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In graph theory, reachability refers to the ability to get from one vertex to another within a graph. A vertex
$$
s
$$
can reach a vertex
$$
t
$$
(and
$$
t
$$
is reachable from
$$
s
$$
) if there exists a sequence of adjacent vertices (i.e. a walk) which starts with
$$
s
$$
and ends with
$$
t
$$
.
In an undir... | https://en.wikipedia.org/wiki/Reachability |
The Alexandrov uniqueness theorem is a rigidity theorem in mathematics, describing three-dimensional convex polyhedra in terms of the distances between points on their surfaces. It implies that convex polyhedra with distinct shapes from each other also have distinct metric spaces of surface distances, and it characteri... | https://en.wikipedia.org/wiki/Alexandrov%27s_uniqueness_theorem |
In fluid dynamics, a wake may either be:
- the region of recirculating flow immediately behind a moving or stationary blunt body, caused by viscosity, which may be accompanied by flow separation and turbulence, or
- the wave pattern on the water surface downstream of an object in a flow, or produced by a moving object ... | https://en.wikipedia.org/wiki/Wake_%28physics%29 |
A waverider is a hypersonic aircraft design that improves its supersonic lift-to-drag ratio by using the shock waves being generated by its own flight as a lifting surface, a phenomenon known as compression lift.
The waverider remains a well-studied design for high-speed aircraft in the Mach 5 and higher hypersonic re... | https://en.wikipedia.org/wiki/Waverider |
In algebraic geometry, a generic point P of an algebraic variety X is a point in a general position, at which all generic properties are true, a generic property being a property which is true for almost every point.
In classical algebraic geometry, a generic point of an affine or projective algebraic variety of dimens... | https://en.wikipedia.org/wiki/Generic_point |
In thermodynamics, a thermodynamic state of a system is its condition at a specific time; that is, fully identified by values of a suitable set of parameters known as state variables, state parameters or thermodynamic variables. Once such a set of values of thermodynamic variables has been specified for a system, the v... | https://en.wikipedia.org/wiki/Thermodynamic_state |
Nuclear medicine (nuclear radiology, nucleology),What is nucleology? is a medical specialty involving the application of radioactive substances in the diagnosis and treatment of disease. Nuclear imaging is, in a sense, radiology done inside out, because it records radiation emitted from within the body rather than radi... | https://en.wikipedia.org/wiki/Nuclear_medicine |
A symbol in computer programming is a primitive data type whose instances have a human-readable form. Symbols can be used as identifiers. In some programming languages, they are called atoms. Uniqueness is enforced by holding them in a symbol table. The most common use of symbols by programmers is to perform language r... | https://en.wikipedia.org/wiki/Symbol_%28programming%29 |
The wave (also Mexican wave outside North America) is a type of metachronal rhythm achieved in a packed stadium or other large seated venue, when successive groups of spectators briefly stand and raise their arms. Immediately upon stretching to full height, the spectator returns to the usual seated position.
The result... | https://en.wikipedia.org/wiki/Wave_%28audience%29 |
In financial econometrics (the application of statistical methods to economic data), the Markov-switching multifractal (MSM) is a model of asset returns developed by Laurent E. Calvet and Adlai J. Fisher that incorporates stochastic volatility components of heterogeneous durations. MSM captures the outliers, log-memory... | https://en.wikipedia.org/wiki/Markov_switching_multifractal |
In mathematics, the polygamma function of order is a meromorphic function on the complex numbers
$$
\mathbb{C}
$$
defined as the th derivative of the logarithm of the gamma function:
$$
\psi^{(m)}(z) := \frac{\mathrm{d}^m}{\mathrm{d}z^m} \psi(z) = \frac{\mathrm{d}^{m+1}}{\mathrm{d}z^{m+1}} \ln\Gamma(z).
$$
Thus
$$
\... | https://en.wikipedia.org/wiki/Polygamma_function |
Clairaut's theorem characterizes the surface gravity on a viscous rotating ellipsoid in hydrostatic equilibrium under the action of its gravitational field and centrifugal force. It was published in 1743 by Alexis Claude Clairaut in a treatise which synthesized physical and geodetic evidence that the Earth is an oblat... | https://en.wikipedia.org/wiki/Clairaut%27s_theorem_%28gravity%29 |
Absorption spectroscopy is spectroscopy that involves techniques that measure the absorption of electromagnetic radiation, as a function of frequency or wavelength, due to its interaction with a sample. The sample absorbs energy, i.e., photons, from the radiating field. The intensity of the absorption varies as a funct... | https://en.wikipedia.org/wiki/Absorption_spectroscopy |
In graph theory and order theory, a comparability graph is an undirected graph that connects pairs of elements that are comparable to each other in a partial order. Comparability graphs have also been called transitively orientable graphs, partially orderable graphs, containment graphs, and divisor graphs.
An incompara... | https://en.wikipedia.org/wiki/Comparability_graph |
A duplex communication system is a point-to-point system composed of two or more connected parties or devices that can communicate with one another in both directions. Duplex systems are employed in many communications networks, either to allow for simultaneous communication in both directions between two connected par... | https://en.wikipedia.org/wiki/Duplex_%28telecommunications%29 |
In the mathematical areas of number theory and analysis, an infinite sequence or a function is said to eventually have a certain property, if it does not have the said property across all its ordered instances, but will after some instances have passed. The use of the term "eventually" can be often rephrased as "for su... | https://en.wikipedia.org/wiki/Eventually_%28mathematics%29 |
In mathematics, Hörmander's condition is a property of vector fields that, if satisfied, has many useful consequences in the theory of partial and stochastic differential equations. The condition is named after the Swedish mathematician Lars Hörmander.
## Definition
Given two C1 vector fields V and W on d-dimensional ... | https://en.wikipedia.org/wiki/H%C3%B6rmander%27s_condition |
Liquid crystal (LC) is a state of matter whose properties are between those of conventional liquids and those of solid crystals. For example, a liquid crystal can flow like a liquid, but its molecules may be oriented in a common direction as in a solid. There are many types of LC phases, which can be distinguished by t... | https://en.wikipedia.org/wiki/Liquid_crystal |
In general relativity, the pp-wave spacetimes, or pp-waves for short, are an important family of exact solutions of Einstein's field equation. The term pp stands for plane-fronted waves with parallel propagation, and was introduced in 1962 by Jürgen Ehlers and Wolfgang Kundt.
## Overview
The pp-waves solutions model ra... | https://en.wikipedia.org/wiki/Pp-wave_spacetime |
A software bug is a design defect (bug) in computer software. A computer program with many or serious bugs may be described as buggy.
The effects of a software bug range from minor (such as a misspelled word in the user interface) to severe (such as frequent crashing).
In 2002, a study commissioned by the US Departmen... | https://en.wikipedia.org/wiki/Software_bug |
In probability and statistics, the Kumaraswamy's double bounded distribution is a family of continuous probability distributions defined on the interval (0,1). It is similar to the beta distribution, but much simpler to use especially in simulation studies since its probability density function, cumulative distribution... | https://en.wikipedia.org/wiki/Kumaraswamy_distribution |
In continuum mechanics, Whitham's averaged Lagrangian method – or in short Whitham's method – is used to study the Lagrangian dynamics of slowly-varying wave trains in an inhomogeneous (moving) medium.
The method is applicable to both linear and non-linear systems. As a direct consequence of the averaging used in the m... | https://en.wikipedia.org/wiki/Averaged_Lagrangian |
The Hann function is named after the Austrian meteorologist Julius von Hann. It is a window function used to perform Hann smoothing or hanning. The function, with length
$$
L
$$
and amplitude
$$
1/L,
$$
is given by:
$$
w_0(x) \triangleq \left\{
\begin{array}{ccl}
\tfrac{1}{L}\left(\tfrac{1}{2} + \tfrac{1}{2} \cos ... | https://en.wikipedia.org/wiki/Hann_function |
Euler's quadrilateral theorem or Euler's law on quadrilaterals, named after Leonhard Euler (1707–1783), describes a relation between the sides of a convex quadrilateral and its diagonals. It is a generalisation of the parallelogram law which in turn can be seen as generalisation of the Pythagorean theorem. Because of t... | https://en.wikipedia.org/wiki/Euler%27s_quadrilateral_theorem |
In mathematics, specifically the theory of Lie algebras, Lie's theorem states that, over an algebraically closed field of characteristic zero, if
$$
\pi: \mathfrak{g} \to \mathfrak{gl}(V)
$$
is a finite-dimensional representation of a solvable Lie algebra, then there is a flag
$$
V = V_0 \supset V_1 \supset \cdots \... | https://en.wikipedia.org/wiki/Lie%27s_theorem |
Bubble sort, sometimes referred to as sinking sort, is a simple sorting algorithm that repeatedly steps through the input list element by element, comparing the current element with the one after it, swapping their values if needed. These passes through the list are repeated until no swaps have to be performed during a... | https://en.wikipedia.org/wiki/Bubble_sort |
Synthetic-aperture radar (SAR) is a form of radar that is used to create two-dimensional images or three-dimensional reconstructions of objects, such as landscapes. SAR uses the motion of the radar antenna over a target region to provide finer spatial resolution than conventional stationary beam-scanning radars. SAR is... | https://en.wikipedia.org/wiki/Synthetic-aperture_radar |
In mathematics and more specifically in field theory, A radical extension of a field
$$
K
$$
is a field extension obtained by a tower of field extensions, each generated by adjoining an nth root of an element from the previous field.
## Definition
A simple radical extension is a simple extension F/K generated by a si... | https://en.wikipedia.org/wiki/Radical_extension |
In the study of image processing, a watershed is a transformation defined on a grayscale image. The name refers metaphorically to a geological watershed, or drainage divide, which separates adjacent drainage basins. The watershed transformation treats the image it operates upon like a topographic map, with the brightne... | https://en.wikipedia.org/wiki/Watershed_%28image_processing%29 |
Clock synchronization is a topic in computer science and engineering that aims to coordinate otherwise independent clocks. Even when initially set accurately, real clocks will differ after some amount of time due to clock drift, caused by clocks counting time at slightly different rates. There are several problems that... | https://en.wikipedia.org/wiki/Clock_synchronization |
In computer science, approximate string matching (often colloquially referred to as fuzzy string searching) is the technique of finding strings that match a pattern approximately (rather than exactly). The problem of approximate string matching is typically divided into two sub-problems: finding approximate substring ... | https://en.wikipedia.org/wiki/Approximate_string_matching |
In complex analysis, a branch of mathematics, the Koebe 1/4 theorem states the following:
Koebe Quarter Theorem. The image of an injective analytic function from the unit disk
onto a subset of the complex plane contains the disk whose center is and whose radius is .
The theorem is named after Paul Koebe, who conjec... | https://en.wikipedia.org/wiki/Koebe_quarter_theorem |
In mathematics, an ordered field is a field together with a total ordering of its elements that is compatible with the field operations. Basic examples of ordered fields are the rational numbers and the real numbers, both with their standard orderings.
Every subfield of an ordered field is also an ordered field in the... | https://en.wikipedia.org/wiki/Ordered_field |
The Dymaxion map projection, also called the Fuller projection, is a kind of polyhedral map projection of the Earth's surface onto the unfolded net of an icosahedron. The resulting map is heavily interrupted in order to reduce shape and size distortion compared to other world maps, but the interruptions are chosen to l... | https://en.wikipedia.org/wiki/Dymaxion_map |
Light, visible light, or visible radiation is electromagnetic radiation that can be perceived by the human eye. Visible light spans the visible spectrum and is usually defined as having wavelengths in the range of 400–700 nanometres (nm), corresponding to frequencies of 750–420 terahertz. The visible band sits adjacent... | https://en.wikipedia.org/wiki/Light |
In computational number theory and computational algebra, Pollard's kangaroo algorithm (also Pollard's lambda algorithm, see
## Naming
below) is an algorithm for solving the discrete logarithm problem. The algorithm was introduced in 1978 by the number theorist John M. Pollard, in the same paper as his better-known ... | https://en.wikipedia.org/wiki/Pollard%27s_kangaroo_algorithm |
An optical fiber, or optical fibre, is a flexible glass or plastic fiber that can transmit light from one end to the other. Such fibers find wide usage in fiber-optic communications, where they permit transmission over longer distances and at higher bandwidths (data transfer rates) than electrical cables. Fibers are us... | https://en.wikipedia.org/wiki/Optical_fiber |
The multi-commodity flow problem is a network flow problem with multiple commodities (flow demands) between different source and sink nodes.
## Definition
Given a flow network
$$
\,G(V,E)
$$
, where edge
$$
(u,v) \in E
$$
has capacity
$$
\,c(u,v)
$$
. There are
$$
\,k
$$
commodities
$$
K_1,K_2,\dots,K_k
$$
, def... | https://en.wikipedia.org/wiki/Multi-commodity_flow_problem |
In automata theory (a branch of theoretical computer science), DFA minimization is the task of transforming a given deterministic finite automaton (DFA) into an equivalent DFA that has a minimum number of states. Here, two DFAs are called equivalent if they recognize the same regular language. Several different algorit... | https://en.wikipedia.org/wiki/DFA_minimization |
A concurrent hash-trie or Ctrie is a concurrent thread-safe lock-free implementation of a hash array mapped trie. It is used to implement the concurrent map abstraction. It has particularly scalable concurrent insert and remove operations and is memory-efficient. It is the first known concurrent data-structure that sup... | https://en.wikipedia.org/wiki/Ctrie |
In mathematics, a polyadic space is a topological space that is the image under a continuous function of a topological power of an Alexandroff one-point compactification of a discrete space.
## History
Polyadic spaces were first studied by S. Mrówka in 1970 as a generalisation of dyadic spaces. The theory was developed... | https://en.wikipedia.org/wiki/Polyadic_space |
In finance, technical analysis is an analysis methodology for analysing and forecasting the direction of prices through the study of past market data, primarily price and volume. As a type of active management, it stands in contradiction to much of modern portfolio theory. The efficacy of technical analysis is disputed... | https://en.wikipedia.org/wiki/Technical_analysis |
In computational complexity theory, randomized polynomial time (RP) is the complexity class of problems for which a probabilistic Turing machine exists with these properties:
RP algorithm (1 run) ≥ 1/2 ≤ 1/2 0 1RP algorithm (n runs) ≥ 1 − 2−n ≤ 2−n 0 1co-RP algorithm (1 run) 1 0 ≤ 1/2 ≥ 1/2
- It always r... | https://en.wikipedia.org/wiki/RP_%28complexity%29 |
In mathematics, the Kodaira vanishing theorem is a basic result of complex manifold theory and complex algebraic geometry, describing general conditions under which sheaf cohomology groups with indices q > 0 are automatically zero. The implications for the group with index q = 0 is usually that its dimension — the numb... | https://en.wikipedia.org/wiki/Kodaira_vanishing_theorem |
In Euclidean geometry, the right triangle altitude theorem or geometric mean theorem is a relation between the altitude on the hypotenuse in a right triangle and the two line segments it creates on the hypotenuse. It states that the geometric mean of those two segments equals the altitude.
## Theorem and its converse
I... | https://en.wikipedia.org/wiki/Geometric_mean_theorem |
A climate spiral (sometimes referred to as a temperature spiral) is an animated data visualization graphic designed as a "simple and effective demonstration of the progression of global warming", especially for general audiences.
The original climate spiral was published on 9 May 2016 by British climate scientist Ed H... | https://en.wikipedia.org/wiki/Climate_spiral |
In finance, a T-forward measure is a pricing measure absolutely continuous with respect to a risk-neutral measure, but rather than using the money market as numeraire, it uses a bond with maturity T. The use of the forward measure was pioneered by Farshid Jamshidian (1987), and later used as a means of calculating the ... | https://en.wikipedia.org/wiki/Forward_measure |
Aerodynamics ( aero (air) + (dynamics)) is the study of the motion of air, particularly when affected by a solid object, such as an airplane wing. It involves topics covered in the field of fluid dynamics and its subfield of gas dynamics, and is an important domain of study in aeronautics. The term aerodynamics is of... | https://en.wikipedia.org/wiki/Aerodynamics |
In mechanics, acceleration is the rate of change of the velocity of an object with respect to time. Acceleration is one of several components of kinematics, the study of motion. Accelerations are vector quantities (in that they have magnitude and direction). The orientation of an object's acceleration is given by the o... | https://en.wikipedia.org/wiki/Acceleration |
A supercomputer is a type of computer with a high level of performance as compared to a general-purpose computer. The performance of a supercomputer is commonly measured in floating-point operations per second (FLOPS) instead of million instructions per second (MIPS). Since 2022, supercomputers have existed which can p... | https://en.wikipedia.org/wiki/Supercomputer |
In abstract algebra, an ordered ring is a (usually commutative) ring R with a total order ≤ such that for all a, b, and c in R:
- if a ≤ b then a + c ≤ b + c.
- if 0 ≤ a and 0 ≤ b then 0 ≤ ab.
## Examples
Ordered rings are familiar from arithmetic. Examples include the integers, the rationals and the real numbers. (T... | https://en.wikipedia.org/wiki/Ordered_ring |
In mathematics, the multiplicative ergodic theorem, or Oseledets theorem provides the theoretical background for computation of Lyapunov exponents of a nonlinear dynamical system. It was proved by Valery Oseledets (also spelled "Oseledec") in 1965 and reported at the International Mathematical Congress in Moscow in 196... | https://en.wikipedia.org/wiki/Oseledets_theorem |
Internal waves are gravity waves that oscillate within a fluid medium, rather than on its surface. To exist, the fluid must be stratified: the density must change (continuously or discontinuously) with depth/height due to changes, for example, in temperature and/or salinity. If the density changes over a small vertical... | https://en.wikipedia.org/wiki/Internal_wave |
Quantum information is the information of the state of a quantum system. It is the basic entity of study in quantum information theory, and can be manipulated using quantum information processing techniques. Quantum information refers to both the technical definition in terms of
#### Von Neumann entropy
and the gener... | https://en.wikipedia.org/wiki/Quantum_information |
The Christofides algorithm or Christofides–Serdyukov algorithm is an algorithm for finding approximate solutions to the travelling salesman problem, on instances where the distances form a metric space (they are symmetric and obey the triangle inequality).
It is an approximation algorithm that guarantees that its solut... | https://en.wikipedia.org/wiki/Christofides_algorithm |
Seam carving (or liquid rescaling) is an algorithm for content-aware image resizing, developed by Shai Avidan, of Mitsubishi Electric Research Laboratories (MERL), and Ariel Shamir, of the Interdisciplinary Center and MERL. It functions by establishing a number of seams (paths of least importance) in an image and autom... | https://en.wikipedia.org/wiki/Seam_carving |
The propensity theory of probability is a probability interpretation in which the probability is thought of as a physical propensity, disposition, or tendency of a given type of situation to yield an outcome of a certain kind, or to yield a long-run relative frequency of such an outcome.
Propensities are not relative f... | https://en.wikipedia.org/wiki/Propensity_probability |
In mathematics, a wavelet series is a representation of a square-integrable (real- or complex-valued) function by a certain orthonormal series generated by a wavelet. This article provides a formal, mathematical definition of an orthonormal wavelet and of the integral wavelet transform.Chui, Charles K. (1992), An Intro... | https://en.wikipedia.org/wiki/Wavelet_transform |
In Euclidean geometry, the intersecting chords theorem, or just the chord theorem, is a statement that describes a relation of the four line segments created by two intersecting chords within a circle.
It states that the products of the lengths of the line segments on each chord are equal.
It is Proposition 35 of Boo... | https://en.wikipedia.org/wiki/Intersecting_chords_theorem |
Lamb waves propagate in solid plates or spheres. They are elastic waves whose particle motion lies in the plane that contains the direction of wave propagation and the direction perpendicular to the plate. In 1917, the English mathematician Horace Lamb published his classic analysis and description of acoustic waves of... | https://en.wikipedia.org/wiki/Lamb_waves |
The Allais paradox is a choice problem designed by to show an inconsistency of actual observed choices with the predictions of expected utility theory. The Allais paradox demonstrates that individuals rarely make rational decisions consistently when required to do so immediately. The independence axiom of expected uti... | https://en.wikipedia.org/wiki/Allais_paradox |
Insertion sort is a simple sorting algorithm that builds the final sorted array (or list) one item at a time by comparisons. It is much less efficient on large lists than more advanced algorithms such as quicksort, heapsort, or merge sort. However, insertion sort provides several advantages:
- Simple implementation: Jo... | https://en.wikipedia.org/wiki/Insertion_sort |
In probability theory, two sequences of probability measures are said to be contiguous if asymptotically they share the same support. Thus the notion of contiguity extends the concept of absolute continuity to the sequences of measures.
The concept was originally introduced by as part of his foundational contribution ... | https://en.wikipedia.org/wiki/Contiguity_%28probability_theory%29 |
In mathematics, the Nørlund–Rice integral, sometimes called Rice's method, relates the nth forward difference of a function to a contour integral on the complex plane. It commonly appears in the theory of finite differences and has also been applied in computer science and graph theory to estimate binary tree lengths. ... | https://en.wikipedia.org/wiki/N%C3%B8rlund%E2%80%93Rice_integral |
A seismic wave is a mechanical wave of acoustic energy that travels through the Earth or another planetary body. It can result from an earthquake (or generally, a quake), volcanic eruption, magma movement, a large landslide and a large man-made explosion that produces low-frequency acoustic energy. Seismic waves are st... | https://en.wikipedia.org/wiki/Seismic_wave |
In general relativity, the monochromatic electromagnetic plane wave spacetime is the analog of the monochromatic plane waves known from Maxwell's theory. The precise definition of the solution is quite complicated but very instructive.
Any exact solution of the Einstein field equation which models an electromagnetic f... | https://en.wikipedia.org/wiki/Monochromatic_electromagnetic_plane_wave |
Memory segmentation is an operating system memory management technique of dividing a computer's primary memory into segments or sections. In a computer system using segmentation, a reference to a memory location includes a value that identifies a segment and an offset (memory location) within that segment. Segments or ... | https://en.wikipedia.org/wiki/Memory_segmentation |
The zodiacal light (also called false dawn when seen before sunrise) is a faint glow of diffuse sunlight scattered by interplanetary dust. Brighter around the Sun, it appears in a particularly dark night sky to extend from the Sun's direction in a roughly triangular shape along the zodiac, and appears with less intensi... | https://en.wikipedia.org/wiki/Zodiacal_light |
Safety engineering is an engineering discipline which assures that engineered systems provide acceptable levels of safety. It is strongly related to industrial engineering/systems engineering, and the subset system safety engineering. Safety engineering assures that a life-critical system behaves as needed, even when ... | https://en.wikipedia.org/wiki/Safety_engineering |
The sunrise problem can be expressed as follows: "What is the probability that the sun will rise tomorrow?" The sunrise problem illustrates the difficulty of using probability theory when evaluating the plausibility of statements or beliefs.
According to the Bayesian interpretation of probability, probability theory ca... | https://en.wikipedia.org/wiki/Sunrise_problem |
In computer science, a Cartesian tree is a binary tree derived from a sequence of distinct numbers. To construct the Cartesian tree, set its root to be the minimum number in the sequence, and recursively construct its left and right subtrees from the subsequences before and after this number. It is uniquely defined as... | https://en.wikipedia.org/wiki/Cartesian_tree |
Open addressing, or closed hashing, is a method of collision resolution in hash tables. With this method a hash collision is resolved by probing, or searching through alternative locations in the array (the probe sequence) until either the target record is found, or an unused array slot is found, which indicates that ... | https://en.wikipedia.org/wiki/Open_addressing |
In the theory of functions of several complex variables, Hartogs's extension theorem is a statement about the singularities of holomorphic functions of several variables. Informally, it states that the support of the singularities of such functions cannot be compact, therefore the singular set of a function of several ... | https://en.wikipedia.org/wiki/Hartogs%27s_extension_theorem |
Geophysics () is a subject of natural science concerned with the physical processes and properties of Earth and its surrounding space environment, and the use of quantitative methods for their analysis. Geophysicists conduct investigations across a wide range of scientific disciplines. The term geophysics classically r... | https://en.wikipedia.org/wiki/Geophysics |
Rossby waves, also known as planetary waves, are a type of inertial wave naturally occurring in rotating fluids. They were first identified by Sweden-born American meteorologist Carl-Gustaf Arvid Rossby in the Earth's atmosphere in 1939. They are observed in the atmospheres and oceans of Earth and other planets, owing ... | https://en.wikipedia.org/wiki/Rossby_wave |
In mathematics, a Hirzebruch surface is a ruled surface over the projective line. They were studied by .
## Definition
The Hirzebruch surface
$$
\Sigma_n
$$
is the
$$
\mathbb{P}^1
$$
-bundle (a projective bundle) over the projective line
$$
\mathbb{P}^1
$$
, associated to the sheaf
$$
\mathcal{O}\oplus \mathcal{O}(... | https://en.wikipedia.org/wiki/Hirzebruch_surface |
As originally stated in terms of direct-current resistive circuits only, Thévenin's theorem states that "Any linear electrical network containing only voltage sources, current sources and resistances can be replaced at terminals by an equivalent combination of a voltage source in a series connection with a resistance... | https://en.wikipedia.org/wiki/Th%C3%A9venin%27s_theorem |
In computability theory, a Turing reduction from a decision problem
$$
A
$$
to a decision problem
$$
B
$$
is an oracle machine that decides problem
$$
A
$$
given an oracle for
$$
B
$$
(Rogers 1967, Soare 1987) in finitely many steps. It can be understood as an algorithm that could be used to solve
$$
A
$$
if ... | https://en.wikipedia.org/wiki/Turing_reduction |
Literate programming (LP) is a programming paradigm introduced in 1984 by Donald Knuth in which a computer program is given as an explanation of how it works in a natural language, such as English, interspersed (embedded) with snippets of macros and traditional source code, from which compilable source code can be gene... | https://en.wikipedia.org/wiki/Literate_programming |
In automata theory and sequential logic, a state-transition table is a table showing what state (or states in the case of a nondeterministic finite automaton) a finite-state machine will move to, based on the current state and other inputs. It is essentially a truth table in which the inputs include the current state a... | https://en.wikipedia.org/wiki/State-transition_table |
Probabilistic logic (also probability logic and probabilistic reasoning) involves the use of probability and logic to deal with uncertain situations. Probabilistic logic extends traditional logic truth tables with probabilistic expressions. A difficulty of probabilistic logics is their tendency to multiply the computat... | https://en.wikipedia.org/wiki/Probabilistic_logic |
Gravitational waves are oscillations of the gravitational field that travel through space at the speed of light; they are generated by the relative motion of gravitating masses. They were proposed by Oliver Heaviside in 1893 and then later by Henri Poincaré in 1905 as the gravitational equivalent of electromagnetic wav... | https://en.wikipedia.org/wiki/Gravitational_wave |
In physics, a redshift is an increase in the wavelength, and corresponding decrease in the frequency and photon energy, of electromagnetic radiation (such as light). The opposite change, a decrease in wavelength and increase in frequency and energy, is known as a blueshift. The terms derive from the colours red and blu... | https://en.wikipedia.org/wiki/Redshift |
Morton's theorem is a poker principle articulated by Andy Morton in a Usenet poker newsgroup. It states that in multi-way pots, a player's expectation may be maximized by an opponent making a correct decision.
The most common application of Morton's theorem occurs when one player holds the best hand, but there are two ... | https://en.wikipedia.org/wiki/Morton%27s_theorem |
In a computer operating system that uses paging for virtual memory management, page replacement algorithms decide which memory pages to page out, sometimes called swap out, or write to disk, when a page of memory needs to be allocated. Page replacement happens when a requested page is not in memory (page fault) and a f... | https://en.wikipedia.org/wiki/Page_replacement_algorithm |
A supernova (: supernovae or supernovas) is a powerful and luminous explosion of a star. A supernova occurs during the last evolutionary stages of a massive star, or when a white dwarf is triggered into runaway nuclear fusion. The original object, called the progenitor, either collapses to a neutron star or black hole,... | https://en.wikipedia.org/wiki/Supernova |
In mathematics, specifically group theory, Cauchy's theorem states that if is a finite group and is a prime number dividing the order of (the number of elements in ), then contains an element of order . That is, there is in such that is the smallest positive integer with = , where is the identity element of . ... | https://en.wikipedia.org/wiki/Cauchy%27s_theorem_%28group_theory%29 |
Peterson's algorithm (or Peterson's solution) is a concurrent programming algorithm for mutual exclusion that allows two or more processes to share a single-use resource without conflict, using only shared memory for communication. It was formulated by Gary L. Peterson in 1981. While Peterson's original formulation wor... | https://en.wikipedia.org/wiki/Peterson%27s_algorithm |
The noncentral t-distribution generalizes Student's t-distribution using a noncentrality parameter. Whereas the central probability distribution describes how a test statistic t is distributed when the difference tested is null, the noncentral distribution describes how t is distributed when the null is false. This le... | https://en.wikipedia.org/wiki/Noncentral_t-distribution |
In traditional logic, a contradiction involves a proposition conflicting either with itself or established fact. It is often used as a tool to detect disingenuous beliefs and bias. Illustrating a general tendency in applied logic, Aristotle's law of noncontradiction states that "It is impossible that the same thing can... | https://en.wikipedia.org/wiki/Contradiction |
The phase velocity of a wave is the rate at which the wave propagates in any medium. This is the velocity at which the phase of any one frequency component of the wave travels. For such a component, any given phase of the wave (for example, the crest) will appear to travel at the phase velocity. The phase velocity is g... | https://en.wikipedia.org/wiki/Phase_velocity |
The wave impedance of an electromagnetic wave is the ratio of the transverse components of the electric and magnetic fields (the transverse components being those at right angles to the direction of propagation). For a transverse-electric-magnetic (TEM) plane wave traveling through a homogeneous medium, the wave imped... | https://en.wikipedia.org/wiki/Wave_impedance |
In mathematics, especially in order theory, a preorder or quasiorder is a binary relation that is reflexive and transitive. The name is meant to suggest that preorders are almost partial orders, but not quite, as they are not necessarily antisymmetric.
A natural example of a preorder is the divides relation "x divides... | https://en.wikipedia.org/wiki/Preorder |
In mathematics, the particular point topology (or included point topology) is a topology where a set is open if it contains a particular point of the topological space. Formally, let X be any non-empty set and p ∈ X. The collection
$$
T = \{S \subseteq X \mid p \in S \} \cup \{\emptyset\}
$$
of subsets of X is the p... | https://en.wikipedia.org/wiki/Particular_point_topology |
Fermat's factorization method, named after Pierre de Fermat, is based on the representation of an odd integer as the difference of two squares:
$$
N = a^2 - b^2.
$$
That difference is algebraically factorable as
$$
(a+b)(a-b)
$$
; if neither factor equals one, it is a proper factorization of N.
Each odd number has suc... | https://en.wikipedia.org/wiki/Fermat%27s_factorization_method |
Vehicle dynamics is the study of vehicle motion, e.g., how a vehicle's forward movement changes in response to driver inputs, propulsion system outputs, ambient conditions, air/surface/water conditions, etc.
Vehicle dynamics is a part of engineering primarily based on classical mechanics.
It may be applied for motorize... | https://en.wikipedia.org/wiki/Vehicle_dynamics |
Dekker's algorithm is the first known correct solution to the mutual exclusion problem in concurrent programming where processes only communicate via shared memory. The solution is attributed to Dutch mathematician Th. J. Dekker by Edsger W. Dijkstra in an unpublished paper on sequential process descriptions and his ma... | https://en.wikipedia.org/wiki/Dekker%27s_algorithm |
In signal processing, group delay and phase delay are functions that describe in different ways the delay times experienced by a signal’s various sinusoidal frequency components as they pass through a linear time-invariant (LTI) system (such as a microphone, coaxial cable, amplifier, loudspeaker, communications system,... | https://en.wikipedia.org/wiki/Group_delay_and_phase_delay |
The Wakeby distribution is a five-parameter probability distribution defined by its quantile function,
$$
W(p) =\xi + \frac{\alpha}{\beta}(1 - (1-p)^{\beta}) - \frac{\gamma}{\delta}(1 - (1-p)^{-\delta})
$$
,
and by its quantile density function,
$$
W'(p) = w(p) = \alpha (1-p)^{\beta - 1} + \gamma (1-p)^{-\delta - 1}
$$... | https://en.wikipedia.org/wiki/Wakeby_distribution |
In computer science, a purely functional data structure is a data structure that can be directly implemented in a purely functional language. The main difference between an arbitrary data structure and a purely functional one is that the latter is (strongly) immutable. This restriction ensures the data structure posses... | https://en.wikipedia.org/wiki/Purely_functional_data_structure |
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