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Plate heat exchanger Design of plate and frame heat exchangers Plate_and_frame_heat_exchanger > Design of plate and frame heat exchangers The plates are pressed to form troughs at right angles to the direction of flow of the liquid which runs through the channels in the heat exchanger. These troughs are arranged so that they interlink with the other plates which forms the channel with gaps of 1.3–1.5 mm between the plates. The plates are compressed together in a rigid frame to form an arrangement of parallel flow channels with alternating hot and cold fluids.
Hermann Hartmann External links and references Hermann_Hartmann > External links and references Kohlmaier (Ed.). Chemische Elementarprozesse. Springer, Berlin (1968) Book H. W. Spiess, H. Haas, H. Hartmann: Anisotropic Chemical Shifts in Cobalt (III) Complexes.
Armored fighting vehicles Armoured vehicle-launched bridge Armored_fighting_vehicles > Modern classification by type and role > Armoured engineering vehicle > Armoured vehicle-launched bridge An armoured vehicle-launched bridge (AVLB) is a combat support vehicle, sometimes regarded as a subtype of combat engineering vehicle, designed to assist militaries in rapidly deploying tanks and other armoured fighting vehicles across rivers. The AVLB is usually a tracked vehicle converted from a tank chassis to carry a folding metal bridge instead of weapons. The AVLB's job is to allow armoured or infantry units to cross water, when a river too deep for vehicles to wade through is reached, and no bridge is conveniently located (or sufficiently sturdy, a substantial concern when moving 60-ton tanks). The bridge layer unfolds and launches its cargo, providing a ready-made bridge across the obstacle in only minutes.
History of systems of units of measurement History History_of_systems_of_units_of_measurement > History Other quantities, such as power and speed, are derived from the base quantities: for example, speed is distance per unit time. Historically a wide range of units was used for the same type of quantity. In different contexts length was measured in inches, feet, yards, fathoms, rods, chains, furlongs, miles, nautical miles, stadia, leagues, with conversion factors that were not based on power of ten.
Physical Sciences Definition Physical_Sciences > Definition Physical science can be described as all of the following: A branch of science (a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe).A branch of natural science – natural science is a major branch of science that tries to explain and predict nature's phenomena, based on empirical evidence. In natural science, hypotheses must be verified scientifically to be regarded as scientific theory. Validity, accuracy, and social mechanisms ensuring quality control, such as peer review and repeatability of findings, are amongst the criteria and methods used for this purpose. Natural science can be broken into two main branches: life science (for example biology) and physical science. Each of these branches, and all of their sub-branches, are referred to as natural sciences.
Concept Theory-theory Concept > Notable theories on the structure of concepts > Theory-theory Theory-theory is a reaction to the previous two theories and develops them further. This theory postulates that categorization by concepts is something like scientific theorizing. Concepts are not learned in isolation, but rather are learned as a part of our experiences with the world around us. In this sense, concepts' structure relies on their relationships to other concepts as mandated by a particular mental theory about the state of the world.
Evolving digital ecological network Overview Evolving_digital_ecological_network > Overview Understanding how individual interactions within networks influence coevolution, and conversely how coevolution influences the overall structure of networks, requires an appreciation for how pair-wise interactions change due to their broader community contexts as well as how this community context shapes selective pressures. Accordingly, research is now focusing on how reciprocal selection influences and is embedded within the structure of multispecies interactive webs, not only on particular species in isolation.Coevolution in a community context can be addressed theoretically via mathematical modeling and simulation, by looking at ancient footprints of evolutionary history via ecological patterns that persist and are observable today, and by performing laboratory experiments with microorganisms.
Robotic Process Automation Historic evolution Robotic_Process_Automation > Historic evolution It is considered to be a significant technological evolution in the sense that new software platforms are emerging which are sufficiently mature, resilient, scalable and reliable to make this approach viable for use in large enterprises (who would otherwise be reluctant due to perceived risks to quality and reputation). A principal barrier to the adoption of self-service is often technological: it may not always be feasible or economically viable to retrofit new interfaces onto existing systems. Moreover, organisations may wish to layer a variable and configurable set of process rules on top of the system interfaces which may vary according to market offerings and the type of customer.
Vitamin K reaction Parental Vitamin K1 Reactions Vitamin_K_reaction > Parental Vitamin K1 Reactions Most of the reactions that are observed, can be maintained by polyoxyethylated caster oil. This oil is composed by reacting castrol oil with ethylene oxide. This emulsifier can act as a stabilizer for other medications like cyclosporine, clotrimazole, miconazole, teniposide and paclitaxel.
Signed graph Other kinds of "signed graph" Signed_graphs > Other kinds of "signed graph" Sometimes the signs are taken to be +1 and −1. This is only a difference of notation, if the signs are still multiplied around a circle and the sign of the product is the important thing. However, there are two other ways of treating the edge labels that do not fit into signed graph theory. The term signed graph is applied occasionally to graphs in which each edge has a weight, w(e) = +1 or −1.
Thermomechanical analysis Static force thermomechanometry experimental Thermomechanical_analysis > Static force thermomechanometry experimental Creep and stress relaxation measures the elasticity, viscoelasticity and viscous behaviour of materials under a selected stress and temperature. Tensile geometry is the most common for creep measurements. A small force is initially imparted to keep the specimen aligned and straight. The selected stress is applied rapidly and held constant for the required time; this may be 1 h or more.
List of moments of inertia List of 3D inertia tensors List_of_moments_of_inertia > List of 3D inertia tensors This list of moment of inertia tensors is given for principal axes of each object. To obtain the scalar moments of inertia I above, the tensor moment of inertia I is projected along some axis defined by a unit vector n according to the formula: n ⋅ I ⋅ n ≡ n i I i j n j , {\displaystyle \mathbf {n} \cdot \mathbf {I} \cdot \mathbf {n} \equiv n_{i}I_{ij}n_{j}\,,} where the dots indicate tensor contraction and the Einstein summation convention is used. In the above table, n would be the unit Cartesian basis ex, ey, ez to obtain Ix, Iy, Iz respectively.
Automatic Performance Control Summary Automatic_Performance_Control To detect knock, a piezoelectric knock sensor (basically a microphone) bolted to the engine block responds to unique frequencies caused by engine knock. The sensor generates a small voltage that is sent to the electronic control unit, which processes the signal to determine if, in fact, knock is occurring. If it is, then the control unit activates a solenoid valve that directs boost pressure to the turbocharger's pneumatically controlled wastegate, that opens to bypass exhaust gases from the turbocharger directly to the exhaust pipe, lowering turbo boost pressure until the knock subsides.
Strategic interaction Description and modeling Games_theory > General and applied uses > Description and modeling The primary use of game theory is to describe and model how human populations behave. Some scholars believe that by finding the equilibria of games they can predict how actual human populations will behave when confronted with situations analogous to the game being studied. This particular view of game theory has been criticized.
Optimal Control Theory Finite time Optimal_Control > Examples > Finite time Consider the problem of a mine owner who must decide at what rate to extract ore from their mine. They own rights to the ore from date 0 {\displaystyle 0} to date T {\displaystyle T} . At date 0 {\displaystyle 0} there is x 0 {\displaystyle x_{0}} ore in the ground, and the time-dependent amount of ore x ( t ) {\displaystyle x(t)} left in the ground declines at the rate of u ( t ) {\displaystyle u(t)} that the mine owner extracts it. The mine owner extracts ore at cost u ( t ) 2 / x ( t ) {\displaystyle u(t)^{2}/x(t)} (the cost of extraction increasing with the square of the extraction speed and the inverse of the amount of ore left) and sells ore at a constant price p {\displaystyle p} . Any ore left in the ground at time T {\displaystyle T} cannot be sold and has no value (there is no "scrap value"). The owner chooses the rate of extraction varying with time u ( t ) {\displaystyle u(t)} to maximize profits over the period of ownership with no time discounting.
Greenhouse General and cited references Greenhouse > General and cited references ; Molina, F.D. ; López, A. (2016).
Menger theorem Summary Menger's_theorem In the mathematical discipline of graph theory, Menger's theorem says that in a finite graph, the size of a minimum cut set is equal to the maximum number of disjoint paths that can be found between any pair of vertices. Proved by Karl Menger in 1927, it characterizes the connectivity of a graph. It is generalized by the max-flow min-cut theorem, which is a weighted, edge version, and which in turn is a special case of the strong duality theorem for linear programs.
Franck–Hertz experiment Early quantum theory Franck–Hertz_experiment > Early quantum theory Every satellite has its own orbit, and practically any orbital distance, and any satellite binding energy, is possible. Since an electron is attracted to the positive charge of the atomic nucleus by a similar force, so-called "classical" calculations suggest that any binding energy should also be possible for electrons. However, Bohr assumed that only a specific series of binding energies occur, which correspond to the "quantum energy levels" for the electron.
Electromagnetic signal Thermal and electromagnetic radiation as a form of heat Electromagnetic_resonance > Thermal and electromagnetic radiation as a form of heat This caveat also applies to UV, even though almost all of it is not ionizing, because UV can damage molecules due to electronic excitation, which is far greater per unit energy than heating effects.Infrared radiation in the spectral distribution of a black body is usually considered a form of heat, since it has an equivalent temperature and is associated with an entropy change per unit of thermal energy. However, "heat" is a technical term in physics and thermodynamics and is often confused with thermal energy. Any type of electromagnetic energy can be transformed into thermal energy in interaction with matter.
Tropocoronand ligand Tropocoronand complexes Tropocoronand_ligand > Tropocoronand complexes Tropocoronand complexes with transition metals (Cu, Zn, Ni, Cd, Co, Rh, Fe, etc.) are synthesized by salt metathesis reactions. Various metals (Zn(II), Cd(II), Co(II), Ni(II), Cu(II), etc.) have been studied in order to determine how the differences in macrocycle ring size, metal ionic radius, and electronic structure can affect the dihedral angle of the tropocoronand ligand. Structural analysis is indicative of a correlation between metal ion size and properties; for example, the relatively large Zn2+ ion prohibits the formation of a four-coordinate metal center with 14-membered tropocoronand complex . Indeed, the tropocoronands with the larger zinc metal center exhibit significantly larger dihedral angles relative to their smaller copper congeners.
P orbitals Hydrogen-like orbitals 1s_electron > Hydrogen-like orbitals Electron states are best represented by time-depending "mixtures" (linear combinations) of multiple orbitals. See Linear combination of atomic orbitals molecular orbital method. The quantum number n first appeared in the Bohr model where it determines the radius of each circular electron orbit.
Kinetic proofreading Summary Kinetic_proofreading Kinetic proofreading (or kinetic amplification) is a mechanism for error correction in biochemical reactions, proposed independently by John Hopfield (1974) and Jacques Ninio (1975). Kinetic proofreading allows enzymes to discriminate between two possible reaction pathways leading to correct or incorrect products with an accuracy higher than what one would predict based on the difference in the activation energy between these two pathways.Increased specificity is obtained by introducing an irreversible step exiting the pathway, with reaction intermediates leading to incorrect products more likely to prematurely exit the pathway than reaction intermediates leading to the correct product. If the exit step is fast relative to the next step in the pathway, the specificity can be increased by a factor of up to the ratio between the two exit rate constants. (If the next step is fast relative to the exit step, specificity will not be increased because there will not be enough time for exit to occur.) This can be repeated more than once to increase specificity further.
Anonymity application Psychological effects Anonymity_application > Psychological effects With few perceived negative consequences, anonymous or semi-anonymous forums often provide a soapbox for disruptive conversational behavior. The term "troll" is sometimes used to refer to those who engage in such disruptive behavior. Relative anonymity is often enjoyed in large crowds.
Interplate earthquake Summary Interplate_earthquake An interplate earthquake is an earthquake that occurs at the boundary between two tectonic plates. Earthquakes of this type account for more than 90 percent of the total seismic energy released around the world. If one plate is trying to move past the other, they will be locked until sufficient stress builds up to cause the plates to slip relative to each other. The slipping process creates an earthquake with relative displacement on either side of the fault, resulting in seismic waves which travel through the Earth and along the Earth's surface.
∂ Names and coding ∂ > Names and coding The symbol is variously referred to as "partial", "curly d", "rounded d", "curved d", "dabba", or "Jacobi's delta", or as "del" (but this name is also used for the "nabla" symbol ∇). It may also be pronounced simply "dee", "partial dee", "doh", or "die".The Unicode character U+2202 ∂ PARTIAL DIFFERENTIAL is accessed by HTML entities ∂ or ∂, and the equivalent LaTeX symbol (Computer Modern glyph: ∂ {\displaystyle \partial } ) is accessed by \partial.
Hepatocyte Lipid metabolism Liver_cell > Function > Lipid metabolism The liver receives many lipids from the systemic circulation and metabolizes chylomicron remnants. It also synthesizes cholesterol from acetate and further synthesizes bile salts. The liver is the sole site of bile salts formation.
Nuclear Magnetic Resonance Summary Nuclear_Magnetic_Resonance Both use applied magnetic fields (B0) of great strength, often produced by large currents in superconducting coils, in order to achieve dispersion of response frequencies and of very high homogeneity and stability in order to deliver spectral resolution, the details of which are described by chemical shifts, the Zeeman effect, and Knight shifts (in metals). The information provided by NMR can also be increased using hyperpolarization, and/or using two-dimensional, three-dimensional and higher-dimensional techniques. NMR phenomena are also utilized in low-field NMR, NMR spectroscopy and MRI in the Earth's magnetic field (referred to as Earth's field NMR), and in several types of magnetometers.
CMOS logic Static dissipation CMOS > Power: switching and leakage > Static dissipation Both NMOS and PMOS transistors have a gate–source threshold voltage (Vth), below which the current (called sub threshold current) through the device drops exponentially. Historically, CMOS designs operated at supply voltages much larger than their threshold voltages (Vdd might have been 5 V, and Vth for both NMOS and PMOS might have been 700 mV). A special type of the transistor used in some CMOS circuits is the native transistor, with near zero threshold voltage.
Plaintext-aware encryption Summary Plaintext-aware_encryption Plaintext-awareness is a notion of security for public-key encryption. A cryptosystem is plaintext-aware if it is difficult for any efficient algorithm to come up with a valid ciphertext without being aware of the corresponding plaintext. From a lay point of view, this is a strange property. Normally, a ciphertext is computed by encrypting a plaintext.
Cyber intrusion Control systems Cyber_intrusion > Infrastructures as targets > Control systems Control systems are responsible for activating and monitoring industrial or mechanical controls. Many devices are integrated with computer platforms to control valves and gates to certain physical infrastructures. Control systems are usually designed as remote telemetry devices that link to other physical devices through internet access or modems. Little security can be offered when dealing with these devices, enabling many hackers or cyberterrorists to seek out systematic vulnerabilities.
Circle of longitude Meridian passage Geographical_meridian > Meridian passage The meridian passage is the moment when a celestial object passes the meridian of longitude of the observer. At this point, the celestial object is at its highest point. When the sun passes two times an altitude while rising and setting can be averaged to give the time of meridian passage.
List of graphs Summary Gallery_of_named_graphs This partial list of graphs contains definitions of graphs and graph families. For collected definitions of graph theory terms that do not refer to individual graph types, such as vertex and path, see Glossary of graph theory. For links to existing articles about particular kinds of graphs, see Category:Graphs. Some of the finite structures considered in graph theory have names, sometimes inspired by the graph's topology, and sometimes after their discoverer. A famous example is the Petersen graph, a concrete graph on 10 vertices that appears as a minimal example or counterexample in many different contexts.
Lithium-ion capacitor Electrolyte Lithium-ion_capacitor > Concept > Electrolyte The third part of nearly any energy storage device is the electrolyte. The electrolyte must be able to transport electrons from one electrode to the other but it must not limit the electrochemical species in its reaction rate. For LIC's the electrolyte ideally has a high ionic conductivity such that lithium ions can easily reach the anode. Normally, one would use aqueous electrolyte to achieve this but water will react with the lithium ions so non-aqueous electrolytes are often used.
Debye–Waller factor Introduction Debye–Waller_factor > Derivation > Introduction Scattering experiments are a common method for learning about crystals. Such experiments typically involve a probe (e.g. X-rays or neutrons) and a crystalline solid. A well-characterized probe propagating towards the crystal may interact and scatter away in a particular manner.
Lagrangian equations of motion Conservation Lagrangian_dynamics > Properties of the Lagrangian > Energy > Conservation In Lagrangian mechanics, the system is closed if and only if its Lagrangian L {\displaystyle L} does not explicitly depend on time. The energy conservation law states that the energy E {\displaystyle E} of a closed system is an integral of motion. More precisely, let q = q ( t ) {\displaystyle \mathbf {q} =\mathbf {q} (t)} be an extremal. (In other words, q {\displaystyle \mathbf {q} } satisfies the Euler-Lagrange equations).
Hosmer–Lemeshow test Calculation of the statistic Hosmer–Lemeshow_test > Introduction > Calculation of the statistic A − E x p e c t e d . A ) 2 E x p e c t e d .
Learning Summary Learning For example, learning may occur as a result of habituation, or classical conditioning, operant conditioning or as a result of more complex activities such as play, seen only in relatively intelligent animals. Learning may occur consciously or without conscious awareness. Learning that an aversive event cannot be avoided or escaped may result in a condition called learned helplessness.
MSI protocol Overview MSI_protocol > Overview Different caching architectures handle this differently. For example, bus architectures often perform snooping, where the read request is broadcast to all of the caches.
Residual stress Applications Residual_stress > Applications A demonstration of the effect is shown by Prince Rupert's Drop, a material-science novelty in which a molten glass globule is quenched in water: Because the outer surface cools and solidifies first, when the volume cools and solidifies, it "wants" to take up a smaller volume than the outer "skin" has already defined; this puts much of the volume in tension, pulling the "skin" in, putting the "skin" in compression. As a result, the solid globule is extremely tough, able to be hit with a hammer, but if its long tail is broken, the balance of forces is upset, causing the entire piece to shatter violently. In certain types of gun barrels made with two tubes forced together, the inner tube is compressed while the outer tube stretches, preventing cracks from opening in the rifling when the gun is fired.
LOOP (programming language) Syntax LOOP_(programming_language) > Formal definition > Syntax LOOP-programs consist of the symbols LOOP, DO, END, :=, + and ; as well as any number of variables and constants. LOOP-programs have the following syntax in modified Backus–Naur form: P ::= x i := 0 | x i := x i + 1 | P ; P | L O O P x i D O P E N D {\displaystyle {\begin{array}{lrl}P&::=&x_{i}:=0\\&|&x_{i}:=x_{i}+1\\&|&P;P\\&|&{\mathtt {LOOP}}\,x_{i}\,{\mathtt {DO}}\,P\,{\mathtt {END}}\end{array}}} Here, V a r := { x 0 , x 1 , . . . } {\displaystyle Var:=\{x_{0},x_{1},...\}} are variable names and c ∈ N {\displaystyle c\in \mathbb {N} } are constants.
Cartan connection Motivation Cartan_connection > Introduction > Motivation In the first case, G/H is the affine plane, with G = Aff(R2) the affine group of the plane, and H = GL(2) the corresponding general linear group. In the second case, G/H is the conformal (or celestial) sphere, with G = O+(3,1) the (orthochronous) Lorentz group, and H the stabilizer of a null line in R3,1.The Cartan geometry of S consists of a copy of the model space G/H at each point of S (with a marked point of contact) together with a notion of "parallel transport" along curves which identifies these copies using elements of G. This notion of parallel transport is generic in the intuitive sense that the point of contact always moves along the curve. In general, let G be a group with a subgroup H, and M a manifold of the same dimension as G/H. Then, roughly speaking, a Cartan connection on M is a G-connection which is generic with respect to a reduction to H.
Retroactive interference Long-term memory Retroactive_interference > Output interference > Research > Long-term memory Even if retrieving items is necessary for a recall, it is not crucial to performance in a recognition tack. Recall of the organized information from long-term memory hurt the following item recalled. In long-term memory, Smith suggests that Output Interference has effects on extra-core material, which is represented as contextual information, rather than the core material, which is highly available as a result of organization.
Pulmonary thromboendarterectomy Recovery and complications Pulmonary_thromboendarterectomy > Recovery and complications Recovery from this procedure can be complex. Thoracic surgery, CBP and cardioplegia are associated with their own complications and management challenges, as is hypothermia. Specifically, endartectomy is associated with reperfusion pulmonary edema and "pulmonary artery steal". Reperfusion pulmonary edema occurs in up to 30% of patients and is a result of changes in permeability to the vascular endothelium.
Separable differential equation Alternative notation Separable_differential_equation > Ordinary differential equations (ODE) > Alternative notation Those who dislike Leibniz's notation may prefer to write this as 1 h ( y ) d y d x = g ( x ) , {\displaystyle {\frac {1}{h(y)}}{\frac {dy}{dx}}=g(x),} but that fails to make it quite as obvious why this is called "separation of variables". Integrating both sides of the equation with respect to x {\displaystyle x} , we have or equivalently, ∫ 1 h ( y ) d y = ∫ g ( x ) d x {\displaystyle \int {\frac {1}{h(y)}}\,dy=\int g(x)\,dx} because of the substitution rule for integrals. If one can evaluate the two integrals, one can find a solution to the differential equation. Observe that this process effectively allows us to treat the derivative d y d x {\displaystyle {\frac {dy}{dx}}} as a fraction which can be separated. This allows us to solve separable differential equations more conveniently, as demonstrated in the example below. (Note that we do not need to use two constants of integration, in equation (A1) as in ∫ 1 h ( y ) d y + C 1 = ∫ g ( x ) d x + C 2 , {\displaystyle \int {\frac {1}{h(y)}}\,dy+C_{1}=\int g(x)\,dx+C_{2},} because a single constant C = C 2 − C 1 {\displaystyle C=C_{2}-C_{1}} is equivalent.)
Algorithmic cooling Heat-bath algorithmic cooling (irreversible algorithmic cooling) Algorithmic_cooling > Heat-bath algorithmic cooling (irreversible algorithmic cooling) The irreversible case is an extension of the reversible case: it uses the reversible algorithm as a subroutine. The irreversible algorithm contains another procedure called "Refresh" and extends the reversible one by using a heat bath. This allows for cooling certain qubits (called "reset qubits") without affecting the others, which results in an overall cooling of all the qubits as a system.
P. vivax Mosquito stage Plasmodium_vivax > Biology > Life cycle > Mosquito stage Parasite life cycle in mosquitoes includes all stages of sexual reproduction: Infection and Gametogenesis Microgametes Macrogametes Fertilization Ookinite Oocyst Sporogony
List of number theory topics L-functions List_of_number_theory_topics > L-functions Riemann zeta function Basel problem on ζ(2) Hurwitz zeta function Bernoulli number Agoh–Giuga conjecture Von Staudt–Clausen theorem Dirichlet series Euler product Prime number theorem Prime-counting function Meissel–Lehmer algorithm Offset logarithmic integral Legendre's constant Skewes' number Bertrand's postulate Proof of Bertrand's postulate Proof that the sum of the reciprocals of the primes diverges Cramér's conjecture Riemann hypothesis Critical line theorem Hilbert–Pólya conjecture Generalized Riemann hypothesis Mertens function, Mertens conjecture, Meissel–Mertens constant De Bruijn–Newman constant Dirichlet character Dirichlet L-series Siegel zero Dirichlet's theorem on arithmetic progressions Linnik's theorem Elliott–Halberstam conjecture Functional equation (L-function) Chebotarev's density theorem Local zeta function Weil conjectures Modular form modular group Congruence subgroup Hecke operator Cusp form Eisenstein series Modular curve Ramanujan–Petersson conjecture Birch and Swinnerton-Dyer conjecture Automorphic form Selberg trace formula Artin conjecture Sato–Tate conjecture Langlands program modularity theorem
Time-independent schrodinger equation Semiclassical limit Schrodinger's_equation > Semiclassical limit In the case of the quantum harmonic oscillator, however, V ′ {\displaystyle V'} is linear and this distinction disappears, so that in this very special case, the expected position and expected momentum do exactly follow the classical trajectories. For general systems, the best we can hope for is that the expected position and momentum will approximately follow the classical trajectories. If the wave function is highly concentrated around a point x 0 {\displaystyle x_{0}} , then V ′ ( ⟨ X ⟩ ) {\displaystyle V'\left(\left\langle X\right\rangle \right)} and ⟨ V ′ ( X ) ⟩ {\displaystyle \left\langle V'(X)\right\rangle } will be almost the same, since both will be approximately equal to V ′ ( x 0 ) {\displaystyle V'(x_{0})} .
Cutoff function Summary Mollifier In mathematics, mollifiers (also known as approximations to the identity) are smooth functions with special properties, used for example in distribution theory to create sequences of smooth functions approximating nonsmooth (generalized) functions, via convolution. Intuitively, given a function which is rather irregular, by convolving it with a mollifier the function gets "mollified", that is, its sharp features are smoothed, while still remaining close to the original nonsmooth (generalized) function.They are also known as Friedrichs mollifiers after Kurt Otto Friedrichs, who introduced them.
Least squares method The method Least_squares_method > History > The method This result is known as the Gauss–Markov theorem. The idea of least-squares analysis was also independently formulated by the American Robert Adrain in 1808. In the next two centuries workers in the theory of errors and in statistics found many different ways of implementing least squares.
Split complex number Isomorphism Hyperbolic_number > Definition > Isomorphism then corresponds under this linear transformation to a squeeze mapping Though lying in the same isomorphism class in the category of rings, the split-complex plane and the direct sum of two real lines differ in their layout in the Cartesian plane. The isomorphism, as a planar mapping, consists of a counter-clockwise rotation by 45° and a dilation by √2. The dilation in particular has sometimes caused confusion in connection with areas of a hyperbolic sector.
Distributed Hash Table History Distributed_Hash_Table > History Queries are likely to be routed through the network to such a cluster without needing to visit many peers. However, Freenet does not guarantee that data will be found. Distributed hash tables use a more structured key-based routing in order to attain both the decentralization of Freenet and Gnutella, and the efficiency and guaranteed results of Napster.
Plasma membrane Intracellular membranes Plasma_membrane > Structures > Intracellular membranes Like the ER, the outer membrane also possesses ribosomes responsible for producing and transporting proteins into the space between the two membranes. The nuclear membrane disassembles during the early stages of mitosis and reassembles in later stages of mitosis.
Primary metabolism Coenzymes Cellular_metabolism > Key biochemicals > Coenzymes These coenzymes are therefore continuously made, consumed and then recycled.One central coenzyme is adenosine triphosphate (ATP), the energy currency of cells. This nucleotide is used to transfer chemical energy between different chemical reactions. There is only a small amount of ATP in cells, but as it is continuously regenerated, the human body can use about its own weight in ATP per day.
Adversarial machine learning Fast gradient sign method Adversarial_machine_learning > Specific attack types > Adversarial examples > White box attacks > Fast gradient sign method Shown below is the equation to generate an adversarial example where x {\textstyle x} is the original image, ϵ {\textstyle \epsilon } is a very small number, Δ x {\textstyle \Delta _{x}} is the gradient function, J {\textstyle J} is the loss function, θ {\textstyle \theta } is the model weights, and y {\textstyle y} is the true label. One important property of this equation is that the gradient is calculated with respect to the input image since the goal is to generate an image that maximizes the loss for the original image of true label y {\textstyle y} . In traditional gradient descent (for model training), the gradient is used to update the weights of the model since the goal is to minimize the loss for the model on a ground truth dataset. The Fast Gradient Sign Method was proposed as a fast way to generate adversarial examples to evade the model, based on the hypothesis that neural networks cannot resist even linear amounts of perturbation to the input.
Surfer Wave conditions for surfing Surfer > The physics of surfing > Wave conditions for surfing Wave section length is the distance between two breaking crests in a wave set. Wave section length can be hard to measure because local winds, non-linear wave interactions, island sheltering, and swell interactions can cause multifarious wave configurations in the surf zone.The parameters breaking wave height, wave peel angle (α), and wave breaking intensity, and wave section length are important because they are standardized by past oceanographers who researched surfing; these parameters have been used to create a guide that matches the type of wave formed and the skill level of surfer. Table 1 shows a relationship of smaller peel angles correlating with a higher skill level of the surfer.
Glossary of artificial intelligence A Glossary_of_artificial_intelligence > A automated machine learning (AutoML) A field of machine learning which aims to automatically configure a machine learning system to maximize its performance (e.g, classification accuracy). automated planning and scheduling Also simply AI planning. A branch of artificial intelligence that concerns the realization of strategies or action sequences, typically for execution by intelligent agents, autonomous robots and unmanned vehicles.
Kepler orbit Mathematical solution of the differential equation (1) above Kepler_orbits > Development of the laws > Mathematical solution of the differential equation (1) above This brings: Taking the time derivative of (3) gets Equations (3) and (4) allow us to eliminate the time derivatives of θ {\displaystyle \theta } . In order to eliminate the time derivatives of r {\displaystyle r} , the chain rule is used to find appropriate substitutions: Using these four substitutions, all time derivatives in (2) can be eliminated, yielding an ordinary differential equation for r {\displaystyle r} as function of θ . {\displaystyle \theta .}
Earth-to-Earth spaceflight Orbital Space_transportation > Types > Orbital A minimal orbital spaceflight requires much higher velocities than a minimal sub-orbital flight, and so it is technologically much more challenging to achieve. To achieve orbital spaceflight, the tangential velocity around the Earth is as important as altitude. In order to perform a stable and lasting flight in space, the spacecraft must reach the minimal orbital speed required for a closed orbit.
Tracing garbage collection Performance Tracing_garbage_collection > Performance Manual memory management (as in C++) and reference counting have a similar issue of arbitrarily long pauses in case of deallocating a large data structure and all its children, though these only occur at fixed times, not depending on garbage collection. Manual heap allocation search for best/first-fit block of sufficient size free list maintenanceGarbage collection locate reachable objects copy reachable objects for moving collectors read/write barriers for incremental collectors search for best/first-fit block and free list maintenance for non-moving collectorsIt is difficult to compare the two cases directly, as their behavior depends on the situation. For example, in the best case for a garbage collecting system, allocation just increments a pointer, but in the best case for manual heap allocation, the allocator maintains freelists of specific sizes and allocation only requires following a pointer.
Diatomic element Excited electronic states Diatomic_molecule > Excited electronic states Λ {\displaystyle \Lambda } takes on values 0, 1, 2, ..., which are represented by the electronic state symbols Σ {\displaystyle \Sigma } , Π {\displaystyle \Pi } , Δ {\displaystyle \Delta } ,.... For example, the following table lists the common electronic states (without vibrational quantum numbers) along with the energy of the lowest vibrational level ( v = 0 {\displaystyle v=0} ) of diatomic nitrogen (N2), the most abundant gas in the Earth's atmosphere.The subscripts and superscripts after Λ {\displaystyle \Lambda } give additional quantum mechanical details about the electronic state. The superscript + {\displaystyle +} or − {\displaystyle -} determines whether reflection in a plane containing the internuclear axis introduces a sign change in the wavefunction. The sub-script g {\displaystyle g} or u {\displaystyle u} applies to molecules of identical atoms, and when reflecting the state along a plane perpendicualr to the molecular axis, states that does not change are labelled g {\displaystyle g} (gerade), and states that change sign are labelled u {\displaystyle u} (ungerade).
Electrical equipment Electrical equipment Electric_device > Electrical equipment Electrical equipment includes any machine powered by electricity. It usually consists of an enclosure, a variety of electrical components, and often a power switch. Examples of these include: Lighting Major appliance Small appliances IT equipment (computers, printers etc.) Motors, pumps and HVAC SystemsMore specifically, electrical equipment refers to the individual components of an electrical distribution system. These components may involve: Electric switchboards Distribution boards Circuit breakers and disconnects Transformers Electricity meter
Inverse multiplexing Summary Inverse_multiplexing An alternative to an inverse multiplexer is to use separate links and load sharing of data between them. In the case of IP, network packets could be sent in round-robin mode between each separate link. Advantages of using inverse multiplexing over separate links include: Lower link latency (one single packet can be spread across all links) Fairer load balancing Network simplicity (no network switch needed between boxes with high-speed interfaces)A simple analogy to transport can help explain the distinction between multiplexing and inverse multiplexing.
Atmospheric optics Fata Morgana Meteorological_optics > Mirage > Fata Morgana This optical phenomenon occurs because rays of light are strongly bent when they pass through air layers of different temperatures in a steep thermal inversion where an atmospheric duct has formed. A thermal inversion is an atmospheric condition where warmer air exists in a well-defined layer above a layer of significantly cooler air. This temperature inversion is the opposite of what is normally the case; air is usually warmer close to the surface, and cooler higher up. In calm weather, a layer of significantly warmer air can rest over colder dense air, forming an atmospheric duct which acts like a refracting lens, producing a series of both inverted and erect images.
Osmotic balance Achieving osmoregulation in vertebrates Osmoregulation > Vertebrate excretory systems > Achieving osmoregulation in vertebrates Four processes occur: filtration – fluid portion of blood (plasma) is filtered from a nephron (functional unit of vertebrate kidney) structure known as the glomerulus into Bowman's capsule or glomerular capsule (in the kidney's cortex) and flows down the proximal convoluted tubule to a "u-turn" called the Loop of Henle (loop of the nephron) in the medulla portion of the kidney. reabsorption – most of the viscous glomerular filtrate is returned to blood vessels that surround the convoluted tubules. secretion – the remaining fluid becomes urine, which travels down collecting ducts to the medullary region of the kidney. excretion – the urine (in mammals) is stored in the urinary bladder and exits via the urethra; in other vertebrates, the urine mixes with other wastes in the cloaca before leaving the body (frogs also have a urinary bladder).
Allostasis Types Allostasis > Types Type 2 allostatic overload does not trigger an escape response, and can only be counteracted through learning and changes in the social structure. Whereas both types of allostasis are associated with increased release of cortisol and catecholamines, they differentially affect thyroid homeostasis: Concentrations of the thyroid hormone triiodothyronine are decreased in type 1 allostasis, but elevated in type 2 allostasis. This may result from type 2 allostatic load increasing the set point of pituitary-thyroid feedback control.
Amino acid score Amino Acid Calculation Amino_acid_score > Amino Acid Calculation Foods that do not meet the requirement need addition nutrition. This is the reason that many people make sure to have a well balanced diet with all the nutrients needed in their daily meals. If a food does not have all the nine amino acids present it is considered an incomplete protein. Everybody's nutritional needs may be different based on age, pregnancy, gender, and protein needs which can affect the diet that is needed.
Autoantibody Diseases Autoantibody > Diseases Although the associated autoimmune disorders are rare, the signs and symptoms they cause are relatively common. Symptoms may include: arthritis-type joint pain, fatigue, fever, rashes, cold or allergy-type symptoms, weight loss, and muscular weakness. Associated conditions include vasculitis which are inflammation of blood vessels and anemia.
Real-root isolation Summary Real-root_isolation In mathematics, and, more specifically in numerical analysis and computer algebra, real-root isolation of a polynomial consist of producing disjoint intervals of the real line, which contain each one (and only one) real root of the polynomial, and, together, contain all the real roots of the polynomial. Real-root isolation is useful because usual root-finding algorithms for computing the real roots of a polynomial may produce some real roots, but, cannot generally certify having found all real roots. In particular, if such an algorithm does not find any root, one does not know whether it is because there is no real root. Some algorithms compute all complex roots, but, as there are generally much fewer real roots than complex roots, most of their computation time is generally spent for computing non-real roots (in the average, a polynomial of degree n has n complex roots, and only log n real roots; see Geometrical properties of polynomial roots § Real roots).
Newtonian fluids Summary Newtonian_Fluid Newtonian fluids are the simplest mathematical models of fluids that account for viscosity. While no real fluid fits the definition perfectly, many common liquids and gases, such as water and air, can be assumed to be Newtonian for practical calculations under ordinary conditions. However, non-Newtonian fluids are relatively common and include oobleck (which becomes stiffer when vigorously sheared) and non-drip paint (which becomes thinner when sheared). Other examples include many polymer solutions (which exhibit the Weissenberg effect), molten polymers, many solid suspensions, blood, and most highly viscous fluids. Newtonian fluids are named after Isaac Newton, who first used the differential equation to postulate the relation between the shear strain rate and shear stress for such fluids.
Learning management system User feedback Learning_management_system > Features > User feedback Students' exchange of feedback both with teachers and their peers is possible through LMS. Teachers may create discussion groups to allow students feedback, share their knowledge on topics and increase the interaction in course. Students' feedback is an instrument which help teachers to improve their work, helps identify what to add or remove from a course, and ensures students feel comfortable and included.
Order (graph theory) Graph Finite_graph > Definitions > Graph The degree or valency of a vertex is the number of edges that are incident to it; for graphs with loops, a loop is counted twice. In a graph of order n, the maximum degree of each vertex is n − 1 (or n + 1 if loops are allowed, because a loop contributes 2 to the degree), and the maximum number of edges is n(n − 1)/2 (or n(n + 1)/2 if loops are allowed). The edges of a graph define a symmetric relation on the vertices, called the adjacency relation.
Gaussian gravitational constant Gauss' constant and Kepler's third law Gaussian_gravitational_constant > Derivation > Gauss' constant and Kepler's third law The Gaussian constant is closely related to Kepler's third law of planetary motion, and one is easily derived from the other. Beginning with the full definition of Gauss' constant, k = 2 π a b P M + m p , {\displaystyle k={\frac {2\pi ab}{P{\sqrt {M+m}}{\sqrt {p}}}},} where a is the semi-major axis of the elliptical orbit, b is the semi-minor axis of the elliptical orbit, P is the orbital period, M is the mass of the primary body, m is the mass of the secondary body, and p is the semi-latus rectum of the elliptical orbit.From the geometry of an ellipse, the semi-latus rectum, p can be expressed in terms of a and b thus: p = b2/a. Therefore, p = b a . {\displaystyle {\sqrt {p}}={\frac {b}{\sqrt {a}}}.}
Fixed point arithmetic Scaling conversion Fixed-precision_arithmetic > Operations > Scaling conversion In fixed-point computing it is often necessary to convert a value to a different scaling factor. This operation is necessary, for example: To store a value into a program variable that has a different implicit scaling factor; To convert two values to the same scaling factor, so that they can be added or subtracted; To restore the original scaling factor of a value after multiplying or dividing it by another; To improve the accuracy of the result of a division; To ensure that the scaling factor of a product or quotient is a simple power like 10n or 2n; To ensure that the result of an operation can be stored into a program variable without overflow; To reduce the cost of hardware that processes fixed-point data.To convert a number from a fixed point type with scaling factor R to another type with scaling factor S, the underlying integer must be multiplied by the ratio R/S. Thus, for example, to convert the value 1.23 = 123/100 from scaling factor R=1/100 to one with scaling factor S=1/1000, the integer 123 must be multiplied by (1/100)/(1/1000) = 10, yielding the representation 1230/1000. If the scaling factor is a power of the base used internally to represent the integer, changing the scaling factor requires only dropping low-order digits of the integer, or appending zero digits.
Safe and Sophie Germain primes Summary Safe_prime In number theory, a prime number p is a Sophie Germain prime if 2p + 1 is also prime. The number 2p + 1 associated with a Sophie Germain prime is called a safe prime. For example, 11 is a Sophie Germain prime and 2 × 11 + 1 = 23 is its associated safe prime. Sophie Germain primes are named after French mathematician Sophie Germain, who used them in her investigations of Fermat's Last Theorem.
Transposon mutagenesis Tn5 transposon system Transposon_mutagenesis > Dynamics > Tn5 transposon system The most likely pathway of Tn 5 transposition is the common pathway for all transposon systems. It begins with Tnp binding the OE and IE sequences of each IS50 sequence. The two ends are brought together, and through oligomerization of DNA, the sequence is cut out of the chromosome.
Metallacarboxylic ester Preparation Hieber_base_reaction > Preparation Metallacarboxylic acids mainly arise by the attack of hydroxide on electrophilic metal carbonyl complexes. An illustrative synthesis is the reaction of a cationic iron carbonyl with a stoichiometric amount of base: BF4 + NaOH → − from iron pentacarbonyl. Fe(CO)5 + NaOH → NaFe(CO)4CO2H NaFe(CO)4CO2H → NaHFe(CO)4 + CO2
Brun's constant In popular culture Brun's_constant > Further results > In popular culture The digits of Brun's constant were used in a bid of $1,902,160,540 in the Nortel patent auction. The bid was posted by Google and was one of three Google bids based on mathematical constants. Furthermore, academic research on the constant ultimately resulted in the Pentium FDIV bug becoming a notable public relations fiasco for Intel.
Heisenberg uncertainty relations Quantum entropic uncertainty principle Quantum_theory_of_measurement > Additional uncertainty relations > Quantum entropic uncertainty principle We take the zeroth bin to be centered near the origin, with possibly some small constant offset c. The probability of lying within the jth interval of width δx is To account for this discretization, we can define the Shannon entropy of the wave function for a given measurement apparatus as Under the above definition, the entropic uncertainty relation is Here we note that δx δp/h is a typical infinitesimal phase space volume used in the calculation of a partition function. The inequality is also strict and not saturated. Efforts to improve this bound are an active area of research.
Dashboard (business) Guidelines for dashboard design Dashboard_(management_information_systems) > Guidelines for dashboard design Another aspect to keep in mind while creating visuals that goes along with information overload is the idea of interaction within your visual. Interacting with the dashboard would allow for further detail to be obtained from the user and allow them to better understand the information on your dashboard. Chart visualization is an important aspect when creating dashboards, diagrams in particular.
CRISPR CRISPR as diagnostic tool CRISPR/Cas9-mediated_genome_editing > Applications > CRISPR as diagnostic tool One example of a coupled technology is SHERLOCK-based Profiling of IN vitro Transcription (SPRINT). SPRINT can be used to detect a variety of substances, such as metabolites in patient samples or contaminants in environmental samples, with high throughput or with portable point-of-care devices.
GNU Build System Usage GNU_Build_System > Usage This makes building such software on the Windows operating system a bit harder than on a Unix-like system which provides the Bourne shell as a standard component. One can install the Cygwin or MSYS system on top of Windows to provide a Unix-like compatibility layer, though, allowing configure scripts to run. Cygwin also provides the GNU Compiler Collection, GNU make, and other software that provides a nearly complete Unix-like system within Windows; MSYS also provides GNU make and other tools designed to work with the MinGW version of GCC.
Genetics Natural selection and evolution Genetic_research > Genetic change > Natural selection and evolution Population genetics studies the distribution of genetic differences within populations and how these distributions change over time. Changes in the frequency of an allele in a population are mainly influenced by natural selection, where a given allele provides a selective or reproductive advantage to the organism, as well as other factors such as mutation, genetic drift, genetic hitchhiking, artificial selection and migration.Over many generations, the genomes of organisms can change significantly, resulting in evolution. In the process called adaptation, selection for beneficial mutations can cause a species to evolve into forms better able to survive in their environment.
Bigraph Directed Bigraphs Bigraph > Extensions and variants > Directed Bigraphs Directed Bigraphs are a generalisation of bigraphs where hyper-edges of the link-graph are directed. Ports and names of the interfaces are extended with a polarity (positive or negative) with the requirement that the direction of hyper-edges goes from negative to positive. Directed bigraphs were introduced as a meta-model for describing computation paradigms dealing with locations and resource communication where a directed link-graph provides a natural description of resource dependencies or information flow. Examples of areas of applications are security protocols, resource access management, and cloud computing.
Lee–Yang theory Summary Lee–Yang_theory In statistical mechanics, Lee–Yang theory, sometimes also known as Yang–Lee theory, is a scientific theory which seeks to describe phase transitions in large physical systems in the thermodynamic limit based on the properties of small, finite-size systems. The theory revolves around the complex zeros of partition functions of finite-size systems and how these may reveal the existence of phase transitions in the thermodynamic limit.Lee–Yang theory constitutes an indispensable part of the theories of phase transitions. Originally developed for the Ising model, the theory has been extended and applied to a wide range of models and phenomena, including protein folding, percolation, complex networks, and molecular zippers.The theory is named after the Nobel laureates Tsung-Dao Lee and Yang Chen-Ning, who were awarded the 1957 Nobel Prize in Physics for their unrelated work on parity non-conservation in weak interaction.
Maximum power theorem Calculus-based proof for purely resistive circuits Maximum_power_theorem > Calculus-based proof for purely resistive circuits In the simplified model of powering a load with resistance RL by a source with voltage VS and source resistance RS, then by Ohm's law the resulting current I is simply the source voltage divided by the total circuit resistance: The power PL dissipated in the load is the square of the current multiplied by the resistance: The value of RL for which this expression is a maximum could be calculated by differentiating it, but it is easier to calculate the value of RL for which the denominator: is a minimum. The result will be the same in either case. Differentiating the denominator with respect to RL: For a maximum or minimum, the first derivative is zero, so or In practical resistive circuits, RS and RL are both positive, so the positive sign in the above is the correct solution.
Radiative Forcing Water vapor Solar_forcing > Basic estimates > Forcing due to changes in atmospheric gas > Water vapor Water vapor is Earth's primary greenhouse gas currently responsible for about half of all atmospheric gas forcing. Its overall atmospheric concentration depends almost entirely on the average planetary temperature, and has the potential to increase by as much as 7% with every degree (°C) of temperature rise (see also: Clausius–Clapeyron relation). Thus over long time scales, water vapor behaves as a system feedback that amplifies the radiative forcing driven by the growth of carbon dioxide and other trace gases.
Glossary of geography terms (A–M) A Glossary_of_geography_terms_(A–M) > A (coordinate system) Any of the reference lines of a Cartesian coordinate system, from which the signed distances to each coordinate are measured, e.g. the x-axis or the y-axis. 2.
Adrenergic blocking agent Beta 3 blocker Adrenergic_blocking_agent > Mechanism of Action > Beta 3 blocker Beta-3 blocker will inactivate beta-3 receptor and stops the following action. Beta 3 receptor is a G-protein coupled receptor, similar to beta-1 and beta-2 receptors. The receptor is involved in G-as activation. The receptor will also stimulate adenylyl cyclase. Eventually, it will lead to effects like increase of tryptophan and 5-hydroxytryptamine level, increase of lipolysis in adipose tissue. Beta-3 blocker will antagonize the receptor, which will stop the signaling pathway(G-as activation, stimulation of adenylyl cyclase).
Metoprolol Precautions Metoprolol > Adverse effects > Precautions Metoprolol reduces long-term mortality and hospitalisation due to worsening heart failure. A meta-analysis further supports reduced incidence of heart failure worsening in patients treated with beta-blockers compared to placebo. However, in some circumstances, particularly when initiating metoprolol in patients with more symptomatic disease, an increased prevalence of hospitalisation and mortality has been reported within the first two months of starting. Patients should monitor for swelling of extremities, fatigue, and shortness of breath.This medicine may cause changes in blood sugar levels or cover up signs of low blood sugar, such as a rapid pulse rate. It also may cause some people to become less alert than they are normally, making it dangerous for them to drive or use machines.
Confusion of the inverse Example 2 Confusion_of_the_inverse > Examples > Example 2 In order to identify individuals having a serious disease in an early curable form, one may consider screening a large group of people. While the benefits are obvious, an argument against such screenings is the disturbance caused by false positive screening results: If a person not having the disease is incorrectly found to have it by the initial test, they will most likely be distressed, and even if they subsequently take a more careful test and are told they are well, their lives may still be affected negatively. If they undertake unnecessary treatment for the disease, they may be harmed by the treatment's side effects and costs. The magnitude of this problem is best understood in terms of conditional probabilities.
Frequency weighting Audio reproduction and broadcasting equipment Frequency_weighting > Audio applications > Audio reproduction and broadcasting equipment Though the noise level of 16-bit audio systems (such as CD players) is commonly quoted (on the basis of calculations that take no account of subjective effect) as −96 dB relative to FS (full scale), the best 468-weighted results are in the region of −68 dB relative to Alignment Level (commonly defined as 18 dB below FS) i.e. −86 dB relative to FS. The use of weighting curves is in no way to be regarded as 'cheating', provided that the proper curve is used. Nothing of relevance is being 'hidden', and even when, for example, hum is present at 50 or 100 Hz at a level above the quoted (weighted) noise floor this is of no importance because our ears are very insensitive to low frequencies at low levels, so it will not be heard. A-weighting is often used to compare and qualify ADCs, for instance, because it more accurately represents the way noise shaping hides dither noise in the ultrasonic range.
Electron shell configuration History Closed_shell > History Bohr's original configurations would seem strange to a present-day chemist: sulfur was given as 2.4.4.6 instead of 1s2 2s2 2p6 3s2 3p4 (2.8.6). Bohr used 4 and 6 following Alfred Werner's 1893 paper. In fact, the chemists believed in atoms long before the physicists.
Transformer (neural network) Decomposable attention Transformer_(machine_learning_model) > Timeline > Decomposable attention In 2016, highly parallelizable decomposable attention was successfully combined with a feedforward network. This indicated that attention mechanisms were powerful in themselves and that sequential recurrent processing of data was not necessary to achieve the quality gains of RNNs with attention. Soon Jakob Uszkoreit from Google Research also proposed replacing RNNs with self-attention and started the effort to evaluate that idea. Transformers, using an attention mechanism, processing all tokens simultaneously, calculated "soft" weights between them in successive layers. Since the attention mechanism only uses information about other tokens from lower layers, it can be computed for all tokens in parallel, which leads to improved training speed.
Matched filter Radar and sonar Matched_filter > Examples > Radar and sonar Matched filters are often used in signal detection. As an example, suppose that we wish to judge the distance of an object by reflecting a signal off it. We may choose to transmit a pure-tone sinusoid at 1 Hz. We assume that our received signal is an attenuated and phase-shifted form of the transmitted signal with added noise.
Consumer choice Assumptions Consumer_choice > Assumptions The behavioral assumption of the consumer theory proposed herein is that all consumers seek to maximize utility. Traditionally in economics, this activity of maximizing utility has been deemed as the "rational" behavior of decision makers. More specifically, in the eyes of economists, all consumers seek to maximize their utility function subject to a budgetary constraint. In other words, economists assume that consumers will always choose the "best" bundle of goods they can afford.
Membrane vesicle trafficking Summary Membrane_vesicle_trafficking Membrane vesicle trafficking in eukaryotic animal cells involves movement of biochemical signal molecules from synthesis-and-packaging locations in the Golgi body to specific release locations on the inside of the plasma membrane of the secretory cell. It takes place in the form of Golgi membrane-bound micro-sized vesicles, termed membrane vesicles (MVs). In this process, the packed cellular products are released or secreted outside the cell, across its plasma membrane. On the other hand, the vesicular membrane is retained and recycled by the secretory cells.
Seam allowance Summary Seam_allowance Seam allowance (sometimes called inlays) is the area between the fabric edge and the stitching line on two (or more) pieces of material being sewn together. Seam allowances can range from 1⁄4 inch (6.4 mm) wide to as much as several inches. Commercial patterns for home sewers have seam allowances ranging from 1⁄4 to 5⁄8 inch (6.4 to 15.9 mm).A 5/8″(1.5cm) seam allowance provides enough extra between the seam line and the cut edge of the fabric to make sure that the fabric will be safely caught as they are being joining together.
Zero-knowledge proof Discrete log of a given value Zero-knowledge_proofs > Practical examples > Discrete log of a given value When Victor challenges her to reveal ( x + r ) mod ( p − 1 ) {\displaystyle (x+r){\bmod {(p-1)}}} , she reveals r ′ {\displaystyle r'} , for which Victor will verify consistency, since he will in turn compute g r ′ mod p {\displaystyle g^{r'}{\bmod {p}}} , which matches C ′ ⋅ y {\displaystyle C'\cdot y} , since Peggy multiplied by the modular multiplicative inverse of y {\displaystyle y} . However, if in either one of the above scenarios Victor issues a challenge other than the one she was expecting and for which she manufactured the result, then she will be unable to respond to the challenge under the assumption of infeasibility of solving the discrete log for this group. If she picked r {\displaystyle r} and disclosed C = g r mod p {\displaystyle C=g^{r}{\bmod {p}}} , then she will be unable to produce a valid ( x + r ) mod ( p − 1 ) {\displaystyle (x+r){\bmod {(p-1)}}} that would pass Victor's verification, given that she does not know x {\displaystyle x} .
Nucleophilic acyl substitution Reactivity trends Nucleophilic_acyl_substitution > Reactivity trends A major factor in determining the reactivity of acyl derivatives is leaving group ability, which is related to acidity. Weak bases are better leaving groups than strong bases; a species with a strong conjugate acid (e.g. hydrochloric acid) will be a better leaving group than a species with a weak conjugate acid (e.g. acetic acid). Thus, chloride ion is a better leaving group than acetate ion.