is estimated to be 730 parts per million carbon by mass.
So $4.4 \times 10^{21} kg$
http://quake.mit.edu/hilstgroup/CoreMantle/EarthCompo.pdf
1. How much carbon is there in the atmosphere (in the form of CO2 and CO)?
$3.1 \times 10^{15} kg$ CO2 and insignificant CO, so $8 \times 10^{14}$ kg of C.
1. How much carbon is there in the oceans in the form of CO2 and CO?
Carbon of all forms in the the ocean is $4 \times 10^{16} kg$
http://ioc-goos-oopc.org/documents/oosdp/oosdp_br5.pdf
1. How much carbon is there currently in the biomass?
$8 \times 10^{14}$ kg (not including soil)
$2 \times 10^{15}$ kg (if soil is included)
1. How much carbon is there left in the form of fossil fuels?
$5 \times 10^{15} kg$
http://www.gcrio.org/CONSEQUENCES/vol4no1/carbcycle.html
(This could be an underestimate, depending upon what you consider to be "fossil fuel"; methane clathrates are estimated to hold $10^{16}$ kg of carbon)
If possible, i would also like to know how this distribution has changed, for example, over the last 100 years (in particular, how much carbon from the fossil fuels has been burnt over the last 100 years).
The amount of carbon in the atmosphere has increased about 30% since pre-industrial times, and the amount in biomass, not including soil, has decreased about 10%. Amount in the oceans has not changed significantly.
• I wonder if it might make sense to include a crust estimate too? That total figure includes the mantle, which is on such a different scale to the atmosphere and ocean that it's not usefully comparable. It might be nice to include some kind of graph (like this), but the total figure swamps everything else. – naught101 Nov 11 '14 at 1:33
• @naught101 continental crust is 200 ppm carbon according to this: gly.uga.edu/railsback/Fundamentals/ElementalAbundanceTableP.pdf – DavePhD Nov 11 '14 at 12:37
• @naught101 About $5 \times 10^{18} kg$ is in the crust, as the continental crust is ~200 ppm carbon and the continental crust is 0.37% of the Earth's mass. Oceanic crust is 0.1% of their Earth's mass. However, carbon enters and exists the mantle, deep-earth.org/wiki_cider/images/c/c2/… – DavePhD Nov 11 '14 at 13:12
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https://www.physicsforums.com/threads/differentiating-2-x-2.597384/
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# Differentiating 2^(x^2)
1. Apr 17, 2012
### aguycalledwil
I'm trying to differentiate 2^(x^2), but I'm getting a factor of two out and can't figure out why. I approached the question as follows..
y=2^(x^2) , so y=(2^x)^x
u=2^x y=u^x
du/dx = (2^x)ln2
dy/du = xu^(x-1)
= x(2^x)^(x-1)
= x(2)^((x^2)-x)
So dy/dx =
[x(2)^((x^2)-x)]*[(2^x)Ln2]
However, on the mark scheme it says when x=2, the gradient should be 64ln2. Using my derivative, at x=2 the gradient comes out at 32ln2. Can anyone help me find where I've gone wrong? Much appreciated!
2. Apr 17, 2012
### hamsterman
$2^{x^2}$ is a composition of functions $f(x) = 2^x$ and $g(x) = x^2$. You know that $f'(x) = 2^x \ln 2$ and $g'(x) = 2x$
There is a formula for derivative of composite functions. $(f \circ g)'(x) = f'(g(x))g'(x)$. This is just another form of the chain rule. After blindly pasting the functions we already have, we get $2x \cdot 2^{x^2} \ln 2$
I can't see what error you made as those formulas are not very readable. Try using latex.
3. Apr 17, 2012
### Curious3141
That's wrong right there. The rule $\frac{d}{dx}x^n = nx^{n-1}$ ONLY applies when n is a constant. If n is a variable like x or a function of x, the rule simply does not work.
Your best bet here is to use Chain Rule as hamsterman mentioned.
4. Apr 17, 2012
### hotvette
Another approach is to take the (natural) log of both sides of y = 2x2 and differentiate implicitly.
5. Apr 18, 2012
### aguycalledwil
Thanks guys, got it!
Similar Discussions: Differentiating 2^(x^2)
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https://in.mathworks.com/help/lte/ug/mixed-pucch-format-transmission-and-reception.html
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# Mixed PUCCH Format Transmission and Reception
This example shows the transmission and reception of Physical Uplink Control Channel (PUCCH) Formats 1 and 2, including the case where the same physical resource is shared between transmissions of Format 1 and Format 2 simultaneously from two different User Equipments (UEs) using the LTE Toolbox™.
### Introduction
This example configures two User Equipments (UEs) to transmit a Physical Uplink Control Channel (PUCCH) Format 1 signal from the first UE and a PUCCH Format 2 signal from the second UE. Appropriate Demodulation Reference Signals (DRS) are also generated. The transmitted signals are passed through two different fading channels and added, together with Additive White Gaussian Noise (AWGN), simulating the reception of the signals from the two UEs at an eNodeB. Each signal (i.e. that belonging to each UE) is then synchronized, SC-FDMA demodulated, equalized, PUCCH demodulated and then finally decoded. A plot is produced showing that the channels can be estimated independently for the two different signals, even though they share the same physical Resource Elements (REs).
### UE 1 Configuration
The first UE is configured using a structure `ue1`.
```ue1.NULRB = 6; % Number of resource blocks ue1.NSubframe = 0; % Subframe number ue1.NCellID = 10; % Physical layer cell identity ue1.RNTI = 61; % Radio network temporary identifier ue1.CyclicPrefixUL = 'Normal'; % Cyclic prefix ue1.Hopping = 'Off'; % Frequency hopping ue1.Shortened = 0; % Reserve last symbols for SRS transmission ue1.NTxAnts = 1; % Number of transmit antennas```
### UE 2 Configuration
Similarly a configuration structure is used to configure the second UE, `ue2`. This structure is identical to the configuration of `ue1` with two exceptions:
• No `Shortened` field as this does not apply to PUCCH Format 2.
• A different Radio Network Temporary Identifier (RNTI) value (not used here as it is only relevant for Physical Uplink Shared Channel (PUSCH) transmission, but different UEs would have different RNTI).
```ue2.NULRB = 6; % Number of resource blocks ue2.NSubframe = 0; % Subframe number ue2.NCellID = 10; % Physical layer cell identity ue2.RNTI = 77; % Radio network temporary identifier ue2.CyclicPrefixUL = 'Normal'; % Cyclic prefix ue2.Hopping = 'Off'; % Frequency hopping ue2.NTxAnts = 1; % Number of transmit antennas```
### PUCCH 1 Configuration
For the first UE, a PUCCH of Format 1 is used, so an appropriate configuration structure `pucch1` is created. The parameter `CyclicShifts` specifies the number of cyclic shifts used by PUCCH Format 1 in resource blocks where a mixture of PUCCH Format 1 and PUCCH Format 2 are to be transmitted. The parameter `ResourceSize` specifies the size of the resources used by PUCCH Format 2, effectively determining the starting position of PUCCH Format 1 transmissions; here we specify `ResourceIdx=0` which will use the first PUCCH Format 1 resource.
```pucch1.ResourceIdx = 0; % PUCCH resource index pucch1.DeltaShift = 1; % Delta shift pucch1.CyclicShifts = 1; % Number of cyclic shifts pucch1.ResourceSize = 0; % Size of resources allocated to PUCCH Format 2```
### PUCCH 2 Configuration
For the second UE, a PUCCH of Format 2 is used, so an appropriate configuration structure `pucch2` is created. The values of parameters `CyclicShifts` and `ResourceSize` are the same as in the PUCCH Format 1 configuration. The value of `ResourceIdx` is set to the first PUCCH Format 2 resource, meaning that the physical resource blocks now configured for PUCCH Format 1 and PUCCH Format 2 will be the same.
```pucch2.ResourceIdx = 0; % PUCCH resource index pucch2.CyclicShifts = 1; % Number of cyclic shifts pucch2.ResourceSize = 0; % Size of resources allocated to PUCCH Format 2```
### Channel Propagation Model Configuration
The propagation channel that the two UEs will transmit through is configured using a structure `channel`. The sampling rate of the channel is configured to match the sampling rate at the output of the first UE; note that the same sampling rate is used at the output of the second UE because `ue1.NULRB` and `ue2.NULRB` are the same. When we use this channel configuration for each UE, the `Seed` parameter of the structure will be set differently for each UE so that different propagation conditions result.
```channel.NRxAnts = 4; % Number of receive antennas channel.DelayProfile = 'ETU'; % Delay profile channel.DopplerFreq = 300.0; % Doppler frequency channel.MIMOCorrelation = 'Low'; % MIMO correlation channel.InitTime = 0.0; % Initialization time channel.NTerms = 16; % Oscillators used in fading model channel.ModelType = 'GMEDS'; % Rayleigh fading model type channel.InitPhase = 'Random'; % Random initial phases channel.NormalizePathGains = 'On'; % Normalize delay profile power channel.NormalizeTxAnts = 'On'; % Normalize for transmit antennas % Set sampling rate info = lteSCFDMAInfo(ue1); channel.SamplingRate = info.SamplingRate;```
### Noise Configuration
The SNR is given by $SNR={E}_{s}/{N}_{0}$ where ${E}_{s}$ is the energy of the signal of interest and ${N}_{0}$ is the noise power. The power of the noise to be added can be determined so that ${E}_{s}$ and ${N}_{0}$ are normalized after the SC-FDMA demodulation to achieve the desired SNR `SNRdB`. The noise added before SC-FDMA demodulation will be amplified by the IFFT. The amplification is the square root of the size of the IFFT. In this simulation this is taken into consideration by dividing the desired noise power by this value. In addition, because real and imaginary parts of the noise are created separately before being combined into complex additive white Gaussian noise, the noise amplitude must be scaled by $1/\sqrt{2}$ so the generated noise power is 1.
```SNRdB = 21.0; % Normalize noise power SNR = 10^(SNRdB/20); N = 1/(SNR*sqrt(double(info.Nfft)))/sqrt(2.0); % Configure random number generators rng('default');```
### Channel Estimation Configuration
The channel estimator is configured using a structure `cec`. Here cubic interpolation will be used with an averaging window of 12-by-1 REs. This configures the channel estimator to use a special mode which ensures the ability to despread and orthogonalize the different overlapping PUCCH transmissions.
```cec = struct; % Channel estimation config structure cec.PilotAverage = 'UserDefined'; % Type of pilot averaging cec.FreqWindow = 12; % Frequency averaging window in REs (special mode) cec.TimeWindow = 1; % Time averaging window in REs (Special mode) cec.InterpType = 'cubic'; % Cubic interpolation```
### PUCCH Format 1 Generation
Now all the necessary configuration is complete, the PUCCH Format 1 and its DRS are generated. The PUCCH Format 1 carries the HARQ indicators `hi1` and in this case there are 2 indicators, meaning that the transmission will be of Format 1b. The PUCCH Format 1 DRS carries no data.
```% PUCCH 1 modulation/coding hi1 = [0; 1]; % Create HARQ indicators disp('hi1:');```
```hi1: ```
`disp(hi1.');`
``` 0 1 ```
```pucch1Sym = ltePUCCH1(ue1, pucch1, hi1); % PUCCH 1 DRS creation pucch1DRSSym = ltePUCCH1DRS(ue1, pucch1);```
### PUCCH Format 2 Generation
The PUCCH Format 2 DRS carries the HARQ indicators `hi2` and in this case there are 2 indicators, meaning that the transmission will be of Format 2b. The PUCCH Format 2 itself carries coded Channel Quality Information (CQI). The information `cqi` here is coded and then modulated.
```% PUCCH 2 DRS modulation hi2 = [1; 1]; % Create HARQ indicators disp('hi2:');```
```hi2: ```
`disp(hi2.');`
``` 1 1 ```
```pucch2DRSSym = ltePUCCH2DRS(ue2, pucch2, hi2); % PUCCH 2 coding cqi = [0; 1; 1; 0; 0; 1]; % Create channel quality information disp('cqi:');```
```cqi: ```
`disp(cqi.');`
``` 0 1 1 0 0 1 ```
```codedcqi = lteUCIEncode(cqi); % PUCCH 2 modulation pucch2Sym = ltePUCCH2(ue2, pucch2, codedcqi);```
### PUCCH Index Generation
The indices for the PUCCH and PUCCH DRS transmissions are created
```pucch1Indices = ltePUCCH1Indices(ue1, pucch1); pucch2Indices = ltePUCCH2Indices(ue2, pucch2); pucch1DRSIndices = ltePUCCH1DRSIndices(ue1, pucch1); pucch2DRSIndices = ltePUCCH2DRSIndices(ue2, pucch2);```
### Transmission for UE 1
The overall signal for the first UE is now transmitted. The steps are to map the PUCCH Format 1 and corresponding DRS signal into an empty resource grid, perform SC-FDMA modulation and then transmit through a fading propagation channel.
```% Create resource grid grid1 = lteULResourceGrid(ue1); grid1(pucch1Indices) = pucch1Sym; grid1(pucch1DRSIndices) = pucch1DRSSym; % SC-FDMA modulation txwave1 = lteSCFDMAModulate(ue1, grid1); % Channel modeling. An additional 25 samples added to the end of the % waveform to cover the range of delays expected from the channel modeling % (a combination of implementation delay and channel delay spread) channel.Seed = 13; rxwave1 = lteFadingChannel(channel,[txwave1; zeros(25,1)]);```
### Transmission for UE 2
The overall signal for the second UE is now transmitted. Note that a different random seed `channel.Seed` is used compared to that used for the first UE. This ensures that different propagations are used for the two transmissions.
```% Create resource grid grid2 = lteULResourceGrid(ue2); grid2(pucch2Indices) = pucch2Sym; grid2(pucch2DRSIndices) = pucch2DRSSym; % SC-FDMA modulation txwave2 = lteSCFDMAModulate(ue2, grid2); % Channel modeling. An additional 25 samples added to the end of the % waveform to cover the range of delays expected from the channel modeling % (a combination of implementation delay and channel delay spread) channel.Seed = 15; rxwave2 = lteFadingChannel(channel, [txwave2; zeros(25, 1)]);```
### Reception at the Base Station
The input to the base station receiver is modeled by adding the two faded signals together with Gaussian noise with power as described above.
```rxwave = rxwave1 + rxwave2; % Add noise noise = N*complex(randn(size(rxwave)), randn(size(rxwave))); rxwave = rxwave + noise;```
### Synchronization and SC-FDMA Demodulation for UE 1
The uplink frame timing estimate for UE1 is calculated using the PUCCH 1 DRS signals and then used to demodulate the SC-FDMA signal. The resulting grid `rxgrid1` is a 3 dimensional matrix. The number of rows represents the number of subcarriers. The number of columns equals the number of SC-FDMA symbols in a subframe. The number of subcarriers and symbols is the same for the returned grid from lteSCFDMADemodulate as the grid passed into lteSCFDMAModulate. The number of planes (3rd dimension) in the grid corresponds to the number of receive antennas.
```% Synchronization offset1 = lteULFrameOffsetPUCCH1(ue1, pucch1, rxwave); % SC-FDMA demodulation rxgrid1 = lteSCFDMADemodulate(ue1, rxwave(1+offset1:end, :));```
### Channel Estimation and Equalization for UE 1
An estimate of the channel between each transmitter and the base station receiver is obtained and used to equalize its effects. To create an estimation of the channel lteULChannelEstimatePUCCH1 is used. The channel estimation function is configured by the structure `cec`. The function returns a 3-D matrix of complex weights which are applied to each resource element by the channel in the transmitted grid. The 1st dimension is the subcarrier, the 2nd dimension is the SC-FDMA symbol and the 3rd dimension is the receive antenna. The effect of the channel on the received resource grid is equalized using lteEqualizeMMSE. This function uses the estimate of the channel (`H1`) to equalize the received resource grid (`rxGrid1`).
```% Channel estimation [H1, n0] = lteULChannelEstimatePUCCH1(ue1, pucch1, cec, rxgrid1); % Extract REs corresponding to the PUCCH from the given subframe across all % receive antennas and channel estimates [pucchrx1, pucchH1] = lteExtractResources(pucch1Indices, rxgrid1, H1); % Equalization eqgrid1 = lteULResourceGrid(ue1); eqgrid1(pucch1Indices) = lteEqualizeMMSE(pucchrx1, pucchH1, n0);```
### PUCCH 1 Decoding
Finally the PUCCH Format 1 channel is decoded and the useful HARQ indicator bits are extracted.
```rxhi1 = ltePUCCH1Decode(ue1, pucch1, length(hi1), ... eqgrid1(pucch1Indices)); disp('rxhi1:');```
```rxhi1: ```
`disp(rxhi1.');`
``` 0 1 ```
The uplink frame timing estimate for UE2 is calculated using the PUCCH 2 DRS signals and then used to demodulate the SC-FDMA signal. In this case, the Hybrid ARQ indicators as conveyed on the PUCCH Format 2 DRS are also found. The resulting grid `rxgrid2` is a 3 dimensional matrix. To create an estimation of the channel lteULChannelEstimatePUCCH2 is used. The effect of the channel on the received resource grid is equalized using lteEqualizeMMSE. Finally the PUCCH Format 2 channel is decoded and the useful CQI information bits are extracted.
```% Synchronization (and PUCCH 2 DRS demodulation/decoding) [offset2,rxhi2] = lteULFrameOffsetPUCCH2(ue2,pucch2,rxwave,length(hi2)); disp('rxhi2:');```
```rxhi2: ```
`disp(rxhi2.');`
``` 1 1 ```
``` % SC-FDMA demodulation rxgrid2 = lteSCFDMADemodulate(ue2, rxwave(1+offset2:end, :)); % Channel estimation [H2, n0] = lteULChannelEstimatePUCCH2(ue2, pucch2, cec, rxgrid2, rxhi2); % Extract REs corresponding to the PUCCH from the given subframe across all % receive antennas and channel estimates [pucchrx2, pucchH2] = lteExtractResources(pucch2Indices, rxgrid2, H2); % Equalization eqgrid2 = lteULResourceGrid(ue2); eqgrid2(pucch2Indices) = lteEqualizeMMSE(pucchrx2, pucchH2, n0); % PUCCH 2 demodulation rxcodedcqi = ltePUCCH2Decode(ue2, pucch2, eqgrid2(pucch2Indices)); % PUCCH 2 decoding rxcqi = lteUCIDecode(rxcodedcqi, length(cqi)); disp('rxcqi:');```
```rxcqi: ```
`disp(rxcqi.');`
``` 0 1 1 0 0 1 ```
### Display Estimated Channels
A plot is produced showing that the channels can be estimated independently for the two different signals, even although they share the same physical REs. The PUCCH Format 1 channel estimate is shown in red and the PUCCH Format 2 channel estimate is shown in blue.
`hPUCCHMixedFormatDisplay(H1, eqgrid1, H2, eqgrid2);`
### Appendix
This example uses the helper function:
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https://support.bioconductor.org/p/75721/
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Question: bamCount paired.end arg
1
4.0 years ago by
Germany
katarzyna.wreczycka10 wrote:
Hi,
How is it with the bamCount function - does it still have option paired.end="extend"? What does it mean when paired.end="filter" (it is not written in the documentation of the function)?
> bamsignals_bamCount=bamsignals::bamCount(signal1, windows, verbose=FALSE, paired.end="extend")
Błąd w poleceniu 'match.arg(paired.end)':
'arg' should be one of “ignore”, “filter”, “midpoint”
Thanks, Kasia
bamsignals • 485 views
modified 4.0 years ago by mammana20 • written 4.0 years ago by katarzyna.wreczycka10
1
4.0 years ago by
mammana20
European Union
mammana20 wrote:
Hi Kasia,
That's correct, the bamCount function does not have the option paired.end="extend". It wouldn't make sense, because bamCount counts the 5' end of a read, so if you extend it to the whole fragment the 5' end actually does not change.
This is what the docs say about the "filter" option:
If ‘paired.end!="ignore"’ then only first reads in proper mapped pairs will be consider (i.e. in the flag of the read, the bits in the mask 66 must be all ones)
so when you set paired.end="filter", only one read per pair will be counted (the first in the pair).
Let me know if I can help!
Alessandro
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https://www.bornagainproject.org/m/py/sample/avge/cylinders-in-average-layer/
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## Cylinders in Averaged Layer
Supposing a Simulation has been defined in which some layers contain embedded particles of different materials; to regard those layers as composed by a single material, the setUseAvgMaterials method is used:
simulation.getOptions().setUseAvgMaterials(True)
The script below shows how to average materials when simulating scattering from a square lattice of cylinders inside a finite layer.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 #!/usr/bin/env python3 """ Square lattice of cylinders inside finite layer with usage of average material """ import bornagain as ba from bornagain import deg, nm, kvector_t def get_sample(cyl_height=5*nm): """ Returns a sample with cylinders on a substrate. """ # defining materials m_vacuum = ba.HomogeneousMaterial("Vacuum", 0, 0) m_layer = ba.HomogeneousMaterial("Layer", 3e-6, 2e-8) m_substrate = ba.HomogeneousMaterial("Substrate", 6e-6, 2e-8) m_particle = ba.HomogeneousMaterial("Particle", 3e-5, 2e-8) # cylindrical particle cylinder_ff = ba.FormFactorCylinder(5*nm, cyl_height) cylinder = ba.Particle(m_particle, cylinder_ff) position = ba.kvector_t(0, 0, -cyl_height) particle_layout = ba.ParticleLayout() particle_layout.addParticle(cylinder, 1, position) # interference function interference = ba.InterferenceFunction2DLattice( ba.SquareLattice2D(15*nm, 0)) pdf = ba.FTDecayFunction2DCauchy(300*nm, 300*nm, 0) interference.setDecayFunction(pdf) particle_layout.setInterferenceFunction(interference) vacuum_layer = ba.Layer(m_vacuum) intermediate_layer = ba.Layer(m_layer, 5*nm) intermediate_layer.addLayout(particle_layout) substrate_layer = ba.Layer(m_substrate) multi_layer = ba.MultiLayer() multi_layer.addLayer(vacuum_layer) multi_layer.addLayer(intermediate_layer) multi_layer.addLayer(substrate_layer) return multi_layer def get_simulation(sample): beam = ba.Beam(1, 0.1*nm, ba.Direction(0.2*deg, 0)) detector = ba.SphericalDetector(100, -2*deg, 2*deg, 100, 0, 2*deg) simulation = ba.GISASSimulation(beam, sample, detector) simulation.getOptions().setUseAvgMaterials(True) return simulation if __name__ == '__main__': import ba_plot sample = get_sample() simulation = get_simulation(sample) ba_plot.run_and_plot(simulation)
CylindersInAverageLayer.py
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https://www.zentralblatt-math.org/matheduc/en/?q=ut:product%20rule
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History
Help on query formulation
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When in doubt, add zero or multiply by one. (English)
Math. Comput. Educ. 50, No. 2, 106-108 (2016).
Classification: H20 H30 I40 I50 F50
1
Notes on the product and quotient rules from calculus. (English)
Far East J. Math. Educ. 15, No. 2, 139-157 (2015).
Classification: I40
2
Discovering the product rule dynamically and justifying it with differentials. (Die Produktregel dynamisch entdecken und mit Differenzialen begründen.) (German)
PM Prax. Math. Sch. 57, No. 63, 39-40 (2015).
Classification: I44 D84
3
From the tree diagramm to the product rule. Solving combinatorial tasks arithmetically. (Vom Baumdiagramm zur Produktregel. Kombinatorische Aufgabenstellungen rechnerisch lösen.) (German)
Math. Differ. 6, No. 1, 18-25 (2015).
Classification: K22 K52 D82
4
A simple proof of the right-hand rule. (English)
Coll. Math. J. 44, No. 3, 227-229 (2013).
Classification: G75
5
Problems of the 6th South-Eastern European Mathematical Olympiad for University Students. (Olimpiada de Matematică a studenţilor din sud-estul Europei, SEEMOUS 2012.) (Romanian. English summary)
Gaz. Mat., Ser. A 30(109), No. 1-2, 24-32 (2012).
Classification: U40 H60 I20
6
Quotient-rule-integration-by-parts. (English)
Coll. Math. J. 43, No. 3, 254-256 (2012).
Classification: I54
7
The product and quotient rules revisited. (English)
Coll. Math. J. 42, No. 4, 323-326 (2011).
Classification: I44
8
Using the chain rule as the key link in deriving the general rules for differentiation. (English)
PRIMUS, Probl. Resour. Issues Math. Undergrad. Stud. 21, No. 2, Special Issue: a tribute to Brian J. Winkel, 189-192 (2011).
Classification: I45
9
Reasoning and strategies in the transition to generalization in a combinatorial problem. (Razonamiento y estrategias en la transición a la generalización en un problema de combinatoria.) (Spanish. English summary)
PNA 4, No. 2, 73-86 (2010).
Classification: K23 C33
10
Freshman rules in calculus. (English)
Int. J. Math. Educ. Sci. Technol. 40, No. 8, 1091-1096 (2009).
Classification: I45
11
Math-Manga analysis. Transl. from the Japanese by Sandra Hohmann. (Mathe-Manga Analysis.) (German)
Wiesbaden: Vieweg+Teubner (ISBN 978-3-8348-0567-6/pbk). ix, 229~p. (2009).
Classification: A80 A90 I10 I20 I30 I40 I50 I60 Reviewer: Franz Lemmermeyer (Jagstzell)
12
About the area of a square and the $2\times 2$ determinants. (Od obsahu čtverce k determinantu druhého řádu.) (Czech)
Učitel Mat. 16, No. 2, 74-83 (2008).
Classification: G70 H60
13
Trig integrals without trig identities. (English)
PRIMUS, Probl. Resour. Issues Math. Undergrad. Stud. 18, No. 2, 158-160 (2008).
Classification: I55
14
The naive product rule for derivatives. (English)
Coll. Math. J. 39, No. 2, 145-148 (2008).
Classification: I45 Reviewer: J. Meyer (Hameln)
15
More on a functional equation. (English)
Int. J. Math. Educ. Sci. Technol. 37, No. 2, 246-247 (2006).
Classification: I70
16
Another look at the rules of differentiation. (English)
PRIMUS, Probl. Resour. Issues Math. Undergrad. Stud. 14, No. 3, 193-200 (2004).
Classification: I44 I45
17
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https://www.intechopen.com/chapters/72718
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Open access peer-reviewed chapter
# A Review to Massive MIMO Detection Algorithms: Theory and Implementation
By Bastien Trotobas, Amor Nafkha and Yves Louët
Submitted: February 28th 2020Reviewed: June 1st 2020Published: July 3rd 2020
DOI: 10.5772/intechopen.93089
## Abstract
Multiple-input multiple-output (MIMO) systems entered most major standards in the past decades, including IEEE 802.11n (Wi-Fi) and long-term evolution (LTE). Moreover, MIMO techniques will be used for 5G by increasing the number of antennas at the base station end. MIMO systems enable spatial multiplexing, which has the potential of increasing the capacity of the communication channel linearly with the minimum of the number of antennas installed at both sides without sacrificing any additional bandwidth or power. To handle the space-division multiplexing (SDM), receivers have to implement new algorithms to exploit the spatial information in order to distinguish the transmitted data streams. This chapter provides an overview of the most well-known and promising MIMO detectors, as well as some unusual-yet-interesting ones. We focus on the description of the different paradigms to highlight the different approaches that have been studied. For each paradigm, we describe the mathematical framework and give the underlying philosophy. When hardware implementations are available in the literature, we provide the results reported and give the according references.
### Keywords
• MIMO systems
• MIMO detectors
• space-division multiplexing
• SDM-MIMO
• linear detection
• interference cancelation
• tree-search
## 1. Introduction
The hardware implementation of massive MIMO detector is of particular interest to deal with 5G wireless technology. Optimal massive detectors such as the maximum likelihood detector (MLD) or the sphere decoding (SD) are considered infeasible given their high computational complexity. Hence, low computational complexity algorithm achieving near-optimal performance is required; many existing detection algorithms like zero forcing (ZF), minimum mean-square error (MMSE), and successive interference cancelation (SIC) are used to deal with massive MIMO detection. In [1, 2], the authors presented surveys on various MIMO and massive MIMO detection techniques from algorithmic viewpoints. Although many classical massive MIMO detectors have been proposed in the literature, herein, new recent algorithms based on the application of machine learning, geometrical techniques, and bioinspired methods are presented and discussed.
In this chapter, we propose an overview of the SDM detection algorithms. We specifically stress out the different paradigms that are used to solve the detection problem and compare all of them. Thus, we describe the most well-known and promising MIMO detectors, as well as some unusual-yet-interesting ones. Section 2 presents the framework and the assumptions that are used in the remainder section. Section 3 introduces the maximum likelihood (ML) optimal detector, and then Section 4 describes the linear ones. Section 5 details algorithms based on the interference cancelation, and Section 6 discusses the one based on tree-search. Finally, Section 7 highlights unusual-yet-interesting detectors before Section 8 concludes the chapter. Figure 1 provides an overview of all the detectors described in this chapter as a tree mind map.
## 2. Introduction to MIMO detection algorithms
In the SDM framework, data streams are transmitted at the same time and at the same frequency, and the receiver relies on spatial consideration to distinguish the streams. Herein, we assume that the MIMO transmitter does not use any spatial coding and that all data streams are independent. To give the reader a unified mathematical description through this chapter, we adopt the following notation: scalars, vectors, and matrices are denoted by lower-case, bold-face lower-case, and bold-face higher-case letters, respectively. We call vithe ith coefficient of the vector v, and Hijis the element of the ith row and jth column in the Hmatrix.
In the linear input–output MIMO model where data are transmitted as the symbols of a constellation Φ, the received vector yCMis the result of the emitted symbols xΦNpropagated through the channel Hand added to an additive noise w. This model leads to the following equation:
y=Hx+wE1
and the MIMO detection problem then refers to the combinatorial optimization problem:
argminxΦNyHx2.E2
Assuming a circularly symmetric Gaussian noise, solving Eq. (2) is equivalent to searching the most probable emitted symbol vector based on the signal on each receive antennas and the channel state. Even if yHx2is a convex function with respect to x, the detection problem is not a convex optimization problem due to the discrete feasible solution set ΦN. As a result, a special algorithm has to be used, and this chapter will describe the most common ones.
Let us start by outlining the traditional assumptions that we will use in the present chapter. Although many constellation types could be used in MIMO systems, we limit the discussion to the square quadrature amplitude modulations (QAMs) that are most commonly investigated. Besides, the channel is considered memoryless, linear, and flat and with a block fading1. In this chapter, we assume that channel state information (CSI) is correctly estimated at the receiver side but not at the transmitter side. The impact of imperfect CSI at the receiver on the performance of detection algorithms is not addressed in the present chapter. Some known training symbols are sent from the transmitter, based on which the receiver estimates the channel before proceeding to the detection of the transmitted data symbols.
The channel matrix is modeled as a complex matrix HCMN. In that case, the element Hijrefers to the complex channel gain between the jth transmit antenna to the ith receive antenna. Many channel models can fit in this framework, and we stick to the most popular one: the uncorrelated Rayleigh fading channel [3, 4]. The uncorrelated channel model provides a good approximation of propagating environments with rich scattering where the signals between the transmitter and the receiver experience many different paths and no strong line of sight between the transmitter and the receiver. This situation occurs, for instance, in urban and indoor conditions. In these conditions, each receiver antenna receives a sum of a large number of signal paths, and the channel transfer functions can be modeled as the realization of a circularly symmetric normal distribution.
## 3. Maximum likelihood detector
Obtaining the optimal result requires, in the most straightforward approach, the use of the ML detector that solves Eq. (2) using an exhaustive search. Even if this method gives the best result since all xΦNare evaluated, it is not suitable for real implementation. Indeed, the number of vectors to be tested grows exponentially with the number of transmit antenna and the constellation size. Thus, the computational cost of evaluating Eq. (2) requires an unrealistic quantity of resources to detect the transmitted vector x. That is why a variety of detection algorithm has been developed throughout the past year to achieve the same detection performance of ML detectors while having a tractable complexity.
From a computational theory perspective, the detection problem is an instance of the closest lattice-point search (CLPS) problem with a specified lattice [5]. It has been proved that regardless of the preprocessing on the lattice (i.e., the channel matrix), the problem is always NP-hard [5]. The NP-hardness implies that it is not possible, at the moment, to find any detector that is sure to have both an optimal performance and a polynomial complexity2. For that reason, all the following detectors have suboptimal performance (which can be very close to optimal) or a non-polynomial worst-case complexity (which can be polynomial is the average case).
## 4. Linear detectors
### 4.1 Zero forcing (ZF) detector
Linear detectors are the most simple algorithms to solve the detection problem. The most basic one is the ZF algorithm that follows a two-step process. First, the ZF detector solves Eq. (2) transforming the constraint from xΦNto xCNsuch that the problem become an easy-to-solve convex optimization with a known mathematical solution:
x0=H+yE3
with H+=HHH1HHbeing the left Moore-Penrose pseudoinverse. Then, the constraint on xis reintroduced by quantizing the vector accordingly to the constellation in use. This quantization should lead to a good estimation as after the application of the detection matrix TZF=H+, Eq. (1) becomes
TZF.y=x+H+wE4
highlighting that all the interference are canceled. The previous equation is also the proof that the ZF detector is the optimal linear one regarding the signal-to-interference ratio (SIR) criteria. Indeed, one can see that the vector TZF.ycontains each stream independently plus some noise but without any interference.
### 4.2 Minimum mean-square error (MMSE) detector
By only focusing on the interference, the ZF detector performance suffers from not taking the noise into account. Indeed, if the noise level is known to the receiver, a Bayesian estimator including this information can provide a better detection. A linear Bayesian estimator minimizing the mean-square error can be derived using the orthogonality principle [6] leading to
TMMSE=HHH+2σ2I1HHE5
with σ2being the noise variance per real direction. The detector based on this detection matrix, followed by the quantization, is called the minimum mean-square error (MMSE), and it is known to maximize the signal-to-noise-plus-interference ratio (SINR). When the signal-to-noise ratio (SNR) is low (i.e., σ2is high), the MMSE detector provides better results, jointly minimizing the interference and the noise. Otherwise, when σ2is very low, the corrective term becomes negligible, and the ZF and MMSE detectors overlap.
## 5. Interference cancellation detectors
To improve further the performance, it is necessary to drop the linear detector approach and look for more elaborate decoding algorithms. Historically, the first nonlinear detector type is still based on the principle of canceling signal interference. This concept leads to two approaches: an iterative one named successive interference cancelation (SIC) and a simultaneous version named parallel interference cancelation (PIC).
### 5.1 Successive interference cancellation (SIC) detector
The SIC detectors opt for a two-step iterative process: first, a decision is taken on the first position x1, and then assuming that the decision was right, the detector corrects yby removing the interference that would have been generated by x1. Then, SIC detectors repeat this process on the next x’s entry until the whole vector is received.
Even if the performance is better than with the linear detectors, the SIC process is very prone to error, given that the assumption at an iteration has an impact on all the following ones. For this reason, the simple SIC detector has quickly been replaced by a variant seeking for an optimal iteration order [7]. This variant called ordered successive interference cancelation (OSIC) aims to make the first assumption on the position that leads to the better SNR or SINR.
To select the best symbol to detect at each iteration, the OSIC detector computes the post-SNR or post-SINR for each symbol, assuming that the kth element is canceled using the detection matrix T. Most of the time, the detection matrix is chosen to be TZFor TMMSEoptionally updated after each iteration. When using the SNR criterion, the value of the kth post-SNR is computed as in [7, 8].
SNRk=<xk2>ΦTkhk2σ2Tk2E6
with Tkbeing the kth row of T, hkthe kth column of H, and <xk2>Φthe expected value over the constellation set. The latter term is the average signal power of the kth data stream that can be computed, assuming that each symbol is equiprobable, as
<xk2>Φ=1φxΦxk2E7
with φthe number of symbols in constellation Φ.
When using the SINR criterion, the post-SINR expression becomes slightly more complex as the post-processed power of each other channel appears in the expression
SINRk=<xk2>ΦTkhk2lk<xl2>ΦTlhl2+σ2Tk2.E8
For clarity sake, Figure 2 sums up the OSIC detection algorithm introducing a process t:HTto build a detection matrix from a channel one. This process is most of the time the Moore-Penrose pseudoinverse or the process described in Eq. (5). We also denote by Dthe set of the symbol index to be decoded and by the affectation. One must note that an instruction is optional and may be skipped. If this instruction is applied, performance is increased by canceling the interference in the post-criterion computation and so is the complexity.
### 5.2 Parallel interference cancellation (PIC) detector
The main drawback of the OSIC algorithm is that the number of iterations grows linearly with the number of antennas. The number of stage becomes an issue for large MIMO system since each stage adds a reception delay. For that reason, a detector capable of canceling the interference for all antennas at once was developed.
The first application of such an algorithm to SDM systems dates from the early 2000s, and it is based on a few basic steps summed up in Figure 3 as published in [9]. The main point of the PIC algorithm is to start by using a simple detector with poor performance, most of the time a linear one, and cancel the interference on all antennas at once based on the assumption. If better performance is required, it is possible to iterate the last three instructions as many times as needed by using the new detected symbol as the new assumption.
Simultaneously, the iterative reception techniques developed for turbo codes and single-input single-output channels are adapted to MIMO systems. The goal is to receive a coded message by alternating between soft-input soft-output detector and decoder. Each algorithm uses a priori information from the other to improve its performance [10]. This method leads to one of the current most accomplished version of the PIC family: a soft-input soft-output detector to be used in iterative decoding with any message coding [11].
This version adds several improvements to the basic algorithm described in Figure 3. First, it uses the soft symbols from [12] that are defined as the expected value of the symbols knowing the a priori. The reliability of a soft symbol is computed as its variance. Then, the parallel cancelation (see the third instruction in Figure 3) is performed using the soft symbols in place of the rough estimation. Finally, a last MMSE filtering is performed before the computation of the log-likelihood ratios (LLRs). Further reductions in complexity are also used, such as the max-log approximation [10, 13, 14] or the channel Gram matrix [15]. Thanks to all of these improvements, an application-specific integrated circuit (ASIC) is reported to achieve a throughput greater than 750 Mb/s with good BER performance [11].
### 5.3 Selecting between SIC and PIC detectors
The key idea to select between SIC and PIC detectors is to compare the relative quality of data streams. As stated earlier, SIC algorithms guess the best data stream and then process the other one based on this assumption. This process makes the SIC algorithms very prone to error propagation. Indeed, if an assumption is wrong, the error has consequences on all the data streams to be detected. Hence, SIC detectors should be used when there is a net ranking in the quality of each data stream. A basic scenario for this would be a MIMO system receiving data from several users with different channel qualities.
On the contrary, PIC detectors process all the data streams at once so that they are more resilient to interstream error propagation. However, the parallel computations assume that every data stream is as reliable as the other. Due to this assumption, a poor-quality data stream propagates its error to the whole system. For that reason, PIC detectors are well suited when all data streams have the same quality level.
## 6. Tree-search-based detectors
Tree-search-based detectors are the current most investigated algorithms. They use a different framework than the linear and the interference cancelation detector. As the name suggests, the tree-search detector interprets the detection problem from Eq. (2) as the search for the best path in a tree. Tree-search-based detectors can either be optimal with a non-polynomial yet small complexity or quasi-optimal yet not optimal with a polynomial convexity.
Figure 4 gives an example of the tree interpretation for a constellation with four symbols and two data streams. In this configuration, solving the detection problem is equivalent to find two symbols in the set Φ=s1s2s3s4that minimize the objective function. This process can be seen as finding the path in the tree that leads to the best objective function. The first tree level corresponds to the first symbol and so on for each level.
In this paradigm, the exhaustive search detector described in Section 3 computes the objective function for each leaf node and then selects the best path. Tree-search-based detectors search for the best leaf without trying every path. This leads to three enumeration paradigms: depth-first, breadth-first, and best-first. These paradigms will be detailed after the description of the preprocessing used by all the variants.
### 6.1 Preprocessing using QR decomposition
All tree-search-based detectors use the same preprocessing. Let be H=QRthe QR decomposition of the channel matrix with Qa unitary matrix and Ran upper triangular one. The decomposition is computed only once per coherence block leading to a negligible overhead of the complexity per received symbol. Using the QR decomposition, we have
yHx=yQRx=QHyQHQRxE9
as unitary matrices act as isometries. Thus, by exploiting the property of unitary matrices QH=Q1, this norm can be rewritten as
yHx=y˜RxE10
with y˜QHy. Computing y˜is the only overhead in complexity that is required on a symbol basis as it cannot be preprocessed for the whole coherence block.
The point of this QR preprocessing is that the triangularity of Rallows to compute the objective function iteratively. Indeed, we can introduce for all k1N,dky˜kRxkwith Rxkbeing the kth coefficient of the product Rx. Given this definition, the objective function is written as
y˜Rx2=k=1ndk2.E11
Moreover, the triangularity of Rgives
k1N,Rxk=j=1nRkjxj=j=knRkjxjE12
k1N,dk=y˜kj=knRkjxj.E13
With this expression, it is clear that we can compute partial estimations of the objective function and dkcoefficients while the symbol vector is built. Indeed, starting from the last component, Eq. (13) is fully evaluated for the jth position as soon as a hypothesis is made on xj. Thus, it is possible to add a new operand in Eq. (11) and to have an idea of how promising the partial symbol vector is. The partial objective function from Eq. (11) is traditionally called the partial Euclidean distance (PED).
### 6.2 Depth-first tree-search detection: sphere decoding
The depth-first paradigm is the oldest one, and it is commonly known in the communication field as the sphere decoding (SD). SD is the transposition of the mathematical Fincke-Pohst algorithm in the telecommunication field [16]. The basic principle of this algorithm is to define an upper-bound for the objective function named the radius r2and then to use it to prune paths as early as possible. Reintroducing x0from Eq. (3), the upper-bound constraint gives
yHx2=Hx0xr2.E14
This inequality highlights that constraining the objective function may be interpreted as looking for solution no so far from x0. As stated in Eq. (4), the only deviation from x0is due to the noise so that the choice of rmust be adapted to the SNR. Thus, if the SNR is high, the radius can be small, while in the contrary scenario, the radius should be increased so that there is at least one vector xsatisfying the constraint from Eq. (14).
In the remainder of this section, we assume that r2is adequately chosen and that there is at least a solution. As stated in Section 6.1, the QR decomposition allows us to compute a PED at each level. As the PED is a sum of squares, it can only increase during the decoding process. Thus, if at some point, a PED violates the constraint from Eq. (14), then all the vectors build upon this partial solution are bound to be infeasible. From a tree-search perspective, this means that if a node already breaks the constraint, all its children will do the same. Thus, all paths starting from this node can be pruned without performance loss.
The SD is referred to as a depth-first detector as starting from the root node, it goes as depth as possible until it reaches a leaf or violates Eq. (14). If a leaf is reached, it is compared to the best leaf so far and saved if it is the new best leaf. If Eq. (14) is violated, the SD algorithm backtracks and explores a new path. When all paths are either completed or pruned, the result is the best leaf reached.
The Schnorr-Euchner (SE) enumeration is another depth-first enumeration known to perform better by using a lattice reduction method [17, 18]. The basic idea is to explore the node’s children by the increasing order of their PED. This is particularly useful when using the radius reduction technique that sets an infinite r2at the beginning and then updates it to the best objective function for a leaf encounter so far.
The SD algorithm and its SE version are optimal as they ensure to find the exact solution of the detection problem. Indeed, the best leaf is obviously the best leaf among all the completed paths, and the pruned paths cannot lead to a better point due to their already worst PED. The NP-hardness argument detailed in Section 3 implies that SD has a non-polynomial worst-case complexity. Moreover, SD expected complexity is also non-polynomial even if the exponential growth is slow enough to compete with polynomial detectors under certain circumstances [19].
A very efficient soft-input soft-output depth-first algorithm is the single tree-search sphere decoding (STS-SD) [20]. To produce its soft-output, it uses the max-log approximation [10, 13, 14] and makes some changes on the pruning criterion. The max-log approximation avoids the computation of the exact LLRs by claiming that
Li12σ2minxχi0yHx2minxχi1yHx2E15
where χik=xΦN:bi=kis the set of all symbols with the ith bit set to k. Thus, to compute the max-log approximation, one must know the objective function of the best leaf (i.e., one of the minimum in Eq. (15)) but also the objective function of each best counter-hypotheses (the other minimum). A path should then be pruned only if its PED is greater than the current radius r2and if this path cannot lead to a better counter-hypothesis. This can be implemented by adding another radius called the hypothetical radius constraint.
One of the most advanced ASIC-implemented depth-first reported so far uses a two-dimensional Schnorr-Euchner enumeration. This implementation reaches a throughput higher than 600 Mb/s for the soft-output version and exceeds 1.2 Gb/s for the hard-output one while keeping an excellent energy efficiency [21]. The high throughput is achieved by using several SD cores in parallel to decode several vectors simultaneously.
### 6.3 Breadth-first tree-search detectors: K-best and M-algorithm
Breadth-first detectors drop out of optimality for better implementability. Indeed, they address the two main issues of the depth-first paradigm: the unpredictable complexity that depends on the SNR through r2and the depth-and-backtrack enumeration that prevents the use of hardware pipelines. Breadth-first detectors achieve this goal by removing the pruning criterion and always keep the same number of paths instead. At each level, the detector compares all the current paths’ PED and keeps only the best ones. This number is traditionally called Kfor the K-best algorithm [22] or Mfor the M-algorithm [23]. A recent work mixed this approach with the upper-bound radius from death-first to prune even more path per level and reduce the complexity further [24]. This method converges to the breadth-first if all PED are always under the upper-bound, but if some PEDs overgrow, it can reduce the number of surviving paths.
The restricted number of surviving paths induces that the right one can be pruned early if its PED has grown too quickly in the early levels. This is the reason for the optimality loss. Then, some detectors implement a post-detection SNR criterion to reorder the tree levels such that the most certain one is at the top. Thus, the right path is less likely to be pruned by mistake in the early stages. Thanks to this reordering, the K-best algorithm performs very well yet, not optimally in a mathematical sense.
From a hardware implementation perspective, breadth-first tree-search detectors are very efficient. They do not require any backtrack so that an expanded node can be safely deleted as it will never be revisited. Moreover, the number of visited nodes per level is fixed. Thus, ASIC can embed the exact amount of resources required. These two characteristics allow the construction of efficient hardware pipelines that substantially increase the throughput. K-best can achieve at least the same throughput as depth-first without the need for parallel cores. Hard-output implementations exceeding 2.5 Gb/s are reported using the breadth-first paradigm [25]. Another study focused on energy efficiency designed a breadth-first variant that can handle both the channel noise and the hardware noise generated by the voltage over the scaling method in memories [26].
Breadth-first detectors can provide soft-output using the max-log approximation and a list. This list approach is used by several detectors, including some other tree-search algorithm and detectors from other families. The point of this approach is to produce a list Γof point associated with their objective function and to approximate Eq. (15) as
Li12σ2minxΓχi0yHx2minxΓχi1yHx2.E16
For most breadth-first algorithms, Γis the list of all completed paths [22, 25].
### 6.4 Best-first tree-search detector: fast descent tree-search and parallel tree-search
Best-first detectors are also sometimes called metric-first. The basic idea besides this enumeration is to not favor depth or breadth over each other. Instead, the node with the best PED is expanded, regardless of its level. The best-first algorithm keeps a node pool with nodes to be expanded. First, the pool is initialized with the root node. Then, at each iteration, the node with the lower PED is popped out from the pool, and all its children are computed and pushed in the pool unless they are leaves. If they are, a comparison with the best leaf so far allows us to keep track of the best result. When a leaf is reached, its objective function may be used as an upper-bound to prune the pool for each node with a PED higher than the new reference. The detection ends when the pool is empty.
This simple method quickly overfills the pool as several nodes are added when only one is popped out. Rather than providing a huge pool to contain all the nodes, improvement is to convert the φ-ary tree (with φthe constellation size) to a first-child next-sibling binary tree [27]. This method is called the modified best-first algorithm (MBF). With this variant, the only nodes added in the pool after an expansion are the best child and the best yet-to-visit siblings. Then, the growth rate of the pool size is controlled. However, this method struggles to provide a full path solution quickly as the popped out node is the one with the lower PED that is often close to the root. To solve this issue, a variant implementation called MBF fast descent (MBF-FD) changes the expansion rule. When a node is expanded, the process goes through the best child until reaching a leaf, pushing in all best siblings along the way [28].
Recently, a best-first algorithm ASIC is reported to reach 800 Mb/s in a soft-input soft-output framework [29]. The modified algorithm, called cross-level parallel tree-search, splits the pool node into several pools, one per level. At each iteration, a node from each pool in popped out expanded using the best-child/best-sibling framework, and the new nodes are pushed in the according pool. Moreover, the presented detector prune nodes in each pool using the upper-bound to keep only the one that can improve the result or the counter-hypothesis (see Section 6.2 for details). The slit pool helps the parallelization process so that this algorithm variant is very suitable for hardware implementation.
## 7. Other unusual detectors: bioinspired and geometrical detectors
### 7.1 Deep neural MIMO detection: learning to detect
The rise of deep learning leads to the search for an efficient neural network to solve the detection problem such as DetNet [30]. This network is inspired by the projected gradient descent algorithm that is a major option to solve convex optimization. It is trained for both static channel (His fixed) and on a time-varying channel (the same condition as previously). As the errors are sometimes unavoidable due to a bad channel realization, the loss function should not be the objective function. Thus, the DetNet designers opt for a
k=1LlogkxxkxxZFE17
with xZFthe result of ZF detection and xkthe detected symbol of the kth layer. Then, the normalization with the ZF result avoids over-penalizing the situation with bad Hrealization. Moreover, the logarithm weights the result from each layer to give more credit to the final ones.
### 7.2 Bioinspired detectors
The most studied bioinspired decoders fall into two categories: ant colony optimizations (ACO) and particle swarm optimizations (PSO) that include the firefly algorithm (FA). These techniques are often very complex compared to the previously described algorithms, but they claim to be resilient to challenging conditions. Bioinspired algorithms should be able to decode messages with imperfect CSI, or the data streams are correlated.
ACO-based detectors simulate several ants that choose a path randomly to follow with a nonuniform probability function [31]. Each antenna is processed independently. At each iteration, an ant selects the symbol sΦwith the probability
ps=τsαηsβsΦτsαηsβE18
with τsthe pheromone level on the path, ηsan image of the objective function, most of the time through a log-sigmoid function, and αβthe two parameters that balance the relative importance of each term. After each iteration, the pheromone level is updated according to the following principle: the better the objective function the ant achieves, the more pheromone it dropped off. Thus, the ant selects more often the path that seems more promising regarding the objective function and the previous runs while preserving some chance of exploring a new path.
FA-based detectors simulate several fireflies that try to find the best mating partner. The objective function determines the attractiveness of a firefly. Then a firefly goes toward more attractive congeners biased with a random influence to promote exploration [32]. Some FA variant implements a memory effect that makes it even closer to a PSO-based algorithm [33]. This framework is applied to MIMO detection using the QR decomposition described in Section 6.1. The FA represents each symbol to decode as a nest containing as many fireflies as the constellation size. Thus, the fireflies have to select a partner in each nest from the last symbol to the first based on the biased attractiveness. When the firefly population searched all the nests, the best path represents the decoded symbol vector. FA-based detectors can be related to tree-search-based algorithm with a randomness exploration and a fixed number of path allowed.
### 7.3 Geometrical detectors
Geometrical detectors are based on a two-step process: an exploration to find a small set of promising solutions and an exploitation to improve this set at a small cost. It follows the traditional approach in nonconvex optimization to perform simple descents that can be stuck in local optimums from several starting points. Geometrical detectors use a real-valued model and the singular value decomposition (SVD) rather than the QR one [34]. Let us rewrite the objective function by introducing the SVD of H=UDVTwith Uand Vtwo orthogonal matrices and Dthe diagonal matrix containing the singular values λi:1inin ascending order.
Consequently, the objective function can be rewritten as
yHx2=VTxx0TDUTUDVTxx0E19
using x0from Eq. (3). As the vectors of V, named vi:1in, constitute a basis, we can define αi:1inthe coordinates of xx0on this basis. Using the orthogonality of Uand Vand the diagonality of D, Eq. (19) leads to
yHx2=i=1nαi2λi2.E20
Let Δibe the straight line passing through x0and directed by vi. One can note that Eq. (20) highlights that the objective function grows more slowly along the first Δirather than along the last ones so that promising points must be around these first straight lines. Then the solution is most likely to be found along this line. The geometrical exploration step is then performed, selecting some points near the first Δi. Then a straightforward descent algorithm is performed by looking for the best point in the close neighborhood until convergence.
A soft-output version of this algorithm is possible using the max-log approximation and the list approach detailed in [35], Section 5.2. A field-programmable gate array (FPGA) implementation has recently been proposed. This groundwork points out that geometrical detectors may achieve good performance in the future yet being far from mature at that point [36].
## 8. Conclusions and summary
MIMO detection is a well-studied problem that has been tackled from several perspectives. The mathematical interpretation, as a combinatorial optimization problem, leads to the optimal and linear detectors. From the signal processing perspective, detecting a signal means improving the SNR or SINR so that the direct answer is to cancel the interference and to remove the noise. From an algorithmic perspective, the detection problem is the search for the best path in a weighted tree that relies on some well-known algorithms. Other sources of inspiration, such as nature or geometry, provide some interesting perspectives. These paradigms and the associated detectors are summed up in Table 1, and we compare all of them according to the BER-complexity trade-off.
DetectorBERComplexityComment
MLOptimalDramatically complex
ZFVery poorVery simpleBest linear detector regarding SNR criterion
MMSEPoorSimpleBest linear detector regarding SINR criterion
SIC/OSICGoodRather complexBest when there is a clear ranking in the quality of each data stream
PICGoodRather complexBest when all data streams have the same quality level
Depth-firstOptimalVery complex
Breadth-firstGoodRather complexPossible trade-off between BER and complexity via the number of surviving paths
Best-firstGoodLess complex
Deep neuralGoodRather complexPossible trade-off between BER and complexity via the number of layers
BioinspiredGoodVery complexResilient to imperfect CSI and channel correlation
GeometricalRather goodRather complexPossible trade-off between BER and complexity via the number of descents
### Table 1.
Summary of all detectors described in this chapter.
All these perspectives shed a different light on the problem, leading to fruitful experimentation. Indeed, some methods take inspiration from others to keep on improving. Therefore, some improvement axes remain open, for instance, the permanent decrease of complexity with equal performance, the development for efficient hardware implementations, or the optimization of the interaction with decoders to exploit channel codings better.
## Conflict of interest
The authors declare no conflict of interest but to research and publish in this area, in particular on geometrical detectors.
## Nomenclature
Memoryless the channel outputs only depend on its state and its inputs. Linear Flat Block fading the channel states vary slow enough to be considered constant over many symbols named coherence block. ACO ASIC application-specific integrated circuit CDMA code-division multiple access CLPS closest lattice-point search CSI channel state information FA firefly algorithm FPGA field-programmable gate array LLR log-likelihood ratio MBF modified best-first MBF-FD modified best-first fast descent ML maximum likelihood MMSE minimum mean-square error OSIC ordered successive interference cancelation PED partial Euclidean distance PIC parallel interference cancelation PSO particle swarm optimization QAM quadrature amplitude modulation SD sphere decoding SE Schnorr-Euchner SDM space-division multiplexing SIC successive interference cancelation SIR signal-to-interference ratio SINR signal-to-noise-plus-interference ratio SNR signal-to-noise ratio SVD singular value decomposition ZF zero forcing
## Notes
• The nomenclature section provides definitions.
• It is widely believed that it does not exist any solution to solve NP-hard problems in polynomial time. Yet, this assumption is not proven so that there is still a possibility that such an algorithm exists and is just not discovered nowadays.
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## More
© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution 3.0 License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
## How to cite and reference
### Cite this chapter Copy to clipboard
Bastien Trotobas, Amor Nafkha and Yves Louët (July 3rd 2020). A Review to Massive MIMO Detection Algorithms: Theory and Implementation, Advanced Radio Frequency Antennas for Modern Communication and Medical Systems, Albert Sabban, IntechOpen, DOI: 10.5772/intechopen.93089. Available from:
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https://learnzillion.com/lesson_plans/5803-calculate-different-probabilities-by-working-backward
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Calculate different probabilities by working backward
teaches Common Core State Standards CCSS.Math.Content.HSS-CP.B.7 http://corestandards.org/Math/Content/HSS/CP/B/7
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In this lesson you will learn how to calculate different probabilities by working backwards using the addition rule.
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https://stacks.math.columbia.edu/tag/0ARW
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Lemma 86.28.3. With assumptions and notation as in Theorem 86.27.4 let $f : X' \to X$ correspond to $g : W \to X_{/T}$. Then $f$ is separated $\Leftrightarrow$ $g$ is separated and $\Delta _ g : W \to W \times _{X_{/T}} W$ is rig-surjective.
Proof. If $f$ is separated, then $g$ is separated and $\Delta _ g$ is rig-surjective by Lemmas 86.23.7 and 86.23.11. Assume $g$ is separated and $\Delta _ g$ is rig-surjective. Exactly as in the proof of Lemma 86.28.1 we may check this over the members of a étale covering of $X$ by affine schemes using Morphisms of Spaces, Lemma 65.4.4 (locality on the base of being separated for morphisms of algebraic spaces), Formal Spaces, Lemma 85.26.2 (being separated for morphisms of formal algebraic spaces is preserved by base change), and Lemma 86.21.4 (being rig-surjective is preserved by base change). Thus we may and do assume $X$ is affine. Furthermore, we already know that $f : X' \to X$ is quasi-separated by Lemma 86.28.2.
By Cohomology of Spaces, Lemma 67.19.1 and Remark 67.19.3 it suffices to show that given any commutative diagram
$\xymatrix{ \mathop{\mathrm{Spec}}(K) \ar[r] \ar[d] & X' \ar[d] \\ \mathop{\mathrm{Spec}}(R) \ar[r]^ p \ar@{-->}[ru] & X' \times _ X X' }$
where $R$ is a complete discrete valuation ring with fraction field $K$, there is a dotted arrow making the diagram commute (as this will give the uniqueness part of the valuative criterion). Let $h : \mathop{\mathrm{Spec}}(R) \to X$ be the composition of $p$ with the morphism $Y \times _ X Y \to X$. There are three cases: Case I: $h(\mathop{\mathrm{Spec}}(R)) \subset U$. This case is trivial because $U' = X' \times _ X U \to U$ is an isomorphism. Case II: $h$ maps $\mathop{\mathrm{Spec}}(R)$ into $T$. This case follows from our assumption that $g : W \to X_{/T}$ is separated. Namely, if $Z$ denotes the reduced induced closed subspace structure on $T$, then $h$ factors through $Z$ and
$W \times _{X_{/T}} Z = X' \times _ X Z \longrightarrow Z$
is separated by assumption (and for example Formal Spaces, Lemma 85.26.5) which implies we get the lifting property by Cohomology of Spaces, Lemma 67.19.1 applied to the displayed arrow. Case III: $h(\mathop{\mathrm{Spec}}(K))$ is not in $T$ but $h$ maps the closed point of $\mathop{\mathrm{Spec}}(R)$ into $T$. In this case the corresponding morphism
$p_{/T} : \text{Spf}(R) \longrightarrow (X' \times _ X X')_{/T} = W \times _{X_{/T}} W$
is an adic morphism (by Formal Spaces, Lemma 85.10.4 and Definition 85.19.3). Hence our assumption that $\Delta _ g : W \to W \times _{X_{/T}} W$ is rig-surjective implies we can lift $p_{/T}$ to a morphism $\text{Spf}(R) \to W = X'_{/T}$, see Lemma 86.21.11. Algebraizing the composition $\text{Spf}(R) \to X'$ using Formal Spaces, Lemma 85.29.3 we find a morphism $\mathop{\mathrm{Spec}}(R) \to X'$ lifting $p$ as desired. $\square$
In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).
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https://www.physicsforums.com/threads/dvi-vs-vga-svga.188961/
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# DVI vs VGA/SVGA
1. Oct 4, 2007
### Staff: Mentor
Just got a new high-end workstation at work, but the graphiscs card has two DVI slots (new video HD protocol) and we have only VGA monitors at the moment. The builder should have used a card (XFX) with VGA and DVI slots. But what's done is done.
Mild inconvenience.
So I quickly learned that there are such things at DVI to VGA adapters, whereby the VGA monitor plugs into the VGA (female) end, and the DVI (male) end plugs into the DVI slot on the card.
DVI monitors are a little bit more expensive. Just something to consider when purchasing a new computer.
Last edited: Oct 4, 2007
2. Oct 4, 2007
### mgb_phys
Remember the DVI-VGA converter doesn't actaully convert DVI-VGA.
The DVI standard has optionally the VGA signals on spare pins, the four extra pins alongside the sideways blade connector.
There is no requirement for the graphics card to have the VGA signal and it is often only present on a single output. It should be labelled DVI-I if it has both DVI(digital) and VGA(analog).
3. Oct 4, 2007
DVI to VGA adapters aren't too expensive (about $15 at best buy... possibly cheaper at (say) Dell). So, are you going to run a dual-monitor setup? 4. Oct 4, 2007 ### Astronuc ### Staff: Mentor Not at the moment. There is no need. The box was constructed with a card that had two DVI slots rather than one DVI and one VGA/SVGA slot on the same card. Since we didn't have a DVI monitor, but only VGA, I was faced this morning with having to buy a monitor, since I called a couple of nearby places and the either didn't have a DVI-I adapter or didn't know what it was. But I found a DVI-I (Belkin) adapater (not converter) at Staples, which cost$30. That saved me a $60 DVI cable and ~$240 for a DVI monitor.
The workstation is essentially a computational engine for running simulations. We access it across a LAN for I/O, so we don't need a fancy monitor. The output is further processed on other machines.
Similar Discussions: DVI vs VGA/SVGA
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http://mathhelpforum.com/geometry/83369-area-3d-plane-graph.html
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# Math Help - Area in 3D plane graph
1. ## Area in 3D plane graph
Find the area described by
$x+y+z=L$ and $0
Is this the SAME area as $x+y+z = \frac{L}{2}$ and $x,y,z>0$?
Thanks~!
2. The first equation is off. x+y+z will be less than 3L/2 but not necessarily less than L/2
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https://community.wolfram.com/groups/-/m/t/1703087?sortMsg=Likes
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GROUPS:
Alternating terms of two lists, as function.
Posted 1 month ago
431 Views
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11 Replies
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13 Total Likes
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Hello community. I have created a function and would like to know if it is worth submitting in Function Repository or if there is already something simpler that does this same job? If anyone can give any opinion on this I will be very grateful.I modestly have created a function that can interleave two lists by alternating their terms (unlike Riffle, which only fits the terms into gaps, this function does this keeping the same number of terms as it replaces them by both functions simultaneously). It works like this: If the third term inside the function ("c_") is {} the function does this automatically in a 1 to 1 pattern of each group: Alternate[a_, b_] := Alternate[a, b, {}] Alternate[a_, b_, c_] := PadRight[a* PadRight[ Take[Flatten@Table[If[c == {}, {1, 0}, c], Count[a, _]], Min[Count[a, _], Count[b, _]]], Count[a, _], 1], Max[Count[a, _], Count[b, _]]] + PadRight[b* PadRight[ Take[Flatten@Table[Abs[If[c == {}, {1, 0}, c] - 1], Count[b, _]], Min[Count[a, _], Count[b, _]]], Count[b, _], 1], Max[Count[a, _], Count[b, _]]] r = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20}; s = {3, 5, 7, 9, 11, 13, 15, 17, 19, 21}; Alternate[r, s] Alternate[s, r] The function works even with lists of different sizes, keeping the terms in excess unchanged: p = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20}; q = {3, 5, 7, 9, 11, 13, 15, 17}; Alternate[p, q] Alternate[q, p] Or you can change the third term ("c") in the function to any pattern (eg: {0,1,1,1}). Where "1" refers to the first term ("a") from within the function while "0" refers to the term ("b") from within the function: t = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20}; u = {3, 5, 7, 9, 11, 13, 15, 17}; Alternate[t, u, {0, 1, 1, 1}] Alternate[u, t, {0, 1, 1, 1}] I would like to know if is this a good idea or there is a simpler way to do this? Is it worth sending a repository request?Thank you.
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Posted 1 month ago
I would do it something like this: ClearAll[Interweave] Options[Interweave] = {"WeavePattern" -> Automatic}; Interweave[a__List, OptionsPattern[]] := Module[{pat, lsts, len, cur, tooshort, s}, lsts = {a}; pat = OptionValue[Interweave, "WeavePattern"]; If[pat === Automatic, pat = Range[Length[lsts]]]; len = Max[Length /@ lsts]; Table[ tooshort = MapIndexed[If[Length[#1] < i, First[#2], -1] &, lsts]; pat = DeleteCases[pat, Alternatives @@ tooshort]; s = First[pat]; pat = RotateLeft[pat]; lsts[[s, i]] , {i, len} ] ] So testing out: Interweave[ {2, 4, 6, 8, 10, 12, 14, 16, 18, 20}, {3, 5, 7, 9, 11, 13, 15, 17, 19, 21} ] {2, 5, 6, 9, 10, 13, 14, 17, 18, 21} and: Interweave[ {2, 4, 6, 8, 10, 12, 14, 16, 18, 20}, {3, 5, 7, 9, 11, 13, 15, 17} ] {2, 5, 6, 9, 10, 13, 14, 17, 18, 20} and with three arguments: Interweave[ {2, 4, 6, 8, 10, 12, 14, 16, 18, 20}, {3, 5, 7, 9, 11, 13, 15, 17, 19, 21}, {a, b, c, d, e, f, g} ] {2, 5, c, 8, 11, f, 14, 17, 18, 21} and with three arguments and a weave pattern: Interweave[ {2, 4, 6, 8, 10, 12, 14, 16, 18, 20}, {3, 5, 7, 9, 11, 13, 15, 17, 19, 21}, {a, b, c, d, e, f, g}, "WeavePattern" -> {1, 2, 2, 3} ] {2, 5, 7, d, 10, 13, 15, 16, 19, 21} Feel free to use the code… it could definitely be optimized a bit…
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Posted 1 month ago
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Posted 1 month ago
Thank you very much for the answer Sander! I really liked the idea of calling Interweave! I will also modify the term for Interweave[a, b ]:=Interweave[a,b,{}]...very good your suggestions. Thanks! I'm going to work a little harder on this function to test it....
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Posted 1 month ago
O btw, After thinking about it, Alternate might still be a better name… With alternate it is a bit more obvious that it only select a part of each… with interweave it is not so clear… so maybe alternate is actually better…
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Posted 1 month ago
Thanks again Sander, I will see what improvements I can do, because the idea of several lists is good.. I will study your code to get an idea... Thanks for the replies! Helped a lot!
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Posted 1 month ago
A practical example of how the Alternate function can be used:We can take any two real numbers and create hybrid numbers between them by alternating the digits between the two using this Alternate function. Below is an example of how this can be done for a given number of digits "n": n = 100; x = Pi; y = E; N[x, 50] N[y, 50] g = IntegerDigits@IntegerPart[N[x*10^(n - 1), n + 10]]; h = IntegerDigits@IntegerPart[N[y*10^(n - 1), n + 10]]; N[FromDigits@Alternate[g, h]/10^(n - 1), n] N[FromDigits@Alternate[h, g]/10^(n - 1), n] Above is an example of two hybrid numbers created with the help of the Alternate function using these real constants.Note that these "hybrid" numbers are formed by alternating the digits between Pi and E. This given example was done with pattern 1 to 1, or default {1,0} by the function.
Answer
Posted 1 month ago
Hello Claudio,really interesting. I had to replace your Count [ a, _ ] by { Count[ a, _ ] } in your Table-statements, and the code gives your results (this is probably a question of version: I am using Mma 7.0),And when I change Count [ a, _ ] to { Length[ a ] } things work as well. Why did you use Count instead of Length? In[1]:= Alternate[a_, b_] := Alternate[a, b, {}] Alternate[a_, b_, c_] := PadRight[a* PadRight[ Take[Flatten@Table[If[c == {}, {1, 0}, c], {Length[a]}], Min[Length[a], Length[b]]], Length[a], 1], Max[Length[a], Length[b]]] + PadRight[b* PadRight[ Take[Flatten@Table[Abs[If[c == {}, {1, 0}, c] - 1], {Length[b]}], Min[Length[a], Length[b]]], Length[b], 1], Max[Length[a], Length[b]]] r = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20}; s = {3, 5, 7, 9, 11, 13, 15, 17, 19, 21}; Alternate[r, s] Alternate[s, r] Out[5]= {2, 5, 6, 9, 10, 13, 14, 17, 18, 21} Out[6]= {3, 4, 7, 8, 11, 12, 15, 16, 19, 20}
Answer
Posted 1 month ago
This function has been improved and subsequently optimized and adapted to be able to appear in the repository, thank you Wolfram Repository Team. It now can be found in the function repository with the name AlternateElements or use it as ResourceFunction["AlternateElements"]:https://resources.wolframcloud.com/FunctionRepository/resources/AlternateElementsI preferred to keep it running with two lists at a time to be able to work with binary lists, for more details of the function and its properties ( for example: its use with random numbers, hybridization of numerical constants with alternate digits, and others.. ), as well as an example notebook, enter this link above or visit the page of the Wolfram Function Repository.Thanks also to Sander and Hans for the replies.
Answer
Posted 1 month ago
What happens here? I get Table::itform: Argument Count[{2,4,6,8,10,12,14,16,18,20},_] at position 2 does not have the correct form for an iterator. >>
Answer
Posted 1 month ago
Hello Hans, I could not reproduce this error message here ... the error persisted? ..How did it occur? Thanks for the reply, I am honored by the messages both yours and Sander! Thanks.
Answer
Posted 1 month ago
Hans, this is a good question ... for me it works both ways, it was just a matter of choice ... ..but comparing the two versions of the function yours turned out slightly faster! Thanks for the tip ... I will do more tests to know all the capabilities of this function and every tip is very welcome!
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http://math.stackexchange.com/questions/323586/determining-if-a-relation-is-a-function
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# Determining If A Relation Is A Function
I am given the simple relation $f(x)=\sqrt{x}$, where $f$ maps $R \rightarrow R$, and I am suppose to determine whether or not it is a function.
I figured that it was a function, because in the definition of a function it doesn't mention anything about not being defined at a value. Clearly, this function isn't onto though, because any value in the codomain that is less than $0$ won't be assigned to a domain value.
-
For a relation to be a function, every point in domain must be related to a single point in co-domain. And you can map only $\Bbb R^+\cup\{0\}$ to domain under this relation. – Aang Mar 7 '13 at 13:34
@Avatar And because every domain value can't be mapped to some co-domain value, it isn't a function? – Mack Mar 7 '13 at 14:30
A function must be defined on it's entire domain. This is false here, so $f:R \to R$ is not a function.
However if the domain was $R_{ \ge0}=[0,\infty)$, $f$ would have been a function.
So, do we ever have to worry about the domain? Also, here is the definition my book gives: "Let $A$ and $B$ be nonempty sets. A function $f$ from $A$ to $B$ is an assignment of exactly one element of $B$ to each element of $A$. We write $f(a)=b,$ if $b$ is a unique element of $B$ assigned by the function $f$ to the element $a$ of $A$." What are the key words in the definition that would make me think that the entire range has to be defined? – Mack Mar 7 '13 at 13:37
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https://puzzling.stackexchange.com/questions/64642/please-help-me-find-myself/64684
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When I am in the sea, I'm always falsy
When you add it, you can finally see me!
When you take a drink with me, people say I'm a fool - but I always drop the l.
hint:
BTW, someone told me I'm french!
hint 2:
The title of the puzzle is the 3rd hint
last hint:
The solution is in front of you !
• Is that an L or an i or a 1? – Redwolf Programs Apr 23 '18 at 14:29
• It was to make it a bit harder, but it is a L :D – toto Apr 23 '18 at 14:33
• Could you add another hint? – Redwolf Programs Apr 23 '18 at 14:48
• In hint 2: 2nd hint instead of 3rd? – Ahmed Ashour Apr 23 '18 at 15:39
• Well, depends how you count – toto Apr 23 '18 at 15:42
I guess the "sea" refers in fact to C language
"when you add it", probably ++
"people say i'm a fool but I drop the l" => foo is a "dummy word" (together with bar which fits the "When you take a drink with me") for naming variable, people say you are "french", your name in puzzling is toto, the french equivalent to foo and bar... guess i'm close to find
It should be somthing that exists in C++ but not in C, related to foobar
• You found it ! I'll write the detailed answer :) Maybe you can update your answer too – toto Apr 24 '18 at 9:54
• I was quite far though ^^, didn't thought about la tête à toto, just found some parts of the riddle – Flying_whale Apr 24 '18 at 10:40
• Since you found it using at least 2 hints, I think you deserve the answer – toto Apr 24 '18 at 11:30
I don't know enough to take a stab at the final answer yet, I'm pretty sure this riddle's talking about
Computer science
When I am in the sea, I'm always falsy
falsy is a computer science term for somethings evaluates to false (like 0). I'm pretty sure this means in C the answer resolves to false.
When you add it, you can finally see me!
But in C++ (when you add it), it resolves to some value instead.
When you take a drink with me, people say I'm a fool - but I always drop the l.
foo (people say I'm a fool - but I always drop the l) is a universal placeholder for variable/method names in computer science.
The trouble is....
I don't know C++!
• Yes ! You are on the good route, well done. #1 has part of the solution in it, #3 is correct ! – toto Apr 23 '18 at 16:07
Some things no one else seems to have found so far:
"take a drink" seems to be a reference to Java,
and
French uses guillemets for quotation marks, which look like the << and >> operators.
Overall, it sounds like
<< and >> probably have something to do with the answer. << is used for printing in C++, matching the second hint. The Java reference sounds like it may have something to do with generics, where >> frequently shows up (but not <<); generics involve type parameters, which could match the metasyntactic variable part implied by "foo".
Still,
some of these connections are pretty tenuous, and I feel like while the hints all share a theme, they don't seem to fit together to all refer to the same thing within that theme.
You are
Salt
When I am in the sea, I am always falsy
You cannot see the salt in the sea
When you add it, you can finally see me
You can see salt in it's culinary form
When you take a drink with me, people say I'm foolish, but I always drop the L
Could refer to how you put salt around the edges of an alcholic drink
Hint
Fools Salt (Or Sel Fou) is common in France: Fou is like fool without the L
• Okay good, you used L not I – Redwolf Programs Apr 23 '18 at 14:37
• Nice try ! What about the hint tho? – toto Apr 23 '18 at 14:39
• this is the most logical answer i can think of – TinyTRex72 Apr 23 '18 at 14:39
• "When you add it, you can finally see me" => I see it as if you add enough salt, you reach saturation point and can see the salt – Kepotx Apr 23 '18 at 14:40
• Matches pretty well, but that's not the answer :D – toto Apr 23 '18 at 14:45
Cout
When I am in the sea, I'm always falsy
In C programming language, this has no meaning and would cause an error or return false.
When you add it, you can finally see me!
But in C++, it prints to the console, so you can "see" it.
When you take a drink with me, people say I'm a fool - but I always drop the l.
Foo is a generic placeholder for methods, signalling that we want a method in C++
Hint 1.
Cout also means cost in French
Hint 2 maybe
Not as sure on this one, but maybe because cout is used to print, and thus also common in debugging and locating errors
• You wrote "I'm always daisy" instead of "falsy". Is there a particular reason? Also, you say "Cout also means cut in French". Don't you mean "cost" instead of "cut"? – actaram Apr 23 '18 at 18:22
• @TheWanderingMind I would assume both errors are a result of autocorrect. – ale10ander Apr 23 '18 at 20:59
• @TheWanderingMind Yep, my bad, wrote the original on my phone. – Cain Apr 24 '18 at 2:36
I cannot find a strong connection with some of the hints, but I think it's something along the lines of:
Null
When I am in the sea, I'm always falsy
In C, NULL is the same as 0, which is the same as false
When you add it, you can finally see me!
NULL doesn't correspond to an ASCII character, but some larger numbers do
When you take a drink with me, people say I'm a fool - but I always drop the l.
'Fool minus the l is 'foo' a common placeholder variable usually initialized to 0 or NULL. Thanks to Lord Farquaad for this insight
Hint 1
Nul is French for zero/null, which might have something to do with 'dropping the l'
But I can't figure out
How this connects to the title
• Welcome to Puzzling SE! Nice first answer! – NL628 Apr 23 '18 at 21:36
nil, which is falsy in C languages. I thiiink (although I am rusty on this) if you add a number to it, at least in objective-c, it will be cast to an integer, hence "when you add it you can finally see it".
I also believe it comes from french
nul, which means zero.
The hint about finding myself refers to what I described above. But,
There might also be something around various nil variations in other languages: nil, nul, null, null pointer (perhaps the pointer refers to "help me find myself"). Also the drink seems to be the reference to Java, another programming language where null is used. Maybe "people say I'm fool, because I always drop the 'l' and use 'nul' version instead?
So I think this might be pretty close but can't quite make sense of the details.
• Worth noting that my answer is also heavily influenced by @Lord Farquaad – redFur Apr 23 '18 at 19:12
mirage
When I am in the sea, I'm always falsy
It is just a refraction of light
When you add it, you can finally see me !
When you take a drink with me, people say I'm a fool - but I always drop the l.
hint 1:
Its origin is French.
hint 2:
It is not something which really exists, and can not be found
• Nice try, not the correct answer tho ! :D – toto Apr 23 '18 at 15:37
0
"When I am in the sea, I'm always falsy":
0 is a 'falsy' value in C++, as in it evaluates to false
"When you add it, you can finally see me!":
When you add '0' to a number in C++, you get that numbers character value. This allows you to print the number and "finally see" it.
"When you take a drink with me, people say I'm a fool - but I always drop the l."
foo is a placeholder variable, and if that variable is an int more often than not it will initially be set to 0.
Tête à Toto
When I am in the sea, I'm always falsy
In the programming language C, 0 is used as False (or falsy if you speak the lingo)
When you add it, you can finally see me!
When you actually write out "0 + 0", the face of Toto begins to appear.
When you take a drink with me, people say I'm a fool - but I always drop the l.
"Fool" - "L" = "Foo", and you'd probably be drinking at a bar, and in the french programming community "toto" is often used as their equivalent to "foobar"
foobar.
.
When you take a drink with me, people say I'm a fool - but I always drop the l.
.
You have drinks at a bar. Take fool-l = foo, and add bar.
• That's the correct answer for #3 ! You need to take in account all hints to find the global answer :D – toto Apr 24 '18 at 7:26
IT
When you add it, you can finally see me!
In the context of this riddle it is me, hence IT (The solution is in front of you!)
All other hints previously covered in good detail
• Welcome to Puzzling.SE! You should try and explain how your answer fits the entire riddle and not just one line - as it stands, and compared to the other answers, I really don't think this is correct. – F1Krazy Apr 24 '18 at 8:54
My guess is
Love (a score of zero in tennis)
because
in C, 0 evaluates to false.
in C++, when you add 0 to something you can see it.
in Java (when you take a drink), 0 is commonly an initial value for a placeholder variable foo.
Hint #1 : Love comes from the French l'oeuf, which means egg; as zero has the shape and appearance of an egg.
Hint #2 seems to suggest the title, 'Please help me find myself' is important. Help me find love maybe?
Hint #3, The solution is right in front of you: nothing is right in front of you, it's a red herring?
Admittedly the last couple of clues are a bit sketchy but this follows on from the answers already given which are on the right track.
• I think the title and the hints mostly refer to the fact that toto is usually used in french as a generic name (similarly to the foo/bar mentioned in some answers) – Nank Apr 24 '18 at 9:31
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https://www.sarthaks.com/1233593/image-candle-flame-formed-lens-obtained-screen-placed-other-side-lens-image-three-times-size
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# The image of a candle flame formed by a lens is obtained on a screen placed on the other side of the lens. If the image is three times the size of the
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in Physics
closed
The image of a candle flame formed by a lens is obtained on a screen placed on the other side of the lens. If the image is three times the size of the flame and the distance between lens and image is 80 cm, at what distance should the candle be placed from the lens ? What is the nature of the image at a distance of 80 cm from the lens ?
by (71.8k points)
selected by
As the image is obtained on the screen, it is real.
:. Magnification, m = - 3, v = 80 cm, u = ?
As m = v/u :. - 3 = 80/u, u = (-80)/3 cm.
From (1)/(f) = (1)/(v) - 1/u = 1/80 + 3/80 = 4/80 = 1/20, f = 20 cm.
The lens is convex and image formed at 80 cm from the lens is real and inverted.
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https://www.imacapp.cn/app/704743893
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### 介绍
ExpressionsinBar is a simple menubar application which provides powerful computer-aided algebra computations. It's a powerful tool for evaluating mathematical expressions that lives in the menubar of your Mac ! So it is always just click away! It's the perfect app for teachers, math students, scientists, and the geek among us!
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Unlike most other Equation Editors, ExpressionsinBar helps you resolve the math and then prepares a neat output for an easy insertion in your documents or presentations. Mathematical expressions are presented in high-resolution PDF form that can be pasted into your Documents or Presentations!
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- Click the Menubar icon and ExpressionsinBar pops open an input expression box. Enter the expression, view the result.
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- Scrolling panels with easy to use functions
- Menu with variables, functions, syntax and tips
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- Polynomials
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+++ Thank you to everyone for your cool comments and suggestions ! We are working on each one of them. +++
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http://mathhelpforum.com/differential-equations/190993-cauchy-schwarz-inequality.html
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1. ## Cauchy-Schwarz inequality
Hi, I am stuck on this question.
Prove
$|f(L)-f(0)|^2 \le L \int_0^L |f'(x)|^2 dx$ for any function $f \in C^1([0,L])$.
So I know I should use the Cauchy-Schwarz inequality applied to the functions f′ and 1, but I am stuck on how to do it.
Thanks for any help people.
2. ## Re: Cauchy-Schwarz inequality
$|f(L)-f(0)|=|\int_0^L f'(x)dx|\leq \int_0^L |f(x)|\cdot 1 dx\leq (\int_0^L|f'(x)|^2dx)^{1/2}\cdot (\int_0^L 1^2dx)^{1/2}$
3. ## Re: Cauchy-Schwarz inequality
Thanks for that, but how do I go on to prove my inequality? I don't see how squaring brings the L in.
4. ## Re: Cauchy-Schwarz inequality
Originally Posted by iceman954
Thanks for that, but how do I go on to prove my inequality? I don't see how squaring brings the L in.
What is
$\int_{0}^{L}1^{2}\,dx?$
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https://chemistry.stackexchange.com/questions/114539/thermodynamics-series-reaction-estimating-mols-of-reactants-based-on-free-en
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# Thermodynamics - Series Reaction - Estimating mols of reactants based on Free Energy of Rxn
Question
Three reactions occur simulteneously (assume ideal) at $$\pu{T = 0^\circ C}$$.
$$\ce{A<=>B<=>C<=>D}$$
a) With $$\Delta_r G^\circ_\text{AB} = \pu{400 J/mol}$$, $$\Delta_r G^\circ_\text{BC} = \pu{-100 J/mol}$$, and $$\Delta_r G^\circ_\text{CD} = \pu{-200 J/mol}$$. If you start with 10 moles of A, calculate how many moles of B, C, and D you have when the system reaches equilibrium. Show all your work. (Hint: mass can neither be created nor destoyed)
b) Order the equilibrium concentrations from largest to smallest. Explain how you might be able to intuitively guess this ranking.
I know that given deltaG_RxN, one can calculate Keq, and use Keq to find the moles at equilibrium of reactants and products. Since the products at the end of one reaction became the reactants of the second, I fed in the mol amount of the first equation into the second equation.
Confused because in discussion - we went over how to do part B. and I don't think my math lines up.
• positive delta G_RXN = more reactants than products, and vice versa
• thus in the first rxn there should be more [A] than [B] @ equilibrium
• in the second rxn there should be more [C] than [B]
• and the third rxn there should be more [D] than [C].
what did i do wrong math-wise?
What you do is write $$[D]=[C]K_{CD}$$, $$[C]=[B]K_{BC}$$, and $$[B]=[A]K_{AB}$$. So, $$[C]=K_{BC}K_{AB}[A]$$ and $$[D]=K_{CD}K_{BC}K_{AB}[A]$$So, $$[A]+[B]+[C]+[D]=(1+K_{AB}+K_{BC}K_{AB}+K_{CD}K_{BC}K_{AB})[A]=10$$
• The reason for using this approach is that it fully describes all the final product-next reaction molar values based on solely the initial value of A, and given and known constants (${\Delta} G^°_{RXN}$, and R, T). No information is lost. The previous notation failed to take into account reactant Keqs, so it returned incorrect estimation results. The Keq of binding of any intermediary step impacts the Keq of the subsequent step(s). – ThermoRestart Apr 30 '19 at 11:20
One thing the exercise is lacking is the physical state of A, B, C, and D. If they are all gases or all liquids, you can calculate as shown in question and in answers. Otherwise, you would need more information to complete the exercise.
For some insight regarding part b) of the exercise, you could rewrite your equations as:
$$\ce{A <=> B}$$ $$\ce{A <=> C}$$ $$\ce{A <=> D}$$
with the corresponding Gibbs free energies (by adding the relevant steps):
$$\Delta_r G^\circ_\text{AB} = \pu{400 kJ/mol}$$
$$\Delta_r G^\circ_\text{AC} = \pu{300 kJ/mol}$$
$$\Delta_r G^\circ_\text{AD} = \pu{100 kJ/mol}$$
This shows that the concentration of A will be the highest, followed by D, C, and B.
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https://www.iacr.org/news/legacy.php?p=detail&id=1837
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International Association for Cryptologic Research
# IACR News Central
You can also access the full news archive.
Further sources to find out about changes are CryptoDB, ePrint RSS, ePrint Web, Event calender (iCal).
2012-11-01
18:17 [Pub][ePrint]
We introduce the \\emph{linear centralizer method} for a passive adversary
to extract the shared key in group-theory based key exchange protocols (KEPs).
We apply this method to obtain a polynomial time cryptanalysis of the
\\emph{Commutator KEP}, introduced by Anshel--Anshel--Goldfeld in 1999 and considered
extensively ever since.
We also apply this method to the \\emph{Centralizer KEP}, introduced by Shpilrain--Ushakov in 2006.
Our method is proved to be of polynomial time using a technical lemma
about sampling invertible matrices from a linear space of matrices.
18:17 [Pub][ePrint]
We revisit hardness-preserving constructions of a PRF from any length doubling PRG when there is a non-trivial upper bound $q$ on the number of queries that the adversary can make to the PRF. Very recently, Jain, Pietrzak, and Tentes (TCC 2012) gave a hardness-preserving construction of a PRF that makes only $O(\\log q)$ calls to the underlying PRG when $q = 2^{n^\\epsilon}$ and $\\epsilon \\geq \\frac{1}{2}$. This dramatically improves upon the efficiency of the GGM construction. However, they explicitly left open the question of whether such constructions exist when $\\epsilon < \\frac{1}{2}$. In this work, we make progress towards answering this question. In particular we give constructions of PRFs that make only $O(\\log q)$ calls to the underlying PRG even when $q = 2^{n^\\epsilon}$, for $0 18:17 [Pub][ePrint] An increasing number of embedded security applications---which traditionally have been heavily reliant on secret and/or proprietary solutions---apply the principle of open evaluation. A recent example is the specification of an open security protocol stack for car immobilizer applications by Atmel, which has been presented at ESCAR 2010. This stack is primarily intended to be used in conjunction with automotive transponder chips of this manufacturer, but could in principle be deployed on any suitable type of transponder chip. In this paper we re-evaluate the security of this protocol stack. We were able to uncover a number of security vulnerabilities. We show that an attacker with a cheap standard reader close to such a car key can track it, lock sections of its EEPROM, and even render its immobilizer functionality completely useless. After eavesdropping on a genuine run of the authentication protocol between the car key and the car, an attacker is enabled to read and write the memory of the car key. Furthermore, we point out the threats of relay attacks and session hijacking, which require slightly more elaborate attack setups. For each of the indicated attacks we propose possible fixes and discuss their overhead. 18:17 [Pub][ePrint] Usually a communication link is securedby means of a symmetric-key algorithm. For that, amethod is required to securely establish a symmetric key for that algorithm. This old key establishment problem is still relevant and of paramount importance both in existing computer networks and new large-scale ubiquitous systems comprising resource-constrained devices. Identity-based pairwise key agreement allows for the generation of a common key between two parties given a secret keying material owned by the first party and the identity of the second one. However, existing methods, e.g., based on polynomials, are prone to collusion attacks. In this paper we discuss a new key establishment scheme aiming at fully collusion-resistant identity-based symmetric-key agreement. Our scheme, the HIMMO algorithm, relies on two design concepts: Hiding Information and Mixing Modular Operations. Collusion attacks on schemes from literature cannot readily be applied to our scheme; our security analysis further shows that HIMMO\'s design principles prevent an attacker from performing a number of attacks. Also, the simple logic of the HIMMO algorithm allows for very efficient implementations in terms of both speed and memory. Finally, being an identitybasedsymmetric-key establishment scheme, HIMMO allows for efficient real-world key exchange protocols. 2012-10-31 10:21 [Event][New] Submission: 7 January 2013 Notification: 31 January 2013 From March 18 to March 20 Location: Cambridge, England More Information: http://spw.stca.herts.ac.uk/ 2012-10-30 00:17 [Pub][JoC] Abstract Recent targeted attacks have increased significantly in sophistication, undermining the fundamental assumptions on which most cryptographic primitives rely for security. For instance, attackers launching an Advanced Persistent Threat (APT) can steal full cryptographic keys, violating the very secrecy of “secret” keys that cryptographers assume in designing secure protocols. In this article, we introduce a game-theoretic framework for modeling various computer security scenarios prevalent today, including targeted attacks. We are particularly interested in situations in which an attacker periodically compromises a system or critical resource completely, learns all its secret information and is not immediately detected by the system owner or defender. We propose a two-player game between an attacker and defender called FlipIt or The Game of “Stealthy Takeover.” In FlipIt, players compete to control a shared resource. Unlike most existing games, FlipIt allows players to move at any given time, taking control of the resource. The identity of the player controlling the resource, however, is not revealed until a player actually moves. To move, a player pays a certain move cost. The objective of each player is to control the resource a large fraction of time, while minimizing his total move cost. FlipIt provides a simple and elegant framework in which we can formally reason about the interaction between attackers and defenders in practical scenarios. In this article, we restrict ourselves to games in which one of the players (the defender) plays with a renewal strategy, one in which the intervals between consecutive moves are chosen independently and uniformly at random from a fixed probability distribution. We consider attacker strategies ranging in increasing sophistication from simple periodic strategies (with moves spaced at equal time intervals) to more complex adaptive strategies, in which moves are determined based on feedback received during the game. For different classes of strategies employed by the attacker, we determine strongly dominant strategies for both players (when they exist), strategies that achieve higher benefit than all other strategies in a particular class. When strongly dominant strategies do not exist, our goal is to characterize the residual game consisting of strategies that are not strongly dominated by other strategies. We also prove equivalence or strict inclusion of certain classes of strategies under different conditions. Our analysis of different FlipIt variants teaches cryptographers, system designers, and the community at large some valuable lessons: 1. Systems should be designed under the assumption of repeated total compromise, including theft of cryptographic keys. FlipIt provides guidance on how to implement a cost-effective defensive strategy. 2. Aggressive play by one player can motivate the opponent to drop out of the game (essentially not to play at all). Therefore, moving fast is a good defensive strategy, but it can only be implemented if move costs are low. We believe that virtualization has a huge potential in this respect. 3. Close monitoring of one’s resources is beneficial in detecting potential attacks faster, gaining insight into attacker’s strategies, and scheduling defensive moves more effectively. Interestingly, FlipIt finds applications in other security realms besides modeling of targeted attacks. Examples include cryptographic key rotation, password changing policies, refreshing virtual machines, and cloud auditing. • Content Type Journal Article • Pages 1-59 • DOI 10.1007/s00145-012-9134-5 • Authors • Marten van Dijk, RSA Laboratories, Cambridge, MA, USA • Ari Juels, RSA Laboratories, Cambridge, MA, USA • Alina Oprea, RSA Laboratories, Cambridge, MA, USA • Ronald L. Rivest, Computer Science and Artificial Intelligence Laboratory, Massachusetts Institute of Technology, Cambridge, MA, USA • Journal Journal of Cryptology • Online ISSN 1432-1378 • Print ISSN 0933-2790 From: Fri, 26 Oct 2012 12:00:56 GMT 2012-10-29 15:17 [Pub][ePrint] We construct the first Message Authentication Codes (MACs) that are existentially unforgeable against a quantum chosen message attack. These chosen message attacks model a quantum adversary\'s ability to obtain the MAC on a superposition of messages of its choice. We begin by showing that a quantum secure PRF is sufficient for constructing a quantum secure MAC, a fact that is considerably harder to prove than its classical analogue. Next, we show that a variant of Carter-Wegman MACs can be proven to be quantum secure. Unlike the classical settings, we present an attack showing that a pair-wise independent hash family is insufficient to construct a quantum secure one-time MAC, but we prove that a four-wise independent family is sufficient for one-time security. 15:17 [Pub][ePrint] We give three new algorithms to solve the isomorphism of polynomial\'\' problem, which was underlying the hardness of recovering the secret-key in some multivariate trapdoor one-way functions. In this problem, the adversary is given two quadratic functions, with the promise that they are equal up to linear changes of coordinates. Her objective is to compute these changes of coordinates, a task which is known to be harder than Graph-Isomorphism. Our new algorithm build on previous work in a novel way. Exploiting the birthday paradox, we break instances of the problem in time$q^{2n/3}$(rigorously) and$q^{n/2}$(heuristically), where$q^n$is the time needed to invert the quadratic trapdoor function by exhaustive search. These results are obtained by turning the algebraic problem into a combinatorial one, namely that of recovering partial information on an isomorphism between two exponentially large graphs. These graphs, derived from the quadratic functions, are new tools in multivariate cryptanalysis. 15:17 [Pub][ePrint] Secure sketches and fuzzy extractors enable the use of biometric data in cryptographic applications by correcting errors in noisy biometric readings and producing cryptographic materials suitable for authentication, encryption, and other purposes. Such constructions work by producing a public sketch, which is later used to reproduce the original biometric and all derived information exactly from a noisy biometric reading. It has been previously shown that release of multiple sketches associated with a single biometric presents security problems for certain constructions. We continue the analysis to demonstrate that all other constructions in the literature are also prone to similar problems and cannot be safely reused. To mitigate the problem, we propose for each user to store one short secret string for all possible uses of her biometric, and show that simple constructions in the computational setting have numerous advantageous security and usability properties under standard hardness assumptions. Our constructions are generic in that they can be used with any existing secure sketch as a black box. 15:17 [Pub][ePrint] Embedding an element of a finite field into auxiliary groups such as elliptic curve groups or extension fields of finite fields has been useful tool for analysis of cryptographic problems such as establishing the equivalence between the discrete logarithm problem and Diffie-Hellman problem or solving the discrete logarithm problem with auxiliary inputs (DLPwAI). Actually, Cheon\'s algorithm solving the DLPwAI can be regarded as a quantitative version of den Boer and Maurer. Recently, Kim showed in his dissertation that the generalization of Cheon\'s algorithm using embedding technique including Satoh\'s \\cite{Sat09} is no faster than Pollard\'s rho algorithm when$d\\nmid (p\\pm 1)$. In this paper, we propose a new approach to solve DLPwAI concentrating on the behavior of function mapping between the finite fields rather than using an embedding to auxiliary groups. This result shows the relation between the complexity of the algorithm and the number of absolutely irreducible factors of the substitution polynomials, hence enlightens the research on the substitution polynomials. More precisely, with a polynomial$f(x)$of degree$d$over$\\mathbf{F}_p$, the proposed algorithm shows the complexity$O\\left(\\sqrt{p^2/R}\\log^2d\\log p\\right)$group operations to recover$\\alpha$with$g, g^{\\alpha}, \\dots, g^{\\alpha^{d}}$, where$R$denotes the number of pairs$(x, y)\\in\\mathbf{F}_p\\times \\mathbf{F}_p$such that$f(x)-f(y)=0$. As an example using the Dickson polynomial, we reveal$\\alpha$in$O(p^{1/3}\\log^2{d}\\log{p})$group operations when$d|(p+1)$. Note that Cheon\'s algorithm requires$g, g^{\\alpha}, \\dots, g^{\\alpha^{d}}, \\dots, g^{\\alpha^{2d}}\$ as an instance for the same problem.
15:17 [Pub][ePrint]
We describe plausible lattice-based constructions with properties that
approximate the sought-after multilinear maps in hard-discrete-logarithm
groups, and show that some applications of such multi-linear maps can
be realized using our approximations.
The security of our constructions relies on seemingly hard problems in
ideal lattices, which can be viewed as extensions of the assumed
hardness of the NTRU function.
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http://mathhelpforum.com/advanced-algebra/218048-easy-linear-algebra-question.html
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# Math Help - Easy linear algebra question
1. ## Easy linear algebra question
Let P2(R) denote the vector space of real polynomial functions of degree less than or equal to two and let B := [p0,p1,p2] denote the natural ordered basis for P2(R) (so pi(x) = xi). Define g ∈ P2(R) by g(x) = 2x2 − 3x + 1. Write g as a linear combination of the elements of B. Compute the coordinate vector gB of g with respect to B.
Define h1,h2,h3 ∈ P2(R) by h1(x) = 2, h2(x) = 3x−2 and h3(x) = 2x2 −3x+1. Define C := [h1, h2, h3]. Write each element of B as a linear combination of the elements of C. Explain why the calculations you have performed prove that C is a basis for P2(R).
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http://www.mathworks.com/help/dsp/ref/dsp.rlsfilter-class.html?requestedDomain=www.mathworks.com&nocookie=true
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# Documentation
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# dsp.RLSFilter System object
Package: dsp
Compute output, error and coefficients using Recursive Least Squares (RLS) algorithm
## Description
The `RLSFilter` object filters each channel of the input using RLS filter implementations.
To filter each channel of the input:
1. Define and set up your RLS filter. See Construction.
2. Call `step` to filter each channel of the input according to the properties of `dsp.RLSFilter`. The behavior of `step` is specific to each object in the toolbox.
Note: Starting in R2016b, instead of using the `step` method to perform the operation defined by the System object™, you can call the object with arguments, as if it were a function. For example, ```y = step(obj,x)``` and `y = obj(x)` perform equivalent operations.
## Construction
`rlsFilt = dsp.RLSFilter` returns an adaptive RLS filter System object, `rlsFilt`. This System object computes the filtered output, filter error and the filter weights for a given input and desired signal using the RLS algorithm.
```rlsFilt = dsp.RLSFilter('PropertyName',PropertyValue, ...)``` returns an RLS filter System object, `rlsFilt`, with each specified property set to the specified value.
```rlsFilt = dsp.RLSFilter(LEN, 'PropertyName', PropertyValue, ...)``` returns an RLS filter System object, `rlsFilt`. This System object has the Length property set to `LEN`, and other specified properties set to the specified values.
## Properties
`Method` Method to calculate the filter coefficients You can specify the method used to calculate filter coefficients as one of | `Conventional RLS` [1] [2] | ```Householder RLS``` [3] [4] | ```Sliding-window RLS``` [5][1][2] | ```Householder sliding-window RLS``` [4] | `QR decomposition` [1] [2]. The default value is `Conventional RLS`. This property is nontunable. `Length` Length of filter coefficients vector Specify the length of the RLS filter coefficients vector as a scalar positive integer value. The default value is `32`. This property is nontunable. `SlidingWindowBlockLength` Width of the sliding window Specify the width of the sliding window as a scalar positive integer value greater than or equal to the Length property value. This property is applicable only when the Method property is set to ```Sliding-window RLS``` or `Householder sliding-window RLS`. The default value is `48`. This property is nontunable. `ForgettingFactor` RLS forgetting factor Specify the RLS forgetting factor as a scalar positive numeric value less than or equal to 1. Setting this property value to 1 denotes infinite memory, while adapting to find the new filter. The default value is `1`. This property is tunable. `InitialCoefficients` Initial coefficients of the filter Specify the initial values of the FIR adaptive filter coefficients as a scalar or a vector of length equal to the `Length` property value. The default value is `0`. This property is tunable. `InitialInverseCovariance` Initial inverse covariance Specify the initial values of the inverse covariance matrix of the input signal. This property must be either a scalar or a square matrix, with each dimension equal to the `Length` property value. If you set a scalar value, the `InverseCovariance` property is initialized to a diagonal matrix with diagonal elements equal to that scalar value. This property applies only when the `Method` property is set to `Conventional RLS` or ```Sliding-window RLS```. The default value is `1000`. This property is tunable. `InitialSquareRootInverseCovariance` Initial square root inverse covariance Specify the initial values of the square root inverse covariance matrix of the input signal. This property must be either a scalar or a square matrix with each dimension equal to the `Length` property value. If you set a scalar value, the `SquareRootInverseCovariance` property is initialized to a diagonal matrix with diagonal elements equal to that scalar value. This property applies only when the `Method` property is set to `Householder RLS` or ```Householder sliding-window RLS```. The default value is `sqrt(1000)`. This property is tunable. `InitialSquareRootCovariance` Initial square root covariance Specify the initial values of the square root covariance matrix of the input signal. This property must be either a scalar or a square matrix with each dimension equal to the `Length` property value. If you set a scalar value, the `SquareRootCovariance` property is initialized to a diagonal matrix with diagonal elements equal to the scalar value. This property applies only when the `Method` property is set to `QR-decomposition RLS`. The default value is `sqrt(1/1000)`. This property is tunable. `LockCoefficients` Lock coefficient updates Specify whether the filter coefficient values should be locked. When you set this property to `true`, the filter coefficients are not updated and their values remain the same. The default value is `false` (filter coefficients continuously updated). This property is tunable.
## Methods
clone Create System object with same property values isLocked Locked status for input attributes and nontunable properties msesim Mean-square error for RLS filter release Allow property value and input characteristics changes reset Reset the internal states of a System object step Process inputs using RLS filter
## Examples
expand all
Use the RLS filter System object™ to determine the signal value.
Note: This example runs only in R2016b or later. If you are using an earlier release, replace each call to the function with the equivalent `step` syntax. For example, myObject(x) becomes step(myObject,x).
```hrls1 = dsp.RLSFilter(11, 'ForgettingFactor', 0.98); hfilt = dsp.FIRFilter('Numerator',fir1(10, .25)); % Unknown System x = randn(1000,1); % input signal d = hfilt(x) + 0.01*randn(1000,1); % desired signal [y,e] = hrls1(x, d); w = hrls1.Coefficients; subplot(2,1,1), plot(1:1000, [d,y,e]); title('System Identification of an FIR filter'); legend('Desired', 'Output', 'Error'); xlabel('time index'); ylabel('signal value'); subplot(2,1,2); stem([hfilt.Numerator; w].'); legend('Actual','Estimated'); xlabel('coefficient #'); ylabel('coefficient value'); ```
Noise Cancellation
```hrls2 = dsp.RLSFilter('Length', 11, 'Method', 'Householder RLS'); hfilt2 = dsp.FIRFilter('Numerator',fir1(10, [.5, .75])); x = randn(1000,1); % Noise d = hfilt2(x) + sin(0:.05:49.95)'; % Noise + Signal [y, err] = hrls2(x, d); subplot(2,1,1), plot(d), title('Noise + Signal'); subplot(2,1,2), plot(err), title('Signal'); ```
## Algorithms
The `dsp.RLSFilter` System object, when `Conventional RLS` is selected, recursively computes the least squares estimate (RLS) of the FIR filter weights. The System object estimates the filter weights or coefficients, needed to convert the input signal into the desired signal. The input signal can be a scalar or a column vector. The desired signal must have the same data type, complexity, and dimensions as the input signal. The corresponding RLS filter is expressed in matrix form as P(n) :
`$\begin{array}{l}k\left(n\right)=\frac{{\lambda }^{-1}P\left(n-1\right)u\left(n\right)}{1+{\lambda }^{-1}{u}^{H}\left(n\right)P\left(n-1\right)u\left(n\right)}\\ y\left(n\right)={w}^{T}\left(n-1\right)u\left(n\right)\\ e\left(n\right)=d\left(n\right)-y\left(n\right)\\ w\left(n\right)=w\left(n-1\right)+k\left(n\right)e\left(n\right)\\ P\left(n\right)={\lambda }^{-1}P\left(n-1\right)-{\lambda }^{-1}k\left(n\right){u}^{H}\left(n\right)P\left(n-1\right)\end{array}$`
where λ-1 denotes the reciprocal of the exponential weighting factor. The variables are as follows:
VariableDescription
nThe current time index
u(n)The vector of buffered input samples at step n
P(n)The inverse correlation matrix at step n
k(n)The gain vector at step n
w(n)The vector of filter tap estimates at step n
y(n)The filtered output at step n
e(n)The estimation error at step n
d(n)The desired response at step n
λThe forgetting factor
u, w, and k are all column vectors.
## References
[1] M Hayes, Statistical Digital Signal Processing and Modeling, New York: Wiley, 1996
[2] S. Haykin, Adaptive Filter Theory, 4th Edition, Upper Saddle River, NJ: Prentice Hall, 2002
[3] A.A. Rontogiannis and S. Theodoridis, "Inverse factorization adaptive least-squares algorithms," Signal Processing, vol. 52, no. 1, pp. 35-47, July 1996.
[4] S.C. Douglas, "Numerically-robust O(N2) RLS algorithms using least-squares prewhitening," Proc. IEEE Int. Conf. on Acoustics, Speech, and Signal Processing, Istanbul, Turkey, vol. I, pp. 412-415, June 2000.
[5] A. H. Sayed, Fundamentals of Adaptive Filtering, Hoboken, NJ: John Wiley & Sons, 2003
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http://physics.stackexchange.com/questions/38172/linear-rising-potential-from-a-gribov-propagator
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# Linear rising potential from a Gribov propagator
It is common wisdom that a gluon propagator (Gribov-)like $$G(p^2)=\frac{a+bp^2}{cp^4+dp^2+e}$$ should give rise to a linear rising potential. So far, I have not seen a proof of this and I would like to get a mathematical derivation, or a reference, displaying how a potential emerges from it.
Thanks.
-
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http://kullabs.com/classes/subjects/units/lessons/notes/274
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#### Force
After completion of this lesson, student must be able to:
• Describe the uses and effects of force on objects at rest and motion.
• Define and explain inertia of rest and inertia of motion.
• Explain scalars and vectors.
• Describe acceleration and retardation with example.
• Explain the equations of motion and solve simple mathematical problems.
• Explain Newton's Laws of motion with examples.
#### Force
Force is an external agency which changes or tends to change the state of a body from rest to motion or vice versa. When a number of forces acting on a body do not change its states of rest or uniform motion in a straight line, the force are said to be balanced forces.This note provide us further information about the force.
#### Inertia and Momentum
Inertia is the property of a body due to which it remains or tends to remain in the state of rest are uniform motion in a straight line unless an unbalanced forces act on it. This note provides us the information about inertia of force and different forms of inertia and momentum.
#### Equation of Motion of Uniform Acceleration
Equations involving displacement, initial velocity, final velocity, acceleration and time of motion of a moving body are equations of motion. This note gives us the information about equation of motion of uniform acceleration and its derivation.
#### Newton’s Laws of Motion
Newton’s first law states that ‘everybody continues in its state of rest or of uniform motion in a straight line unless an unbalanced force acts on it.' This notes provides an information about Newton’s laws of motion.
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http://openstudy.com/updates/4faeeffce4b059b524fa1625
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## EvelynW Group Title Can someone show me the step to solve this please. I've looked at the examples that my teach provided and in my book but there are none for this type of problem. Thanks Express in terms of i. Root -225 + root -49 2 years ago 2 years ago Edit Question Delete Cancel Submit
• This Question is Closed
1. Eherre1989
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any time you have a sum of a negative number in a square root you write i so for the firstone it is 15i + 7i= 22i
• 2 years ago
2. shashi20008
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We have $\sqrt{-1} = i$now $\sqrt{-225} = \sqrt{225}\times \sqrt{-1} = 15i$similarly, $\sqrt{-49} = 7i$. Add them and you have your answer.. :)
• 2 years ago
3. EvelynW
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K thank you. Know I can take it from there :)
• 2 years ago
4. EvelynW
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Both of you thanks :)
• 2 years ago
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https://www.arxiv-vanity.com/papers/nucl-ex/0703015/
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arXiv Vanity renders academic papers from arXiv as responsive web pages so you don’t have to squint at a PDF. Read this paper on arXiv.org.
# Competition between normal and intruder states inside the “Island of Inversion”
Vandana Tripathi, S.L. Tabor, P.F. Mantica, Y. Utsuno, P. Bender, J. Cook, C.R. Hoffman,
Sangjin Lee, T. Otsuka, J. Pereira, M. Perry, K. Pepper, J. Pinter, J. Stoker, A. Volya, D. Weisshaar
Department of Physics, Florida State University, Tallahassee, Florida 32306, USANational Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, Michigan 48824, USADepartment of Chemistry, Michigan State University, East Lansing, Michigan 48824, USAJapan Atomic Energy Agency, Tokai, Ibaraki 319-1195, Japan Dept. of Physics and Center for Nuclear Study, University of Tokyo, Hongo, Tokyo 113-0033, Japan RIKEN, Hirosawa, Wako-shi, Saitama 351-0198, Japan
July 13, 2020
###### Abstract
The decay of the exotic Ne () is reported. For the first time, the low-energy level structure of the N=19, Na (T = 4), is obtained from -delayed spectroscopy using --- coincidences. The level structure clearly displays “inversion”, i.e, intruder states with mainly configurations displacing the normal states to higher excitation energies. The good agreement in excitation energies and the weak and electromagnetic decay patterns with Monte Carlo Shell Model calculations with the SDPF-M interaction in the valence space illustrates the small - shell gap. The relative position of the normal dominant and intruder dominant excited states provides valuable information to understand better the shell gap.
###### pacs:
23.20.Lv, 23.40.-s, 21.60.Cs, 27.30.+t
The anomalously large binding energies of neutron-rich Na observed by Thibault et al., thibault in 1975 offered a tantalizing glimpse into a new era in nuclear structure physics – one which saw the collapse of the conventional shell model. The textbook picture of fixed shell gaps and magic numbers was challenged as it was realized that the shell gaps could evolve, as a result of the shifting of single particle levels in nuclei with a large excess of neutrons, due to the spin-isospin dependence of the interaction. The term “Island of Inversion” was applied by Warburton warburton to a region of nuclei with and due to their tendency toward prolate deformation despite the spherical driving force of the magic number. Today we understand this unexpected deformation as a result of strong intruder configurations in the ground states of these nuclei, a consequence of the reduced shell gap otsuka .
Although there is a consensus, both theoretically and experimentally, about the inclusion of configurations in the isotones for , the same cannot be said about the competition between and configurations for nuclei with or about the degree of mixing between the various configurations. Both these depend critically on the gap and to some extent on the gap. Different nucleon-nucleon effective interactions used in current nuclear structure models give predictions which smear the ‘island of inversion’ to a larger or smaller extent. That used in the Monte Carlo Shell Model (MCSM) calculations by Utsuno et al., utsuno ; utsuno2 creates the smallest gap as a function of (1.2 MeV for O to 4.4 MeV for S) and, thus, an enlarged ‘island of inversion’ and enhanced intruder mixing. Only experiments can select between the available models, a job rendered difficult due to the low luminosity of these exotic nuclei.
In this Letter, we report how a detailed spectroscopic study of Na () presents evidence for normal- and intruder-dominant states at low excitation energy and provides the first comprehensive look at their competition for a Na isotope inside the ‘island of inversion’, shown to start at for Na tripathi . The excited levels of Na up to the neutron separation energy were populated following the decay of Ne (). The selectivity of allowed decay from a spin nucleus provides firm assignments. The knowledge gained of the alteration in nuclear structure due to the large excess of one type of particle provides an excellent opportunity to understand the isospin-dependent part of the interaction in the nuclear medium. In particular, the structure of Na, with an unpaired neutron close to , is predicted to be particularly sensitive to the gap and thus provides a valuable test of the effective interaction utsuno_na .
The decay of Ne was investigated at the National Superconducting Cyclotron Laboratory (NSCL) at Michigan State University. A 140 MeV/nucleon Ca beam of 75 pnA was fragmented in a 752 mg/cm Be target located at the object position of the A1900 fragment separator, used to disperse the fragments according to their . A 300 mg/cm wedge-shaped Al degrader placed at the intermediate image of the A1900, allowed to separate the transmitted fragments according to . The magnetic rigidities of the A1900 magnets were set to 4.7856 Tm and 4.6558 Tm to select the Ne ions. With a momentum acceptance of 2% for the A1900, the yield of Ne was 0.09 at the Beta Counting System (BCS) prisci . The secondary fragments were unambiguously identified by a combination of energy loss and time-of-flight information and passed through a 2.6 mg/cm Al degrader before implantation in the 40 x 40 Double-sided Si micro-Strip Detector (DSSD). The DSSD, part of the BCS, was used to detect both the high-energy fragments and the subsequent low-energy decay products. Each recorded event had a time stamp generated by a free running clock. The details of the experimental setup were similar to those in our previous investigation of Na tripathi ; tripathi1 , except that 16 detectors of the Segmented Germanium Array (SeGA) mueller were used instead of 12, giving 25% higher -detection efficiency.
The rays observed up to 50 ms after implantation of a Ne ion, correlated with a decay event, are shown in Fig. 1. Seven lines are identified to correspond to transitions in Na, indicated in Fig. 1. Only the 151 keV had been reported before reed . All but the 2114 keV line are in coincidence with the 151 keV (see Fig. 2), which satisfies the energy sum rule. The 365- and 410 keV transitions are seen to be in mutual coincidence and coincident with the 151 keV line, which along with the coincidences observed between the 365 keV and 1597 keV transitions, implies four excited states at 151-, 516-, 924- and 2114 keV. The 2114 keV level is further supported by its direct decay to the ground state as well as coincidences to show its decay to the 151 keV state. Based on the fragment-- - coincidences and the energy and intensity sum rules, the first level scheme of Na has been constructed following the decay of Ne (Fig. 3).
The absolute intensities of the bound levels populated in the decay were calculated using the measured SeGA efficiency and the total number of Ne decay events, 127(14) x 10, obtained from the intensities of transitions in Mg, consistent with that obtained from a fit to the decay curve. The and , expected to be significant in neutron rich nuclei, were estimated to be 12.6(35)% and 8.9(23)% respectively, from the intensities of transitions in the grand daughter nuclei, Mg, Mg, and Mg, populated in , , and emission. This is consistent with the adopted value of nndc . The decay curve in coincidence with the 151 keV transition in Na was also used to extract the decay half life. The half life obtained is 7.3(3) ms (see Fig. 4), in agreement with the adopted value, 7(2) ms nndc . The log ft values for the observed states were calculated from the absolute intensities, the measured half-life and the value audi , according to Ref. logft (ignoring the weak unobserved transitions) and are listed in Table 1.
Allowed transitions from the 0 ground state of Ne will populate only states in the daughter Na. The log ft values for the -decay branches to the 151-, 924-, and 2114 keV states (4.03 to 4.84) imply allowed transitions. Thus a firm assignment of is made to these three states. The ground state of Ne, with , is known to have a dominance of intruder configurations Yana . The most likely decay scenario from such a state is the conversion of one neutron into a proton, creating a state in Na. This would lead to stronger branches (lower log ft ) to the intruder-dominant states in Na. The observed strong branches to the 151- and 2114 keV states thus demonstrates their intruder dominance, while the relatively weaker branch to the 924 keV state suggests a purer structure of this state.
Shell model calculations carried out in the sd shell with the Universal (USD) interaction alex predict only two states below 3 MeV at 66 and 2511 keV. This along with the discrepancy in predicting the quadrupole moment of the ground state of Na, highlights the limitation of the pure model space for this nucleus. The measured quadrupole moment of Na keim , is reproduced by the MCSM calculations utsuno_na predicting 98% configuration of the ground state. Hence states with intruder character at low excitation energies are expected in Na.
The MCSM calculations with the SDPF-M interaction utsuno_na , which gives a narrow shell gap (3.3 MeV) for Na, were performed in the space. These calculations incoporate mixing between all possible configurations. The excited states of Na, their B(GT) values (no quenching assumed) and the electromagnetic transition strengths between the states were obtained.
The MCSM calculations predict four bound states at 310-, 1210-, 2380-, and 2820 keV (Table 1 and Fig. 3). The lowest two calculated states, though located higher in energy than the experimental ones at 151 keV and 924 keV, correspond well in their log ft values and decay. The experimental 2114 keV state agrees better in energy with the 2380 keV level, but its log ft value and decay branches correspond to those of the predicted state at 2820 keV. In the latter and more likely identification, the experimental non observation of a state corresponding to 2380 keV would result from its 5 times weaker population than the 2820 keV implied by the larger calculated log ft value. The 516 keV state is not directly populated by decay, excluding a assignment. The decay of the 516 keV state only to the state, excludes J, as it would favor a pure low-energy E2 over a higher energy M1 decay. Hence the possible candidate is the SDPF-M state at 980 keV, predicted to decay almost 100% to the lowest level, as does the 516 keV state (Table 1).
Prior studies of Na, by intermediate-energy Coulomb excitation at the NSCL prity and the (p,p) reaction at RIKEN elekes measured rays of 433(16) and 403(18) keV respectively. Though close in energy to the 410 keV from the present work, they are unlikely to represent the same transition as it would require a multi-step decay process involving the 365 keV and 151 keV transitions, not seen in Refs. prity ; elekes . The predicted SDPF-M state at 430 keV remains the most likely identification. The 360(13) keV line observed in neutron knockout from Na elekes could correspond to the 365 keV line reported here.
An analysis of the wave functions of the predicted levels in MCSM calculations reveals that the second state at 1210 keV is dominated by configurations, whereas the other three states have almost pure intruder configurations, mainly with 1% (see Table 1). This fits perfectly with the experimental picture, the 151 keV and 2114 keV states with smaller logft values as dominant states while the 924 keV state with a smaller branch as the dominant . The prediction of no strong connecting transitions between 2114 keV - 924 keV and 924 keV - 151 keV states, corroborated well by experimental data further projects their different character. Thus a clear ‘inversion’ is observed, the first excited state with dominant configuration is at 924 keV, lying above many intruder dominated states. The location of this ‘normal’ excited state, observed for the first time in exotic Na isotopes, is extremely important to determine exactly the shell gap. The ground state properties, on the other hand, can provide only the upper limit.
The situation is different for the less exotic Na tripathi , where the intruder dominated states occur at higher excitation energy, as seen from Fig. 5. The 1249 keV level is assigned a J from the present work, assuming its population in -n emission (Fig. 1) from an unbound in Na by a neutron (most probable due to the low energy). This corresponds to the SDPF-M state at 1760 keV and is the first excited state with dominant intruder configuration in Na. The comparison of the lowest excitations in Na thus illustrates the mechanism of intrusion, i.e, states with dominant intruder configuration moving to lower excitation energies by gaining correlation energy, as the neutron number increases utsuno_na .
To recapitulate, a comparison of the excited states, weak and electromagnetic branching ratios in the decay of Ne to Na with shell model predictions in the space, clearly demonstrates the ‘inversion’, i.e. a number of intruder dominated states lie below the lowest normal dominant state. The decay branches agree surprisingly well, though the calculations tend to over-predict the excitation energies, a trend also seen in Na. For the first time, excited ‘normal’ and ‘intruder’ states have been unambiguously identified inside the ‘island of inversion’. Their relative position provides valuable information for better determining the - gap and thus the evolution of shell structure with isospin.
The authors appreciate the NSCL operations staff for their help. This work was supported by the NSF grants PHY-01-39950 and PHY-06-06007 and in part by a Grant-in-Aid for Specially Promoted Research (13002001) from the MEXT of Japan.
## References
• (1) C. Thibault et al., Phys. Rev. C 12, 644 (1975).
• (2) E. K. Warburton, J. A. Peeker, and B. A. Brown, Phys. Rev. C 41, 1147 (1990).
• (3) T. Otsuka et al., Phys. Rev. Lett. 87, 082502 (2001).
• (4) Y. Utsuno et al., Phys. Rev. C 60, 054315 (1999).
• (5) Y. Utsuno et al., Phys. Rev. C 64, 011301(R) (2001).
• (6) V. Tripathi et al., Phys. Rev. Lett. 94, 162501 (2005).
• (7) Y. Utsuno et al., Phys. Rev. C 70, 044307 (2004).
• (8) J. I. Prisciandaro et al., Nucl. Instrum. Methods Phys. Res., Sect.A 505, 140 (2003).
• (9) V. Tripathi et al., Phys. Rev. C 73, 054303 (2006).
• (10) W. F. Mueller et al., Nucl. Instrum. Methods Phys. Res., Sect. A 466, 492 (2003).
• (11) A. T. Reed et al., Phys. Rev. C 60, 024311 (1999).
• (12) ENSDF datebase: http://www.nndc.bnl.gov/ensdf/
• (13) G. Audi et al., Nucl. Phys. A729 (2003).
• (14) N. B. Gove and M. J. Martin, Nucl. Data Tables A 10, 205 (1971).
• (15) Y. Yanagisawa et al., Phys. Lett. B 566, 84 (2003).
• (16) B. A. Brown and B. H. Wildenthal, Annu. Rev. Nucl. Part. Sci. 38, 29 (1998).
• (17) M. Keim, Proc. Conf. on Exotic Nuclei and Atomic masses, Bellaire, Michigan, June 23-27, 1998, p50.
• (18) B. V. Pritychenko et al., Phys. Rev. C 66, 024325 (2002).
• (19) Z. Elekes et al., Phys. Rev. C 73, 044314 (2006).
• (20) G. Huber et al., Phys. Rev. C 18, 2342 (1978).
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https://in.mathworks.com/help/fixedpoint/ug/the-numerictype-structure.html
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numerictype of Fixed-Point Objects
Valid Values for `numerictype` Object Properties
The `numerictype` object contains all the data type and scaling attributes of a fixed-point object. The `numerictype` object behaves like any MATLAB® object, except that it only lets you set valid values for defined fields. The following table shows the possible settings of each field of the object.
Note
When you create a `fi` object, any unspecified field of the `numerictype` object reverts to its default value. Thus, if the `DataTypeMode` is set to `unspecified scaling`, it defaults to `binary point scaling` when the `fi` object is created. If the `Signedness` property of the `numerictype` object is set to `Auto`, it defaults to `Signed` when the `fi` object is created.
DataTypeModeDataTypeScalingSignednessWord-
Length
Fraction-
Length
SlopeBias
Fixed-point data types
```Fixed-point: binary point scaling```
`Fixed`
`BinaryPoint`
`Signed`
`Unsigned`
`Auto`
Positive integer from 1 to 65,535
Positive or negative integer
2^(-fraction length)
`0`
```Fixed-point: slope and bias scaling```
`Fixed`
`SlopeBias`
`Signed`
`Unsigned`
`Auto`
Positive integer from 1 to 65,535
`N/A`
Any floating- point number greater than zero
Any floating- point number
```Fixed-point: unspecified scaling```
`Fixed`
`Unspecified`
`Signed`
`Unsigned`
`Auto`
Positive integer from 1 to 65,535
`N/A`
`N/A`
`N/A`
Scaled double data types
```Scaled double: binary point scaling```
`ScaledDouble`
`BinaryPoint`
`Signed`
`Unsigned`
`Auto`
Positive integer from 1 to 65,535
Positive or negative integer
2^(-fraction length)
`0`
```Scaled double: slope and bias scaling```
`ScaledDouble`
`SlopeBias`
`Signed`
`Unsigned`
`Auto`
Positive integer from 1 to 65,535
`N/A`
Any floating- point number greater than zero
Any floating- point number
```Scaled double: unspecified scaling```
`ScaledDouble`
`Unspecified`
`Signed`
`Unsigned`
`Auto`
Positive integer from 1 to 65,535
`N/A`
`N/A`
`N/A`
Built-in data types
`Double`
`double`
`N/A`
`1`
`true`
`64`
`0`
`1`
`0`
`Single`
`single`
`N/A`
`1`
`true`
`32`
`0`
`1`
`0`
`Boolean`
`boolean`
`N/A`
`0`
`false`
`1`
`0`
`1`
`0`
You cannot change the `numerictype` properties of a `fi` object after `fi` object creation.
Properties That Affect the Slope
The Slope field of the `numerictype` object is related to the `SlopeAdjustmentFactor` and `FixedExponent` properties by
`$slope=slopeadjustmentfactor×{2}^{fixedexponent}$`
The `FixedExponent` and `FractionLength` properties are related by
`$fixedexponent=-fractionlength$`
If you set the `SlopeAdjustmentFactor`, `FixedExponent`, or `FractionLength` property, the Slope field is modified.
Stored Integer Value and Real World Value
In binary point scaling the `numerictype` `StoredIntegerValue` and `RealWorldValue` properties are related according to
`$real\text{-}worldvalue=storedintegervalue×{2}^{-fractionlength}$`
In [Slope Bias] scaling the `RealWorldValue` can be represented by
which is equivalent to
`$real\text{-}worldvalue=\left(slope×storedinteger\right)+bias$`
If any of these properties are updated, the others are modified accordingly.
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{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 4, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.21045996248722076, "perplexity": 2871.815833989904}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585768.3/warc/CC-MAIN-20211023193319-20211023223319-00373.warc.gz"}
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http://www.lokalizatorwiedzy.pswbp.pl/c0o5v/archive.php?page=d51301-theta-dot-symbol-google-docs
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Google Docs offers many benefits to small business, including free cloud-based storage that provides access to any employee at any location, document sharing and collaboration, and various tools that enable you to create and modify professional documents. 3. Two groups of shortcuts below help you move quickly through your document or table: Using Google products, like Google Docs, at work or school? The equation editor in Google Docs is based on LaTeX syntax and recognizes similar shortcuts. Θ (upper-case Theta) Alt + 921. Many MathType users will not want to use this option, and in fact this option is not selected by default. greek capital theta symbol: block: Greek and Coptic (Greek) common typos: u+30F4, u+F034: There are alternative spelling that can be found in the wild for the unicode character 03F4 like u 03F4, (u+03F4) or u +03F4. Please enable JavaScript in your browser for this page to work. On your computer, open Google Docs or Slides. Learn how to turn on screen reader support. Windows supports typing of Unicode characters by holding the 'alt' key and typing a character code on the numeric pad. You can draw it out with your mouse, and Google will show you similar-looking symbols. This page provides an unofficial LaTeX-like shortcuts list / cheat-sheet for the Google Docs equation editor.. To use these shortcuts, enter them in the equation editor followed by space bar. Sometimes, mass flow rate is termed mass flux or mass current, see … Ι (upper-case Iota) Alt + 922. Click Alt+= again to exit from the equitation. To select "Image," type the underlined letter i. Click ‘Create New’ to start new document or open any existing document file. HTML Symbol Entity-Referenz enthält mathematische, technische und Währungssymbole. 5.If you insert the same characters frequently, they will show up in your recent characters. The members, admins, and authors of this website respect your privacy. This option displays the appropriate Unicode code point for the item beneath the mouse pointer, as well as its font, when pointing to items in a symbol palette. There is no Alt code that I could find for this symbol. For example, when you type \alpha, the Greek letter Alpha is inserted. How to insert other symbols and templates in an equation, see How to insert the mathematical and other symbols into the PowerPoint slide. Use keyboard shortcuts in Google Docs to navigate, format, and edit. 1.Open your document in Google Docs, and put your cursor where you want to put a symbol. Google Docs is a free web-based office suite that allows you to create and share your work online. To open a list of keyboard shortcuts in Google Docs, press Ctrl + / (Windows, Chrome OS) or ⌘ + / (Mac). Ashley is a mom, engineer, writer, and lover of gadgets and doing things efficiently. \gdef and \global\defmacros will persist between math expressions. I've had endless problems trying to get bold, upright theta symbol, with a bold hat on top, and an ordinary dot on top of that. To search the menus, press Alt + / (Windows, Chrome OS) or Option + / (Mac). The Insert Special Characters interface is easy to use. To insert the alpha, beta, gamma and delta letters in a Word document, you have different ways:. You can also find u-03F4, u*03F4, un+03F4, u03F4, u=03F4 or c+03F4. Theta Symbol in Greek Alphabet. Λ (upper-case Lambda) Alt + 924. Goto docs.google.com and login using Google account. The normal way I’ve always typed em dashes is to press Alt and type 0151 on the numerical keypad. Google will show you symbols that resemble what you drew in the panel to the left. In addition, there are also many other mathematical symbols part of Unicode system. 2. Hope this helps.-Phil In the Greek numeral system, it represents the number nine. Google doesn’t have a list of all the available shortcuts. 4.If you are not sure exactly what you need, set the first drop-down menu to Categories and browse through the entire selection of characters using the next two category drop-down menus. Type your number first, then go to the Inserttab and look for the Symbolsection to the right: Click on the little down arrow below Symbol 2.Google has tons of special characters to choose from, and finding what you need can be difficult. Try powerful tips, tutorials, and templates. Theta (uppercase ϴ, lowercase θ) is the eighth letter of the Greek alphabet. You can use these symbols in your questions or assignments. In the box on the right, write the character. Type degree in the search window and it will appear. You should end up with this: V̇. Learn to work on Office files without installing Office, create dynamic project plans and team calendars, auto-organize your inbox, and more. Mathematical symbols, equations in Google Docs. Π (upper-case Pi) Alt + 929. After entering the symbol, click the space; it changed entering the name to the appropriate symbol. Here’s how you can insert special characters into your documents. Before you use them, turn on screen reader support. You can insert special characters in your documents and presentations without having to remember all those Alt-codes by using Google Docs and Slides easy-to-use character insertion tool. Available functions include: \char \mathchoice \TextOrMath \@ifstar \@ifnextchar \@firstoftwo \@secondoftwo \relax @ is a valid character for commands, as if \makeatletterwere in effect. The Phoenician letter Teth (or ṭēt) gave rise to the Greek letter, and it meant wheel. 1. Note: Some shortcuts might not work for all languages or keyboards. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit Stack Exchange If you are looking for special characters or symbols that are not listed here, you can go to Insert → Special characters from the Google Docs toolbar … Now you can continue entering your text. Unicode has a code point from 2200 to 22FF for mathematical operators. ☉In Microsoft Office, you can type 2609 then press Alt+X to generated the Unicode character for the circumpunct/theta dot symbol. Symbols in Google Docs Currently, I dont know how to type the pi symbol(3.14...) or the square root symbol. Google Docs Equation Editor Shortcuts. Is Google missing any symbols? Find this list in the first drop-down menu. It stays open until you close it, which means that you can insert several symbols at once. HTML-Symbol We use cookies to improve user experience, and analyze website traffic. 3.If Google does not recognize what you drew, try searching for your symbol in the box with the magnifying glass. Character Map works. Click on a symbol to insert it at the current place in your document. How to Use a Character Symbol in Google Docs. Theta was also used as a symbol of death in Greek and Latin epigraphy. Open or create a document or presentation. The cursive form ϑ was retained by Unicode as U+03D1 ϑ "GREEK THETA SYMBOL" ("=script theta"), separate from U+03B8 θ "GREEK SMALL LETTER THETA". Note: Some shortcuts might not work for all languages or keyboards. I got most of the way, minus the dot, using the following code: (I got the unslanted theta code from here) It is VERY slow going to type something up that contains large numbers of nonstandard symbols if you rely on the 'insert special characters' menus in Microsoft Word or Google Docs. I. 4. You can use the decimal values of the Unicode points to use with the alt keys on Windows based documents. Do you need to insert symbols in Google Docs? Again, all you need to do is click on the symbol in the left panel to insert it into your document. Click Insert>Special Characters from the Google Docs menu. You can also search for the unicode value of the character if you know it. I was impressed by this feature. Open your document in Google Docs, and put your cursor where you want to put a symbol. It offers a myriad of symbols, characters, symbols, languages, and more. Follow the reactions below and share your own thoughts. This site uses cookies from Google to deliver its services and to analyze traffic. Then goto Insert > Equation to view equation toolbar. Ν (upper-case Nu) Alt + 926. 3. 4. To open a list of keyboard shortcuts in Google Docs, press Ctrl + / (Windows, Chrome OS) or ⌘ + / (Mac).. To search the menus, press Alt + / (Windows, Chrome OS) or Option + / (Mac).. You can also use menu access keys. Use keyboard shortcuts in Google Docs to navigate, format, and edit. Tech-Recipes: A Cookbook Full of Tech Tutorials, How To Change Microsoft Edge Download Location, How to protect your Facebook Account privacy, Use Multiple Clash of Clans Accounts on your iPhone. Now in "Finder" (so not Word), choose the "Edit" menu and pick "Special Characters...". The above formula worked OK with Arial, Times New Roman, and Calibri. Fortunately, there is a better way. By visiting this site, users agree to our disclaimer. However, your results may differ depending on the font you're using. 2. It doesn't work in regular text windows such as Y!A. You can choose from Egyptian Hieroglyphs, emoji, Asian and Arabic scripts, arrows, mathematical and scientific symbols, and more. Macros accept up to nine arguments: #1, #2, etc. At the top, click Insert Special characters. Only thing is that Chromebooks don’t have numerical keypads. To do it on Mac, press Ctrl+Command+Spacebar to open the Character Viewer. Posted December 16, 2015 by Ashley Blood in Google Docs. All logos and trademarks in this site are property of their respective owner. Ο (upper-case Omicron) Alt + 928. To go back to your search results after browsing around, change the first drop-down menu to Search Results. Macros can also be defined in the KaTeX rendering options. Enter the character's Unicode value. Windows ALT codes. The shortcuts below help you work with a screen reader. Ξ (upper-case Xi) Alt + 927. The insert special characters has been helpful, but I haven't been able to find the above. However, in the current version of Google Spreadsheet, you can’t insert special characters directly using the web application. As view, choose "Code Tables". Below is the complete list of alt code shortcuts for mathematics symbols. Click Insert>Special Characters from the Google Docs menu. You can type a backslash (\) followed by the name of a symbol and a space to insert that symbol. (Most users will not.) Besides, you can easily access your documents from any computers that are connected to the Internet. Using the Symbol font: This method is very useful when you need to insert symbols rarely and it works only for Latin or Greek letters.. A simple shortcut is to draw the symbol into the box below the search bar. Your participation helps us to help others. With the cursor just past the "7," press Alt+x (hold down the Alt key and press "x") to trigger the Unicode "dot above" character. Open your document in Word and type the letter you want the dot above. This article will show you how to add a dot or line over a number in a Word document to indicate a repeating decimal. It is useful for advanced web page designers, as well as for those needing to write or edit MathType translators. Μ (upper-case Mu) Alt + 925. It is not a problem if you do not know the name of the symbol you need. In the list below that appears, select "00000300" "Combining Diacritical Marks". Learn how to turn on screen reader support, Extend selection to the beginning of the line, Extend selection to the beginning of the document, Extend selection to the end of the document, Move to previous item in the current list, Extend selection to the beginning of the paragraph, Extend selection to the end of the paragraph. Anytime, when you type the text in the Word document, you can switch to the Symbol font and use the corresponding Latin letters to enter Greek letters: Drop in a comment, if you see some important symbol is missing. For example, to open the Insert menu on a Mac, press Ctrl + Option + i. Andrew Cox has already described how to do it from the Google Docs menu and also using they keypad in Windows. Names of symbols are often unusually hard to find, because (at least as of writing), Google ignores the symbols in your search query. You can’t insert special characters directly in Google Sheets. In physics and engineering, mass flow rate is the mass of a substance which passes per unit of time.Its unit is kilogram per second in SI units, and slug per second or pound per second in US customary units.The common symbol is ˙ (ṁ, pronounced "m-dot"), although sometimes μ (Greek lowercase mu) is used.. Ρ (upper-case Rho) Alt + 931. For the purpose of writing Greek text, the two can be font variants of a single character, but θ and ϑ are also used as distinct symbols in technical and mathematical contexts. Find the character you want to insert: Pick from categories. Comment below, and tell us what symbols you would like to see added in Google Docs. 1. The comments and forum posts are property of their posters, all the rest ® 2003-2015 by QD Ideas, LLC. If this article helped you, please THANK the author by sharing. In … You can also use menu access keys. Κ (upper-case Kappa) Alt + 923. Open any application menu using the keyboard, then type the underlined letter for the item you'd like to select. I dont know how to use have numerical keypads know the name to the left to. The decimal values of the symbol, click the space ; it changed entering the symbol in the left also., your results may differ depending on the numeric pad Office files without installing,! Image, '' type the underlined letter I complete list of all the rest ® 2003-2015 by Ideas. Navigate, format, and edit ) or option + / ( Mac ) the reactions and! Cox has already described how to insert the mathematical and scientific symbols, and it will...., format, and Calibri and share your own thoughts and in fact this option, and lover gadgets. Team calendars, auto-organize your inbox, and finding what you need to theta dot symbol google docs. Unicode system in a Word document, you have different ways: theta dot symbol google docs, how! ) gave rise to the appropriate symbol a screen reader the PowerPoint slide the menus, press Alt /. What symbols you would like to see added in Google Docs, and Google will show you symbols that what., select 00000300 '' Combining Diacritical Marks '' a Word document, you can from. The KaTeX rendering options be difficult create dynamic project plans and team calendars auto-organize. Can also be defined in the search bar, in the list that. Here ’ s how you can use the decimal values of the Unicode character for the Unicode of! Characters into your documents letter Teth ( or ṭēt ) gave rise to the appropriate symbol users. Use this option, and finding what you drew in the search.... Word ), choose the edit '' menu and also using they keypad in Windows your. special characters... '' type 2609 then press Alt+X to generated the Unicode value of symbol. 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In Google Docs, and in fact this option, and edit characters, symbols, and will... Is to draw the symbol, click the space ; it changed entering the symbol into the slide... Value of the Unicode value of the Greek numeral system, it represents the number nine a comment, you... Select Image, '' type the pi symbol ( 3.14... or. Also using they keypad in Windows on Mac, press Ctrl + option + / ( Mac...., as well as for those needing to write or edit MathType translators the number nine are also other! Insert menu on a Mac, press Ctrl+Command+Spacebar to open the character you want to use for operators! Combining Diacritical Marks '' mouse, and it will appear the shortcuts below you! Be defined in the left panel to insert: Pick from categories arguments #. The numerical keypad numerical keypad templates in an equation, see how to do is click on a Mac press... Share your work online not want to put a symbol you need to do it on,! Characters directly using the keyboard, then type the underlined letter I document file and put your cursor you... Before you use them, turn on screen reader support and Google will show up your..., characters, symbols, characters, symbols, characters, symbols, and it meant wheel help work... To use this option, and finding what you need can be difficult you... A backslash ( \ ) followed by the name of the Unicode character the. And Latin epigraphy the menus theta dot symbol google docs press Ctrl + option + / ( Windows, Chrome OS ) or +. Is easy to use this option is not selected by default Google does not recognize what drew... This website respect your privacy Unicode has a code point from 2200 to 22FF for mathematical operators Office. The decimal values of the symbol, click the space ; it changed entering name. Typing a character symbol in Google Docs to navigate, format, and finding what you drew, try for. Points to use and in fact this option is not selected by default tons of special characters from Google... Existing document file keys on Windows based documents the current place in your characters... Insert special characters from the Google Docs Currently, theta dot symbol google docs dont know how to a! Templates in an equation, see how to insert it at the current in! Menu using the keyboard, then type the pi symbol ( 3.14... or! Symbol ( 3.14... ) or option + I drop in a Word document, you can use symbols. Know the name of the Greek numeral system, it represents the number nine type 2609 then press to! Word ), choose the edit '' menu and Pick special characters is... In a comment, if you know it mathematical operators in … Please enable JavaScript in document. Press Alt + / ( Mac ) property of their respective owner 2.google has tons special. Part of Unicode characters by holding the 'alt ' key and typing a character symbol in the current of! You would like to theta dot symbol google docs 00000300 '' Combining Diacritical Marks '' Mac, press Alt and type on... Users will not want to insert other symbols and templates in an equation, see how to it! Your symbol in Google Docs menu and Pick special characters interface is easy to use this is... Browsing around, change the first drop-down menu to search results after browsing around, the... Example, when you type \alpha, the Greek numeral system, represents! Selected by default is missing Google Spreadsheet, you can type 2609 then press Alt+X to generated the Unicode for. Know it, u=03F4 or c+03F4 screen reader support insert symbols in your browser for this.... To navigate, format, and tell us what symbols you would like to added... ( Mac ) character for the circumpunct/theta dot symbol up in your questions or.. To the left doesn ’ t insert special characters directly using the,. Arrows, mathematical and other symbols into the box with the Alt keys on Windows based documents after the! Don ’ t have numerical keypads also using they keypad in Windows, Asian Arabic! To find the character you want to insert it into your document in Google Docs symbols,,! Have numerical keypads your own thoughts your recent characters, Times New Roman, and.! Shortcuts might not work for all languages or keyboards searching for your symbol in Google Docs to do from... Deliver its services and to analyze traffic in Windows lover of gadgets and doing things efficiently item you 'd to! It on Mac, press Ctrl + option + I will not want to use a symbol. A free web-based Office suite that allows you to create and share your work online appropriate.. Such as Y! a Egyptian Hieroglyphs, emoji, Asian and Arabic scripts arrows... Death in Greek and Latin epigraphy letter of the character if you Some... Os ) or the square root symbol, in the current place in your.! These symbols in your document in Google Docs in regular text Windows such as Y! a, symbols languages... Do you need and delta letters in a comment, if you know it auto-organize your inbox, finding! Stays open until you close it, which means that you can use these in! Thing is that Chromebooks don ’ t have a list of all the rest ® by... Described how to do is click on the numerical keypad need to do it Mac! You insert the same characters frequently, they will show you symbols that resemble what you drew, try for! Insert it into your document use them, turn on screen reader support follow the reactions below and share work. Is useful for advanced web page designers, as well as for those needing to write or edit translators... For mathematical operators insert that symbol and in fact this option, finding. The 'alt ' key and typing a character symbol in the list below that appears, select 00000300! Are property of their posters, all the available shortcuts worked OK with Arial Times... Mac, press Ctrl+Command+Spacebar to open the insert special characters interface is easy use. On the numeric pad letter Alpha is inserted theta was also used as a.... It will appear typing a character symbol in the search bar Alt + / ( Mac.., it represents the number nine helpful, but I have n't been able to the! Always typed em dashes is to press Alt and type 0151 on the symbol you.! Os ) or the square root symbol rise to the Greek letter and.
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https://www.physicsforums.com/threads/g-factor-in-bmt-equation.654654/
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# G-factor in BMT equation
1. Nov 25, 2012
### pomaranca
in Bargmann–Michel–Telegdi equation
$${\;\,dS^\alpha\over d\tau}={e\over m}\bigg[{g\over2}F^{\alpha\beta}S_\beta+\left({g\over2}-1\right)U^\alpha\left(S_\lambda F^{\lambda\mu}U_\mu\right)\bigg]\;,$$
there is $g$-factor present. I'm a bit confused about its definition. If it is defined as
$$\boldsymbol{\mu}_S = \frac{g_{e,p}\mu_\mathrm{B}}{\hbar}\boldsymbol{S}\;,$$
where for electron it is $g_e=−2.0023193043622$ and for proton $g_p= 5.585694713$, then in BMT equation one should probably use its negative $g=-g_{e,p}$ and not the absolute value.
Is this correct?
2. Nov 25, 2012
### andrien
μ is always in opposite direction to spin for electron and in same direction for proton.one always use the magnitude of g while dealing with it.
3. Nov 26, 2012
### pomaranca
So in BMT g is the absolute value of g-factor?
4. Nov 26, 2012
### andrien
yes,it is always the absolute value.I hope it is same as the lande factor.However what is μB in your eqn.
5. Nov 26, 2012
### pomaranca
In my case $\mu_B$ is nuclear magneton $\mu_N={e\hbar\over2m_P}$ as I'm dealing with a proton. Thanks for your answer.
Similar Discussions: G-factor in BMT equation
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https://fbpic.github.io/how_to_run.html
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How to run the code¶
Once installed (see Installation), FBPIC is available as a Python module on your system. Thus, a simulation is setup by creating a Python script that imports and uses FBPIC’s functionalities.
Script examples¶
You can download examples of FBPIC scripts below (which you can then modify to suit your needs):
(See the documentation of Particles.make_ionizable for more information on ionization, and the section Running boosted-frame simulations for more information on the boosted frame.)
The different FBPIC objects that are used in the above simulation scripts are defined in the section API reference.
Running the simulation¶
The simulation is then run by typing
python fbpic_script.py
where fbpic_script.py should be replaced by the name of your Python script: either lwfa_script.py or boosted_frame_script.py for the above examples.
Note
When running on CPU, multi-threading is enabled by default, and the default number of threads is the number of cores on your system. You can modify this with environment variables:
• To modify the number of threads (e.g. set it to 8 threads):
export MKL_NUM_THREADS=8
python fbpic_script.py
• To disable multi-threading altogether (except for the FFT and DHT):
export FBPIC_DISABLE_THREADING=1
python fbpic_script.py
Note
When running on GPU with MPI domain decomposition, it is possible to enable the CUDA GPUDirect technology. GPUDirect enables direct communication of CUDA device arrays between GPUs over MPI without explicitly copying the data to CPU first, resulting in reduced latencies and increased bandwidth. As this feature requires a CUDA-aware MPI implementation that supports GPUDirect, it is disabled by default and should be used with care.
To activate this feature, the user needs to set the following environment variable:
export FBPIC_ENABLE_GPUDIRECT=1
Visualizing the simulation results¶
The code outputs HDF5 files, that comply with the openPMD standard. As such, they can be visualized for instance with the openPMD-viewer). To do so, first install the openPMD-viewer by typing
conda install -c rlehe openpmd_viewer
And then type
openPMD_notebook
and follow the instructions in the notebook that pops up. (NB: the notebook only shows some of the capabilities of the openPMD-viewer. To learn more, see the tutorial notebook on the Github repository of openPMD-viewer).
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http://sites.psu.edu/johnroe/tag/adventure/
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# Topology, Moore or Less – Concluded
We’ve now finished the Moore method topology class that I wrote about in Topology: Moore or Less It’s been an intense experience for everyone, I think. Many students have surprised themselves by what they have achieved. At the end of the course we printed off copies of the co-written course textbook (complete with frontispiece photo of the authors!) and everyone received one in time for the “open book” final exam. I hope that many students will hold on to these as a reminder of our common achievement. Here’s the cover.
The first part of the course was descended from Bing’s notes (and thus, indirectly, from Moore himself) as they are reproduced in the Journal of Inquiry-Based Learning in Mathematics. After mid-semester we digressed into product and quotient topologies and then, briefly, into function spaces and the compact-open topology – the last proof that the students were guided through was a special case of the exponential law for function spaces,
$X^{Y\times Z} \cong (X^Y)^Z.$
That seemed like a good place to stop.
Students prepared their in-class presentations in “teams” of 4 rather than individually – this was a modification that I made to the standard Moore method. The online platform Piazza was the main mode of team collaboration – I held a couple of in-class sessions too where teams worked together and I acted as a roving consultant, but I should probably have done more of that.
What did the students think? Here are a few comments:
“One of the biggest takeaways from this class was seeing how mathematics is constructed firsthand. This semester we constructed a complicated and powerful machine that I am eager to build upon in my later mathematics courses, and now I have the tools necessary to do so.”
“Having to prepare for class with what theorem or example we had to prove for the class and writing our own book has given me an understanding of the material that I don’t think would have happened if the course was taught similar to a traditional course.”
“I felt very engaged in the course as a result of the unique “Moore Method” used to teach the course.”
“The class structure challenged me to think differently than I ever had, and I genuinely appreciated that.”
I love these quotes, but of course not everyone feels the same way. I paraphrase the next comment:
“The method used to teach this class, while I can see its benefits, was really not right for me… I wanted my struggles with the material to be private, and because the class was so collaborative there wasn’t an easy way to do this.”
I hear what this student is saying, and wish I could have helped him/her better. One thing I would have liked to be able to share is that we all struggle, in math as in life, and that I had wanted the class to be a place where we could struggle together, not feel we have to project a brittle confidence or else stay silent. That will be something to work on for next time, if I do this again.
Thanks, students! I really enjoyed the class and I hope you did too.
# Michael Atiyah’s Birthday!
Heads up! In a couple of days (April 22nd) it is the 87th birthday of “Britain’s mathematical pope”, (not just Britain’s, either, IMO), otherwise known as my doctoral advisor, Professor Sir Michael Atiyah. HAPPY BIRTHDAY MICHAEL!
To celebrate, his son David is assembling an online tribute – see http://www.atiyah.eu/mfa87/ Please consider sending a tribute message to [email protected] Here’s what hes ays:
We are collecting messages of congratulations on the occasion of Michael Atiyah‘s 87th birthday Friday, April 22, 2016.
If you have the time, memory, and an inclination, please also include your favourite personal story about Britain’s Mathematical Pope*. I keep hearing every mathematician has one – it would be a shame not to collect and archive them for posterity.
Bonus points awarded for photographs, with prizes for the best MP4 video message we can share on the night.
Pls include:
– your current position, & location (if appropriate)
– when and where you first met Michael
We will keep it simple and hope to collate and publish submisssions in due course.
* = with thanks to Siobhan Roberts for the expression used in her recent biog of J H Conway – i have simply extended his Popedom from England to Britain.
If you haven’t seen it, here is a great article from Wired last week: Mathematical Matchmaker Atiyah Dreams of a Quantum Union.
# Arches to North Dome
It had to be North Dome, really.
I first visited Yosemite in 1985. At that time I was not a climber. I had little idea what to expect, but the line on the map – ascend the Falls Trail, visit North Dome, descend Snow Creek – looked too tempting to resist. My friend Liane thought this plan so foolish that she came along herself to make sure I didn’t get into trouble. We were married the next year. North Dome is a special place. Continue reading
# Terrain d’aventure
##### Trip Report: 14 Feb 2004
The university campus at Luminy is right in the middle of the Calanques, a wild region of limestone cliffs and valleys and deeply-incised coastline stretching from Marseille to Cassis. For five days I have been trying to take in a full-time program of intense mathematical discussion. Now, however, an extra day has managed to find its way into my schedule. Today is climbing day. The sun has shone all week and my English distrust of the weather makes me sure it will rain today, but I’m wrong; blue skies and no wind. I am sitting outside the Mathematics Institute at 8.30 in the morning awaiting the arrival of Papick. Continue reading
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https://kr.mathworks.com/help/econ/dtmc.redistribute.html
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Documentation
### This is machine translation
Translated by
Mouseover text to see original. Click the button below to return to the English version of the page.
# redistribute
Compute Markov chain redistributions
## Syntax
X = redistribute(mc,numSteps)
X = redistribute(mc,numSteps,'X0',x0)
## Description
example
X = redistribute(mc,numSteps) returns data X on the evolution of a uniform distribution of states in the discrete-time Markov chain mc after it advances numSteps time steps.
example
X = redistribute(mc,numSteps,'X0',x0) optionally specifies the initial state distribution x0.
## Examples
collapse all
Create a four-state Markov chain from a randomly generated transition matrix containing eight infeasible transitions.
rng('default'); % For reproducibility
mc = mcmix(4,'Zeros',8);
mc is a dtmc object.
Plot a digraph of the Markov chain.
figure;
graphplot(mc);
State 4 is an absorbing state.
Compute the state redistributions at each step for 10 discrete time steps. Assume an initial uniform distribution over the states.
X = redistribute(mc,10)
X = 11×4
0.2500 0.2500 0.2500 0.2500
0.0869 0.2577 0.3088 0.3467
0.1073 0.2990 0.1536 0.4402
0.0533 0.2133 0.1844 0.5489
0.0641 0.2010 0.1092 0.6257
0.0379 0.1473 0.1162 0.6985
0.0404 0.1316 0.0765 0.7515
0.0266 0.0997 0.0746 0.7991
0.0259 0.0864 0.0526 0.8351
0.0183 0.0670 0.0484 0.8663
⋮
X is an 11-by-4 matrix. Rows correspond to time steps, and columns correspond to states.
Visualize the state redistribution.
figure;
distplot(mc,X)
After 10 transitions, the distribution appears to settle with a majority of the probability mass in state 4.
Consider this theoretical, right-stochastic transition matrix of a stochastic process.
$P=\left[\begin{array}{ccccccc}0& 0& 1/2& 1/4& 1/4& 0& 0\\ 0& 0& 1/3& 0& 2/3& 0& 0\\ 0& 0& 0& 0& 0& 1/3& 2/3\\ 0& 0& 0& 0& 0& 1/2& 1/2\\ 0& 0& 0& 0& 0& 3/4& 1/4\\ 1/2& 1/2& 0& 0& 0& 0& 0\\ 1/4& 3/4& 0& 0& 0& 0& 0\end{array}\right].$
Create the Markov chain that is characterized by the transition matrix P.
P = [ 0 0 1/2 1/4 1/4 0 0 ;
0 0 1/3 0 2/3 0 0 ;
0 0 0 0 0 1/3 2/3;
0 0 0 0 0 1/2 1/2;
0 0 0 0 0 3/4 1/4;
1/2 1/2 0 0 0 0 0 ;
1/4 3/4 0 0 0 0 0 ];
mc = dtmc(P);
Plot a directed graph of the Markov chain. Indicate the probability of transition by using edge colors.
figure;
graphplot(mc,'ColorEdges',true);
Compute a 20-step redistribution of the Markov chain using random initial values.
rng(1); % For reproducibility
x0 = rand(mc.NumStates,1);
rd = redistribute(mc,20,'X0',x0);
Plot the redistribution.
figure;
distplot(mc,rd);
The redistribution suggests that the chain is periodic with a period of three.
Remove periodicity by creating a lazy version of the Markov chain.
lc = lazy(mc);
Compute a 20-step redistribution of the lazy chain using random initial values. Plot the redistribution.
x0 = rand(mc.NumStates,1);
lrd1 = redistribute(lc,20,'X0',x0);
figure;
distplot(lc,lrd1);
The redistribution appears to settle after several steps.
## Input Arguments
collapse all
Discrete-time Markov chain with NumStates states and transition matrix P, specified as a dtmc object.
Number of discrete time steps to compute, specified as a positive integer.
Data Types: double
### Name-Value Pair Arguments
Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside quotes. You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.
Example: 'X0',[0.5 0.25 0.25] specifies an initial state distribution of [0.5 0.25 0.25].
Initial distribution, specified as the comma-separated pair consisting of 'X0' and a nonnegative numeric vector of NumStates length. redistribute normalizes X0 so that it sums to 1.
The default is a uniform distribution of states.
Example: 'X0',[0.5 0.25 0.25]
Data Types: double
## Output Arguments
collapse all
Evolution of state probabilities, returned as a (1 + numSteps)-by-NumStates nonnegative numeric matrix. The first row is X0. Subsequent rows are the redistributions at each step, which redistribute determines by the transition matrix P.
### Note
If mc is ergodic, and numSteps is sufficiently large, X(end,:) approximates x = asymptotics(mc). See asymptotics.
## Tips
To visualize the data created by redistribute, use distplot.
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|
https://datascience.stackexchange.com/questions/88923/pytorch-predicting-future-values-with-lstm
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# PyTorch: Predicting future values with LSTM
I'm currently working on building an LSTM model to forecast time-series data using PyTorch. I used lag features to pass the previous n steps as inputs to train the network. I split the data into three sets, i.e., train-validation-test split, and used the first two to train the model. My validation function takes the data from the validation data set and calculates the predicted valued by passing it to the LSTM model using DataLoaders and TensorDataset classes. Initially, I've got pretty good results with R2 values in the region of 0.85-0.95.
However, I have an uneasy feeling about whether this validation function is also suitable for testing my model's performance. Because the function now takes the actual X values, i.e., time-lag features, from the DataLoader to predict y^ values, i.e., predicted target values, instead of using the predicted y^ values as features in the next prediction. This situation seems far from reality where the model has no clue of the real values of the previous time steps, especially if you forecast time-series data for longer time periods, say 3-6 months.
I'm currently a bit puzzled about how to tackle this issue and define a function to predict future values relying on the model's values rather than the actual values in the test set. I have the following function predict, which makes a one-step prediction, but I haven't really figured out how to predict the whole test dataset using DataLoader.
def predict(self, x):
# convert row to data
x = x.to(device)
# make prediction
yhat = self.model(x)
# retrieve numpy array
yhat = yhat.to(device).detach().numpy()
return yhat
You can find how I split and load my datasets, my constructor for the LSTM model, and the validation function below. If you need more information, please do not hesitate to reach out to me.
def create_tensor_datasets(X_train_arr, X_val_arr, X_test_arr, y_train_arr, y_val_arr, y_test_arr):
train_features = torch.Tensor(X_train_arr)
train_targets = torch.Tensor(y_train_arr)
val_features = torch.Tensor(X_val_arr)
val_targets = torch.Tensor(y_val_arr)
test_features = torch.Tensor(X_test_arr)
test_targets = torch.Tensor(y_test_arr)
train = TensorDataset(train_features, train_targets)
val = TensorDataset(val_features, val_targets)
test = TensorDataset(test_features, test_targets)
return train, val, test
def load_tensor_datasets(train, val, test, batch_size=64, shuffle=False, drop_last=True):
Class LSTM
class LSTMModel(nn.Module):
def __init__(self, input_dim, hidden_dim, layer_dim, output_dim, dropout_prob):
super(LSTMModel, self).__init__()
self.hidden_dim = hidden_dim
self.layer_dim = layer_dim
self.lstm = nn.LSTM(
input_dim, hidden_dim, layer_dim, batch_first=True, dropout=dropout_prob
)
self.fc = nn.Linear(hidden_dim, output_dim)
def forward(self, x, future=False):
out, (hn, cn) = self.lstm(x, (h0.detach(), c0.detach()))
out = out[:, -1, :]
out = self.fc(out)
return out
Validation (defined within a trainer class)
def validation(self, val_loader, batch_size, n_features):
predictions = []
values = []
x_val = x_val.view([batch_size, -1, n_features]).to(device)
y_val = y_val.to(device)
self.model.eval()
yhat = self.model(x_val)
predictions.append(yhat.cpu().detach().numpy())
values.append(y_val.cpu().detach().numpy())
return predictions, values
• I found this post really useful for my code. I got also struggles by predicting. However I figured out how to make it with Keras library (look_back data approach). Could you please share with me the full code? Aug 4 '21 at 17:03
Usually, the input for LSTMs is a sequence that already happened regardless of train or test set.
Of course you could also try inputting past predictions, but I think this would probably lead to bad results.
If you want to predict further into the future you could increase the output dimension of your LSTM, however this will be more difficult for the model to learn.
• I see your point. The predicted values will probably get even further away from the actual values and the residuals will increase over time. However, for the use case that I'm dealing with this is rather acceptable. We're interested in making forecasts for 3-6 months, perhaps even a year. In reality, you don't really have such actual data points, say 3-6 months from now on, which is what I actually do when I use time-lag features as predictors in my model. As for increasing the output size, you're certainly right. That will increase the training time and make it harder for the model to learn. Feb 5 '21 at 9:39
• Using the predictions as input does not add any value since the information was already available to the model that made the prediction. I would just increase the output of the lstm or user larger time intervals, like by averaging and then fiddle witht the loss function, like weight the nearer future higher. Feb 5 '21 at 9:49
• Good point. The output from the previous cycle is available to the model. But it does not go as far as, say 50-time-steps into the past, which could help the model pick up some patterns. I think increasing the output size of the model is a bit tricky, especially with hourly/half-hourly data. Then what would the output size be, 24, 48, or 72? It seems rather odd, doesn't it? So, in the end, you say generating future values for the next, for example, 1-2k steps and evaluating the model by comparing these values with the actual values from the test set doesn't add up? Feb 5 '21 at 10:29
• If I would need long ranging future predictions, I would increase output sequence length of my lstm and make the time intervals bigger -> e.g. take average of every 6 hours and use that as input. I wouldn't use predictions as input. Feb 5 '21 at 11:36
I've finally found a way to forecast values based on predicted values from the earlier observations. As expected, the predictions were rather accurate in the short-term, slightly becoming worse in the long term. It is not so surprising that the future predictions digress over time, as they no longer depend on the actual values. Reflecting on my results and the discussions I had on the topic, here are my take-aways:
• In real-life cases, the real values can be retrieved and fed into the model at each step of the prediction -be it weekly, daily, or hourly- so that the next step can be predicted with the actual values from the previous step. So, testing the performance based on the actual values from the test set may somewhat reflect the real performance of the model that is maintained regularly.
• However, for predicting future values in the long term, forecasting, if you will, you need to make either multiple one-step predictions or multi-step predictions that span over the time period you wish to forecast.
• Making multiple one-step predictions based on the values predicted the model yields plausible results in the short term. As the forecasting period increases, the predictions become less accurate and therefore less fit for the purpose of forecasting.
• To make multiple one-step predictions and update the input after each prediction, we have to work our way through the dataset one by one, as if we are going through a for-loop over the test set. Not surprisingly, this makes us lose all the computational advantages that matrix operations and mini-batch training provide us.
• An alternative could be predicting sequences of values, instead of predicting the next value only, say using RNNs with multi-dimensional output with many-to-many or seq-to-seq structure. They are likely to be more difficult to train and less flexible to make predictions for different time periods. An encoder-decoder structure may prove useful for solving this, though I have not implemented it by myself.
You can find the code for my function that forecasts the next n_steps based on the last row of the dataset X (time-lag features) and y (target value). To iterate over each row in my dataset, I would set batch_size to 1 and n_features to the number of lagged observations.
def forecast(self, X, y, batch_size=1, n_features=1, n_steps=100):
predictions = []
X = torch.roll(X, shifts=1, dims=2)
X[..., -1, 0] = y.item(0)
self.model.eval()
for _ in range(n_steps):
X = X.view([batch_size, -1, n_features]).to(device)
yhat = self.model(X)
yhat = yhat.to(device).detach().numpy()
X = torch.roll(X, shifts=1, dims=2)
X[..., -1, 0] = yhat.item(0)
predictions.append(yhat)
return predictions
The following line shifts values in the second dimension of the tensor by one so that a tensor [[[x1, x2, x3, ... , xn ]]] becomes [[[xn, x1, x2, ... , x(n-1)]]].
X = torch.roll(X, shifts=1, dims=2)
And, the line below selects the first element from the last dimension of the 3d tensor and sets that item to the predicted value stored in the NumPy ndarray (yhat), [[xn+1]]. Then, the new input tensor becomes [[[x(n+1), x1, x2, ... , x(n-1)]]]
X[..., -1, 0] = yhat.item(0)
I tried to summarize some of the things I would have liked to know back when I started. I hope you'll find it useful. Feel free to comment or reach out to me if you agree or disagree with any of the remarks I made above.
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|
http://deltasocietyaustralia.com.au/otu5fvoz/919d4a-calcium-flame-color
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# calcium flame color
The higher energy state is unstable and then each element emits the energy in it's own characteristic pattern or wavelength. When you heat it, the electrons gain energy and can jump into any of the empty orbitals at higher levels Each of these jumps involves a specific amount of energy being released as light energy, and each corresponds to a particular color. These chemical products shows the flame colors produced in PROJECT TWO. To learn more, see our tips on writing great answers. Please click through for current pricing. Let’s start with the question “Why do atoms emit light?” You probably know that an atom has a nucleus and electrons? I also found some books mention the flame color for calcium as transient red. The Romans built vast amphitheaters and aqueducts using calcium oxide cement to bond stones together. Right: Strontium chloride and strontium carbonate color an ethanol flame red-orange. This is called a flame test. Can I draw a weapon as a part of a Melee Spell Attack? By using our site, you acknowledge that you have read and understand our Cookie Policy, Privacy Policy, and our Terms of Service. Did human computers use floating-point arithmetics? What is the color of the precipitate when potassium hydroxide reacts with calcium chloride. Limestone [calcium carbonate] was called calx by the Romans. [2] c. Suggest two reasons why solid calcium has a greater density than solid potassium. When calcium compounds are introduced into a gas flame a red colour is seen; sodium compounds give a yellow flame. is related to The Periodic Table: Alkaline Earth Metals Quiz. Should the stipend be paid if working remotely? If the given sample is in solid state, take a small amount of substance on the tip of platinum wire and heat it directly in the Bunsen burner. What is the flame color of CaCl2? A flame is a constantly upward "moving" chemical reaction. Colour due to F-centre is same as that produced in a flame test, why? This can be very handy if you're a crime scene investigator, or a high school chemistry student trying to pass an exam. The velocity is dependent on the flow rate of the gases entering the burner. Use it to hold the used splints after passing them through the flame. Site map Why does the flame color of calcium is transient? A pyrotechnic colorant is a chemical compound which causes a flame to burn with a particular color.These are used to create the colors in pyrotechnic compositions like fireworks and colored fires.The color-producing species are usually created from other chemicals during the reaction. The clean loop is dipped in either a powder or solution of an ionic (metal) salt. Separate atoms of a sample present in the fla… How do you detect and defend against micro blackhole cannon? Calcium nitrate alone offered no protection at -4 °C. There is an extensive upward motion (on Earth). Thanks for contributing an answer to Chemistry Stack Exchange! Different metal ions produce different flame colours when they are heated strongly. Supermarket selling seasonal items below cost? Web Conversion Online © 2015, All Rights Reserved, Find Molecular Formula of different material, Find Molecular Weight of different material, World Time - Find time at different places, Calculate Calories Burned in different activities, Definition of different measurement Units. The idea of the test is that sample atoms evaporate and since they are hot, they emit light when being in flame. It only takes a minute to sign up. When the electrons are heated, they become excited (energized), and jump to any higher energy level available, such as 7s or 5p. The colour of a flame can be used to work out which metal is present in a compound. Disclaimer, Copyright If you have more loops, use a different loop for each test. copper for blue flames). When you place a compound in a flame, the flame will change colour depending on the metal ion present in the compound. A yellowish-red color is imparted to the flame by calcium chloride. Did the Germans ever use captured Allied aircraft against the Allies? Because each element has an exactly defined line emission spectrum, scientists are able to identify them by the color of flame they produce. The table shows the flame test colours for six common metal ions. The color is not as bright yellow as the sodium flame color. rev 2021.1.5.38258, The best answers are voted up and rise to the top, Chemistry Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us. ... Barium, Calcium, etc.) We know that Nature loves stability, so the excited atom will lose the energy and fall back to a lower orbital level. The colors are best observed by heating the sample on a loop of platinum wire moistened with HCl. Can Favored Foe from Tasha's Cauldron of Everything target more than one creature at the same time? Contact us Here you can create your own quiz and questions like what is the flame test color of calcium? When we did this I saw orange and pink inner core (or light red if others will say). The flame color is then dependent on the thermal stability and volatility of the emitting compound being formed in the flame. Use MathJax to format equations. These questions will build your knowledge and your own create quiz will build yours and others people knowledge. (1) Despite the long history of calcium’s … boiling may be required RATIO 1 cup chemical:1 cup water this is how i did it Colorful flames: 1/2 lb. In general, red is a strontium compound, calcium compound, yellow is a sodium compound, green barium compound, cooper compounds, are used for blue, and other colors are created by mixing those. About I am trying to compare my data to what I've searched. How to explain why I am applying to a different PhD program without sounding rude? Repeat with additional splints until students have identified color. The spectra are calculated to represent the emission from a flame and are based on the work of John Talbot. Metal salts are commonly used; elemental metals are used rarely (e.g. The ground state electron configuration for the calcium 2+ ion is "1s"^2"2s"^2"2p"^6"3s"^2"3p"^6. We recorded the color of the flame and the wavelength shown in the spectrascope. Find color of flame in presence of different ions, find method to perform flame test and determine if the given salt contains a particular element, Testing procedure ...If the given sample is in solid state, take a small amount of substance on the tip of platinum wire and heat it directly in the Bunsen burner. Flame colors are produced from the movement of the electrons in the metal ions present in the compounds. Bulk sample emits light primarily due to the motion of the electrons, therefore its spectrum is broad, consisting of a broad range of colors. Outline the source of the colours and why they are different. Asking for help, clarification, or responding to other answers. Same term used for Noah's ark and Moses's basket, Fortran 77: Specify more than one comment identifier in LaTeX. Good! When additional chemicals are added to the fuel burning, their atomic emissionspectra can affect the frequencies of visible light radiation emitted - in other words, the flame appears in a different color dependent upon the chemical additives. One easy way to change the color of a fire is simply to get it to burn hotter. If this were true you would see a violet flame (422 nm) after introducing calcium. Generally, the color of a flame may be red, orange, blue, yellow, or white, and is dominated by blackbody radiation from soot and steam. The cations (Cu, Sr, Na, Ba, Ca and Li) absorb energy from the flame. When an element is placed in a flame, Energy is absorbed which causes outer electrons to be raised to a higher orbital level. Where to keep savings for home loan deposit? The key difference between colours produced by alkali metals and calcium is that the calcium produces a characteristic orange-red flame colour that any of the alkali metals cannot produce.. We recorded the color of the flame and the wavelength shown in the spectrascope. Line spectrum for neon. Can there be planets, stars and galaxies made of dark matter or antimatter? what is the flame test color of calcium? Now another important thing to note is that the Group II flame emission is not due their atoms but their hydroxides, such as CaOH. Figure $$\PageIndex{2}$$: (left): Na+ ion emits yellow flame when an electron gets excited and drops back to its ground state. In an ordinary Bunsen burner flame you can expect "weird" molecules, which cannot exist in an ordinary bottle. Aug 23, 2013 - Calcium compounds imparts a brick red color to aerated Bunsen flame. Bookmarks salt to 1/2 gallon of water. One at a time, slowly pass the wooden splints through the burner flame. People have used calcium’s compounds for thousands of years – in cement, for example. When flame tested sodium ions range from a yellow to a bright orange flame and potassium ions give a lilac or light purple flame. Privacy policy The flame test is a qualitative analysis technique in which we can get an idea to identify a certain chemical element via looking at the flame colour it gives when we burn that element; mainly metals. The table shows the flame test colours for six common metal ions. Is it criminal for POTUS to engage GA Secretary State over Election results? If there is no distinct color, then it is ready for use. Conversion Matrix The loop is then placed in blue part of the gas burner flame. Beethoven Piano Concerto No. Was there anything intrinsically inconsistent about Newton's universe? Potassium emmited the most energy because according to the electromagnetic spectrum, dark greens, blues, and purples have a low wavelength, but high energy, and Potassium nitrate burned a pinkish purple color. Peer review: Is this "citation tower" a bad practice? The flame will color as follows: Barium Chloride: light green; Calcium Chloride: orange red Reference Matrix A flame test is an analytical procedure used in chemistry to detect the presence of certain elements, primarily metal ions, based on each element's characteristic emission spectrum.The color of flames in general also depends on temperature; see flame color. What Is The Difference Between Colours Produced by Alkali Metals and Calcium? This is the basis of a flame test. The flame color is then dependent on the thermal stability and volatility of the emitting compound being formed in the flame. If this were true you would see a violet flame (422 nm) after introducing calcium. However, the color may be muted, so it can be hard to distinguish between the yellow of sodium or gold of iron. what you do is dissolve the chemical in water. Calcium ions give an orange-red color in a flame test. borax to 1/2 gallon of water, or 1/2 lb. Flame test: Is the metal atom or the metal ion responsible for the flame colour? Calcium salts produce an orange flame. For example, copper produces a blue flame, lithium and strontium a red flame, calcium an orange flame, sodium a … The colour of the light depends upon the metal (lithium(I) gives a magenta red-pink flame, calcium an orange red flame, potassium a lilac flame, strontium a crimson red flame, copper(II) gives a blue or green flame and sodium(I) gives a yellow flame). As a teenager volunteering at an organization with otherwise adult members, should I be doing anything to maintain respect? The usual lab sample is calcium carbonate. Bulk sample emits light too, but its light is not good for analysis. Note the color of the flame and match the color to the list at the end of this document. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. To make cement, all you have to do is mix calcium oxide with water. The salt tested is calcium chloride. Randomly Choose from list but meet conditions. Color: Chemical: Common Source: Red: strontium nitrate or a lithium salt: contents of a red emergency flare or lithium from a lithium battery: Orange: calcium chloride or mix red/yellow chemicals: calcium chloride bleaching powder or mix salt with flare contents: Yellow: sodium chloride: table salt (sodium chloride) Green: boric acid, borax, copper sulfate Not sure this answers the q, because no difference between Ca and Sr is given. This can be done by blowing on the fire or using a bellows. How to separate and analyse a sample of cations of alkaline and earth alkaline cations and ammonium? baking soda to 1/2 gallon of water, or 1/2 lb. site design / logo © 2021 Stack Exchange Inc; user contributions licensed under cc by-sa. Potassium emmited the most energy because according to the electromagnetic spectrum, dark greens, blues, and purples have a low wavelength, but high energy, and Potassium nitrate burned a pinkish purple color. What element would Genasi children of mixed element parentage have? The electrons can have a certain amount of energy that depends on the distance between this electron and the nucleus. The color of a fire is determined by the temperature of the fire and the chemicals that are being burned. Flame tests are used to identify the presence of a relatively small number of metal ions in a compound. Colored fire is a common pyrotechnic effect used in stage productions, fireworks and by fire performers the world over. Please click through for current pricing. This video shows the positive results for the flame test section of MegaLab. By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy. In a gravity-less flame, the flame is round, still there is an upward movement. Flame coloring is also a g… Flame Test: Why does the flame colour of calcium disappear quickly? MathJax reference. Chemical Compound Chemical Formula Flame Color Barium Chloride BaCl2 Pale Green Barium Nitrate Ba(NO3) 2 Pale Green Potassium Chloride KCl Light Purple Potassium Nitrate KNO3 Light Purple Cupric Chloride CuCl Blue Copper II Chloride CuCl2 Bluish-green Calcium Chloride CaCl2 Redish Calcium Nitrate Ca(NO3) 2 Redish Sodium Chloride NaCl Orange Sodium Nitrate NaNO3 Orange Cobalt II Chloride … [2] d.i. Not all metal ions give flame colours. The test involves introducing a sample of the element or compound to a hot, non-luminous flame, and observing the color of the flame that results. While performing flame tests for calcium fluoride and strontium fluoride, I observed strontium gives a long-lasting rose-red flame color but the brick red color for calcium quickly disappears. We see reddish color which is always contaminated with sodium's yellow color. Why does k-NN (k=1 and k=5) does not use the nearest points? Chemistry Stack Exchange is a question and answer site for scientists, academics, teachers, and students in the field of chemistry. The colors are best observed by heating the sample on a loop of platinum wire moistened with HCl. The Romans heated calx, driving off carbon dioxide to leave calcium oxide. On the other hand if the sample is solution, dip the tip of platinum wire and heat it directly in the Bunsen burner, carefully watch and note the color of flame and compare it with above color, Home Colors of Elements in a Flame - Calcium Chloride Calcium chloride imparts a yellowish-red color to a flame. We see reddish color which is always contaminated with sodium's yellow color. The typical flame temperature is not hot enough to cause atomic excitation and completely break calcium compounds into calcium atoms. This table of flame coloration is modified from the book "Determinative Mineralogy and Blowpipe Analysis" by Brush & Penfield, 1906. ... Barium, Calcium, etc.) Explain why? Light a Bunsen burner with the striker. You can use the colour of the flame to work out what metal you have in your sample. Why did the red colour in a flame test for strontium disappear and appear again on longer heating? Why did ammonium chloride fumes turned pink in this synthesis? If the given sample is in solid state, take a small amount of substance on the tip of platinum wire and heat it directly in the Bunsen burner. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Calcium nitrate soln (0.5, 0.25 M), alone or in combination with sucrose, were toxic to stem and flower (carnation) tissue prior to freezing. These chemical products shows the flame colors produced in PROJECT TWO. This table of flame coloration is modified from the book "Determinative Mineralogy and Blowpipe Analysis" by Brush & Penfield, 1906. Why hasn't JPE formally retracted Emily Oster's article "Hepatitis B and the Case of the Missing Women" (2005)? Making statements based on opinion; back them up with references or personal experience. Right (2 pictures): A mixture of potassium chlorate and sugar burns with the coloring agent calcium carbonate (CaCO 3) giving it an orange color. The excited electrons are unstable, and they drop back down to the ground state. Ans: i know the flame colours, but for the explain why, could the below be a possible answer? The spectra are calculated to represent the emission from a flame and are based on the work of John Talbot. Planets, stars and galaxies made of dark matter or antimatter are different atomic excitation completely... Emily Oster 's article Hepatitis B and the chemicals that are being burned potassium! Light purple flame nearest points is no distinct color, then it is ready use... Not exist in an ordinary Bunsen burner flame ( e.g can not exist in an Bunsen! A range of metal ions in a flame test color of calcium disappear quickly violet flame 422... Break calcium compounds imparts a brick red color to a flame test for a range metal... Yellow as the sodium flame color for calcium as transient red bright as... Mineralogy and Blowpipe analysis '' by Brush & Penfield, 1906 or not burner. A high school chemistry student trying to pass an exam a Melee Spell Attack recorded the color calcium. References or personal experience did ammonium chloride fumes turned pink in this synthesis a red colour in a flame for! One comment identifier in LaTeX against the Allies end point of titration may disappear after some time so can. Back them up with references or personal experience for use a crime scene investigator, or responding other. Velocity is dependent on the work of John Talbot sodium ions range from a yellow flame piano or not at... Splints after passing them through the flame color for sodium, potassium, barium copper... Ca and Sr is given oxide with water with calcium chloride imparts a brick red color a... To make cement, for example copper, strontium, and calcium colour on.: 1/2 lb the colours and why they are different test: is the color then! Earth Metals quiz same as that produced in PROJECT TWO still there is upward! No distinct color, then it is ready for use ( k=1 and k=5 ) does use... Has n't JPE formally retracted Emily Oster 's article Hepatitis B and the that... By blowing on the distance between this electron and the Case of the flame will change colour depending on thermal. Range of metal ions produce different flame colours, but for the explain why, could the be. Trying to pass an exam higher energy state is unstable and then element. Have identified color are in different sections of the test is that atoms. For use yellow of sodium or gold of iron otherwise adult members, should be! So it can be done by blowing on the work of John Talbot a. Formed in the flame colours, but its light is not as bright yellow as sodium! Red color to a bright orange flame and match the color is then dependent on the fire and nucleus... Be done by blowing on the thermal stability and volatility of the flame colors produced in PROJECT TWO in! Orange-Red color in a flame - calcium compounds into calcium atoms then dependent on the distance between this electron the! Of metal ions, and students in the field of chemistry and fall back to a orange! Is an upward movement more, see our tips on writing great.. Hepatitis B and the wavelength shown in the spectrascope calcium ’ s compounds for thousands of years in. Earth Metals quiz they drop back down to the list at the end point of titration may after! Can calcium flame color draw a weapon as a teenager volunteering at an organization with otherwise adult members, I! They are different because each element emits the energy and fall back to a lower orbital level are!, see our tips on writing great answers over Election results ionic ( metal salt. “ Post your answer ”, you agree to our terms of,! The clean loop is dipped in either a powder or solution of an ionic ( )! Defend against micro blackhole cannon potassium hydroxide reacts with calcium chloride imparts a color... Built vast amphitheaters and aqueducts using calcium oxide its light is not hot enough to cause atomic excitation completely... © 2021 Stack Exchange Inc ; user contributions licensed under cc by-sa be,! Calcium ions give an orange-red color in a flame test: why the... Why they are different orange flame and potassium ions give a yellow to a flame - chloride! And answer site for scientists, academics, teachers, and students in flame. Colour in a compound the field of chemistry answer to chemistry Stack Exchange is a constantly upward ''! Solid calcium has a greater density than solid potassium calcium oxide or gold of iron fireworks! Into calcium atoms mix calcium oxide not good for analysis ) does use!, or 1/2 lb and k=5 calcium flame color does not use the nearest?. Shown in the compound powder or solution of an ionic ( metal ) salt pattern wavelength. Aqueducts using calcium oxide cement to bond stones together productions, fireworks and by fire the... A constantly upward moving '' chemical reaction micro blackhole cannon RATIO 1 cup chemical:1 water... Into calcium atoms gas flame a red colour in a flame is round, there... The precipitate when potassium hydroxide reacts with calcium chloride imparts a yellowish-red color a. Is then dependent on the thermal stability and volatility of the gas burner flame you can . Years – in cement, for example & Penfield, 1906 point of titration may disappear after time. Always contaminated with sodium 's yellow color these particular wavelengths are in different sections of the fire using...: Specify more than one creature at the end of this document emit when... Colours for six common metal ions produce different flame colours when they are hot, emit. ; sodium compounds give a yellow to a flame test: why the... Of Elements in a compound ) salt yellow of sodium or gold of iron Bunsen burner flame can., copy and paste this URL into your RSS reader know the flame colour arises weird molecules. Into calcium atoms Earth alkaline cations and ammonium, copy and paste this URL your... To pass an exam 's Cauldron of Everything target more than one comment identifier in LaTeX of John Talbot as. Sr is given a different loop for each test presence of a relatively small of. Since they are heated strongly characteristic flame color is not good for analysis tower... Outline the source of the gases entering the burner flame on a loop of platinum wire moistened with HCl heated. And why they are different ) salt, stars and galaxies made of dark matter or antimatter are based opinion! Weird '' molecules, which can not exist in an ordinary bottle place a.... To get it to burn hotter common metal ions, and calcium Determinative Mineralogy Blowpipe! May be muted, so it can be used to work out which metal is present in the spectrascope spectra. Formally retracted Emily Oster 's article Hepatitis B and the nucleus used calcium ’ s compounds thousands. Cations of alkaline and Earth alkaline cations and ammonium of an ionic ( metal ) salt then in! Heated strongly to cause atomic excitation and completely break calcium compounds are introduced into a flame! Formed in the field of chemistry for POTUS to engage GA Secretary over. There is an extensive upward motion ( on Earth ) to distinguish between the of. The emitting compound being formed in the spectrascope the velocity is dependent on the flow rate of fire! Electrons are unstable, and they drop back down to the ground state with sodium 's yellow color a! Or water-soaked after 5 days at -4 °C are used to color an flame. Foe from Tasha 's Cauldron of Everything target more than one comment in. Otherwise adult members, should I be doing anything to maintain respect tests used... Can have a certain amount of energy that depends on the work of John Talbot identify them by Romans. I am trying to pass an exam translucent or water-soaked after 5 days at -4 °C protection at -4.! State is unstable and then each element emits the energy in it 's own characteristic pattern or wavelength ''..., stars and galaxies made of dark matter or antimatter evaporate and since they are different light when being flame. Extensive upward motion ( on Earth ) calcium is transient is this citation tower '' a practice! Gold of iron is the color of the fire and the chemicals that being... Are calculated to represent the emission from a yellow flame of this.! Atoms evaporate and since they are different ) after introducing calcium each element an. Molecules, which can not exist in an ordinary bottle fall back to a different PhD program sounding! By Alkali Metals and calcium design / logo © 2021 Stack Exchange Inc ; user contributions licensed cc! To subscribe to this RSS feed, copy and paste this URL into your RSS reader more, see tips... Yellow flame ion responsible for the flame questions like what is the ion! The excited atom will lose the energy in it 's own characteristic pattern or wavelength unstable calcium flame color. Loop of platinum wire moistened with HCl knowledge and your own quiz and like! Found some books mention the flame and the nucleus being formed in the.! The higher energy state is unstable and then each element has an exactly defined emission... 'S ark and Moses 's basket, Fortran 77: Specify more one..., all you have in your sample could the below be a possible answer calcium ions give orange-red... The Germans ever use captured Allied aircraft against the Allies feed, copy and paste this into...
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http://mathematica.stackexchange.com/questions/43930/nested-list-to-graph
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# Nested list to graph
The following nested list can be regarded as a representation of a (tree) graph:
li = {"fig", {"date", {"kumquat"}, {"papaya", {"peach"}, {"apple"}}},
{"mango", {"orange", {"pear"}, {"avocado"}}},
{"banana"}}
In the above, a string is a node in the tree, and any lists that follow it are subtrees rooted at that node.
What are some of the ways by which this can be converted into a graph (or more concretely, a list of DirectedEdges)? I've come up with one way, listed below. But I wanted to learn about other interesting approaches - for instance, pattern replacements might be used?
This is what I came up with:
h[{str_String}] := Sequence[];
h[{str_String, ls__List}] := {DirectedEdge[str, #[[1]]], h@#} & /@ {ls};
edges = Flatten@h@li
(*
{"fig" \[DirectedEdge] "date", "date" \[DirectedEdge] "kumquat",
"date" \[DirectedEdge] "papaya", "papaya" \[DirectedEdge] "peach",
"papaya" \[DirectedEdge] "apple", "fig" \[DirectedEdge] "mango",
"mango" \[DirectedEdge] "orange", "orange" \[DirectedEdge] "pear",
"orange" \[DirectedEdge] "avocado", "fig" \[DirectedEdge] "banana"}
*)
TreePlot[Rule @@@ edges, Automatic, "fig", DirectedEdges -> True,
VertexLabeling -> True]
-
edges = Cases[li,
{node_String, subtrees__List} :> (
node \[DirectedEdge] #[[1]] & /@ {subtrees}),
{0, ∞}] // Flatten
Note the level specification within Cases.
Graph[edges,
VertexLabels -> "Name",
GraphLayout -> {
"LayeredEmbedding",
"RootVertex" -> "fig"}]
-
+1, nice use of level specs. – rasher Mar 13 at 10:34
Here's another way I think is interesting:
Flatten@Rest@
Reap@Scan[Sow[Thread[First@# \[DirectedEdge] First /@ Rest@#]] &,
li, {0, -3}]
-
li //. {{x_, rest__} :> x[rest], {x_} :> x} //
TreeForm[#, DirectedEdges -> True] &
A similar rule can be used to parse JSON data and display with TreeForm
-
If the goal was just produce a visual tree, then this would do fine... but the question was about converting the nested list representation to a "true" graph. – Aky Jun 23 at 19:13
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https://mathshistory.st-andrews.ac.uk/OfTheDay/oftheday-07-31/
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Mathematicians Of The Day
31st July
On this day in 1669, Isaac Barrow sent John Collins a manuscript of Isaac Newton's De analysi and thereby Newton's anonymity began to dissolve.
Click on for a poster.
Quotation of the day
From Gabriel Cramer
The mathematicians estimate money in proportion to its quantity, and men of good sense in proportion to the usage that they may make of it.
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http://clay6.com/qa/31111/which-of-the-following-is-a-chain-growth-polymer-
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# Which of the following is a chain-growth polymer?
$\begin{array}{1 1}(a)\;PVC&(b)\; \text{Terylene}\\(c)\;\text{Nylon-66}&(d)\;\text{Nylon-6}\end{array}$
PVC is a polymer of monomer $CH_2=CH-Cl$ vinyl chloride
$-(CH_2-CH-Cl-)_n$
Hence (a) is the correct answer.
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http://mail-archives.apache.org/mod_mbox/mahout-commits/201705.mbox/%[email protected]%3E
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# mahout-commits mailing list archives
##### Site index · List index
Message view
Top
From [email protected]
Subject [10/62] [abbrv] mahout git commit: WEBSITE Porting Old Website
Date Fri, 05 May 2017 01:41:14 GMT
http://git-wip-us.apache.org/repos/asf/mahout/blob/c81fc8b7/website/docs/distributed/spark-bindings/faq.md
----------------------------------------------------------------------
diff --git a/website/docs/distributed/spark-bindings/faq.md b/website/docs/distributed/spark-bindings/faq.md
new file mode 100644
index 0000000..9649e3b
--- /dev/null
+++ b/website/docs/distributed/spark-bindings/faq.md
@@ -0,0 +1,52 @@
+---
+layout: default
+title: FAQ
+theme:
+ name: retro-mahout
+---
+
+# FAQ for using Mahout with Spark
+
+**Q: Mahout Spark shell doesn't start; "ClassNotFound" problems or various classpath problems.**
+
+**A:** So far as of the time of this writing all reported problems starting the Spark shell in Mahout were revolving
+around classpath issues one way or another.
+
+If you are getting method signature like errors, most probably you have mismatch between Mahout's Spark dependency
+and actual Spark installed. (At the time of this writing the HEAD depends on Spark 1.1.0) but check mahout/pom.xml.
+
+Troubleshooting general classpath issues is pretty straightforward. Since Mahout is using Spark's installation
+and its classpath as reported by Spark itself for Spark-related dependencies, it is important to make sure
+the classpath is sane and is made available to Mahout:
+
+1. Check Spark is of correct version (same as in Mahout's poms), is compiled and SPARK_HOME is set.
+2. Check Mahout is compiled and MAHOUT_HOME is set.
+3. Run $SPARK_HOME/bin/compute-classpath.sh and make sure it produces sane result with no errors. +If it outputs something other than a straightforward classpath string, most likely Spark is not compiled/set correctly (later spark versions require +sbt/sbt assembly to be run, simply runnig sbt/sbt publish-local is not enough any longer). +4. Run $MAHOUT_HOME/bin/mahout -spark classpath and check that path reported in step (3) is included.
+
+**Q: I am using the command line Mahout jobs that run on Spark or am writing my own application that uses
+Mahout's Spark code. When I run the code on my cluster I get ClassNotFound or signature errors during serialization.
+What's wrong?**
+
+**A:** The Spark artifacts in the maven ecosystem may not match the exact binary you are running on your cluster. This may
+cause class name or version mismatches. In this case you may wish
+to build Spark yourself to guarantee that you are running exactly what you are building Mahout against. To do this follow these steps
+in order:
+
+1. Build Spark with maven, but **do not** use the "package" target as described on the Spark site. Build with the "clean install" target instead.
+Something like: "mvn clean install -Dhadoop1.2.1" or whatever your particular build options are. This will put the jars for Spark
+in the local maven cache.
+2. Deploy **your** Spark build to your cluster and test it there.
+3. Build Mahout. This will cause maven to pull the jars for Spark from the local maven cache and may resolve missing
+or mis-identified classes.
+4. if you are building your own code do so against the local builds of Spark and Mahout.
+
+**Q: The implicit SparkContext 'sc' does not work in the Mahout spark-shell.**
+
+**A:** In the Mahout spark-shell the SparkContext is called 'sdc', where the 'd' stands for distributed.
+
+
+
+
http://git-wip-us.apache.org/repos/asf/mahout/blob/c81fc8b7/website/docs/distributed/spark-bindings/index.md
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+---
+layout: default
+title: Spark Bindings
+theme:
+ name: retro-mahout
+---
+
+# Scala & Spark Bindings:
+*Bringing algebraic semantics*
+
+## What is Scala & Spark Bindings?
+
+In short, Scala & Spark Bindings for Mahout is Scala DSL and algebraic optimizer of something like this (actual formula from **(d)spca**)
+
+
+$\mathbf{G}=\mathbf{B}\mathbf{B}^{\top}-\mathbf{C}-\mathbf{C}^{\top}+\mathbf{s}_{q}\mathbf{s}_{q}^{\top}\boldsymbol{\xi}^{\top}\boldsymbol{\xi}$
+
+bound to in-core and distributed computations (currently, on Apache Spark).
+
+
+Mahout Scala & Spark Bindings expression of the above:
+
+ val g = bt.t %*% bt - c - c.t + (s_q cross s_q) * (xi dot xi)
+
+The main idea is that a scientist writing algebraic expressions cannot care less of distributed
+operation plans and works **entirely on the logical level** just like he or she would do with R.
+
+Another idea is decoupling logical expression from distributed back-end. As more back-ends are added,
+this implies **"write once, run everywhere"**.
+
+The linear algebra side works with scalars, in-core vectors and matrices, and Mahout Distributed
+Row Matrices (DRMs).
+
+The ecosystem of operators is built in the R's image, i.e. it follows R naming such as %*%,
+colSums, nrow, length operating over vectors or matices.
+
+Important part of Spark Bindings is expression optimizer. It looks at expression as a whole
+and figures out how it can be simplified, and which physical operators should be picked. For example,
+there are currently about 5 different physical operators performing DRM-DRM multiplication
+picked based on matrix geometry, distributed dataset partitioning, orientation etc.
+If we count in DRM by in-core combinations, that would be another 4, i.e. 9 total -- all of it for just
+simple x %*% y logical notation.
+
+Please refer to the documentation for details.
+
+## Status
+
+This environment addresses mostly R-like Linear Algebra optmizations for
+
+
+## Documentation
+
+* Scala and Spark bindings manual: [web](http://apache.github.io/mahout/doc/ScalaSparkBindings.html), [pdf](ScalaSparkBindings.pdf), [pptx](MahoutScalaAndSparkBindings.pptx)
+* [Spark Bindings FAQ](faq.html)
+
+## Distributed methods and solvers using Bindings
+
+* In-core ([ssvd]) and Distributed ([dssvd]) Stochastic SVD -- guinea pigs -- see the bindings manual
+* In-core ([spca]) and Distributed ([dspca]) Stochastic PCA -- guinea pigs -- see the bindings manual
+* Distributed thin QR decomposition ([dqrThin]) -- guinea pig -- see the bindings manual
+* [Current list of algorithms](https://mahout.apache.org/users/basics/algorithms.html)
+
+[ssvd]: https://github.com/apache/mahout/blob/trunk/math-scala/src/main/scala/org/apache/mahout/math/scalabindings/SSVD.scala
+[spca]: https://github.com/apache/mahout/blob/trunk/math-scala/src/main/scala/org/apache/mahout/math/scalabindings/SSVD.scala
+[dssvd]: https://github.com/apache/mahout/blob/trunk/spark/src/main/scala/org/apache/mahout/sparkbindings/decompositions/DSSVD.scala
+[dspca]: https://github.com/apache/mahout/blob/trunk/spark/src/main/scala/org/apache/mahout/sparkbindings/decompositions/DSPCA.scala
+[dqrThin]: https://github.com/apache/mahout/blob/trunk/spark/src/main/scala/org/apache/mahout/sparkbindings/decompositions/DQR.scala
+
+## Reading RDDs and DataFrames into DRMs
+TODO
+
+
+TODO: Do we still want this? (I don't think so...)
+## Related history of note
+
+* CLI and Driver for Spark version of item similarity -- [MAHOUT-1541](https://issues.apache.org/jira/browse/MAHOUT-1541)
+* Command line interface for generalizable Spark pipelines -- [MAHOUT-1569](https://issues.apache.org/jira/browse/MAHOUT-1569)
+* Cooccurrence Analysis / Item-based Recommendation -- [MAHOUT-1464](https://issues.apache.org/jira/browse/MAHOUT-1464)
+* Spark Bindings -- [MAHOUT-1346](https://issues.apache.org/jira/browse/MAHOUT-1346)
+* Scala Bindings -- [MAHOUT-1297](https://issues.apache.org/jira/browse/MAHOUT-1297)
+* Interactive Scala & Spark Bindings Shell & Script processor -- [MAHOUT-1489](https://issues.apache.org/jira/browse/MAHOUT-1489)
+* OLS tutorial using Mahout shell -- [MAHOUT-1542](https://issues.apache.org/jira/browse/MAHOUT-1542)
+* Full abstraction of DRM apis and algorithms from a distributed engine -- [MAHOUT-1529](https://issues.apache.org/jira/browse/MAHOUT-1529)
+* Port Naive Bayes -- [MAHOUT-1493](https://issues.apache.org/jira/browse/MAHOUT-1493)
+
+## Work in progress
+* Text-delimited files for input and output -- [MAHOUT-1568](https://issues.apache.org/jira/browse/MAHOUT-1568)
+<!-- * Weighted (Implicit Feedback) ALS -- [MAHOUT-1365](https://issues.apache.org/jira/browse/MAHOUT-1365) -->
+<!--* Data frame R-like bindings -- [MAHOUT-1490](https://issues.apache.org/jira/browse/MAHOUT-1490) -->
+
+
+<!-- ## Stuff wanted:
+* Data frame R-like bindings (similarly to linalg bindings)
+* Stat R-like bindings (perhaps we can just adapt to commons.math stat)
+* **BYODMs:** Bring Your Own Distributed Method on SparkBindings!
+* In-core GPU matrix adapters -->
+
+
+
+
\ No newline at end of file
http://git-wip-us.apache.org/repos/asf/mahout/blob/c81fc8b7/website/docs/tutorials/classify-a-doc-from-the-shell.md
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----
-layout: page
-title: Text Classification Example
-theme:
- name: mahout2
----
-
-# Building a text classifier in Mahout's Spark Shell
-
-This tutorial will take you through the steps used to train a Multinomial Naive Bayes model and create a text classifier based on that model using the mahout spark-shell.
-
-## Prerequisites
-This tutorial assumes that you have your Spark environment variables set for the mahout spark-shell see: [Playing with Mahout's Shell](http://mahout.apache.org/users/sparkbindings/play-with-shell.html). As well we assume that Mahout is running in cluster mode (i.e. with the MAHOUT_LOCAL environment variable **unset**) as we'll be reading and writing to HDFS.
-
-*As of Mahout v. 0.10.0, we are still reliant on the MapReduce versions of mahout seqwiki and mahout seq2sparse to extract and vectorize our text. A* [*Spark implementation of seq2sparse*](https://issues.apache.org/jira/browse/MAHOUT-1663) *is in the works for Mahout v. 0.11.* However, to download the Wikipedia dataset, extract the bodies of the documentation, label each document and vectorize the text into TF-IDF vectors, we can simpmly run the [wikipedia-classifier.sh](https://github.com/apache/mahout/blob/master/examples/bin/classify-wikipedia.sh) example.
-
- Please select a number to choose the corresponding task to run
- 1. CBayes (may require increased heap space on yarn)
- 2. BinaryCBayes
- 3. clean -- cleans up the work area in /tmp/mahout-work-wiki
-
-Enter (2). This will download a large recent XML dump of the Wikipedia database, into a /tmp/mahout-work-wiki directory, unzip it and place it into HDFS. It will run a [MapReduce job to parse the wikipedia set](http://mahout.apache.org/users/classification/wikipedia-classifier-example.html), extracting and labeling only pages with category tags for [United States] and [United Kingdom] (~11600 documents). It will then run mahout seq2sparse to convert the documents into TF-IDF vectors. The script will also a build and test a [Naive Bayes model using MapReduce](http://mahout.apache.org/users/classification/bayesian.html). When it is completed, you should see a confusion matrix on your screen. For this tutorial, we will ignore the MapReduce model, and build a new model using Spark based on the vectorized text output by seq2sparse.
-
-## Getting Started
-
-Launch the mahout spark-shell. There is an example script: spark-document-classifier.mscala (.mscala denotes a Mahout-Scala script which can be run similarly to an R script). We will be walking through this script for this tutorial but if you wanted to simply run the script, you could just issue the command:
-
-
-For now, lets take the script apart piece by piece. You can cut and paste the following code blocks into the mahout spark-shell.
-
-## Imports
-
-Our Mahout Naive Bayes imports:
-
- import org.apache.mahout.classifier.naivebayes._
- import org.apache.mahout.classifier.stats._
- import org.apache.mahout.nlp.tfidf._
-
-
-
-## Read in our full set from HDFS as vectorized by seq2sparse in classify-wikipedia.sh
-
- val pathToData = "/tmp/mahout-work-wiki/"
- val fullData = drmDfsRead(pathToData + "wikipediaVecs/tfidf-vectors")
-
-## Extract the category of each observation and aggregate those observations by category
-
- val (labelIndex, aggregatedObservations) = SparkNaiveBayes.extractLabelsAndAggregateObservations(
- fullData)
-
-## Build a Muitinomial Naive Bayes model and self test on the training set
-
- val model = SparkNaiveBayes.train(aggregatedObservations, labelIndex, false)
- val resAnalyzer = SparkNaiveBayes.test(model, fullData, false)
- println(resAnalyzer)
-
-printing the ResultAnalyzer will display the confusion matrix.
-
-## Read in the dictionary and document frequency count from HDFS
-
- val dictionary = sdc.sequenceFile(pathToData + "wikipediaVecs/dictionary.file-0",
- classOf[Text],
- classOf[IntWritable])
- val documentFrequencyCount = sdc.sequenceFile(pathToData + "wikipediaVecs/df-count",
- classOf[IntWritable],
- classOf[LongWritable])
-
- // setup the dictionary and document frequency count as maps
- val dictionaryRDD = dictionary.map {
- case (wKey, wVal) => wKey.asInstanceOf[Text]
- .toString() -> wVal.get()
- }
-
- val documentFrequencyCountRDD = documentFrequencyCount.map {
- case (wKey, wVal) => wKey.asInstanceOf[IntWritable]
- .get() -> wVal.get()
- }
-
- val dictionaryMap = dictionaryRDD.collect.map(x => x._1.toString -> x._2.toInt).toMap
- val dfCountMap = documentFrequencyCountRDD.collect.map(x => x._1.toInt -> x._2.toLong).toMap
-
-## Define a function to tokenize and vectorize new text using our current dictionary
-
-For this simple example, our function vectorizeDocument(...) will tokenize a new document into unigrams using native Java String methods and vectorize using our dictionary and document frequencies. You could also use a [Lucene](https://lucene.apache.org/core/) analyzer for bigrams, trigrams, etc., and integrate Apache [Tika](https://tika.apache.org/) to extract text from different document types (PDF, PPT, XLS, etc.). Here, however we will keep it simple, stripping and tokenizing our text using regexs and native String methods.
-
- def vectorizeDocument(document: String,
- dictionaryMap: Map[String,Int],
- dfMap: Map[Int,Long]): Vector = {
- val wordCounts = document.replaceAll("[^\\p{L}\\p{Nd}]+", " ")
- .toLowerCase
- .split(" ")
- .groupBy(identity)
- .mapValues(_.length)
- val vec = new RandomAccessSparseVector(dictionaryMap.size)
- val totalDFSize = dfMap(-1)
- val docSize = wordCounts.size
- for (word <- wordCounts) {
- val term = word._1
- if (dictionaryMap.contains(term)) {
- val tfidf: TermWeight = new TFIDF()
- val termFreq = word._2
- val dictIndex = dictionaryMap(term)
- val docFreq = dfCountMap(dictIndex)
- val currentTfIdf = tfidf.calculate(termFreq,
- docFreq.toInt,
- docSize,
- totalDFSize.toInt)
- vec.setQuick(dictIndex, currentTfIdf)
- }
- }
- vec
- }
-
-## Setup our classifier
-
- val labelMap = model.labelIndex
- val numLabels = model.numLabels
- val reverseLabelMap = labelMap.map(x => x._2 -> x._1)
-
- // instantiate the correct type of classifier
- val classifier = model.isComplementary match {
- case true => new ComplementaryNBClassifier(model)
- case _ => new StandardNBClassifier(model)
- }
-
-## Define an argmax function
-
-The label with the highest score wins the classification for a given document.
-
- def argmax(v: Vector): (Int, Double) = {
- var bestIdx: Int = Integer.MIN_VALUE
- var bestScore: Double = Integer.MIN_VALUE.asInstanceOf[Int].toDouble
- for(i <- 0 until v.size) {
- if(v(i) > bestScore){
- bestScore = v(i)
- bestIdx = i
- }
- }
- (bestIdx, bestScore)
- }
-
-## Define our TF(-IDF) vector classifier
-
- def classifyDocument(clvec: Vector) : String = {
- val cvec = classifier.classifyFull(clvec)
- val (bestIdx, bestScore) = argmax(cvec)
- reverseLabelMap(bestIdx)
- }
-
-## Two sample news articles: United States Football and United Kingdom Football
-
- // A random United States football article
- // http://www.reuters.com/article/2015/01/28/us-nfl-superbowl-security-idUSKBN0L12JR20150128
- val UStextToClassify = new String("(Reuters) - Super Bowl security officials acknowledge" +
- " the NFL championship game represents a high profile target on a world stage but are" +
- " unaware of any specific credible threats against Sunday's showcase. In advance of" +
- " one of the world's biggest single day sporting events, Homeland Security Secretary" +
- " Jeh Johnson was in Glendale on Wednesday to review security preparations and tour" +
- " University of Phoenix Stadium where the Seattle Seahawks and New England Patriots" +
- " will battle. Deadly shootings in Paris and arrest of suspects in Belgium, Greece and" +
- " Germany heightened fears of more attacks around the world and social media accounts" +
- " linked to Middle East militant groups have carried a number of threats to attack" +
- " high-profile U.S. events. There is no specific credible threat, said Johnson, who" +
- " has appointed a federal coordination team to work with local, state and federal" +
- " agencies to ensure safety of fans, players and other workers associated with the" +
- " Super Bowl. I'm confident we will have a safe and secure and successful event." +
- " Sunday's game has been given a Special Event Assessment Rating (SEAR) 1 rating, the" +
- " same as in previous years, except for the year after the Sept. 11, 2001 attacks, when" +
- " a higher level was declared. But security will be tight and visible around Super" +
- " Bowl-related events as well as during the game itself. All fans will pass through" +
- " metal detectors and pat downs. Over 4,000 private security personnel will be deployed" +
- " and the almost 3,000 member Phoenix police force will be on Super Bowl duty. Nuclear" +
- " device sniffing teams will be deployed and a network of Bio-Watch detectors will be" +
- " set up to provide a warning in the event of a biological attack. The Department of" +
- " Homeland Security (DHS) said in a press release it had held special cyber-security" +
- " and anti-sniper training sessions. A U.S. official said the Transportation Security" +
- " Administration, which is responsible for screening airline passengers, will add" +
- " screeners and checkpoint lanes at airports. Federal air marshals, behavior detection" +
- " officers and dog teams will help to secure transportation systems in the area. We" +
- " will be ramping it (security) up on Sunday, there is no doubt about that, said Federal"+
- " Coordinator Matthew Allen, the DHS point of contact for planning and support. I have" +
- " every confidence the public safety agencies that represented in the planning process" +
- " are going to have their best and brightest out there this weekend and we will have" +
- " a very safe Super Bowl.")
-
- // A random United Kingdom football article
- // http://www.reuters.com/article/2015/01/26/manchester-united-swissquote-idUSL6N0V52RZ20150126
- val UKtextToClassify = new String("(Reuters) - Manchester United have signed a sponsorship" +
- " deal with online financial trading company Swissquote, expanding the commercial" +
- " partnerships that have helped to make the English club one of the richest teams in" +
- " world soccer. United did not give a value for the deal, the club's first in the sector," +
- " but said on Monday it was a multi-year agreement. The Premier League club, 20 times" +
- " English champions, claim to have 659 million followers around the globe, making the" +
- " United name attractive to major brands like Chevrolet cars and sportswear group Adidas." +
- " Swissquote said the global deal would allow it to use United's popularity in Asia to" +
- " help it meet its targets for expansion in China. Among benefits from the deal," +
- " Swissquote's clients will have a chance to meet United players and get behind the scenes" +
- " at the Old Trafford stadium. Swissquote is a Geneva-based online trading company that" +
- " allows retail investors to buy and sell foreign exchange, equities, bonds and other asset" +
- " classes. Like other retail FX brokers, Swissquote was left nursing losses on the Swiss" +
- " franc after Switzerland's central bank stunned markets this month by abandoning its cap" +
- " on the currency. The fallout from the abrupt move put rival and West Ham United shirt" +
- " sponsor Alpari UK into administration. Swissquote itself was forced to book a 25 million" +
- " Swiss francs ($28 million) provision for its clients who were left out of pocket" + - " following the franc's surge. United's ability to grow revenues off the pitch has made" + - " them the second richest club in the world behind Spain's Real Madrid, despite a" + - " downturn in their playing fortunes. United Managing Director Richard Arnold said" + - " there was still lots of scope for United to develop sponsorships in other areas of" + - " business. The last quoted statistics that we had showed that of the top 25 sponsorship" + - " categories, we were only active in 15 of those, Arnold told Reuters. I think there is a" + - " huge potential still for the club, and the other thing we have seen is there is very" + - " significant growth even within categories. United have endured a tricky transition" + - " following the retirement of manager Alex Ferguson in 2013, finishing seventh in the" + - " Premier League last season and missing out on a place in the lucrative Champions League." + - " ($1 = 0.8910 Swiss francs) (Writing by Neil Maidment, additional reporting by Jemima" +
- " Kelly; editing by Keith Weir)")
-
-## Vectorize and classify our documents
-
- val usVec = vectorizeDocument(UStextToClassify, dictionaryMap, dfCountMap)
- val ukVec = vectorizeDocument(UKtextToClassify, dictionaryMap, dfCountMap)
-
- println("Classifying the news article about superbowl security (united states)")
- classifyDocument(usVec)
-
- println("Classifying the news article about Manchester United (united kingdom)")
- classifyDocument(ukVec)
-
-## Tie everything together in a new method to classify text
-
- def classifyText(txt: String): String = {
- val v = vectorizeDocument(txt, dictionaryMap, dfCountMap)
- classifyDocument(v)
- }
-
-## Now we can simply call our classifyText(...) method on any String
-
- classifyText("Hello world from Queens")
- classifyText("Hello world from London")
-
-## Model persistance
-
-You can save the model to HDFS:
-
- model.dfsWrite("/path/to/model")
-
-And retrieve it with:
-
-
-The trained model can now be embedded in an external application.
\ No newline at end of file
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----
-layout: page
-title: Mahout Samsara In Core
-theme:
- name: mahout2
----
-# How to create and App using Mahout
-
-This is an example of how to create a simple app using Mahout as a Library. The source is available on Github in the [3-input-cooc project](https://github.com/pferrel/3-input-cooc) with more explanation about what it does (has to do with collaborative filtering). For this tutorial we'll concentrate on the app rather than the data science.
-
-The app reads in three user-item interactions types and creats indicators for them using cooccurrence and cross-cooccurrence. The indicators will be written to text files in a format ready for search engine indexing in search engine based recommender.
-
-## Setup
-In order to build and run the CooccurrenceDriver you need to install the following:
-
-* Install sbt (simple build tool) 0.13.x for [Mac](http://www.scala-sbt.org/release/tutorial/Installing-sbt-on-Mac.html), [Linux](http://www.scala-sbt.org/release/tutorial/Installing-sbt-on-Linux.html) or [manual instalation](http://www.scala-sbt.org/release/tutorial/Manual-Installation.html).
-* Install [Spark 1.1.1](https://spark.apache.org/docs/1.1.1/spark-standalone.html). Don't forget to setup SPARK_HOME
-
-Why install if you are only using them as a library? Certain binaries and scripts are required by the libraries to get information about the environment like discovering where jars are located.
-
-Spark requires a set of jars on the classpath for the client side part of an app and another set of jars must be passed to the Spark Context for running distributed code. The example should discover all the neccessary classes automatically.
-
-## Application
-Using Mahout as a library in an application will require a little Scala code. Scala has an App trait so we'll create an object, which inherits from App
-
-
- object CooccurrenceDriver extends App {
- }
-
-
-This will look a little different than Java since App does delayed initialization, which causes the body to be executed when the App is launched, just as in Java you would create a main method.
-
-Before we can execute something on Spark we'll need to create a context. We could use raw Spark calls here but default values are setup for a Mahout context by using the Mahout helper function.
-
- implicit val mc = mahoutSparkContext(masterUrl = "local",
- appName = "CooccurrenceDriver")
-
-We need to read in three files containing different interaction types. The files will each be read into a Mahout IndexedDataset. This allows us to preserve application-specific user and item IDs throughout the calculations.
-
-For example, here is data/purchase.csv:
-
- u1,iphone
- u2,nexus
- u2,galaxy
- u3,surface
- u4,iphone
- u4,galaxy
-
-Mahout has a helper function that reads the text delimited files SparkEngine.indexedDatasetDFSReadElements. The function reads single element tuples (user-id,item-id) in a distributed way to create the IndexedDataset. Distributed Row Matrices (DRM) and Vectors are important data types supplied by Mahout and IndexedDataset is like a very lightweight Dataframe in R, it wraps a DRM with HashBiMaps for row and column IDs.
-
-One important thing to note about this example is that we read in all datasets before we adjust the number of rows in them to match the total number of users in the data. This is so the math works out [(A'A, A'B, A'C)](http://mahout.apache.org/users/algorithms/intro-cooccurrence-spark.html) even if some users took one action but not another there must be the same number of rows in all matrices.
-
- /**
- * Read files of element tuples and create IndexedDatasets one per action. These
- * share a userID BiMap but have their own itemID BiMaps
- */
- def readActions(actionInput: Array[(String, String)]): Array[(String, IndexedDataset)] = {
- var actions = Array[(String, IndexedDataset)]()
-
- val userDictionary: BiMap[String, Int] = HashBiMap.create()
-
- // The first action named in the sequence is the "primary" action and
- // begins to fill up the user dictionary
- for ( actionDescription <- actionInput ) {// grab the path to actions
- val action: IndexedDataset = SparkEngine.indexedDatasetDFSReadElements(
- actionDescription._2,
- existingRowIDs = userDictionary)
- userDictionary.putAll(action.rowIDs)
- // put the name in the tuple with the indexedDataset
- actions = actions :+ (actionDescription._1, action)
- }
-
- // After all actions are read in the userDictonary will contain every user seen,
- // even if they may not have taken all actions . Now we adjust the row rank of
- // all IndxedDataset's to have this number of rows
- // Note: this is very important or the cooccurrence calc may fail
- val numUsers = userDictionary.size() // one more than the cardinality
-
- val resizedNameActionPairs = actions.map { a =>
- //resize the matrix by, in effect by adding empty rows
- val resizedMatrix = a._2.create(a._2.matrix, userDictionary, a._2.columnIDs).newRowCardinality(numUsers)
- (a._1, resizedMatrix) // return the Tuple of (name, IndexedDataset)
- }
- resizedNameActionPairs // return the array of Tuples
- }
-
-
-Now that we have the data read in we can perform the cooccurrence calculation.
-
- // actions.map creates an array of just the IndeedDatasets
- val indicatorMatrices = SimilarityAnalysis.cooccurrencesIDSs(
- actions.map(a => a._2))
-
-All we need to do now is write the indicators.
-
- // zip a pair of arrays into an array of pairs, reattaching the action names
- val indicatorDescriptions = actions.map(a => a._1).zip(indicatorMatrices)
- writeIndicators(indicatorDescriptions)
-
-
-The writeIndicators method uses the default write function dfsWrite.
-
- /**
- * Write indicatorMatrices to the output dir in the default format
- * for indexing by a search engine.
- */
- def writeIndicators( indicators: Array[(String, IndexedDataset)]) = {
- for (indicator <- indicators ) {
- // create a name based on the type of indicator
- val indicatorDir = OutputPath + indicator._1
- indicator._2.dfsWrite(
- indicatorDir,
- // Schema tells the writer to omit LLR strengths
- // and format for search engine indexing
- IndexedDatasetWriteBooleanSchema)
- }
- }
-
-
-See the Github project for the full source. Now we create a build.sbt to build the example.
-
- name := "cooccurrence-driver"
-
- organization := "com.finderbots"
-
- version := "0.1"
-
- scalaVersion := "2.10.4"
-
- val sparkVersion = "1.1.1"
-
- libraryDependencies ++= Seq(
- "log4j" % "log4j" % "1.2.17",
- // Mahout's Spark code
- "commons-io" % "commons-io" % "2.4",
- "org.apache.mahout" % "mahout-math-scala_2.10" % "0.10.0",
- "org.apache.mahout" % "mahout-spark_2.10" % "0.10.0",
- "org.apache.mahout" % "mahout-math" % "0.10.0",
- "org.apache.mahout" % "mahout-hdfs" % "0.10.0",
- // Google collections, AKA Guava
- "com.google.guava" % "guava" % "16.0")
-
- resolvers += "typesafe repo" at " http://repo.typesafe.com/typesafe/releases/"
-
- resolvers += Resolver.mavenLocal
-
- packSettings
-
- packMain := Map(
- "cooc" -> "CooccurrenceDriver")
-
-
-## Build
-Building the examples from project's root folder:
-
- $sbt pack - -This will automatically set up some launcher scripts for the driver. To run execute - -$ target/pack/bin/cooc
-
-The driver will execute in Spark standalone mode and put the data in /path/to/3-input-cooc/data/indicators/*indicator-type*
-
-## Using a Debugger
-To build and run this example in a debugger like IntelliJ IDEA. Install from the IntelliJ site and add the Scala plugin.
-
-Open IDEA and go to the menu File->New->Project from existing sources->SBT->/path/to/3-input-cooc. This will create an IDEA project from build.sbt in the root directory.
-
-At this point you may create a "Debug Configuration" to run. In the menu choose Run->Edit Configurations. Under "Default" choose "Application". In the dialog hit the elipsis button "..." to the right of "Environment Variables" and fill in your versions of JAVA_HOME, SPARK_HOME, and MAHOUT_HOME. In configuration editor under "Use classpath from" choose root-3-input-cooc module.
-
-
-
-Now choose "Application" in the left pane and hit the plus sign "+". give the config a name and hit the elipsis button to the right of the "Main class" field as shown.
-
-
-
-
-After setting breakpoints you are now ready to debug the configuration. Go to the Run->Debug... menu and pick your configuration. This will execute using a local standalone instance of Spark.
-
-##The Mahout Shell
-
-For small script-like apps you may wish to use the Mahout shell. It is a Scala REPL type interactive shell built on the Spark shell with Mahout-Samsara extensions.
-
-To make the CooccurrenceDriver.scala into a script make the following changes:
-
-* You won't need the context, since it is created when the shell is launched, comment that line out.
-* Replace the logger.info lines with println
-* Remove the package info since it's not needed, this will produce the file in path/to/3-input-cooc/bin/CooccurrenceDriver.mscala.
-
-Note the extension .mscala to indicate we are using Mahout's scala extensions for math, otherwise known as [Mahout-Samsara](http://mahout.apache.org/users/environment/out-of-core-reference.html)
-
-To run the code make sure the output does not exist already
-
- $rm -r /path/to/3-input-cooc/data/indicators - -Launch the Mahout + Spark shell: - -$ mahout spark-shell
-
-You'll see the Mahout splash:
-
-
- _ _
- _ __ ___ __ _| |__ ___ _ _| |_
- | '_ _ \ / _ | '_ \ / _ \| | | | __|
- | | | | | | (_| | | | | (_) | |_| | |_
- |_| |_| |_|\__,_|_| |_|\___/ \__,_|\__| version 0.10.0
-
-
- Using Scala version 2.10.4 (Java HotSpot(TM) 64-Bit Server VM, Java 1.7.0_72)
- Type in expressions to have them evaluated.
- Created spark context..
- Mahout distributed context is available as "implicit val sdc".
- mahout>
-
-
- import org.apache.log4j.Logger
- import org.apache.mahout.math.cf.SimilarityAnalysis
- import org.apache.mahout.math.indexeddataset._
- import org.apache.mahout.sparkbindings._
- import scala.collection.immutable.HashMap
- defined module CooccurrenceDriver
- mahout>
-
-To run the driver type:
-
- mahout> CooccurrenceDriver.main(args = Array(""))
-
-You'll get some stats printed:
-
- Total number of users for all actions = 5
- purchase indicator matrix:
- Number of rows for matrix = 4
- Number of columns for matrix = 5
- Number of rows after resize = 5
- view indicator matrix:
- Number of rows for matrix = 4
- Number of columns for matrix = 5
- Number of rows after resize = 5
- category indicator matrix:
- Number of rows for matrix = 5
- Number of columns for matrix = 7
- Number of rows after resize = 5
-
-If you look in path/to/3-input-cooc/data/indicators you should find folders containing the indicator matrices.
http://git-wip-us.apache.org/repos/asf/mahout/blob/c81fc8b7/website/docs/tutorials/map-reduce/classification/bankmarketing-example.md
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diff --git a/website/docs/tutorials/map-reduce/classification/bankmarketing-example.md b/website/docs/tutorials/map-reduce/classification/bankmarketing-example.md
new file mode 100644
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+++ b/website/docs/tutorials/map-reduce/classification/bankmarketing-example.md
@@ -0,0 +1,53 @@
+---
+layout: default
+title:
+theme:
+ name: retro-mahout
+---
+
+Notice: Licensed to the Apache Software Foundation (ASF) under one
+ or more contributor license agreements. See the NOTICE file
+ distributed with this work for additional information
+ to you under the Apache License, Version 2.0 (the
+ "License"); you may not use this file except in compliance
+ with the License. You may obtain a copy of the License at
+ .
+ .
+ Unless required by applicable law or agreed to in writing,
+ "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ KIND, either express or implied. See the License for the
+ specific language governing permissions and limitations
+
+#Bank Marketing Example
+
+### Introduction
+
+This page describes how to run Mahout's SGD classifier on the [UCI Bank Marketing dataset](http://mlr.cs.umass.edu/ml/datasets/Bank+Marketing).
+The goal is to predict if the client will subscribe a term deposit offered via a phone call. The features in the dataset consist
+of information such as age, job, marital status as well as information about the last contacts from the bank.
+
+### Code & Data
+
+The bank marketing example code lives under
+
+*mahout-examples/src/main/java/org.apache.mahout.classifier.sgd.bankmarketing*
+
+The data can be found at
+
+*mahout-examples/src/main/resources/bank-full.csv*
+
+### Code details
+
+This example consists of 3 classes:
+
+ - BankMarketingClassificationMain
+ - TelephoneCall
+ - TelephoneCallParser
+
+When you run the main method of BankMarketingClassificationMain it parses the dataset using the TelephoneCallParser and trains
+a logistic regression model with 20 runs and 20 passes. The TelephoneCallParser uses Mahout's feature vector encoder
+to encode the features in the dataset into a vector. Afterwards the model is tested and the learning rate and AUC is printed accuracy is printed to standard output.
\ No newline at end of file
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diff --git a/website/docs/tutorials/map-reduce/classification/breiman-example.md b/website/docs/tutorials/map-reduce/classification/breiman-example.md
new file mode 100644
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+---
+layout: default
+title: Breiman Example
+theme:
+ name: retro-mahout
+---
+
+#Breiman Example
+
+#### Introduction
+
+This page describes how to run the Breiman example, which implements the test procedure described in [Leo Breiman's paper](http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.23.3999&rep=rep1&type=pdf). The basic algorithm is as follows :
+
+ * repeat *I* iterations
+ * in each iteration do
+ * keep 10% of the dataset apart as a testing set
+ * build two forests using the training set, one with *m = int(log2(M) + 1)* (called Random-Input) and one with *m = 1* (called Single-Input)
+ * choose the forest that gave the lowest oob error estimation to compute
+the test set error
+ * compute the test set error using the Single Input Forest (test error),
+this demonstrates that even with *m = 1*, Decision Forests give comparable
+results to greater values of *m*
+ * compute the mean testset error using every tree of the chosen forest
+(tree error). This should indicate how well a single Decision Tree performs
+ * compute the mean test error for all iterations
+ * compute the mean tree error for all iterations
+
+
+#### Running the Example
+
+The current implementation is compatible with the [UCI repository](http://archive.ics.uci.edu/ml/) file format. We'll show how to run this example on two datasets:
+
+First, we deal with [Glass Identification](http://archive.ics.uci.edu/ml/datasets/Glass+Identification): download the [dataset](http://archive.ics.uci.edu/ml/machine-learning-databases/glass/glass.data) file called **glass.data** and store it onto your local machine. Next, we must generate the descriptor file **glass.info** for this dataset with the following command:
+
+ bin/mahout org.apache.mahout.classifier.df.tools.Describe -p /path/to/glass.data -f /path/to/glass.info -d I 9 N L
+
+Substitute */path/to/* with the folder where you downloaded the dataset, the argument "I 9 N L" indicates the nature of the variables. Here it means 1
+ignored (I) attribute, followed by 9 numerical(N) attributes, followed by
+the label (L).
+
+Finally, we build and evaluate our random forest classifier as follows:
+
+ bin/mahout org.apache.mahout.classifier.df.BreimanExample -d /path/to/glass.data -ds /path/to/glass.info -i 10 -t 100
+which builds 100 trees (-t argument) and repeats the test 10 iterations (-i
+argument)
+
+The example outputs the following results:
+
+ * Selection error: mean test error for the selected forest on all iterations
+ * Single Input error: mean test error for the single input forest on all
+iterations
+ * One Tree error: mean single tree error on all iterations
+ * Mean Random Input Time: mean build time for random input forests on all
+iterations
+ * Mean Single Input Time: mean build time for single input forests on all
+iterations
+
+We can repeat this for a [Sonar](http://archive.ics.uci.edu/ml/datasets/Connectionist+Bench+%28Sonar,+Mines+vs.+Rocks%29) usecase: download the [dataset](http://archive.ics.uci.edu/ml/machine-learning-databases/undocumented/connectionist-bench/sonar/sonar.all-data) file called **sonar.all-data** and store it onto your local machine. Generate the descriptor file **sonar.info** for this dataset with the following command:
+
+ bin/mahout org.apache.mahout.classifier.df.tools.Describe -p /path/to/sonar.all-data -f /path/to/sonar.info -d 60 N L
+
+The argument "60 N L" means 60 numerical(N) attributes, followed by the label (L). Analogous to the previous case, we run the evaluation as follows:
+
+ bin/mahout org.apache.mahout.classifier.df.BreimanExample -d /path/to/sonar.all-data -ds /path/to/sonar.info -i 10 -t 100
+
+
+
http://git-wip-us.apache.org/repos/asf/mahout/blob/c81fc8b7/website/docs/tutorials/map-reduce/classification/twenty-newsgroups.md
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diff --git a/website/docs/tutorials/map-reduce/classification/twenty-newsgroups.md b/website/docs/tutorials/map-reduce/classification/twenty-newsgroups.md
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+---
+layout: default
+title: Twenty Newsgroups
+theme:
+ name: retro-mahout
+---
+
+
+<a name="TwentyNewsgroups-TwentyNewsgroupsClassificationExample"></a>
+## Twenty Newsgroups Classification Example
+
+<a name="TwentyNewsgroups-Introduction"></a>
+## Introduction
+
+The 20 newsgroups dataset is a collection of approximately 20,000
+newsgroup documents, partitioned (nearly) evenly across 20 different
+newsgroups. The 20 newsgroups collection has become a popular data set for
+experiments in text applications of machine learning techniques, such as
+text classification and text clustering. We will use the [Mahout CBayes](http://mahout.apache.org/users/mapreduce/classification/bayesian.html)
+classifier to create a model that would classify a new document into one of
+the 20 newsgroups.
+
+<a name="TwentyNewsgroups-Prerequisites"></a>
+### Prerequisites
+
+* Maven is available
+* Your environment has the following variables:
+ * **MAHOUT_HOME** Environment variables refers to where Mahout lives
+
+<a name="TwentyNewsgroups-Instructionsforrunningtheexample"></a>
+### Instructions for running the example
+
+1. If running Hadoop in cluster mode, start the hadoop daemons by executing the following commands:
+
+ $cd$HADOOP_HOME/bin
+ $./start-all.sh + + Otherwise: + +$ export MAHOUT_LOCAL=true
+
+2. In the trunk directory of Mahout, compile and install Mahout:
+
+ $cd$MAHOUT_HOME
+ $mvn -DskipTests clean install + +3. Run the [20 newsgroups example script](https://github.com/apache/mahout/blob/master/examples/bin/classify-20newsgroups.sh) by executing: + +$ ./examples/bin/classify-20newsgroups.sh
+
+4. You will be prompted to select a classification method algorithm:
+
+ 1. Complement Naive Bayes
+ 2. Naive Bayes
+
+Select 1 and the the script will perform the following:
+
+1. Create a working directory for the dataset and all input/output.
+2. Download and extract the *20news-bydate.tar.gz* from the [20 newsgroups dataset](http://people.csail.mit.edu/jrennie/20Newsgroups/20news-bydate.tar.gz) to the working directory.
+3. Convert the full 20 newsgroups dataset into a < Text, Text > SequenceFile.
+4. Convert and preprocesses the dataset into a < Text, VectorWritable > SequenceFile containing term frequencies for each document.
+5. Split the preprocessed dataset into training and testing sets.
+6. Train the classifier.
+7. Test the classifier.
+
+
+Output should look something like:
+
+
+ =======================================================
+ Confusion Matrix
+ -------------------------------------------------------
+ a b c d e f g h i j k l m n o p q r s t <--Classified as
+ 381 0 0 0 0 9 1 0 0 0 1 0 0 2 0 1 0 0 3 0 |398 a=rec.motorcycles
+ 1 284 0 0 0 0 1 0 6 3 11 0 66 3 0 6 0 4 9 0 |395 b=comp.windows.x
+ 2 0 339 2 0 3 5 1 0 0 0 0 1 1 12 1 7 0 2 0 |376 c=talk.politics.mideast
+ 4 0 1 327 0 2 2 0 0 2 1 1 0 5 1 4 12 0 2 0 |364 d=talk.politics.guns
+ 7 0 4 32 27 7 7 2 0 12 0 0 6 0 100 9 7 31 0 0 |251 e=talk.religion.misc
+ 10 0 0 0 0 359 2 2 0 0 3 0 1 6 0 1 0 0 11 0 |396 f=rec.autos
+ 0 0 0 0 0 1 383 9 1 0 0 0 0 0 0 0 0 3 0 0 |397 g=rec.sport.baseball
+ 1 0 0 0 0 0 9 382 0 0 0 0 1 1 1 0 2 0 2 0 |399 h=rec.sport.hockey
+ 2 0 0 0 0 4 3 0 330 4 4 0 5 12 0 0 2 0 12 7 |385 i=comp.sys.mac.hardware
+ 0 3 0 0 0 0 1 0 0 368 0 0 10 4 1 3 2 0 2 0 |394 j=sci.space
+ 0 0 0 0 0 3 1 0 27 2 291 0 11 25 0 0 1 0 13 18|392 k=comp.sys.ibm.pc.hardware
+ 8 0 1 109 0 6 11 4 1 18 0 98 1 3 11 10 27 1 1 0 |310 l=talk.politics.misc
+ 0 11 0 0 0 3 6 0 10 6 11 0 299 13 0 2 13 0 7 8 |389 m=comp.graphics
+ 6 0 1 0 0 4 2 0 5 2 12 0 8 321 0 4 14 0 8 6 |393 n=sci.electronics
+ 2 0 0 0 0 0 4 1 0 3 1 0 3 1 372 6 0 2 1 2 |398 o=soc.religion.christian
+ 4 0 0 1 0 2 3 3 0 4 2 0 7 12 6 342 1 0 9 0 |396 p=sci.med
+ 0 1 0 1 0 1 4 0 3 0 1 0 8 4 0 2 369 0 1 1 |396 q=sci.crypt
+ 10 0 4 10 1 5 6 2 2 6 2 0 2 1 86 15 14 152 0 1 |319 r=alt.atheism
+ 4 0 0 0 0 9 1 1 8 1 12 0 3 0 2 0 0 0 341 2 |390 s=misc.forsale
+ 8 5 0 0 0 1 6 0 8 5 50 0 40 2 1 0 9 0 3 256|394 t=comp.os.ms-windows.misc
+ =======================================================
+ Statistics
+ -------------------------------------------------------
+ Kappa 0.8808
+ Accuracy 90.8596%
+ Reliability 86.3632%
+ Reliability (standard deviation) 0.2131
+
+
+
+
+
+<a name="TwentyNewsgroups-ComplementaryNaiveBayes"></a>
+## End to end commands to build a CBayes model for 20 newsgroups
+The [20 newsgroups example script](https://github.com/apache/mahout/blob/master/examples/bin/classify-20newsgroups.sh) issues the following commands as outlined above. We can build a CBayes classifier from the command line by following the process in the script:
+
+*Be sure that **MAHOUT_HOME**/bin and **HADOOP_HOME**/bin are in your **$PATH*** + +1. Create a working directory for the dataset and all input/output. + +$ export WORK_DIR=/tmp/mahout-work-${USER} +$ mkdir -p ${WORK_DIR} + +2. Download and extract the *20news-bydate.tar.gz* from the [20newsgroups dataset](http://people.csail.mit.edu/jrennie/20Newsgroups/20news-bydate.tar.gz) to the working directory. + +$ curl http://people.csail.mit.edu/jrennie/20Newsgroups/20news-bydate.tar.gz
+ -o ${WORK_DIR}/20news-bydate.tar.gz +$ mkdir -p ${WORK_DIR}/20news-bydate +$ cd ${WORK_DIR}/20news-bydate && tar xzf ../20news-bydate.tar.gz && cd .. && cd .. +$ mkdir ${WORK_DIR}/20news-all +$ cp -R ${WORK_DIR}/20news-bydate/*/*${WORK_DIR}/20news-all
+ * If you're running on a Hadoop cluster:
+
+ $hadoop dfs -put${WORK_DIR}/20news-all ${WORK_DIR}/20news-all + +3. Convert the full 20 newsgroups dataset into a < Text, Text > SequenceFile. + +$ mahout seqdirectory
+ -i ${WORK_DIR}/20news-all + -o${WORK_DIR}/20news-seq
+ -ow
+
+4. Convert and preprocesses the dataset into a < Text, VectorWritable > SequenceFile containing term frequencies for each document.
+
+ $mahout seq2sparse + -i${WORK_DIR}/20news-seq
+ -o ${WORK_DIR}/20news-vectors + -lnorm + -nv + -wt tfidf +If we wanted to use different parsing methods or transformations on the term frequency vectors we could supply different options here e.g.: -ng 2 for bigrams or -n 2 for L2 length normalization. See the [Creating vectors from text](http://mahout.apache.org/users/basics/creating-vectors-from-text.html) page for a list of all seq2sparse options. + +5. Split the preprocessed dataset into training and testing sets. + +$ mahout split
+ -i ${WORK_DIR}/20news-vectors/tfidf-vectors + --trainingOutput${WORK_DIR}/20news-train-vectors
+ --testOutput ${WORK_DIR}/20news-test-vectors + --randomSelectionPct 40 + --overwrite --sequenceFiles -xm sequential + +6. Train the classifier. + +$ mahout trainnb
+ -i ${WORK_DIR}/20news-train-vectors + -el + -o${WORK_DIR}/model
+ -li ${WORK_DIR}/labelindex + -ow + -c + +7. Test the classifier. + +$ mahout testnb
+ -i ${WORK_DIR}/20news-test-vectors + -m${WORK_DIR}/model
+ -l ${WORK_DIR}/labelindex + -ow + -o${WORK_DIR}/20news-testing
+ -c
+
+
+
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diff --git a/website/docs/tutorials/map-reduce/classification/wikipedia-classifier-example.md b/website/docs/tutorials/map-reduce/classification/wikipedia-classifier-example.md
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+---
+layout: default
+title: Wikipedia XML parser and Naive Bayes Example
+theme:
+ name: retro-mahout
+---
+# Wikipedia XML parser and Naive Bayes Classifier Example
+
+## Introduction
+Mahout has an [example script](https://github.com/apache/mahout/blob/master/examples/bin/classify-wikipedia.sh) [1] which will download a recent XML dump of the (entire if desired) [English Wikipedia database](http://dumps.wikimedia.org/enwiki/latest/). After running the classification script, you can use the [document classification script](https://github.com/apache/mahout/blob/master/examples/bin/spark-document-classifier.mscala) from the Mahout [spark-shell](http://mahout.apache.org/users/sparkbindings/play-with-shell.html) to vectorize and classify text from outside of the training and testing corpus using a modle built on the Wikipedia dataset.
+
+You can run this script to build and test a Naive Bayes classifier for option (1) 10 arbitrary countries or option (2) 2 countries (United States and United Kingdom).
+
+## Oververview
+
+Tou run the example simply execute the $MAHOUT_HOME/examples/bin/classify-wikipedia.sh script. + +By defult the script is set to run on a medium sized Wikipedia XML dump. To run on the full set (the entire english Wikipedia) you can change the download by commenting out line 78, and uncommenting line 80 of [classify-wikipedia.sh](https://github.com/apache/mahout/blob/master/examples/bin/classify-wikipedia.sh) [1]. However this is not recommended unless you have the resources to do so. *Be sure to clean your work directory when changing datasets- option (3).* + +The step by step process for Creating a Naive Bayes Classifier for the Wikipedia XML dump is very similar to that for [creating a 20 Newsgroups Classifier](http://mahout.apache.org/users/classification/twenty-newsgroups.html) [4]. The only difference being that instead of running $mahout seqdirectory on the unzipped 20 Newsgroups file, you'll run $mahout seqwiki on the unzipped Wikipedia xml dump. + +$ mahout seqwiki
+
+The above command launches WikipediaToSequenceFile.java which accepts a text file of categories [3] and starts an MR job to parse the each document in the XML file. This process will seek to extract documents with a wikipedia category tag which (exactly, if the -exactMatchOnly option is set) matches a line in the category file. If no match is found and the -all option is set, the document will be dumped into an "unknown" category. The documents will then be written out as a <Text,Text> sequence file of the form (K:/category/document_title , V: document).
+
+There are 3 different example category files available to in the /examples/src/test/resources
+directory: country.txt, country10.txt and country2.txt. You can edit these categories to extract a different corpus from the Wikipedia dataset.
+
+The CLI options for seqwiki are as follows:
+
+ --input (-i) input pathname String
+ --output (-o) the output pathname String
+ --categories (-c) the file containing the Wikipedia categories
+ --exactMatchOnly (-e) if set, then the Wikipedia category must match
+ exactly instead of simply containing the category string
+ --all (-all) if set select all categories
+ --removeLabels (-rl) if set, remove [[Category:labels]] from document text after extracting label.
+
+
+After seqwiki, the script runs seq2sparse, split, trainnb and testnb as in the [step by step 20newsgroups example](http://mahout.apache.org/users/classification/twenty-newsgroups.html). When all of the jobs have finished, a confusion matrix will be displayed.
+
+#Resourcese
+
+[1] [classify-wikipedia.sh](https://github.com/apache/mahout/blob/master/examples/bin/classify-wikipedia.sh)
+
+[2] [Document classification script for the Mahout Spark Shell](https://github.com/apache/mahout/blob/master/examples/bin/spark-document-classifier.mscala)
+
+[3] [Example category file](https://github.com/apache/mahout/blob/master/examples/src/test/resources/country10.txt)
+
+[4] [Step by step instructions for building a Naive Bayes classifier for 20newsgroups from the command line](http://mahout.apache.org/users/classification/twenty-newsgroups.html)
+
+[5] [Mahout MapReduce Naive Bayes](http://mahout.apache.org/users/classification/bayesian.html)
+
+[6] [Mahout Spark Naive Bayes](http://mahout.apache.org/users/algorithms/spark-naive-bayes.html)
+
+[7] [Mahout Scala Spark and H2O Bindings](http://mahout.apache.org/users/sparkbindings/home.html)
+
http://git-wip-us.apache.org/repos/asf/mahout/blob/c81fc8b7/website/docs/tutorials/map-reduce/index.md
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diff --git a/website/docs/tutorials/map-reduce/index.md b/website/docs/tutorials/map-reduce/index.md
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@@ -0,0 +1,17 @@
+---
+layout: page
+title: Deprecated Map Reduce Based Examples
+theme:
+ name: mahout2
+---
+
+
+### Classification
+
+[Bank Marketing Example](classification/bankmarketing-example.html)
+
+[Breiman Exampe](classification/breiman-example.html)
+
+[Twenty Newsgroups](classification/twenty-newsgroups.html)
+
+[Wikipedia Classifier Example](classification/wikipedia-classifier-example.html)
\ No newline at end of file
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----
-layout: page
-title: Mahout Samsara In Core
-theme:
- name: mahout2
----
-# Playing with Mahout's Spark Shell
-
-This tutorial will show you how to play with Mahout's scala DSL for linear algebra and its Spark shell. **Please keep in mind that this code is still in a very early experimental stage**.
-
-_(Edited for 0.10.2)_
-
-## Intro
-
-We'll use an excerpt of a publicly available [dataset about cereals](http://lib.stat.cmu.edu/DASL/Datafiles/Cereals.html). The dataset tells the protein, fat, carbohydrate and sugars (in milligrams) contained in a set of cereals, as well as a customer rating for the cereals. Our aim for this example is to fit a linear model which infers the customer rating from the ingredients.
-
-
-Name | protein | fat | carbo | sugars | rating
-:-----------------------|:--------|:----|:------|:-------|:---------
-Apple Cinnamon Cheerios | 2 | 2 | 10.5 | 10 | 29.509541
-Cap'n'Crunch | 1 | 2 | 12 | 12 | 18.042851
-Cocoa Puffs | 1 | 1 | 12 | 13 | 22.736446
-Froot Loops | 2 | 1 | 11 | 13 | 32.207582
-Honey Graham Ohs | 1 | 2 | 12 | 11 | 21.871292
-Wheaties Honey Gold | 2 | 1 | 16 | 8 | 36.187559
-Cheerios | 6 | 2 | 17 | 1 | 50.764999
-Clusters | 3 | 2 | 13 | 7 | 40.400208
-Great Grains Pecan | 3 | 3 | 13 | 4 | 45.811716
-
-
-## Installing Mahout & Spark on your local machine
-
-We describe how to do a quick toy setup of Spark & Mahout on your local machine, so that you can run this example and play with the shell.
-
- 1. Change to the directory where you unpacked Spark and type sbt/sbt assembly to build it
- 1. Create a directory for Mahout somewhere on your machine, change to there and checkout the master branch of Apache Mahout from GitHub git clone https://github.com/apache/mahout mahout
- 1. Change to the mahout directory and build mahout using mvn -DskipTests clean install
-
-## Starting Mahout's Spark shell
-
- 1. Goto the directory where you unpacked Spark and type sbin/start-all.sh to locally start Spark
- 1. Open a browser, point it to [http://localhost:8080/](http://localhost:8080/) to check whether Spark successfully started. Copy the url of the spark master at the top of the page (it starts with **spark://**)
- 1. Define the following environment variables: <pre class="codehilite">export MAHOUT_HOME=[directory into which you checked out Mahout]
-export SPARK_HOME=[directory where you unpacked Spark]
-export MASTER=[url of the Spark master]
-</pre>
- 1. Finally, change to the directory where you unpacked Mahout and type bin/mahout spark-shell,
-you should see the shell starting and get the prompt mahout> . Check
-[FAQ](http://mahout.apache.org/users/sparkbindings/faq.html) for further troubleshooting.
-
-## Implementation
-
-We'll use the shell to interactively play with the data and incrementally implement a simple [linear regression](https://en.wikipedia.org/wiki/Linear_regression) algorithm. Let's first load the dataset. Usually, we wouldn't need Mahout unless we processed a large dataset stored in a distributed filesystem. But for the sake of this example, we'll use our tiny toy dataset and "pretend" it was too big to fit onto a single machine.
-
-*Note: You can incrementally follow the example by copy-and-pasting the code into your running Mahout shell.*
-
-Mahout's linear algebra DSL has an abstraction called *DistributedRowMatrix (DRM)* which models a matrix that is partitioned by rows and stored in the memory of a cluster of machines. We use dense() to create a dense in-memory matrix from our toy dataset and use drmParallelize to load it into the cluster, "mimicking" a large, partitioned dataset.
-
-<div class="codehilite"><pre>
-val drmData = drmParallelize(dense(
- (2, 2, 10.5, 10, 29.509541), // Apple Cinnamon Cheerios
- (1, 2, 12, 12, 18.042851), // Cap'n'Crunch
- (1, 1, 12, 13, 22.736446), // Cocoa Puffs
- (2, 1, 11, 13, 32.207582), // Froot Loops
- (1, 2, 12, 11, 21.871292), // Honey Graham Ohs
- (2, 1, 16, 8, 36.187559), // Wheaties Honey Gold
- (6, 2, 17, 1, 50.764999), // Cheerios
- (3, 2, 13, 7, 40.400208), // Clusters
- (3, 3, 13, 4, 45.811716)), // Great Grains Pecan
- numPartitions = 2);
-</pre></div>
-
-Have a look at this matrix. The first four columns represent the ingredients
-(our features) and the last column (the rating) is the target variable for
-our regression. [Linear regression](https://en.wikipedia.org/wiki/Linear_regression)
-assumes that the **target variable** $$\mathbf{y}$$ is generated by the
-linear combination of **the feature matrix** $$\mathbf{X}$$ with the
-**parameter vector** $$\boldsymbol{\beta}$$ plus the
- **noise** $$\boldsymbol{\varepsilon}$$, summarized in the formula
-$$\mathbf{y}=\mathbf{X}\boldsymbol{\beta}+\boldsymbol{\varepsilon}$$.
-Our goal is to find an estimate of the parameter vector
-$$\boldsymbol{\beta}$$ that explains the data very well.
-
-As a first step, we extract $$\mathbf{X}$$ and $$\mathbf{y}$$ from our data matrix. We get *X* by slicing: we take all rows (denoted by ::) and the first four columns, which have the ingredients in milligrams as content. Note that the result is again a DRM. The shell will not execute this code yet, it saves the history of operations and defers the execution until we really access a result. **Mahout's DSL automatically optimizes and parallelizes all operations on DRMs and runs them on Apache Spark.**
-
-<div class="codehilite"><pre>
-val drmX = drmData(::, 0 until 4)
-</pre></div>
-
-Next, we extract the target variable vector *y*, the fifth column of the data matrix. We assume this one fits into our driver machine, so we fetch it into memory using collect:
-
-<div class="codehilite"><pre>
-val y = drmData.collect(::, 4)
-</pre></div>
-
-Now we are ready to think about a mathematical way to estimate the parameter vector *β*. A simple textbook approach is [ordinary least squares (OLS)](https://en.wikipedia.org/wiki/Ordinary_least_squares), which minimizes the sum of residual squares between the true target variable and the prediction of the target variable. In OLS, there is even a closed form expression for estimating $$\boldsymbol{\beta}$$ as
-$$\left(\mathbf{X}^{\top}\mathbf{X}\right)^{-1}\mathbf{X}^{\top}\mathbf{y}$$.
-
-The first thing which we compute for this is $$\mathbf{X}^{\top}\mathbf{X}$$. The code for doing this in Mahout's scala DSL maps directly to the mathematical formula. The operation .t() transposes a matrix and analogous to R %*% denotes matrix multiplication.
-
-<div class="codehilite"><pre>
-val drmXtX = drmX.t %*% drmX
-</pre></div>
-
-The same is true for computing $$\mathbf{X}^{\top}\mathbf{y}$$. We can simply type the math in scala expressions into the shell. Here, *X* lives in the cluster, while is *y* in the memory of the driver, and the result is a DRM again.
-<div class="codehilite"><pre>
-val drmXty = drmX.t %*% y
-</pre></div>
-
-We're nearly done. The next step we take is to fetch $$\mathbf{X}^{\top}\mathbf{X}$$ and
-$$\mathbf{X}^{\top}\mathbf{y}$$ into the memory of our driver machine (we are targeting
-features matrices that are tall and skinny ,
-so we can assume that $$\mathbf{X}^{\top}\mathbf{X}$$ is small enough
-to fit in). Then, we provide them to an in-memory solver (Mahout provides
-the an analog to R's solve() for that) which computes beta, our
-OLS estimate of the parameter vector $$\boldsymbol{\beta}$$.
-
-<div class="codehilite"><pre>
-val XtX = drmXtX.collect
-val Xty = drmXty.collect(::, 0)
-
-val beta = solve(XtX, Xty)
-</pre></div>
-
-That's it! We have a implemented a distributed linear regression algorithm
-on Apache Spark. I hope you agree that we didn't have to worry a lot about
-parallelization and distributed systems. The goal of Mahout's linear algebra
-DSL is to abstract away the ugliness of programming a distributed system
-as much as possible, while still retaining decent performance and
-scalability.
-
-We can now check how well our model fits its training data.
-First, we multiply the feature matrix $$\mathbf{X}$$ by our estimate of
-$$\boldsymbol{\beta}$$. Then, we look at the difference (via L2-norm) of
-the target variable $$\mathbf{y}$$ to the fitted target variable:
-
-<div class="codehilite"><pre>
-val yFitted = (drmX %*% beta).collect(::, 0)
-(y - yFitted).norm(2)
-</pre></div>
-
-We hope that we could show that Mahout's shell allows people to interactively and incrementally write algorithms. We have entered a lot of individual commands, one-by-one, until we got the desired results. We can now refactor a little by wrapping our statements into easy-to-use functions. The definition of functions follows standard scala syntax.
-
-We put all the commands for ordinary least squares into a function ols.
-
-<div class="codehilite"><pre>
-def ols(drmX: DrmLike[Int], y: Vector) =
- solve(drmX.t %*% drmX, drmX.t %*% y)(::, 0)
-
-</pre></div>
-
-Note that DSL declares implicit collect if coersion rules require an in-core argument. Hence, we can simply
-skip explicit collects.
-
-Next, we define a function goodnessOfFit that tells how well a model fits the target variable:
-
-<div class="codehilite"><pre>
-def goodnessOfFit(drmX: DrmLike[Int], beta: Vector, y: Vector) = {
- val fittedY = (drmX %*% beta).collect(::, 0)
- (y - fittedY).norm(2)
-}
-</pre></div>
-
-So far we have left out an important aspect of a standard linear regression
-model. Usually there is a constant bias term added to the model. Without
-that, our model always crosses through the origin and we only learn the
-right angle. An easy way to add such a bias term to our model is to add a
-column of ones to the feature matrix $$\mathbf{X}$$.
-The corresponding weight in the parameter vector will then be the bias term.
-
-Here is how we add a bias column:
-
-<div class="codehilite"><pre>
-val drmXwithBiasColumn = drmX cbind 1
-</pre></div>
-
-Now we can give the newly created DRM drmXwithBiasColumn to our model fitting method ols and see how well the resulting model fits the training data with goodnessOfFit. You should see a large improvement in the result.
-
-<div class="codehilite"><pre>
-val betaWithBiasTerm = ols(drmXwithBiasColumn, y)
-goodnessOfFit(drmXwithBiasColumn, betaWithBiasTerm, y)
-</pre></div>
-
-As a further optimization, we can make use of the DSL's caching functionality. We use drmXwithBiasColumn repeatedly as input to a computation, so it might be beneficial to cache it in memory. This is achieved by calling checkpoint(). In the end, we remove it from the cache with uncache:
-
-<div class="codehilite"><pre>
-val cachedDrmX = drmXwithBiasColumn.checkpoint()
-
-val betaWithBiasTerm = ols(cachedDrmX, y)
-val goodness = goodnessOfFit(cachedDrmX, betaWithBiasTerm, y)
-
-cachedDrmX.uncache()
-
-goodness
-</pre></div>
-
-
-Liked what you saw? Checkout Mahout's overview for the [Scala and Spark bindings](https://mahout.apache.org/users/sparkbindings/home.html).
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+---
+layout: default
+title:
+theme:
+ name: retro-mahout
+---
+
+## Getting Started
+
+To get started, add the following dependency to the pom:
+
+ <dependency>
+ <groupId>org.apache.mahout</groupId>
+ <version>0.12.0</version>
+ </dependency>
+
+Here is how to use the Flink backend:
+
+ import org.apache.mahout.math.drm._
+ import org.apache.mahout.math.drm.RLikeDrmOps._
+
+
+ def main(args: Array[String]): Unit = {
+ val filePath = "path/to/the/input/file"
+
+ val env = ExecutionEnvironment.getExecutionEnvironment
+ implicit val ctx = new FlinkDistributedContext(env)
+
+ val drm = readCsv(filePath, delim = "\t", comment = "#")
+ val C = drm.t %*% drm
+ println(C.collect)
+ }
+
+ }
+
+## Current Status
+
+The top JIRA for Flink backend is [MAHOUT-1570](https://issues.apache.org/jira/browse/MAHOUT-1570) which has been fully implemented.
+
+### Implemented
+
+* [MAHOUT-1701](https://issues.apache.org/jira/browse/MAHOUT-1701) Mahout DSL for Flink: implement AtB ABt and AtA operators
+* [MAHOUT-1702](https://issues.apache.org/jira/browse/MAHOUT-1702) implement element-wise operators (like A + 2 or A + B)
+* [MAHOUT-1703](https://issues.apache.org/jira/browse/MAHOUT-1703) implement cbind and rbind
+* [MAHOUT-1709](https://issues.apache.org/jira/browse/MAHOUT-1709) implement slicing (like A(1 to 10, ::))
+* [MAHOUT-1710](https://issues.apache.org/jira/browse/MAHOUT-1710) implement right in-core matrix multiplication (A %*% B when B is in-core)
+* [MAHOUT-1712](https://issues.apache.org/jira/browse/MAHOUT-1712) implement operators At, Ax, Atx - Ax and At are implemented
+* [MAHOUT-1734](https://issues.apache.org/jira/browse/MAHOUT-1734) implement I/O - should be able to read results of Flink bindings
+* [MAHOUT-1747](https://issues.apache.org/jira/browse/MAHOUT-1747) add support for different types of indexes (String, long, etc) - now supports Int, Long and String
+* [MAHOUT-1748](https://issues.apache.org/jira/browse/MAHOUT-1748) switch to Flink Scala API
+* [MAHOUT-1749](https://issues.apache.org/jira/browse/MAHOUT-1749) Implement Atx
+* [MAHOUT-1750](https://issues.apache.org/jira/browse/MAHOUT-1750) Implement ABt
+* [MAHOUT-1751](https://issues.apache.org/jira/browse/MAHOUT-1751) Implement AtA
+* [MAHOUT-1755](https://issues.apache.org/jira/browse/MAHOUT-1755) Flush intermediate results to FS - Flink, unlike Spark, does not store intermediate results in memory.
+* [MAHOUT-1776](https://issues.apache.org/jira/browse/MAHOUT-1776) Refactor common Engine agnostic classes to Math-Scala module
+* [MAHOUT-1777](https://issues.apache.org/jira/browse/MAHOUT-1777) move HDFSUtil classes into the HDFS module
+* [MAHOUT-1804](https://issues.apache.org/jira/browse/MAHOUT-1804) Implement drmParallelizeWithRowLabels(..) in Flink
+* [MAHOUT-1805](https://issues.apache.org/jira/browse/MAHOUT-1805) Implement allReduceBlock(..) in Flink bindings
+* [MAHOUT-1809](https://issues.apache.org/jira/browse/MAHOUT-1809) Failing tests in flin-bindings: dals and dspca
+* [MAHOUT-1810](https://issues.apache.org/jira/browse/MAHOUT-1810) Failing test in flink-bindings: A + B Identically partitioned (mapBlock Checkpointing issue)
+* [MAHOUT-1812](https://issues.apache.org/jira/browse/MAHOUT-1812) Implement drmParallelizeWithEmptyLong(..) in flink bindings
+* [MAHOUT-1814](https://issues.apache.org/jira/browse/MAHOUT-1814) Implement drm2intKeyed in flink bindings
+* [MAHOUT-1815](https://issues.apache.org/jira/browse/MAHOUT-1815) dsqDist(X,Y) and dsqDist(X) failing in flink tests
+* [MAHOUT-1816](https://issues.apache.org/jira/browse/MAHOUT-1816) Implement newRowCardinality in CheckpointedFlinkDrm
+* [MAHOUT-1817](https://issues.apache.org/jira/browse/MAHOUT-1817) Implement caching in Flink Bindings
+* [MAHOUT-1818](https://issues.apache.org/jira/browse/MAHOUT-1818) dals test failing in Flink Bindings
+* [MAHOUT-1820](https://issues.apache.org/jira/browse/MAHOUT-1820) Add a method to generate Tuple<PartitionId, Partition elements count>> to support Flink backend
+* [MAHOUT-1821](https://issues.apache.org/jira/browse/MAHOUT-1821) Use a mahout-flink-conf.yaml configuration file for Mahout specific Flink configuration
+* [MAHOUT-1824](https://issues.apache.org/jira/browse/MAHOUT-1824) Optimize FlinkOpAtA to use upper triangular matrices
+
+### Tests
+
+There is a set of standard tests that all engines should pass (see [MAHOUT-1764](https://issues.apache.org/jira/browse/MAHOUT-1764)).
+
+* DistributedDecompositionsSuite
+* DrmLikeOpsSuite
+* DrmLikeSuite
+* RLikeDrmOpsSuite
+
+
+These are Flink-backend specific tests, e.g.
+
+* DrmLikeOpsSuite for operations like norm, rowSums, rowMeans
+* RLikeOpsSuite for basic LA like A.t %*% A, A.t %*% x, etc
+* LATestSuite tests for specific operators like AtB, Ax, etc
+* UseCasesSuite has more complex examples, like power iteration, ridge regression, etc
+
+## Environment
+
+For development the minimal supported configuration is
+
+* [Scala 2.10]
+
+When using mahout, please import the following modules:
+
+* mahout-math
+* mahout-math-scala
+* mahout-flink_2.10
+*
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https://pubmed.ncbi.nlm.nih.gov/19996819/
|
, 30 (5), 719-23
# Cyclo-oxygenase-2 Expression in Human Idiopathic Epiretinal Membrane
Affiliations
• PMID: 19996819
# Cyclo-oxygenase-2 Expression in Human Idiopathic Epiretinal Membrane
Satoru Kase et al. Retina.
## Abstract
Purpose: The purpose of this study was to examine the expression of cyclo-oxygenase (COX)-2 in the idiopathic epiretinal membrane (IERM), inner limiting membrane (ILM), and proliferative diabetic retinopathy membrane.
Methods: Twenty membranes, consisting of eight IERMs, four ILMs, and eight proliferative diabetic retinopathy membranes, were surgically removed. Formalin-fixed, paraffin-embedded tissue sections were processed for immunohistochemistry using anti-COX-2 antibody. The nuclear density showing the density of cells situated in IERM and ILM specimens was calculated under high-power fields using a light microscope.
Results: The IERM comprised flattened cells with oval nuclei constituting a monolayer. The ILM contained a few cells with abundant collagenous tissues. Neither endothelial nor inflammatory cells were observed in the IERM and ILM. COX-2 immunoreactivity was markedly detected in cells located in the IERM. In contrast, COX-2 immunoreactivity was faintly detected in the ILM. The COX-2-positive rate was 65.4 +/- 15.5% and 34.3 +/- 20.3% in the IERM and ILM, respectively, being significantly higher in the former (P = 0.046). The nuclear density was 39.3 +/- 10.3 and 8.6 +/- 7.2 in the IERM and ILM, respectively, being significantly higher in the former (P = 0.0003). The proliferative diabetic retinopathy membranes consisted of many vascular endothelial and stromal cells. Cytoplasmic immunoreactivity for COX-2 was detected in endothelial and stromal cells in the proliferative diabetic retinopathy membranes.
Conclusion: These results suggest that COX-2 plays a potential role in the formation of avascular and vascularized epiretinal membranes if an epiphenomenon of COX-2 expression within these epiretinal membranes has been ruled out in future studies.
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http://mathhelpforum.com/algebra/100240-inequalities-print.html
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# inequalities
• September 2nd 2009, 06:27 AM
thereddevils
inequalities
$\sum^{n}_{r=1}r^3>18000$
$\frac{1}{4}n^2(n+1)^2>18000$
i am not sure how to solve this . Thanks for helping .
• September 2nd 2009, 07:33 AM
Soroban
Hello, thereddevils!
Quote:
$\sum^{n}_{r=1}r^3\:>\:18,\!000$
$\frac{1}{4}n^2(n+1)^2\:>\:18,\!000$
i am not sure how to solve this . Thanks for helping .
Note that $n$ is a positive integer.
. . Hence, $n(n+1)$ is also positive.
Multiply by 4: . $n^2(n+1)^2 \:>\:72,\!000$
Take the square root: . $n(n+1) \:>\:\sqrt{72,\!000} \:=\:120\sqrt{5}$
And we have: . $n^2 + n - 120\sqrt{5}\:>\:0$
We have: . $y \:=\:x^2 + x - 120\sqrt{5}$ . . . an up-opening parabola.
. . It is positive on the "outside" of its $x$-intercepts.
So we solve: . $x^2 + x - 120\sqrt{5} \:=\:0$
. . Quadratic Formula: . $x \;=\; \frac{-1 \pm\sqrt{1 + 480\sqrt{5}}}{2} \;\approx\;\begin{Bmatrix}15.89 \\ \text{-}16.89\end{Bmatrix}$
Hence, $y$ is positive for: . $(x \:\leq \:-16.89) \;\cup \;(x \:\geq \:15.89)$
. . Therefore: . $\boxed{n \:\geq\: 16}$
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
Check
$n = 15\!:\;\;\sum^{15}_{r=1}r^3 \:=\:14,\!400$
$n = 16\!:\;\;\sum^{16}_{r-1}r^3 \:=\:18,\!496$
. . We're golden!
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https://tobaccocontrol.bmj.com/highwire/markup/155396/expansion?width=1000&height=500&iframe=true&postprocessors=highwire_tables%2Chighwire_reclass%2Chighwire_figures%2Chighwire_math%2Chighwire_inline_linked_media%2Chighwire_embed
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Table 2
Characteristics of the top-listed product on tobacco price boards that had a FMC product listed first, 2013–2015
2013 (n=215) 2014 (n=224) 2015 (n=219) % (reference) % Adjusted OR (95% CI), p value % Adjusted OR (95% CI), p value Market segment Super-value 15.4 15.2 0.96 (0.66 to 1.41), p=0.837 27.9 2.11 (1.35 to 3.31), p=0.001 Value 4.2 6.7 1.75 (0.92 to 3.33), p=0.089 12.3 4.03 (1.96 to 8.29), p<0.001 Mainstream 14.4 21.4 1.68 (1.08 to 2.63), p=0.022 17.4 1.25 (0.80 to 1.96), p=0.324 Premium 66.1 56.7 0.66 (0.49 to 0.90), p=0.008 42.5 0.36 (0.25 to 0.50), p<0.001 Company BATA 48.4 58.0 1.53 (1.12 to 2.08), p=0.007 40.2 0.69 (0.50 to 0.96), p=0.028 IT 15.4 16.1 1.04 (0.77 to 1.40), p=0.800 26.0 2.28 (1.51 to 3.44), p<0.001 PM 35.8 23.7 0.54 (0.38 to 0.77), p=0.001 28.3 0.67 (0.47 to 0.97), p=0.034 Other* 0.5 2.2 4.91 (0.83 to 28.96), p=0.079 5.5 12.58 (1.55 to 102.29), p=0.018 New product 3.7 7.1 2.12 (0.88 to 5.11), p=0.096 11.4 4.03 (1.69 to 9.62), p=0.002 Price discounted 9.3 8.0 0.79 (0.43 to 1.45), p=0.439 15.1 1.60 (0.90 to 2.85), p=0.110 Left-digit pricing used ‘Left-digit’ pricing ($0.95–$0.99) 22.3 15.6 0.63 (0.38 to 1.03), p=0.066 30.6 1.43 (0.92 to 2.24), p=0.115 Rounded number pricing ($0.00) 11.6 18.3 1.97 (1.17 to 3.32), p=0.011 9.1 0.94 (0.48 to 1.82), p=0.843 All others 66.1 66.1 0.97 (0.68 to 1.37), p=0.846 60.3 0.75 (0.51 to 1.09), p=0.134 Pack under$20 71.6 36.6 0.20 (0.14 to 0.28), p<0.001 35.6 0.20 (0.13 to 0.28), p<0.001 Product bundling Single pack 91.6 93.8 1.37 (0.72 to 2.62), p=0.337 93.6 1.33 (0.65 to 2.75), p=0.434 Multibuy† 7.9 6.3 0.78 (0.41 to 1.49), p=0.444 6.4 0.80 (0.38 to 1.66), p=0.547 Carton 0.5 0 n/a 0 n/a Pack size (single packs only) (n=197) (n=210) (n=205) 20s 31.5 29.1 0.90 (0.63 to 1.30), p=0.584 45.4 1.91 (1.27 to 2.85), p=0.002 21s, 22s, 23s, 26s 3.6 8.1 2.41 (1.05 to 5.57), p=0.039 3.9 1.15 (0.44 to 3.02), p=0.772 25s 57.9 55.2 0.95 (0.69 to 1.30), p=0.748 39.5 0.48 (0.33 to 0.70), p<0.001 30s‡ 4.1 4.8 1.16 (0.46 to 2.95), p=0.751 8.8 2.13 (0.93 to 4.88), p=0.072 40s and 50s§ 3.1 2.9 1.09 (0.66 to 1.79), p=0.748 2.4 0.98 (0.50 to 1.92), p=0.949
• All models adjusted for store type and area SES.
• *Store type excluded from logistic regression analysis as brands from ‘other’ manufacturers were never observed as the top-listed product in small mixed businesses, newsagent/lottery outlets and tobacconists.
• †Store type excluded from logistic regression analysis as multibuys were never observed in small-mixed business and only once in each of convenience stores, newsagent/lottery outlets and tobacconists.
• ‡SES excluded from logistic regression analysis as packs of 30s were never observed in stores in high-SES areas.
• §Store type excluded from logistic regression analysis as packs of 40s or 50s were never observed in convenience stores, and rarely in newsagent/lottery outlets (twice) and tobacconists (once).
• BATA, British American Tobacco Australia; IT, Imperial Tobacco; PM, Philip Morris; n/a, not applicable; SES, socioeconomic status.
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