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Field of algebraic numbers Closed-form number Algebraic_numbers > Related fields > Closed-form number Algebraic numbers are all numbers that can be defined explicitly or implicitly in terms of polynomials, starting from the rational numbers. One may generalize this to "closed-form numbers", which may be defined in various ways. Most broadly, all numbers that can be defined explicitly or implicitly in terms of polynomials, exponentials, and logarithms are called "elementary numbers", and these include the algebraic numbers, plus some transcendental numbers. Most narrowly, one may consider numbers explicitly defined in terms of polynomials, exponentials, and logarithms – this does not include all algebraic numbers, but does include some simple transcendental numbers such as e or ln 2.
Hadronic matter Based on atoms Ordinary_matter > Definition > Based on atoms A definition of "matter" based on its physical and chemical structure is: matter is made up of atoms. Such atomic matter is also sometimes termed ordinary matter. As an example, deoxyribonucleic acid molecules (DNA) are matter under this definition because they are made of atoms. This definition can be extended to include charged atoms and molecules, so as to include plasmas (gases of ions) and electrolytes (ionic solutions), which are not obviously included in the atoms definition. Alternatively, one can adopt the protons, neutrons, and electrons definition.
Oestrous cycle Anestrus Estrous_cycle > Four phases > Anestrus Anestrus refers to the phase when the sexual cycle rests. This is typically a seasonal event and controlled by light exposure through the pineal gland that releases melatonin. Melatonin may repress stimulation of reproduction in long-day breeders and stimulate reproduction in short-day breeders. Melatonin is thought to act by regulating the hypothalamic pulse activity of the gonadotropin-releasing hormone.
Fundamental theorem of the calculus Generalizations Fundamental_theorem_of_the_calculus > Generalizations In that case, we can conclude that the function F is differentiable almost everywhere and F′(x) = f(x) almost everywhere. On the real line this statement is equivalent to Lebesgue's differentiation theorem. These results remain true for the Henstock–Kurzweil integral, which allows a larger class of integrable functions.In higher dimensions Lebesgue's differentiation theorem generalizes the Fundamental theorem of calculus by stating that for almost every x, the average value of a function f over a ball of radius r centered at x tends to f(x) as r tends to 0.
Polynomial factorization Formulation of the question Factorization_of_polynomials > Formulation of the question For example, the fundamental theorem of algebra, which states that every polynomial with complex coefficients has complex roots, implies that a polynomial with integer coefficients can be factored (with root-finding algorithms) into linear factors over the complex field C. Similarly, over the field of reals, the irreducible factors have degree at most two, while there are polynomials of any degree that are irreducible over the field of rationals Q. The question of polynomial factorization makes sense only for coefficients in a computable field whose every element may be represented in a computer and for which there are algorithms for the arithmetic operations. However, this is not a sufficient condition: Fröhlich and Shepherdson give examples of such fields for which no factorization algorithm can exist.The fields of coefficients for which factorization algorithms are known include prime fields (that is, the field of the rational number and the fields of the integers modulo a prime number) and their finitely generated field extensions. Integer coefficients are also tractable.
Axiom of countable choice Overview Axiom_of_countable_choice > Overview For instance, in order to prove that every accumulation point x of a set S ⊆ R is the limit of some sequence of elements of S \ {x}, one needs (a weak form of) the axiom of countable choice. When formulated for accumulation points of arbitrary metric spaces, the statement becomes equivalent to ACω. For other statements equivalent to ACω, see Herrlich (1997) and Howard & Rubin (1998).
4CAPS Overview and Assumptions 4CAPS > Overview and Assumptions In particular, according to Just and Varma, 4CAPS is based on four characteristic assumptions: Each cortical area can perform multiple cognitive functions. Each cortical area has a limited capacity for computational resources. The cortical network of regions that is responsible for carrying out a particular task changes dynamically as the regions' capacity resources are saturated. Communications between cortical regions are also subject to specific constraints, similar to bandwidth limitations along information channels.
Wikipedia:Manual of Style/Diagrams and maps Summary Wikipedia:Manual_of_Style/Diagrams_and_maps On the other hand, diagrams should avoid the inclusion of big areas of empty, non-informative space inside the image. Maps should present necessary geographic details, not every possible detail. The level of detail on a map should be selected so as to make the map useful to experts familiar with the subject, and also to users who are not at all familiar with it.
B-1 cell Types B1_cell > Types In contrast, B1b cells appear to be the primary source of dynamic T cell independent (TI) antibody production and long-term protection after bacterial infection such as Borrelia hermsii and Streptococcus pneumoniae. These studies indicate preexisting subset differences in B-cell receptor (BCR) specificity and antigen-driven B cell fate that remain important unresolved features of the system.
Open system (computing) Summary Open_system_(computing) The definition of "open system" can be said to have become more formalized in the 1990s with the emergence of independently administered software standards such as The Open Group's Single UNIX Specification. Although computer users today are used to a high degree of both hardware and software interoperability, in the 20th century the open systems concept could be promoted by Unix vendors as a significant differentiator. IBM and other companies resisted the trend for decades, exemplified by a now-famous warning in 1991 by an IBM account executive that one should be "careful about getting locked into open systems".However, in the first part of the 21st century many of these same legacy system vendors, particularly IBM and Hewlett-Packard, began to adopt Linux as part of their overall sales strategy, with "open source" marketed as trumping "open system". Consequently, an IBM mainframe with Linux on IBM Z is marketed as being more of an open system than commodity computers using closed-source Microsoft Windows—or even those using Unix, despite its open systems heritage. In response, more companies are opening the source code to their products, with a notable example being Sun Microsystems and their creation of the OpenOffice.org and OpenSolaris projects, based on their formerly closed-source StarOffice and Solaris software products.
Software brittleness Causes Software_brittleness > Causes These systems often rely on significant assumptions about the input data. When these assumptions aren't met – and, because they may not be stated, this may easily be the case – then the system will respond in completely unpredictable ways.
Signs and symptoms of Graves' disease Sub-clinical hyperthyroidism Signs_and_symptoms_of_Graves'_disease > Sub-clinical hyperthyroidism Also, hypersensitivity of the central nervous system to low-grade hyperthyroidism can result in an anxiety disorder before other Graves' disease symptoms emerge. E.g., panic disorder has been reported to precede Graves' hyperthyroidism by 4 to 5 years in some cases, although it is not known how frequently this occurs.However, while clinical hyperthyroidism is associated with frank neuropsychological and affective alterations, the occurrence of these alterations and their treatment in mild and sub-clinical hyperthyroidism remains a controversial issue. Regardless of the inconsistent findings, a 2007 study by Andersen et al. states that the distinction between sub-clinical and overt thyroid disease is in any case somewhat arbitrary. Sub-clinical hyperthyroidism has been reported in 63% of euthyroid Graves' disease, but only in 4% of cases where Graves' disease was in remission.
Earth's energy budget Earth's internal heat sources and other small effects Radiation_budget > Earth's energy flows > Earth's internal heat sources and other small effects A similar flow of thermal energy is released over the course of a year when plants are used as food or fuel. Other minor sources of energy are usually ignored in the calculations, including accretion of interplanetary dust and solar wind, light from stars other than the Sun and the thermal radiation from space. Earlier, Joseph Fourier had claimed that deep space radiation was significant in a paper often cited as the first on the greenhouse effect.
Empirical method Scientific research Empirical_study > Usage > Scientific research The outcome of empirical research using statistical hypothesis testing is never proof. It can only support a hypothesis, reject it, or do neither.
Database index Covering index Clustered_index > Covering index To reduce such index size, some systems allow including non-key fields in the index. Non-key fields are not themselves part of the index ordering but only included at the leaf level, allowing for a covering index with less overall index size. This can be done in SQL with CREATE INDEX my_index ON my_table (id) INCLUDE (name);.
Insecure channel Secure channels in the real world Insecure_channel > Secure channels in the real world There are no perfectly secure channels in the real world. There are, at best, only ways to make insecure channels (e.g., couriers, homing pigeons, diplomatic bags, etc.) less insecure: padlocks (between courier wrists and a briefcase), loyalty tests, security investigations, and guns for courier personnel, diplomatic immunity for diplomatic bags, and so forth. In 1976, two researchers proposed a key exchange technique (now named after them)—Diffie–Hellman key exchange (D-H). This protocol allows two parties to generate a key only known to them, under the assumption that a certain mathematical problem (e.g., the Diffie–Hellman problem in their proposal) is computationally infeasible (i.e., very very hard) to solve, and that the two parties have access to an authentic channel.
Differential rotation matrix Discussion Infinitesimal_rotation_matrix > Discussion An infinitesimal rotation matrix is a skew-symmetric matrix where: As any rotation matrix has a single real eigenvalue, which is equal to +1, the corresponding eigenvector defines the rotation axis. Its module defines an infinitesimal angular displacement.The shape of the matrix is as follows:
Reporter gene Gene expression assays Reporter_gene > Gene expression assays Reporter genes can be used to assay for the expression of a gene of interest that is normally difficult to quantitatively assay. Reporter genes can produce a protein that has little obvious or immediate effect on the cell culture or organism. They are ideally not present in the native genome to be able to isolate reporter gene expression as a result of the gene of interest's expression.To activate reporter genes, they can be expressed constitutively, where they are directly attached to the gene of interest to create a gene fusion. This method is an example of using cis-acting elements where the two genes are under the same promoter elements and are transcribed into a single messenger RNA molecule.
Fourth dimension in literature Early influence Fourth_dimension_in_literature > Early influence Edgar Allan Poe wrote an essay on cosmology titled Eureka (1848) which said that "space and duration are one". This is the first known instance of suggesting space and time to be different perceptions of one thing. Poe arrived at this conclusion after approximately 90 pages of reasoning but employed no mathematics.Theoretical physicist James Clerk Maxwell is best known for his work in formulating the equations of electromagnetism. He was also a prize-winning poet, and in his last poem Paradoxical Ode; Maxwell muses on connections between science, religion and nature, touching upon higher-dimensions along the way: In the Brothers Karamazov, Dostoevsky's last work completed in 1880, the fourth dimension is used to signify that which is ungraspable to someone with earthly (or three-dimensional) concerns.
Complex value Solutions of polynomial equations Complex_arithmetic > Properties > Solutions of polynomial equations Given any complex numbers (called coefficients) a0, ..., an, the equation has at least one complex solution z, provided that at least one of the higher coefficients a1, ..., an is nonzero. This is the statement of the fundamental theorem of algebra, of Carl Friedrich Gauss and Jean le Rond d'Alembert. Because of this fact, C {\displaystyle \mathbb {C} } is called an algebraically closed field. This property does not hold for the field of rational numbers Q {\displaystyle \mathbb {Q} } (the polynomial x2 − 2 does not have a rational root, since √2 is not a rational number) nor the real numbers R {\displaystyle \mathbb {R} } (the polynomial x2 + a does not have a real root for a > 0, since the square of x is positive for any real number x).
Neural circuitry Unsupervised learning Neural_nets > Models > Learning paradigms > Unsupervised learning In unsupervised learning, input data is given along with the cost function, some function of the data x {\displaystyle \textstyle x} and the network's output. The cost function is dependent on the task (the model domain) and any a priori assumptions (the implicit properties of the model, its parameters and the observed variables). As a trivial example, consider the model f ( x ) = a {\displaystyle \textstyle f(x)=a} where a {\displaystyle \textstyle a} is a constant and the cost C = E {\displaystyle \textstyle C=E} . Minimizing this cost produces a value of a {\displaystyle \textstyle a} that is equal to the mean of the data.
Lexical scoping Lexical scope vs. dynamic scope Lexical_scope > Lexical scope vs. dynamic scope The use of local variables — of variable names with limited scope, that only exist within a specific function — helps avoid the risk of a name collision between two identically named variables. However, there are two very different approaches to answering this question: What does it mean to be "within" a function? In lexical scope (or lexical scoping; also called static scope or static scoping), if a variable name's scope is a certain function, then its scope is the program text of the function definition: within that text, the variable name exists, and is bound to the variable's value, but outside that text, the variable name does not exist. By contrast, in dynamic scope (or dynamic scoping), if a variable name's scope is a certain function, then its scope is the time-period during which the function is executing: while the function is running, the variable name exists, and is bound to its value, but after the function returns, the variable name does not exist.
Meiotic non-disjunction Sex chromosome aneuploidy Meiotic_non-disjunction > Consequences > Sex chromosome aneuploidy The term sex chromosome aneuploidy summarizes conditions with an abnormal number of sex chromosomes, i.e., other than XX (female) or XY (male). Formally, X chromosome monosomy (Turner syndrome, see above) can also be classified as a form of sex chromosome aneuploidy.
Quantity equation Conversion factor Quantity_of_matter > Conversion factor In dimensional analysis, a ratio which converts one unit of measure into another without changing the quantity is called a conversion factor. For example, kPa and bar are both units of pressure, and 100 kPa = 1 bar. The rules of algebra allow both sides of an equation to be divided by the same expression, so this is equivalent to 100 kPa / 1 bar = 1. Since any quantity can be multiplied by 1 without changing it, the expression "100 kPa / 1 bar" can be used to convert from bars to kPa by multiplying it with the quantity to be converted, including the unit. For example, 5 bar × 100 kPa / 1 bar = 500 kPa because 5 × 100 / 1 = 500, and bar/bar cancels out, so 5 bar = 500 kPa.
Virtual twin Summary Virtual_twin Virtual twins are two children who are generally the same age and who are not genetic siblings, yet they are "reared together since infancy". Others have defined virtual twins as "unrelated children born within nine months of each other who enter a family, through birth or adoption, in the first year of life.This phenomenon has led to the creation of the Fullerton Virtual Twin Study (FVTS) at California State University, Fullerton (CSUF). == References ==
Centrality Percolation centrality Closeness_(graph_theory) > Percolation centrality However, a node may very well be centrally located in terms of betweenness centrality or another centrality measure, but may not be ‘centrally’ located in the context of a network in which there is percolation. Percolation of a ‘contagion’ occurs in complex networks in a number of scenarios. For example, viral or bacterial infection can spread over social networks of people, known as contact networks.
Lie detection Eye-tracking Lie_detection > Non-verbal behavior > Eye-tracking John Kircher, Doug Hacker, Anne Cook, Dan Woltz and David Raskin have developed eye-tracking technology at the University of Utah that they consider a polygraph alternative. This is not an emotional reaction like the polygraph and other methods but rather a cognitive reaction. This technology measures pupil dilation, response time, reading and rereading time, and errors. Data is recorded while subjects answer true or false questions on a computer.They have found that more effort is required by lying than giving the truth and thus their aim is to find indications of hard work. Individuals not telling the truth might, for instance, have dilated pupils while also taking longer to answer the question.Eye-tracking claims to offer several benefits over the polygraph: lower cost, 1/5th of the time to conduct, subjects do not need to be "hooked up" to anything, and it does not require qualified polygraph examiners to give the test. The technology has not been subject to peer review.
Chronic stress Summary Chronic_stress Chronic stress can cause the allostasis system to overstimulate in response to the persistent threat. And such overstimulation can lead to an adverse impact. To illustrate, the long-term exposure to stress creates a high level of these hormones.
Mutual organization Conversion Mutual_organization > Conversion Mutualization or mutualisation is the process by which a joint stock company changes legal form to a mutual organization or a cooperative, so that the majority of the stock is owned by employees or customers.Demutualization (or privatization) is the reverse process, in which a mutual may convert itself to a non-mutual through the process. This process became increasingly common in the 1980s as a result of deregulation. In the United States, conversion may be full, to a public company, or, in many states, partial, to a mutual holding company.
Multiple complex developmental disorder Neurological symptoms Multiple_complex_developmental_disorder > Diagnostic criteria > Neurological symptoms Because these are frequently found in cases of autistic disorders, criteria could be met for multiple neurological disorders, or cause severe symptoms. Some examples include: Learning difficulties symptoms such as dyslexia, dysgraphia, dyscalcula, NVLD, slow learning, poor memory, etc. AD/HD symptoms such as poor concentration, poor decision making, poor judgement, impulsiveness, difficulty sitting still, etc. Synesthesia. Neurological sleep disorders such as narcolepsy, insomnia, circadian rhythm disorder, etc. Conditions affecting perceptions and/or cognition, such as agnosia, aphasia, etc. Tourette syndrome or Tic disorder. Epilepsy or Seizure disorder. Parkinsonian syndrome features such as tremors, stiff movements, etc.
Kahn process network Closed and open systems Kahn_process_networks > Properties > Closed and open systems A closed KPN has no external input or output channels. Processes that have no input channels act as data sources and processes that have no output channels act as data sinks. In an open KPN each process has at least one input and output channel.
Application-level virtualization Description Application_virtualization > Description Full application virtualization requires a virtualization layer. Application virtualization layers replace part of the runtime environment normally provided by the operating system. The layer intercepts all disk operations of virtualized applications and transparently redirects them to a virtualized location, often a single file.
Graph structure theorem Summary Graph_structure_theorem In mathematics, the graph structure theorem is a major result in the area of graph theory. The result establishes a deep and fundamental connection between the theory of graph minors and topological embeddings. The theorem is stated in the seventeenth of a series of 23 papers by Neil Robertson and Paul Seymour. Its proof is very long and involved. Kawarabayashi & Mohar (2007) and Lovász (2006) are surveys accessible to nonspecialists, describing the theorem and its consequences.
Epitope mapping Methods Epitope_mapping > Methods These residues are mapped onto structures of the target protein to visualize the epitope. Benefits of high-throughput shotgun mutagenesis epitope mapping include: 1) the ability to identify both linear and conformational epitopes, 2) a shorter assay time than other methods, 3) the presentation of properly folded and post-translationally modified proteins, and 4) the ability to identify key amino acids that drive the energetic interactions (energetic "hot spots" of the epitope). Hydrogen–deuterium exchange (HDX).
Ambrose–Singer holonomy theorem Holonomy of a connection in a vector bundle De_Rham_decomposition_theorem > Definitions > Holonomy of a connection in a vector bundle Choosing different identifications of Ex with Rk also gives conjugate subgroups. Sometimes, particularly in general or informal discussions (such as below), one may drop reference to the basepoint, with the understanding that the definition is good up to conjugation. Some important properties of the holonomy group include: Hol 0 ⁡ ( ∇ ) {\displaystyle \operatorname {Hol} ^{0}(\nabla )} is a connected Lie subgroup of GL(k, R).
Topology of uniform convergence Properties Topology_of_uniform_convergence > 𝒢-topologies on spaces of continuous linear maps > Properties {\displaystyle X.} if X {\displaystyle X} is quasi-complete (meaning that closed and bounded subsets are complete), then the bounded subsets of L ( X ; Y ) {\displaystyle L(X;Y)} are identical for all G {\displaystyle {\mathcal {G}}} -topologies where G {\displaystyle {\mathcal {G}}} is any family of bounded subsets of X {\displaystyle X} covering X . {\displaystyle X.}
Bernoulli's equation Compressible flow in thermodynamics Bernoulli’s_principle > Compressible flow equation > Compressible flow in thermodynamics The most general form of the equation, suitable for use in thermodynamics in case of (quasi) steady flow, is:: § 3.5: § 5: § 5.9 Here w is the enthalpy per unit mass (also known as specific enthalpy), which is also often written as h (not to be confused with "head" or "height"). Note that where e is the thermodynamic energy per unit mass, also known as the specific internal energy. So, for constant internal energy e {\displaystyle e} the equation reduces to the incompressible-flow form. The constant on the right-hand side is often called the Bernoulli constant and denoted b. For steady inviscid adiabatic flow with no additional sources or sinks of energy, b is constant along any given streamline.
Conformal gravity Weyl-squared theories Conformal_gravity > Weyl-squared theories The simplest theory in this category has the square of the Weyl tensor as the Lagrangian S = ∫ d 4 x − g C a b c d C a b c d , {\displaystyle {\mathcal {S}}=\int \,\mathrm {d} ^{4}x\,{\sqrt {-g\;}}\,C_{abcd}\,C^{abcd}~,} where C a b c d {\displaystyle \;C_{abcd}\;} is the Weyl tensor. This is to be contrasted with the usual Einstein–Hilbert action where the Lagrangian is just the Ricci scalar. The equation of motion upon varying the metric is called the Bach tensor, 2 ∂ a ∂ d C a b c d + R a d C a b c d = 0 , {\displaystyle 2\,\partial _{a}\,\partial _{d}\,{{C^{a}}_{bc}}^{d}~~+~~R_{ad}\,{{C^{a}}_{bc}}^{d}~=~0~,} where R a b {\displaystyle \;R_{ab}\;} is the Ricci tensor. Conformally flat metrics are solutions of this equation.
Biomagnetics Summary Biomagnetics Biomagnetics is a field of biotechnology. It has actively been researched since at least 2004. Although the majority of structures found in living organisms are diamagnetic, the magnetic field itself, as well as magnetic nanoparticles, microstructures and paramagnetic molecules can influence specific physiological functions of organisms under certain conditions. The effect of magnetic fields on biosystems is a topic of research that falls under the biomagnetic umbrella, as well as the construction of magnetic structures or systems that are either biocompatible, biodegradable or biomimetic. Magnetic nanoparticles and magnetic microparticles are known to interact with certain prokaryotes and certain eukaryotes.Magnetic nanoparticles under the influence of magnetic and electromagnetic fields were shown to modulate redox reactions for the inhibition or the promotion of animal tumor growth. The mechanism underlying nanomagnetic modulation involves the convergence of magnetochemical and magneto-mechanical reactions.
Spectral resolution Summary Spectral_resolution The spectral resolution of a spectrograph, or, more generally, of a frequency spectrum, is a measure of its ability to resolve features in the electromagnetic spectrum. It is usually denoted by Δ λ {\displaystyle \Delta \lambda } , and is closely related to the resolving power of the spectrograph, defined as where Δ λ {\displaystyle \Delta \lambda } is the smallest difference in wavelengths that can be distinguished at a wavelength of λ {\displaystyle \lambda } . For example, the Space Telescope Imaging Spectrograph (STIS) can distinguish features 0.17 nm apart at a wavelength of 1000 nm, giving it a resolution of 0.17 nm and a resolving power of about 5,900. An example of a high resolution spectrograph is the Cryogenic High-Resolution IR Echelle Spectrograph (CRIRES+) installed at ESO's Very Large Telescope, which has a spectral resolving power of up to 100,000.
Ableism United States Ableism > History > United States Much like many minority groups, disabled Americans were often segregated and denied certain rights for a majority of American history. In the 1800s, a shift from a religious view to a more scientific view took place and caused more individuals with disabilities to be examined. Public stigma began to change after World War II when many Americans returned home with disabilities. In the 1960s, following the civil rights movement in America, the world began the disabled rights movement.
Finite element solver A-FEM Finite_elements > Various types of finite element methods > A-FEM Yang and Lui introduced the Augmented-Finite Element Method, whose goal was to model the weak and strong discontinuities without needing extra DoFs, as PuM stated.
Intelligent Speed Adaptation (ISA) Other references Intelligent_speed_adaptation > References > Other references Carsten O (2001) "ISA: the Best Collision Avoidance System? ", Proceedings of 17th Conference on the Enhanced Safety of Vehicles, Netherlands. Carsten O (2004) "ISA – From Fields Trials to Reality", PACTS conference Targets 2010: No Room for Complacency, London, 10 February 2004.
Regular function Examples Biregular_map > Examples The regular functions on An are exactly the polynomials in n variables and the regular functions on Pn are exactly the constants. Let X be the affine curve y = x 2 {\displaystyle y=x^{2}} . Then is a morphism; it is bijective with the inverse g ( x ) = ( x , x 2 ) {\displaystyle g(x)=(x,x^{2})} . Since g is also a morphism, f is an isomorphism of varieties.
Data Protection Protection of privacy in information systems Information_privacy > Protection of privacy in information systems The same applies to any kind of traffic generated on the Internet, including web browsing, instant messaging, and others. In order not to give away too much personal information, e-mails can be encrypted and browsing of webpages as well as other online activities can be done traceless via anonymizers, or by open source distributed anonymizers, so-called mix networks.
Kepler 10b Nomenclature and history Kepler-10b > Nomenclature and history The transit method of discovering exoplanets relies upon carefully monitoring the brightness of a star. If a planet is present and crosses the line of sight between Earth and the star, the star will dim at a regular interval by an amount that depends upon the radius of the transiting planet.
Iamblichus Attribution Iamblichus > Attribution Vol. 14 (11th ed.). Cambridge University Press. pp. 213–215.
Ellipse Area Ellipse > Metric properties > Area The area A ellipse {\displaystyle A_{\text{ellipse}}} enclosed by an ellipse is: where a {\displaystyle a} and b {\displaystyle b} are the lengths of the semi-major and semi-minor axes, respectively. The area formula π a b {\displaystyle \pi ab} is intuitive: start with a circle of radius b {\displaystyle b} (so its area is π b 2 {\displaystyle \pi b^{2}} ) and stretch it by a factor a / b {\displaystyle a/b} to make an ellipse. This scales the area by the same factor: π b 2 ( a / b ) = π a b . {\displaystyle \pi b^{2}(a/b)=\pi ab.}
Switching regulators Electronic voltage regulators Voltage_regulators > Electronic voltage regulators Any difference is amplified and used to control the regulation element in such a way as to reduce the voltage error. This forms a negative feedback control loop; increasing the open-loop gain tends to increase regulation accuracy but reduce stability. (Stability is avoidance of oscillation, or ringing, during step changes.)
Financial derivatives Forwards Derivative_contract > Types > Forwards The price of the underlying instrument, in whatever form, is paid before control of the instrument changes. This is one of the many forms of buy/sell orders where the time and date of trade is not the same as the value date where the securities themselves are exchanged. The forward price of such a contract is commonly contrasted with the spot price, which is the price at which the asset changes hands on the spot date.
Theories of gravitation Scientific revolution Theory_of_gravitation > History > Scientific revolution Galileo postulated that air resistance is the reason that objects with a low density and high surface area fall more slowly in an atmosphere. In 1604, Galileo correctly hypothesized that the distance of a falling object is proportional to the square of the time elapsed. This was later confirmed by Italian scientists Jesuits Grimaldi and Riccioli between 1640 and 1650. They also calculated the magnitude of the Earth's gravity by measuring the oscillations of a pendulum.
Algorithmic synthesis History High-level_synthesis > History Early academic work extracted scheduling, allocation, and binding as the basic steps for high-level-synthesis. Scheduling partitions the algorithm in control steps that are used to define the states in the finite-state machine. Each control step contains one small section of the algorithm that can be performed in a single clock cycle in the hardware. Allocation and binding maps the instructions and variables to the hardware components, multiplexers, registers and wires of the data path.
NT Object Manager Architecture NT_Object_Manager > Architecture Object Manager is the centralized resource broker in the Windows NT line of operating systems, which keeps track of the resources allocated to processes. It is resource-agnostic and can manage any type of resource, including device and file handles. All resources are represented as objects, each belonging to a logical namespace for categorization and having a type that represents the type of the resource, which exposes the capabilities and functionalities via properties. An object is kept available until all processes are done with it; Object Manager maintains the record of which objects are currently in use via reference counting, as well as the ownership information.
Parametrization (atmospheric modeling) Eddies Parametrization_(climate) > Eddies The ocean (and, although more variably, the atmosphere) is stratified through density. At rest, surfaces of constant density (known as isopycnals in the ocean) will be parallel to surfaces of constant pressure (isobars). However, various processes such as geostrophy and upwelling can result in isopycnals becoming tilted relative to isobars. These tilted density surfaces represent a source of potential energy and, if the slope becomes steep enough, a fluid instability known as baroclinic instability can be triggered.
Crop factor Estimating sensor performance Crop_factor > Estimating sensor performance For a given exposure, for example for a fixed focal-plane illuminance and exposure time, larger image sensors capture more photons and hence produce images with less image noise and greater dynamic range than smaller sensors. Due to the statistics of photon shot noise, the desirable properties of signal-to-noise ratio (SNR) and sensor unity gain both scale with the square root of pixel area.Since crop factor is inversely proportional to the square root of sensor area (to within a small aspect ratio-dependent factor), it is useful for estimating image sensor performance. For example, if two different-sized image sensors have the same aspect ratio and a resolution of 10 megapixels, and are made using similar technology, the larger sensor will have better signal-to-noise ratio by a factor equal to the ratio of the two sensors' crop factors. The larger sensor has the smaller crop factor and the higher signal-to-noise ratio.
Cluster File Systems Release history Cluster_File_Systems > Release history The Lazy Size on MDT (LSOM) feature allows storing an estimate of the file size on the MDT for use by policy engines, filesystem scanners, and other management tools that can more efficiently make decisions about files without a fully accurate file sizes or blocks count without having to query the OSTs for this information. This release also added the ability to manually restripe an existing directory across multiple MDTs, to allow migration of directories with large numbers of files to use the capacity and performance of several MDS nodes. The Lustre RPC data checksum added SCSI T10-PI integrated data checksums from the client to the kernel block layer, SCSI host adapter, and T10-enabled hard drives.
Gliquidone Pharmacokinetics Gliquidone > Pharmacokinetics Gliquidone is fully metabolized by the liver. Its metabolites are excreted virtually completely with bile (even with long-term administration), thus allowing the use of medication in diabetic patients with kidney disease and diabetic nephropathy. == References ==
Jump discontinuity Essential discontinuity Removable_discontinuity > Classification > Essential discontinuity (This is distinct from an essential singularity, which is often used when studying functions of complex variables). Supposing that f {\displaystyle f} is a function defined on an interval I ⊆ R , {\displaystyle I\subseteq \mathbb {R} ,} we will denote by D {\displaystyle D} the set of all discontinuities of f {\displaystyle f} on I . {\displaystyle I.}
Santiago Calatrava Margaret Hunt Hill Bridge (2007–2012) and Peace Bridge (2008–2012) Santiago_Calatrava > Recent major projects (2011–) > Margaret Hunt Hill Bridge (2007–2012) and Peace Bridge (2008–2012) Calatrava constructed a series of extraordinary bridges, the type of structure which originally brought him global attention, for cities around the world that wanted a symbol of modernity and daring. Among the largest and dramatic are three bridges over the Trinity River in Dallas, Texas. The first of these was the Margaret Hunt Hill Bridge, opened for traffic in March 2012. The bridge, carrying six lanes of traffic, is 209 metres (686 ft) long, with the appearance of being suspended from an arc-shaped tubular steel pylon forty stories or 136 metres (446 ft) high by fifty-eight cables, ranging in length from 119 to 196 metres (390 to 643 ft).
Cyclopropyl group Structure and bonding Cyclopropyl_group > Structure and bonding Here the two sp-hybrids forming the ring bond are separated into one sp2-hybrid and one pure p-orbital. This corresponds to the π bond description of C=C double bonds. Cyclopropyl groups are good donors in hyperconjugation resulting in a considerable stabilization of carbocations.
Windows Vista I/O technologies Summary Windows_Vista_I/O_technologies Windows Vista introduced a number of new I/O functions to the Microsoft Windows line of operating systems. They are intended to shorten the time taken to boot the system, improve the responsiveness of the system, and improve the reliability of data storage.
History of the International System of Units General rules History_of_the_International_System_of_Units > Lexicographic conventions > Unit symbols and the values of quantities > General rules Unit symbols are written using roman (upright) type, regardless of the type used in the surrounding text. Symbols for derived units formed by multiplication are joined with a centre dot (⋅) or a non-breaking space; e.g., N⋅m or N m. Symbols for derived units formed by division are joined with a solidus (/), or given as a negative exponent. E.g., the "metre per second" can be written m/s, m s−1, m⋅s−1, or m/s.
Living anionic polymerization Additional reading Anionic_addition_polymerization > Additional reading (2015). Anionic Polymerization Principles, Practice, Strength, Consequences and Applications. Springer. ISBN 978-4-431-54186-8. == References ==
Actuator Mechanical Actuator > Types of actuators > Mechanical A mechanical actuator functions to execute movement by converting one kind of motion, such as rotary motion, into another kind, such as linear motion. An example is a rack and pinion. The operation of mechanical actuators is based on combinations of structural components, such as gears and rails, or pulleys and chains.
Official statistics Confidentiality Official_statistics > Quality criteria to be respected > Confidentiality All data collected by the national statistical office must protect the privacy of individual respondents, whether persons or businesses. But on the contrary, government units such as institutions cannot invoke statistical confidentiality. All respondents have to be informed about the purpose and legal basis of the survey and especially about the confidentiality measures.
Proton therapy Surgery Proton_therapy > Comparison with other treatments > Surgery The benefit of external beam proton radiation is in the dosimetric difference from external beam X-ray radiation and brachytherapy in cases where use of radiation therapy is already indicated, rather than as a direct competition with surgery. In prostate cancer, the most common indication for proton beam therapy, no clinical study directly comparing proton therapy to surgery, brachytherapy, or other treatments has shown any clinical benefit for proton beam therapy. Indeed, the largest study to date showed that IMRT compared with proton therapy was associated with less gastrointestinal morbidity.
Devices Profile for Web Services DPWS standardization Devices_Profile_for_Web_Services > DPWS standardization Hosted services are mostly functional and depend on their hosting device for discovery. In addition to these hosted services, DPWS specifies a set of built-in services: Discovery services: used by a device connected to a network to advertise itself and to discover other devices. Support of discovery has led some to dub DPWS as "the USB for Ethernet."
Cranfield experiments Summary Cranfield_experiments The queries were generated by the authors of the papers in the collection and then translated into index lookups by experts in those systems. In this series, one method went from least efficient to most efficient after making minor changes to the arrangement of the way the data was recorded on the index cards. The conclusion appeared to be that the underlying methodology seemed less important than specific details of the implementation.
C4H12Si Uses in NMR spectroscopy C4H12Si > Uses in NMR spectroscopy The majority of compounds studied by 1H NMR spectroscopy absorb downfield of the TMS signal, thus there is usually no interference between the standard and the sample. Similarly, all four carbon atoms in a tetramethylsilane molecule are equivalent.
Min-priority queue Summary Priority_queuing In computer science, a priority queue is an abstract data-type similar to a regular queue or stack data structure. Each element in a priority queue has an associated priority. In a priority queue, elements with high priority are served before elements with low priority. In some implementations, if two elements have the same priority, they are served in the same order in which they were enqueued.
Glossary of aerospace engineering N Glossary_of_aerospace_engineering > N They were developed over several decades of progressively building the theories, from 1822 (Navier) to 1842–1850 (Stokes).The Navier–Stokes equations mathematically express conservation of momentum and conservation of mass for Newtonian fluids. They are sometimes accompanied by an equation of state relating pressure, temperature and density. They arise from applying Isaac Newton's second law to fluid motion, together with the assumption that the stress in the fluid is the sum of a diffusing viscous term (proportional to the gradient of velocity) and a pressure term—hence describing viscous flow.
Uncertainty Principle (Numbers) Plot summary Uncertainty_Principle_(Numbers) > Plot summary Don sends Charlie home to get some rest. Instead, Charlie begins working on P vs. NP in the family garage, a problem that he had worked on during the three months before his mother died of cancer.
Julianna Lisziewicz Langerhans cell-targeting DNA vaccines Julianna_Lisziewicz > Research > Langerhans cell-targeting DNA vaccines When these nanoparticles are applied topically to human subjects, a strong immune response was observed. This vaccine has been clinically proven, and it opens the door for more new dendritic cell-targeting vaccines to be created for the treatment of cancers. == References ==
Introduction to the Higgs field Other proposals Higgs_Field > Public discussion > Naming > Other proposals A renaming competition by British newspaper The Guardian in 2009 resulted in their science correspondent choosing the name "the champagne bottle boson" as the best submission: "The bottom of a champagne bottle is in the shape of the Higgs potential and is often used as an illustration in physics lectures. So it's not an embarrassingly grandiose name, it is memorable, and has some physics connection too." The name Higgson was suggested as well, in an opinion piece in the Institute of Physics' online publication physicsworld.com.
Diagonal spread Summary Diagonal_spread In derivatives trading, the term diagonal spread is applied to an options spread position that shares features of both a calendar spread and a vertical spread. It is established by simultaneously buying and selling equal amount of option contracts of the same type (call options or put options) but with different strike prices and expiration dates.
Deoxyribonucleic Acid Polymerases Phosphodiester_backbone > Interactions with proteins > DNA-modifying enzymes > Polymerases In the active site of these enzymes, the incoming nucleoside triphosphate base-pairs to the template: this allows polymerases to accurately synthesize the complementary strand of their template. Polymerases are classified according to the type of template that they use. In DNA replication, DNA-dependent DNA polymerases make copies of DNA polynucleotide chains.
Energies per unit mass Summary Energy-to-weight_ratio Energy per unit volume has the same physical units as pressure and in many situations is synonymous. For example, the energy density of a magnetic field may be expressed as and behaves like a physical pressure. Likewise, the energy required to compress a gas to a certain volume may be determined by multiplying the difference between the gas pressure and the external pressure by the change in volume. A pressure gradient describes the potential to perform work on the surroundings by converting internal energy to work until equilibrium is reached.
Low-cycle fatigue Notable failures Low_cycle_fatigue > Notable failures Many structural elements such as beams, walls and columns failed due to fatigue, exposing the steel reinforcements used in the design with clear signs of longitudinal buckling. This event caused Chilean seismic design standards to be updated based on observations on damaged structures caused by the earthquake. == References ==
Islamic optics Impetus Islamic_optics > Mechanics > Impetus John Philoponus had rejected the Aristotelian view of motion, and argued that an object acquires an inclination to move when it has a motive power impressed on it. In the eleventh century Ibn Sina had roughly adopted this idea, believing that a moving object has force which is dissipated by external agents like air resistance. Ibn Sina made distinction between 'force' and 'inclination' (called "mayl"), he claimed that an object gained mayl when the object is in opposition to its natural motion. So he concluded that continuation of motion is attributed to the inclination that is transferred to the object, and that object will be in motion until the mayl is spent.
Epidemiology of tuberculosis History Giant_multinucleated_cell > History It was called bacille Calmette–Guérin (BCG). The BCG vaccine was first used on humans in 1921 in France, but achieved widespread acceptance in the US, Great Britain, and Germany only after World War II.Tuberculosis caused widespread public concern in the 19th and early 20th centuries as the disease became common among the urban poor. In 1815, one in four deaths in England was due to "consumption".
Volumetric analysis Measuring the endpoint of a titration Volumetric_titration > Measuring the endpoint of a titration Potentiometer: An instrument that measures the electrode potential of the solution. These are used for redox titrations; the potential of the working electrode will suddenly change as the endpoint is reached.pH meter: A potentiometer with an electrode whose potential depends on the amount of H+ ion present in the solution. (This is an example of an ion-selective electrode.)
Tribasic acid Polyprotic acids Dibasic_acid > Chemical characteristics > Polyprotic acids H2A (aq) + H2O (l) ⇌ H3O+ (aq) + HA− (aq) Ka1 HA− (aq) + H2O (l) ⇌ H3O+ (aq) + A2− (aq) Ka2The first dissociation constant is typically greater than the second (i.e., Ka1 > Ka2). For example, sulfuric acid (H2SO4) can donate one proton to form the bisulfate anion (HSO−4), for which Ka1 is very large; then it can donate a second proton to form the sulfate anion (SO2−4), wherein the Ka2 is intermediate strength. The large Ka1 for the first dissociation makes sulfuric a strong acid.
Predictive engineering analytics Enabling processes and technologies Predictive_engineering_analytics > Enabling processes and technologies Dealing with these challenges is exactly the aim of a predictive engineering analytics approach for product development. It refers to a combination of tools deployment and a good alignment of processes. Manufacturers gradually deploy the following methods and technologies, to an extent that their organization allows it and their products require it:
Power line carrier communication Long haul, low frequency Power_line_communication > Long haul, low frequency Utility companies use special coupling capacitors to connect radio transmitters and receivers to the AC power carrying conductors. Power meters often use small transformers with linear amplifiers in the range of tens of watts. Most of the expense of any PLC system is the power electronics. By comparison, the electronics to encode and decode is usually small, in a special purpose integrated circuit.
Industrial robots Robot programming and interfaces Industrial_robots > Technical description > Robot programming and interfaces It can also increase the level of safety associated with robotic equipment since various "what if" scenarios can be tried and tested before the system is activated. Robot simulation software provides a platform to teach, test, run, and debug programs that have been written in a variety of programming languages. Robot simulation tools allow for robotics programs to be conveniently written and debugged off-line with the final version of the program tested on an actual robot.
Buffer underrun Multimedia playback Buffer_under-run > Multimedia playback An error handling routine (e.g. blue screen of death) may eventually stop the audio controller. Intentionally imitating this audio glitch during the creation of music or sound art, either by manually splicing audio or re-triggering samples, or by using plugins, is called the Stutter edit. == References ==
Autoimmune response Causes Autoimmune_disorders > Causes The exact causes of autoimmune diseases remain largely unknown; however, research has suggested that a combination of genetic, environmental, and hormonal factors, as well as certain infections, may contribute to the development of these disorders.The human immune system is equipped with several mechanisms to maintain a delicate balance between defending against foreign invaders and protecting its own cells. To achieve this, it generates both T cells and B cells, which are capable of reacting with self-proteins. However, in a healthy immune response, self-reactive cells are generally either eliminated before they become active, rendered inert via a process called anergy, or their activities are suppressed by regulatory cells.
Non-covalent bonding Ionic Non-covalent_bonding > Electrostatic interactions > Ionic Ionic interactions involve the attraction of ions or molecules with full permanent charges of opposite signs. For example, sodium fluoride involves the attraction of the positive charge on sodium (Na+) with the negative charge on fluoride (F−). However, this particular interaction is easily broken upon addition to water, or other highly polar solvents. In water ion pairing is mostly entropy driven; a single salt bridge usually amounts to an attraction value of about ΔG =5 kJ/mol at an intermediate ion strength I, at I close to zero the value increases to about 8 kJ/mol. The ΔG values are usually additive and largely independent of the nature of the participating ions, except for transition metal ions etc.These interactions can also be seen in molecules with a localized charge on a particular atom. For example, the full negative charge associated with ethoxide, the conjugate base of ethanol, is most commonly accompanied by the positive charge of an alkali metal salt such as the sodium cation (Na+).
Active learning Active learning exercises Active_learning > Active learning exercises Think-pair-share is helpful for the instructor as it enables organizing content and tracking students on where they are relative to the topic being discussed in class, saves time so that he/she can move to other topics, helps to make the class more interactive, provides opportunities for students to interact with each other (Radhakrishna, Ewing, and Chikthimmah, 2012). A learning cell is an effective way for a pair of students to study and learn together. The learning cell was developed by Marcel Goldschmid of the Swiss Federal Institute of Technology in Lausanne (Goldschmid, 1971).
Unified Medical Language System Semantic Network Unified_Medical_Language_System > Knowledge Sources > Semantic Network The links among semantic types define the structure of the network and show important relationships between the groupings and concepts. The primary link between semantic types is the "isa" link, establishing a hierarchy of types. The network also has 5 major categories of non-hierarchical (or associative) relationships, which constitute the remaining 53 relationship types.
Lagrangian multiplier Single constraint Method_of_Lagrange_multipliers > Single constraint The constrained extrema of f are critical points of the Lagrangian L {\displaystyle {\mathcal {L}}} , but they are not necessarily local extrema of L {\displaystyle \ {\mathcal {L}}\ } (see Example 2 below). One may reformulate the Lagrangian as a Hamiltonian, in which case the solutions are local minima for the Hamiltonian. This is done in optimal control theory, in the form of Pontryagin's minimum principle. The fact that solutions of the Lagrangian are not necessarily extrema also poses difficulties for numerical optimization. This can be addressed by computing the magnitude of the gradient, as the zeros of the magnitude are necessarily local minima, as illustrated in Example 5: Numerical optimization.
DeepDream Process DeepDream > Process The software is designed to detect faces and other patterns in images, with the aim of automatically classifying images. However, once trained, the network can also be run in reverse, being asked to adjust the original image slightly so that a given output neuron (e.g. the one for faces or certain animals) yields a higher confidence score. This can be used for visualizations to understand the emergent structure of the neural network better, and is the basis for the DeepDream concept. This reversal procedure is never perfectly clear and unambiguous because it utilizes a one-to-many mapping process.
Infrared Nanospectroscopy (AFM-IR) Summary Infrared_Nanospectroscopy_(AFM-IR) Then, the use of modern pulsed optical parametric oscillators and quantum cascade lasers, in combination with top-illumination, have enabled to investigate samples on any substrate and with increase sensitivity and spatial resolution. As most recent advances, AFM-IR has been proved capable to acquire chemical maps and nanoscale resolved spectra at the single-molecule scale from macromolecular self-assemblies and biomolecules with circa 10 nm diameter, as well as to overcome limitations of IR spectroscopy and measure in aqueous liquid environments.Recording the amount of infrared absorption as a function of wavelength or wavenumber, AFM-IR creates an infrared absorption spectra that can be used to chemically characterize and even identify unknown samples. Recording the infrared absorption as a function of position can be used to create chemical composition maps that show the spatial distribution of different chemical components.
Applications of artificial intelligence Healthcare Applications_of_artificial_intelligence > Health > Healthcare Current research has indicated that non-cardiac vascular illnesses are also being treated with artificial intelligence (AI). For certain disorders, AI algorithms can assist with diagnosis, recommended treatments, outcome prediction, and patient progress tracking.
Force dynamics Limitations and criticism Force_dynamics > Limitations and criticism As the field of cognitive linguistics is still in a state of theoretical flux, no systematic account addresses this issue yet. However, it is an objection many cognitive linguists are aware of. Some cognitive linguists have replied to such objections by pointing out that the goal of Cognitive Linguistics is not to construct a formal system in which theorems are proved, but rather to better understand the cognitive basis of language (cf. Newman 1996:xii). Jackendoff (1990, 1996:120–3), in the process of incorporating aspects of force dynamics into his theory of conceptual semantics, has proposed a reconfiguration of some of its basic notions. In Jackendoff’s view, this reconfiguration "conforms better to the syntax of force-dynamic verbs" (1996:121).
Generalized velocity Bibliography of cited references Generalized_coordinates > Bibliography of cited references ISBN 978-0-521-88303-0. Goldstein, Herbert; Poole, Charles; Safko, John (2002). Classical Mechanics (3rd ed.).
C macro Including files C_macro > Phases > Including files C compilers and programming environments all have a facility that allows the programmer to define where include files can be found. This can be introduced through a command-line flag, which can be parameterized using a makefile, so that a different set of include files can be swapped in for different operating systems, for instance. By convention, include files are named with either a .h or .hpp extension.
Cloud computing issues Compliance Cloud_computing_issues > Compliance To comply with regulations including FISMA, HIPAA, and SOX in the United States, the Data Protection Directive in the EU and the credit card industry's PCI DSS, users may have to adopt community or hybrid deployment modes that are typically more expensive and may offer restricted benefits. This is how Google is able to "manage and meet additional government policy requirements beyond FISMA" and Rackspace Cloud or QubeSpace are able to claim PCI compliance.Many providers also obtain a SAS 70 Type II audit, but this has been criticised on the grounds that the hand-picked set of goals and standards determined by the auditor and the auditee are often not disclosed and can vary widely. Providers typically make this information available on request, under non-disclosure agreement.Customers in the EU contracting with cloud providers outside the EU/EEA have to adhere to the EU regulations on export of personal data.A multitude of laws and regulations have forced specific compliance requirements onto many companies that collect, generate or store data. These policies may dictate a wide array of data storage policies, such as how long information must be retained, the process used for deleting data, and even certain recovery plans.
Orbit determination Orbit determination from a state vector Orbit_determination > Methods > Orbit determination from a state vector The basic orbit determination task is to determine the classical orbital elements or Keplerian elements, a , e , i , Ω , ω , ν {\displaystyle a,e,i,\Omega ,\omega ,\nu } , from the orbital state vectors , of an orbiting body with respect to the reference frame of its central body. The central bodies are the sources of the gravitational forces, like the Sun, Earth, Moon and other planets. The orbiting bodies, on the other hand, include planets around the Sun, artificial satellites around the Earth, and spacecraft around planets. Newton's laws of motion well explain the trajectory of an orbiting body, known as Keplerian orbit.
Crystallization methods Methods Crystallization_processes > Methods A typical laboratory technique for crystal formation is to dissolve the solid in a solution in which it is partially soluble, usually at high temperatures to obtain supersaturation. The hot mixture is then filtered to remove any insoluble impurities. The filtrate is allowed to slowly cool.

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