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Induction coils Interrupter Ruhmkorff_coil > Construction and function > Interrupter After a time, the magnetic attraction overcomes the armature's spring force, and the armature begins to move. When the armature has moved far enough, the pair of contacts (K) in the primary circuit open and disconnect the primary current. Disconnecting the current causes the magnetic field to collapse and create the spark.
Aplanatic lens Summary Aplanatic_lens An aplanatic lens is a lens that is free of both spherical and coma aberrations. Aplanatic lenses can be made by combining two or three lens elements. A single-element aplanatic lens is an aspheric lens whose surfaces are surfaces of revolution of a cartesian oval. == References ==
Transcription translation feedback loop Drosophila melanogaster Transcription_translation_feedback_loop > Prominent models > Drosophila melanogaster Secondary feedback loops interact with this primary feedback loop. CLOCKWORK ORANGE (CWO) binds the E-boxes to act as a direct competitor of CYC-CLK, therefore inhibiting transcription.
Einstein–Infeld–Hoffmann equations Summary Einstein–Infeld–Hoffmann_equations The acceleration of a particular body depends on the accelerations of all the other bodies. Since the quantity on the left hand side also appears in the right hand side, this system of equations must be solved iteratively. In practice, using the Newtonian acceleration instead of the true acceleration provides sufficient accuracy.
Synaptic transistor Summary Synaptic_transistor A synaptic transistor is an electrical device that can learn in ways similar to a neural synapse. It optimizes its own properties for the functions it has carried out in the past. The device mimics the behavior of the property of neurons called spike-timing-dependent plasticity, or STDP.
Higgs potential Landau model Electroweak_symmetry_breaking > Examples > Landau model This was mysterious for a long time, because it implies that electromagnetic forces somehow become short-range inside the superconductor. Contrast this with the behavior of an ordinary metal. In a metal, the conductivity shields electric fields by rearranging charges on the surface until the total field cancels in the interior.
Principles of Motion Sensing Accelerometers Principles_of_Motion_Sensing > Motion Sensors > Accelerometers Accelerometers measure linear acceleration and tilt angle. Single and multi-axis accelerometers detect the combined magnitude and direction of linear, rotational and gravitational acceleration. They can be used to provide limited motion sensing functionality.
Industrial scale Overview Industrial_scale > Overview Economies of scale also play a role in a "natural monopoly". There is a distinction between two types of economies of scale: internal and external. An industry that exhibits an internal economy of scale is one where the costs of production fall when the number of firms in the industry drops, but the remaining firms increase their production to match previous levels.
Epigenetic modifications Supplemental effects of methylation with DNMTs Epigenetics_in_stem-cell_differentiation > Supplemental effects of methylation with DNMTs DNA methylation is controlled by certain methyltransferases, DMNTs, which perform different functions depending on each one. DNMT3A and DNMT3B have both been linked to a role in the establishment of DNA methylation pattern in the early development of the stem cell, whereas DNMT1 is required to methylate a newly synthesized strand of DNA after the cell has undergone replication in order to sustain the epigenetic regulatory state. Numerous proteins can physically interact with DNMTs themselves, which help target DNMT1 to hemi-methylated DNA.
Flat file system Device file systems File_access > Types of file systems > Special file systems > Device file systems A device file system represents I/O devices and pseudo-devices as files, called device files. Examples in Unix-like systems include devfs and, in Linux 2.6 systems, udev. In non-Unix-like systems, such as TOPS-10 and other operating systems influenced by it, where the full filename or pathname of a file can include a device prefix, devices other than those containing file systems are referred to by a device prefix specifying the device, without anything following it.
Faà di Bruno's formula Research works Faà_di_Bruno's_formula > References > Research works Arbogast, L. F. A. (1800), Du calcul des derivations (in French), Strasbourg: Levrault, pp. xxiii+404, Entirely freely available from Google books. Faà di Bruno, F.
Coordination (linguistics) Coordinators Coordination_(linguistics) > Coordinators A coordinator or a coordinating conjunction, often appears between the conjuncts, usually at least between the penultimate and ultimate conjunct of the coordinate structure. The words and and or are by far the most frequently occurring coordinators in English. Other coordinators occur less often and have unique properties, e.g. but, as well as, then, etc. The coordinator usually serves to link the conjuncts and indicate the presence of a coordinate structure.
Step (software) Description Step_(software) > Description Step is based on bodies and forces placed by the user: Bodies range from tiny particles to huge polygons, and each body has unique properties that influence the outcome of the simulation, such as mass and velocity, and their derivations such as kinetic energy. Forces can be either placed directly by the user or produced by adding gravitation, Coulomb force or other effects.The program also features springs and soft bodies. Step allows reverting after simulation, so the user can modify the bodies and forces and see how the outcome of the simulation is affected.
Quantum measurement theory Measurement-based quantum computation Quantum_measurement > Quantum information and computation > Measurement-based quantum computation Measurement-based quantum computation (MBQC) is a model of quantum computing in which the answer to a question is, informally speaking, created in the act of measuring the physical system that serves as the computer. : 317
Capacitor Lifespan Parallel_plate_capacitor > Non-ideal behavior > Lifespan Electrolytic capacitors generally have the shortest lifespans. Electrolytic capacitors are affected very little by vibration or humidity, but factors such as ambient and operational temperatures play a large role in their failure, which gradually occur as an increase in ESR (up to 300%) and as much as a 20% decrease in capacitance. The capacitors contain electrolytes which will eventually diffuse through the seals and evaporate.
Resting heart rate Correlation with cardiovascular mortality risk Heart_Rate > Clinical significance > Correlation with cardiovascular mortality risk In each case, the authors are actually referring to instantaneous HR, which is the number of times the heart would beat if successive RR intervals were constant. Lifestyle and pharmacological regimens may be beneficial to those with high resting heart rates. Exercise is one possible measure to take when an individual's heart rate is higher than 80 beats per minute.
Energy recovery ventilator Methods of transfer Energy_recovery_ventilation > Methods of transfer Subsequently, this air cools the condenser coil at a lower temperature than if the rejected heat had not entered the exhaust airstream. During the heating seasons, the system works in reverse. Instead of discharging the heat into the exhaust airstream, the system draws heat from the exhaust airstream in order to pre-heat the incoming air.
Inverse function theorem Statements Inverse_function_theorem > Statements For functions of a single variable, the theorem states that if f {\displaystyle f} is a continuously differentiable function with nonzero derivative at the point a {\displaystyle a} ; then f {\displaystyle f} is injective (or bijective onto the image) in a neighborhood of a {\displaystyle a} , the inverse is continuously differentiable near b = f ( a ) {\displaystyle b=f(a)} , and the derivative of the inverse function at b {\displaystyle b} is the reciprocal of the derivative of f {\displaystyle f} at a {\displaystyle a}: It can happen that a function f {\displaystyle f} may be injective near a point a {\displaystyle a} while f ′ ( a ) = 0 {\displaystyle f'(a)=0} . An example is f ( x ) = ( x − a ) 3 {\displaystyle f(x)=(x-a)^{3}} . In fact, for such a function, the inverse cannot be differentiable at b = f ( a ) {\displaystyle b=f(a)} , since if f − 1 {\displaystyle f^{-1}} were differentiable at b {\displaystyle b} , then, by the chain rule, 1 = ( f − 1 ∘ f ) ′ ( a ) = ( f − 1 ) ′ ( b ) f ′ ( a ) {\displaystyle 1=(f^{-1}\circ f)'(a)=(f^{-1})'(b)f'(a)} , which implies f ′ ( a ) ≠ 0 {\displaystyle f'(a)\neq 0} . (The situation is different for holomorphic functions; see #Holomorphic inverse function theorem below.)
Bacterial cell structure Plasma membrane Bacterial_cell_structure > Plasma membrane Gram-negative and mycobacteria have an inner and outer bacteria membrane. As a phospholipid bilayer, the lipid portion of the bacterial outer membrane is impermeable to charged molecules. However, channels called porins are present in the outer membrane that allow for passive transport of many ions, sugars and amino acids across the outer membrane.
SustainableEnergy Objectives SustainableEnergy > Objectives SustainableEnergy has a strong engagement: to influence the development of the Danish energy policy to be more resource- and environment-conscious especially by facilitating the use of renewable energy. to get the people informed of their possibilities to make their own action by installing renewable-energy systems in their own homes or institutions in Denmark.
Dynamic scoping Java Lexically_scoped > By language > Java The loop's variables (local to that loop) are destroyed as soon as the loop ends.Member variables also called fields are variables declared within the class, outside of any method. By default, these variables are available for all methods within that class and also for all classes in the package.Parameters are variables in method declarations.In general, a set of brackets defines a particular scope, but variables at top level within a class can differ in their behavior depending on the modifier keywords used in their definition. The following table shows the access to members permitted by each modifier.
Perfect graph Algorithms Perfect_graph > Algorithms More efficient combinatorial algorithms are known for many special cases.For many years the complexity of recognizing Berge graphs and perfect graphs remained open. From the definition of Berge graphs, it follows immediately that their recognition is in co-NP. Finally, subsequent to the proof of the strong perfect graph theorem, a polynomial time algorithm was discovered by Chudnovsky, Cornuéjols, Liu, Seymour, and Vušković.
Split gene theory Spliceosomal machinery and eukaryotic nucleus Split_gene_theory > Spliceosomal machinery and eukaryotic nucleus Senapathy addressed the origin of the spliceosomal machinery that edits out the introns from RNA transcripts. If the split genes had originated from random DNA, then the introns would have become an unnecessary but integral part of eukaryotic genes along with the splice junctions. The spliceosomal machinery would be required to remove them and to enable the short exons to be linearly spliced together as a contiguously coding mRNA that can be translated into a complete protein. Thus, the split gene theory argues that spliceosomal machinery exists to remove the unnecessary introns.Blake states, “Work by Senapathy, when applied to RNA, comprehensively explains the origin of the segregated form of RNA into coding and noncoding regions. It also suggests why a splicing mechanism was developed at the start of primordial evolution.”
Bernoulli's rule Derivative of denominator is zero Bernoulli's_rule > Cases where theorem cannot be applied (Necessity of conditions) > Derivative of denominator is zero The necessity of the condition that g ′ ( x ) ≠ 0 {\displaystyle g'(x)\neq 0} near c {\displaystyle c} can be seen by the following counterexample due to Otto Stolz. Let f ( x ) = x + sin ⁡ x cos ⁡ x {\displaystyle f(x)=x+\sin x\cos x} and g ( x ) = f ( x ) e sin ⁡ x . {\displaystyle g(x)=f(x)e^{\sin x}.} Then there is no limit for f ( x ) / g ( x ) {\displaystyle f(x)/g(x)} as x → ∞ .
Batch normalization Summary Batch_normalization Recently, some scholars have argued that batch normalization does not reduce internal covariate shift, but rather smooths the objective function, which in turn improves the performance. However, at initialization, batch normalization in fact induces severe gradient explosion in deep networks, which is only alleviated by skip connections in residual networks. Others maintain that batch normalization achieves length-direction decoupling, and thereby accelerates neural networks.
Method inlining Implementation Method_inlining > Implementation Run-time inlining can use dynamic profiling information to make better decisions about which functions to inline, as in the Java Hotspot compiler.Here is a simple example of inline expansion performed "by hand" at the source level in the C programming language: Before inlining: After inlining: Note that this is only an example. In an actual C application, it would be preferable to use an inlining language feature such as parameterized macros or inline functions to tell the compiler to transform the code in this way. The next section lists ways to optimize this code.
Material point method Disadvantages of MPM Material_point_method > Disadvantages of MPM MPM is more expensive in terms of storage than other methods, as MPM makes use of mesh as well as particle data. MPM is more computationally expensive than FEM, as the grid must be reset at the end of each MPM calculation step and reinitialised at the beginning of the following step. Spurious oscillation may occur as particles cross the boundaries of the mesh in MPM, although this effect can be minimized by using generalized interpolation methods (GIMP). In MPM as in FEM, the size and orientation of the mesh can impact the results of a calculation: for example, in MPM, strain localisation is known to be particularly sensitive to mesh refinement. One stability problem in MPM that does not occur in FEM is the cell-crossing errors and null-space errors because the number of integration points (material points) does not remain constant in a cell.
Force-sensing capacitor Uses Force-sensing_capacitor > Uses Force-sensing capacitors can be used to create low-profile force-sensitive buttons. They have been used in medical imaging to map pressures in the esophagus and to image breast and prostate cancer. == References ==
Symmetry in biology Evolution of symmetry in animals Bilateral_symmetry > Evolution of symmetry > Evolution of symmetry in animals Symmetry is often selected for in the evolution of animals. This is unsurprising since asymmetry is often an indication of unfitness – either defects during development or injuries throughout a lifetime. This is most apparent during mating during which females of some species select males with highly symmetrical features.
Electrolytic detector History Electrolytic_detector > History The variations in the amplitude of the radio wave that represent the sound waveform will cause variations in the current, and thus can be converted to sound by an earphone. To do this a rectifier is required, an electrical component that conducts electric current in only one direction and blocks current in the opposite direction.
RNA transcription Background Transcription_inhibitor > Background This directionality is because RNA polymerase can only add nucleotides to the 3' end of the growing mRNA chain. This use of only the 3' → 5' DNA strand eliminates the need for the Okazaki fragments that are seen in DNA replication. This also removes the need for an RNA primer to initiate RNA synthesis, as is the case in DNA replication.
Robot locomotion Approaches Robot_locomotion > Approaches Product optimization Motion planning Motion capture may be performed on humans, insects and other organisms. Machine learning, typically with reinforcement learning.
Secure Copy Secure Copy Protocol Secure_copy_protocol > Secure Copy Protocol The SCP is a network protocol, based on the BSD RCP protocol, which supports file transfers between hosts on a network. SCP uses Secure Shell (SSH) for data transfer and uses the same mechanisms for authentication, thereby ensuring the authenticity and confidentiality of the data in transit. A client can send (upload) files to a server, optionally including their basic attributes (permissions, timestamps). Clients can also request files or directories from a server (download). SCP runs over TCP port 22 by default. Like RCP, there is no RFC that defines the specifics of the protocol.
Decidability (logic) Decidability of a logical system Decidability_(logic) > Decidability of a logical system Each logical system comes with both a syntactic component, which among other things determines the notion of provability, and a semantic component, which determines the notion of logical validity. The logically valid formulas of a system are sometimes called the theorems of the system, especially in the context of first-order logic where Gödel's completeness theorem establishes the equivalence of semantic and syntactic consequence. In other settings, such as linear logic, the syntactic consequence (provability) relation may be used to define the theorems of a system. A logical system is decidable if there is an effective method for determining whether arbitrary formulas are theorems of the logical system.
Functional Programming Efficiency issues Functional_program > Comparison to imperative programming > Efficiency issues For purely functional languages, the worst-case slowdown is logarithmic in the number of memory cells used, because mutable memory can be represented by a purely functional data structure with logarithmic access time (such as a balanced tree). However, such slowdowns are not universal. For programs that perform intensive numerical computations, functional languages such as OCaml and Clean are only slightly slower than C according to The Computer Language Benchmarks Game.
Quantum limit Displacement measurement Standard_quantum_limit > Examples > Displacement measurement (2 and 5) that the position measurement error Δ x m e a s {\displaystyle \Delta x_{\mathrm {meas} }} and the momentum perturbation Δ p b . a . {\displaystyle \Delta p_{\mathrm {b.a.}
Prophase I Leptotene Metaphase_I > Phases > Meiosis I > Prophase I > Leptotene The first stage of prophase I is the leptotene stage, also known as leptonema, from Greek words meaning "thin threads". : 27 In this stage of prophase I, individual chromosomes—each consisting of two replicated sister chromatids—become "individualized" to form visible strands within the nucleus. : 27: 353 The chromosomes each form a linear array of loops mediated by cohesin, and the lateral elements of the synaptonemal complex assemble forming an "axial element" from which the loops emanate. Recombination is initiated in this stage by the enzyme SPO11 which creates programmed double strand breaks (around 300 per meiosis in mice). This process generates single stranded DNA filaments coated by RAD51 and DMC1 which invade the homologous chromosomes, forming inter-axis bridges, and resulting in the pairing/co-alignment of homologues (to a distance of ~400 nm in mice).
Telomerase reverse transcriptase Enhancement Telomerase_reverse_transcriptase > Stem cells > Enhancement Hence, not all stem cells will have increased stem-cell properties. For example, research has shown that telomerase can be upregulated in CD34+ Umbilical Cord Blood Cells through hTERT over-expression. The survival of these stem cells was enhanced, although there was no increase in the amount of population doubling.
Bench (furniture) Types Bench_(furniture) > Types These tables may have table legs which are collapsible, in order to expedite transport and storage. Scenic benches are situated to provide a more comfortable means of enjoying the contemplation of a beautiful landscape, a busy street scene, or less commonly a specific event.
Igor Shafarevich Mathematics Igor_Shafarevich > Mathematics From his early years, Shafarevich made fundamental contributions to several parts of mathematics including algebraic number theory, algebraic geometry and arithmetic algebraic geometry. In particular, in algebraic number theory, the Shafarevich–Weil theorem extends the commutative reciprocity map to the case of Galois groups, which are central extensions of abelian groups by finite groups. Shafarevich was the first mathematician to give a completely self-contained formula for the Hilbert pairing, thus initiating an important branch of the study of explicit formulas in number theory. Another famous (and slightly incomplete) result is Shafarevich's theorem on solvable Galois groups, giving the realization of every finite solvable group as a Galois group over the rationals.
Cold core ring Formation Cold_core_ring > Formation Mesoscale eddies are usually seen in areas of intense, meandering currents such as the Gulf Stream and the Antarctic Circumpolar Current that feeds into the South Pacific and Indian oceans, but in general can be caused by a combination of factors such as cooling of sea surface temperature, convection, direct generation from wind, or water flow past an irregular or jagged coastline. Cyclonic cold-core eddies are frequently formed at the polar front by the Gulf Stream and Labrador Current. The cold, nutrient-rich waters from the Labrador Sea flow south and get caught in the eastward meandering of the Gulf Stream, traveling east across the Atlantic Ocean. Generally, cold core rings are formed when meanders expanding southeast are pinched from the Gulf Stream.
Differentiable manifold Atlases Differentiable_manifolds > Definition > Atlases Relative to the given atlas, this facilitates a notion of differentiable mappings whose domain or range is M, as well as a notion of the derivative of such maps. Formally, the word "differentiable" is somewhat ambiguous, as it is taken to mean different things by different authors; sometimes it means the existence of first derivatives, sometimes the existence of continuous first derivatives, and sometimes the existence of infinitely many derivatives.
Simulation of production systems Automobiles Simulation_of_production_systems > More examples of simulation > Automobiles For novice drivers, truck simulators provide an opportunity to begin their career by applying best practice. For mature drivers, simulation provides the ability to enhance good driving or to detect poor practice and to suggest the necessary steps for remedial action. For companies, it provides an opportunity to educate staff in the driving skills that achieve reduced maintenance costs, improved productivity and, most importantly, to ensure the safety of their actions in all possible situations.
Mathematical model of computation Functional models Mathematical_model_of_computation > Models > Functional models Functional models include: Abstract rewriting systems Combinatory logic General recursive functions Lambda calculus
Inorganic chemist Descriptive inorganic chemistry Inorganic_Chemistry > Descriptive inorganic chemistry Descriptive inorganic chemistry focuses on the classification of compounds based on their properties. Partly the classification focuses on the position in the periodic table of the heaviest element (the element with the highest atomic weight) in the compound, partly by grouping compounds by their structural similarities.
Software entropy Summary Software_entropy Software entropy is the idea that software eventually rots as it is changed if sufficient care is not taken to maintain coherence with product design and established design principles. The common usage is only tangentially related to entropy as defined in classical thermodynamics and statistical physics. Another aspect can be found in what is perceived to be a decay in the quality of otherwise static software that is the result of the inevitable changes to its environment, that often occur as operating systems and other components are upgraded or retired.
Varicap diode Tuning circuits Varicap > Use in a circuit > Tuning circuits Generally the use of a varicap diode in a circuit requires connecting it to a tuned circuit, usually in parallel with any existing capacitance or inductance. A DC voltage is applied as reverse bias across the varicap to alter its capacitance. The DC bias voltage must be blocked from entering the tuned circuit. This can be accomplished by placing a DC blocking capacitor with a capacitance about 100 times greater than the maximum capacitance of the varicap diode in series with it and by applying DC from a high impedance source to the node between the varicap cathode and the blocking capacitor as shown in the upper left circuit in the accompanying diagram.
Bevel gear Applications Bevel_gear > Applications The bevel gear has many diverse applications such as locomotives, marine applications, automobiles, printing presses, cooling towers, power plants, steel plants, railway track inspection machines, etc. For examples, see the following articles on: Bevel gears are used in differential drives, which can transmit power to two axles spinning at different speeds, such as those on a cornering automobile. Bevel gears are used as the main mechanism for a hand drill. As the handle of the drill is turned in a vertical direction, the bevel gears change the rotation of the chuck to a horizontal rotation. The bevel gears in a hand drill have the added advantage of increasing the speed of rotation of the chuck and this makes it possible to drill a range of materials.
Computer emulator Comparison with simulation Software_emulation > Comparison with simulation In contrast, a simulator could be a program which runs on a PC, so that old Atari games can be simulated on it. Purists continue to insist on this distinction, but currently the term "emulation" often means the complete imitation of a machine executing binary code while "simulation" often refers to computer simulation, where a computer program is used to simulate an abstract model. Computer simulation is used in virtually every scientific and engineering domain and Computer Science is no exception, with several projects simulating abstract models of computer systems, such as network simulation, which both practically and semantically differs from network emulation.
Tetraview Summary Tetraview A tetraview is an attempt to graph a complex function of a complex variable, by a method invented by Davide P. Cervone. A graph of a real function of a real variable is the set of ordered pairs (x,y) such that y = f(x). This is the ordinary two-dimensional Cartesian graph studied in school algebra.
Guar gum Solubility and viscosity Guar_gum > Properties > Solubility and viscosity Strong acids cause hydrolysis and loss of viscosity and alkalies in strong concentration also tend to reduce viscosity. It is insoluble in most hydrocarbon solvents. The viscosity attained is dependent on time, temperature, concentration, pH, rate of agitation and particle size of the powdered gum used.
Primitive matrix Perron projection as a limit: Ak/rk Perron–Frobenius_theorem > Proof methods > Perron projection as a limit: Ak/rk Trace of projector equals the dimension of its image. It was proved before that it is not more than one-dimensional. From the definition one sees that P acts identically on the r-eigenvector for M. So it is one-dimensional. So choosing (wTv) = 1, implies P = vwT.
Kleene–Brouwer order Recursion theory Kleene–Brouwer_order > Recursion theory In recursion theory, the Kleene–Brouwer order may be applied to the computation trees of implementations of total recursive functionals. A computation tree is well-founded if and only if the computation performed by it is total recursive. Each state x {\displaystyle x} in a computation tree may be assigned an ordinal number \| \| x \| \| {\displaystyle \|\|x\|\|} , the supremum of the ordinal numbers 1 + \| \| y \| \| {\displaystyle 1+\|\|y\|\|} where y {\displaystyle y} ranges over the children of x {\displaystyle x} in the tree. In this way, the total recursive functionals themselves can be classified into a hierarchy, according to the minimum value of the ordinal at the root of a computation tree, minimized over all computation trees that implement the functional. The Kleene–Brouwer order of a well-founded computation tree is itself a recursive well-ordering, and at least as large as the ordinal assigned to the tree, from which it follows that the levels of this hierarchy are indexed by recursive ordinals.
Hunting oscillation Limitation of simplified analysis Hunting_oscillation > Railway wheelsets > Limitation of simplified analysis The motion of a wheel set is much more complicated than this analysis would indicate. There are additional restraining forces applied by the vehicle suspension and, at high speed, the wheel set will generate additional gyroscopic torques, which will modify the estimate of the critical speed. Conventionally a railway vehicle has stable motion in low speeds, when it reaches to high speeds stability changes to unstable form. The main purpose of nonlinear analysis of rail vehicle system dynamics is to show the view of analytical investigation of bifurcation, nonlinear lateral stability and hunting behavior of rail vehicles in a tangent track.
Pulse-Doppler radar Performance Pulse_doppler_radar > Special consideration > Performance The value D is added to the standard radar range equation to account for both pulse-Doppler signal processing and transmitter FM noise reduction. Detection range is increased proportional to the fourth root of the number of filters for a given power consumption. Alternatively, power consumption is reduced by the number of filters for a given detection range.
Body moment Summary Body_moment In mechanics, a moment is a measure of the turning effect of a force about some point in space. In most practical examples, moments are the results of forces acting at a distance from the point of interest. The stress on the body on which the force acts is then symmetric. If the moment results from a strong body force, such as that produced in a magnetic material in a strong magnetic field, the stress tensor is non-symmetric.
Zermelo-Fraenkel axioms 8. Axiom of power set Zermelo–Fraenkel_axiomatization > Axioms > 8. Axiom of power set Alternative forms of these axioms are often encountered, some of which are listed in Jech (2003). Some ZF axiomatizations include an axiom asserting that the empty set exists. The axioms of pairing, union, replacement, and power set are often stated so that the members of the set x {\displaystyle x} whose existence is being asserted are just those sets which the axiom asserts x {\displaystyle x} must contain. The following axiom is added to turn ZF into ZFC:
Effective Lagrangian Summary Effective_Lagrangian Effective field theories typically work best when there is a large separation between length scale of interest and the length scale of the underlying dynamics. Effective field theories have found use in particle physics, statistical mechanics, condensed matter physics, general relativity, and hydrodynamics. They simplify calculations, and allow treatment of dissipation and radiation effects.
PTC rubber Applications PTC_rubber > Applications These heaters will provide high power when they are cold and rapidly heat up themselves to a constant temperature and remain there virtually unaffected by changes in the ambient conditions. They can be powered with any voltage between 5 and 230 V, AC or DC. The PTC rubber material is a self-regulating heater.
Mammary carcinoma Prognostic factors Breast_carcinoma > Prognosis > Prognostic factors The stage of the breast cancer is the most important component of traditional classification methods of breast cancer, because it has a greater effect on the prognosis than the other considerations. Staging takes into consideration size, local involvement, lymph node status and whether metastatic disease is present. The higher the stage at diagnosis, the poorer the prognosis. The stage is raised by the invasiveness of disease to lymph nodes, chest wall, skin or beyond, and the aggressiveness of the cancer cells.
Half bond Summary Covalent_bond The prefix co- means jointly, associated in action, partnered to a lesser degree, etc.; thus a "co-valent bond", in essence, means that the atoms share "valence", such as is discussed in valence bond theory. In the molecule H2, the hydrogen atoms share the two electrons via covalent bonding. Covalency is greatest between atoms of similar electronegativities. Thus, covalent bonding does not necessarily require that the two atoms be of the same elements, only that they be of comparable electronegativity. Covalent bonding that entails the sharing of electrons over more than two atoms is said to be delocalized.
Reduced Planck Constant Origin of the constant Reduced_Planck’s_constant > Origin of the constant Planck's constant was formulated as part of Max Planck's successful effort to produce a mathematical expression that accurately predicted the observed spectral distribution of thermal radiation from a closed furnace (black-body radiation). This mathematical expression is now known as Planck's law. In the last years of the 19th century, Max Planck was investigating the problem of black-body radiation first posed by Kirchhoff some 40 years earlier.
Glossary of string theory B Glossary_of_string_theory > B Short for boson. 3. Short for baryon.
Lamport's Bakery algorithm Pseudocode Lamport's_Bakery_algorithm > Implementation of the algorithm > Code examples > Pseudocode This primitive is often referred to as yield. Lamport's bakery algorithm assumes a sequential consistency memory model. Few, if any, languages or multi-core processors implement such a memory model. Therefore, correct implementation of the algorithm typically requires inserting fences to inhibit reordering.
Edible vaccines Immune response Edible_vaccines > Immune response The activated B-cells then move to the mesenteric lymph nodes where they become plasma cells and move to the mucous membrane to produce immunoglobulin A (IgA) (a type of antibody). Then the M-cells channel the antigen. As the cells go toward the lumen, the IgA combine with secretary components to make secretory IgA (sIgA). Then, the sIgA and the specific antigenic epitopes work together to eliminate the unwanted pathogen.
Social information processing (theory) Origin Social_information_processing_(theory) > Key concepts and features > Warranting > Origin Partial warranting is another example. It is information that, though provided by the user, contains easily verifiable facts. Numerical information, such as height, weight, age, or address constitutes as partial warranting, as these figures are easily checked and provide little room for gray area.
Ozone Layer Protection Effect Phase-out_of_hydrochlorofluorocarbons > Effect The Montreal Protocol currently calls for a complete phase-out of HCFCs by 2030, but does not place any restriction on HFCs. Since the CFCs themselves are equally powerful greenhouse gases, the mere substitution of HFCs for CFCs does not significantly increase the rate of anthropogenic climate change, but over time a steady increase in their use could increase the danger that human activity will change the climate.Policy experts have advocated for increased efforts to link ozone protection efforts to climate protection efforts. Policy decisions in one arena affect the costs and effectiveness of environmental improvements in the other.
Noise equivalent power Summary Noise_equivalent_power For example, a detector with an NEP of 10 − 12 W / H z {\displaystyle 10^{-12}\mathrm {W} /{\sqrt {\mathrm {Hz} }}} can detect a signal power of one picowatt with a signal-to-noise ratio (SNR) of one after one half second of averaging. The SNR improves as the square root of the averaging time, and hence the SNR in this example can be improved by a factor of 10 by averaging 100-times longer, i.e. for 50 seconds. If the NEP refers to the signal power absorbed in the detector, it is known as the electrical NEP. If instead it refers to the signal power incident on the detector system, it is called the optical NEP. The optical NEP is equal to the electrical NEP divided by the optical coupling efficiency of the detector system.
GEH statistic Development of the SQV statistic GEH_statistic > Development of the SQV statistic An alternative measure to the GEH statistic is the Scalable Quality Value (SQV), which solves the above-mentioned problems: It is applicable to various indicators, it is symmetric, it has no units, and it has a range of values between 0 and 1. Moreover, Friedrich et al. derive the relationship between GEH statistic and normal distribution, and thus the relationship between SQV statistic and normal distribution. The SQV statistic is calculated using an empirical formula with a scaling factor f {\textstyle f} :
Rule-based language Logic-based languages Rule-based_language > Logic-based languages Logic-based languages specify a set of attributes that a solution must-have, rather than a set of steps to obtain a solution. Notable languages following this programming paradigm include: ALF Alma-0 Curry Datalog Fril Flix (a functional programming language with first-class Datalog constraints) Janus λProlog (a logic programming language featuring polymorphic typing, modular programming, and higher-order programming) Oz, and Mozart Programming System cross-platform Oz Prolog (formulates data and the program evaluation mechanism as a special form of mathematical logic called Horn logic and a general proving mechanism called logical resolution) Mercury (based on Prolog) Visual Prolog (object-oriented Prolog extension) ROOP Soufflé
Limit state design Factor development Limit_state_design > Factor development These factors can differ significantly for different materials or even between differing grades of the same material. Wood and masonry typically have smaller factors than concrete, which in turn has smaller factors than steel. The factors applied to resistance also account for the degree of scientific confidence in the derivation of the values — i.e. smaller values are used when there isn't much research on the specific type of failure mode).
ATP generation Eukaryotic electron transport chains Oxidative_phosphorylation > Eukaryotic electron transport chains Many catabolic biochemical processes, such as glycolysis, the citric acid cycle, and beta oxidation, produce the reduced coenzyme NADH. This coenzyme contains electrons that have a high transfer potential; in other words, they will release a large amount of energy upon oxidation. However, the cell does not release this energy all at once, as this would be an uncontrollable reaction. Instead, the electrons are removed from NADH and passed to oxygen through a series of enzymes that each release a small amount of the energy.
Ring of endomorphisms Description Endomorphism_ring > Description Let (A, +) be an abelian group and we consider the group homomorphisms from A into A. Then addition of two such homomorphisms may be defined pointwise to produce another group homomorphism. Explicitly, given two such homomorphisms f and g, the sum of f and g is the homomorphism f + g: x ↦ f(x) + g(x). Under this operation End(A) is an abelian group. With the additional operation of composition of homomorphisms, End(A) is a ring with multiplicative identity.
Hydrogen bond catalysis Anion binding Hydrogen_bond_catalysis > Catalytic strategies > Anion binding It is thought that under the reaction conditions, the chloroether can epimerize and thiourea can stereoselectively bind chloride to form a closely associated ion pair. This asymmetric ion pair is then attacked by the silane to generate alkylated product.
Neurophilosophy Historical overview Neurophilosophy > Computation and representation in the brain > Historical overview Behaviorism had dominated the psychology until the 1950s when new developments in a variety of fields overturned behaviorist theory in favor of a cognitive theory. From the beginning of the cognitive revolution, computational theory played a major role in theoretical developments. Minsky and McCarthy's work in artificial intelligence, Newell and Simon's computer simulations, and Noam Chomsky's importation of information theory into linguistics were all heavily reliant on computational assumptions.
Bochner integral Definition Bochner_integral > Definition If μ ( E i ) {\displaystyle \mu \left(E_{i}\right)} is finite whenever b i ≠ 0 , {\displaystyle b_{i}\neq 0,} then the simple function is integrable, and the integral is then defined by exactly as it is for the ordinary Lebesgue integral. A measurable function f: X → B {\displaystyle f:X\to B} is Bochner integrable if there exists a sequence of integrable simple functions s n {\displaystyle s_{n}} such that where the integral on the left-hand side is an ordinary Lebesgue integral. In this case, the Bochner integral is defined by It can be shown that the sequence { ∫ X s n d μ } n = 1 ∞ {\displaystyle \left\{\int _{X}s_{n}\,d\mu \right\}_{n=1}^{\infty }} is a Cauchy sequence in the Banach space B , {\displaystyle B,} hence the limit on the right exists; furthermore, the limit is independent of the approximating sequence of simple functions { s n } n = 1 ∞ .
Pramipexole Research Pramipexole > Research Pramipexole has been evaluated for the treatment of sexual dysfunction experienced by some users of selective serotonin reuptake inhibitor (SSRI) antidepressants. Pramipexole has shown effects on pilot studies in a placebo-controlled proof of concept study in bipolar disorder. It is also being investigated for the treatment of clinical depression and fibromyalgia.
Imaginary part Conjugate Real_and_imaginary_parts > Relations and operations > Conjugate This process is sometimes called "rationalization" of the denominator (although the denominator in the final expression might be an irrational real number), because it resembles the method to remove roots from simple expressions in a denominator. The real and imaginary parts of a complex number z can be extracted using the conjugation: Moreover, a complex number is real if and only if it equals its own conjugate. Conjugation distributes over the basic complex arithmetic operations: Conjugation is also employed in inversive geometry, a branch of geometry studying reflections more general than ones about a line. In the network analysis of electrical circuits, the complex conjugate is used in finding the equivalent impedance when the maximum power transfer theorem is looked for.
Radiation levels Beta particles Hard_radiation > Directly ionizing radiation > Beta particles Beta particles are less penetrating than gamma radiation, but more penetrating than alpha particles. High-energy beta particles may produce X-rays known as bremsstrahlung ("braking radiation") or secondary electrons (delta ray) as they pass through matter. Both of these can cause an indirect ionization effect. Bremsstrahlung is of concern when shielding beta emitters, as the interaction of beta particles with some shielding materials produces Bremsstrahlung. The effect is greater with material having high atomic numbers, so material with low atomic numbers is used for beta source shielding.
Riemann Hypothesis Numerical calculations Critical_line_theorem > Zeros on the critical line > Numerical calculations So far all zeros that have been checked are on the critical line and are simple. (A multiple zero would cause problems for the zero finding algorithms, which depend on finding sign changes between zeros.) For tables of the zeros, see Haselgrove & Miller (1960) or Odlyzko.
Space research International Gamma-Ray Astrophysics Laboratory Space_research > Space research from artificial satellites > International Gamma-Ray Astrophysics Laboratory INTEGRAL is one of the most powerful gamma-ray observatories, launched by the European Space Agency in 2002, and continuing to operate (as of March 2019). INTEGRAL provides insight into the most energetic cosmological formations in space including, black holes, neutron stars, and supernovas. INTEGRAL plays an important role researching gamma-rays, one of the most exotic and energetic phenomena in space.
Maleylacetic acid Summary Maleylacetic_acid Maleylacetic acid is a chemical compound produced in the biodegradation of catechin by Bradyrhizobium japonicum. The enzyme maleylacetate reductase uses 3-oxoadipate, NAD+, and NADP+ to produce 2-maleylacetate, NADH, NADPH, and H+.
Motor cortex Components of the motor cortex Motor_cortex > Components of the motor cortex 2. The premotor cortex is responsible for some aspects of motor control, possibly including the preparation for movement, the sensory guidance of movement, the spatial guidance of reaching, or the direct control of some movements with an emphasis on control of proximal and trunk muscles of the body. Located anterior to the primary motor cortex.
Critical angle (optics) Fresnel and the phase shift Frustrated_total_internal_reflection > History > Fresnel and the phase shift Although this reasoning was applied without the benefit of knowing that light waves were electromagnetic, it passed the test of experiment, and survived remarkably intact after James Clerk Maxwell changed the presumed nature of the waves. Meanwhile, Fresnel's success inspired James MacCullagh and Augustin-Louis Cauchy, beginning in 1836, to analyze reflection from metals by using the Fresnel equations with a complex refractive index. The imaginary part of the complex index represents absorption.The term critical angle, used for convenience in the above narrative, is anachronistic: it apparently dates from 1873.In the 20th century, quantum electrodynamics reinterpreted the amplitude of an electromagnetic wave in terms of the probability of finding a photon. In this framework, partial transmission and frustrated TIR concern the probability of a photon crossing a boundary, and attenuated total reflectance concerns the probability of a photon being absorbed on the other side. Research into the more subtle aspects of the phase shift in TIR, including the Goos–Hänchen and Imbert–Fedorov effects and their quantum interpretations, has continued into the 21st century.
Determination of equilibrium constants The chemical model Determination_of_equilibrium_constants > Computational methods > The chemical model H 2 O ↽ − − ⇀ H + + OH − {\displaystyle {\ce {H2O <=> H+ + OH-}}}: K W ′ = {\displaystyle K_{\mathrm {W} }^{'}={\frac {}{}}} With dilute solutions the concentration of water is assumed constant, so the equilibrium expression is written in the form of the ionic product of water. K W = {\displaystyle K_{\mathrm {W} }={\ce {}}\,} When both H+ and OH− must be considered as reactants, one of them is eliminated from the model by specifying that its concentration be derived from the concentration of the other. Usually the concentration of the hydroxide ion is given by = K W {\displaystyle ={\frac {K_{{\ce {W}}}}{}}\,} In this case the equilibrium constant for the formation of hydroxide has the stoichiometric coefficients −1 in regard to the proton and zero for the other reactants.
Torque wrenches ASME Pneumatic_torque_wrench > Torque wrench standardization > ASME The American Society of Mechanical Engineers maintains standard ASME B107.300. This standard has the same type designation as the ISO standard with the addition of the type 3, (limiting) torque tool. This type will release the drive once the desired torque is met so that no more torque can be applied. This standard, however, uses different class designations within each type as well as additional style and design variants within each class.
White blood cell differential Procedure White_blood_cell_differential > Types > Manual differential > Procedure The smear is examined in a systematic pattern, scanning from side to side within the feathered edge and counting cells consecutively. The differential is typically performed at 400x or 500x magnification, but 1000x magnification may be used if abnormal cells are present. Cells are identified based on their morphologic features, such as the size and structure of their nucleus and the colour and texture of their cytoplasm.
Valve actuators Process control functions Electric_actuator > Functions > Process control functions Due to increasing decentralisation in automation technology and the introduction of micro processors, more and more functions have been transferred from the DCS to the field devices. The data volume to be transmitted was reduced accordingly, in particular by the introduction of fieldbus technology. Electric actuators whose functions have been considerably expanded are also affected by this development.
Embrittlement Low temperature embrittlement Embrittlement > Embrittlement of metals > Low temperature embrittlement At low temperatures, some metals can undergo a ductile-brittle transition which makes the material brittle and could lead to catastrophic failure during operation. This temperature is commonly called a ductile-brittle transition temperature or embrittlement temperature. Research has shown that low temperature embrittlement and brittle fracture only occurs under these specific criteria: There is enough stress to nucleate a crack. The stress at the crack exceeds a critical value that will open up the crack (also known as Griffith's criterion for crack opening).
Schottky problem Summary Schottky_problem In mathematics, the Schottky problem, named after Friedrich Schottky, is a classical question of algebraic geometry, asking for a characterisation of Jacobian varieties amongst abelian varieties.
Structure–activity relationship Summary Structure_activity_relationship Medicinal chemists use the techniques of chemical synthesis to insert new chemical groups into the biomedical compound and test the modifications for their biological effects. This method was refined to build mathematical relationships between the chemical structure and the biological activity, known as quantitative structure–activity relationships (QSAR). A related term is structure affinity relationship (SAFIR).
Functional Programming History Functional_language > History The lambda calculus, developed in the 1930s by Alonzo Church, is a formal system of computation built from function application. In 1937 Alan Turing proved that the lambda calculus and Turing machines are equivalent models of computation, showing that the lambda calculus is Turing complete. Lambda calculus forms the basis of all functional programming languages. An equivalent theoretical formulation, combinatory logic, was developed by Moses Schönfinkel and Haskell Curry in the 1920s and 1930s.Church later developed a weaker system, the simply-typed lambda calculus, which extended the lambda calculus by assigning a data type to all terms.
Model Based Design Steps Model-based_design > Steps The main steps in model-based design approach are: Plant modeling. Plant modeling can be data-driven or based on first principles. Data-driven plant modeling uses techniques such as System identification. With system identification, the plant model is identified by acquiring and processing raw data from a real-world system and choosing a mathematical algorithm with which to identify a mathematical model.
Post transcriptional gene silencing Three prime untranslated regions and microRNAs RNA_Interference > Cellular mechanism > Three prime untranslated regions and microRNAs Three prime untranslated regions (3′UTRs) of mRNAs often contain regulatory sequences that post-transcriptionally cause RNAi. Such 3′-UTRs often contain both binding sites for miRNAs as well as for regulatory proteins. By binding to specific sites within the 3′-UTR, miRNAs can decrease gene expression of various mRNAs by either inhibiting translation or directly causing degradation of the transcript. The 3′-UTR also may have silencer regions that bind repressor proteins that inhibit the expression of a mRNA.
Nernst heat theorem The theorem Nernst_heat_theorem > The theorem For a change from reactants to products at constant temperature and pressure the equation becomes Δ G = Δ H − T Δ S {\displaystyle \Delta G=\Delta H-T\Delta S} . In the limit of T = 0 the equation reduces to just ΔG = ΔH, as illustrated in the figure shown here, which is supported by experimental data. However, it is known from thermodynamics that the slope of the ΔG curve is -ΔS. Since the slope shown here reaches the horizontal limit of 0 as T → 0 then the implication is that ΔS → 0, which is the Nernst heat theorem. The significance of the Nernst heat theorem is that it was later used by Max Planck to give the third law of thermodynamics, which is that the entropy of all pure, perfectly crystalline homogeneous materials in complete internal equilibrium is 0 at absolute zero.
Contract lifecycle management Stages Contract_lifecycle_management > Stages There are many different phases of each contract – no matter the size or importance of any particular document, they must all go through each stage in order to be completed properly. Aswell as formation of contracts, contract lifecycle management addresses processes after contract signature or execution such as ensure parties comply with their contractual obligations, continuing compliance and dispute resolution.The stages of the contract lifecycle management process include: Requests - The start of every contract involves the actual request. This is the phase where involved parties gather all the relevant information and data they need in order to create a contract that works for both sides. The request stage is arguably one of the most important stages of the contract lifecycle and can take some time depending on who is involved.
Will to Believe Doctrine Criticism Will_to_Believe_Doctrine > Criticism However, the chemist adopting a hypothesis to guide years of study is certainly only a special case of hypothesis adoption. A more general defense of (1) could also be constructed from James' behaviorist theory of belief. James takes believing a proposition to consist in acting as if it were true, so if James considers testing a proposition as acting as if it were true to see if it leads to successful action, then James would be committed to seeing an act of hypothesis adoption as necessarily an act of belief adoption as well.
Drug design Summary Drug_design Drug design, often referred to as rational drug design or simply rational design, is the inventive process of finding new medications based on the knowledge of a biological target. The drug is most commonly an organic small molecule that activates or inhibits the function of a biomolecule such as a protein, which in turn results in a therapeutic benefit to the patient. In the most basic sense, drug design involves the design of molecules that are complementary in shape and charge to the biomolecular target with which they interact and therefore will bind to it. Drug design frequently but not necessarily relies on computer modeling techniques.
Factor (chord) Summary Factor_(chord) The chord factor called the "fifth" (pitch name "G") is represented in voice 2 (shown in red). The chord factor that is in the bass determines the inversion of the chord. For example, if the third is in the bass it is a first inversion chord (figured bass: 63) while if the seventh is in the bass the chord is in third inversion (42).
Cyclic sequence Unrolling and covers Cyclically_ordered_set > Further constructions > Unrolling and covers Starting from a cyclically ordered set K, one may form a linear order by unrolling it along an infinite line. This captures the intuitive notion of keeping track of how many times one goes around the circle. Formally, one defines a linear order on the Cartesian product Z × K, where Z is the set of integers, by fixing an element a and requiring that for all i: If , then ai < xi < yi < ai + 1.For example, the months January 2023, May 2023, September 2023, and January 2024 occur in that order. This ordering of Z × K is called the universal cover of K. Its order type is independent of the choice of a, but the notation is not, since the integer coordinate "rolls over" at a. For example, although the cyclic order of pitch classes is compatible with the A-to-G alphabetical order, C is chosen to be the first note in each octave, so in note-octave notation, B3 is followed by C4.

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