text stringlengths 2.13k 184k | source stringlengths 31 108 |
|---|---|
In logic, false (Its noun form is falsity) or untrue is the state of possessing negative truth value and is a nullary logical connective. In a truth-functional system of propositional logic, it is one of two postulated truth values, along with its negation, truth. Usual notations of the false are 0 (especially in Bool... | https://en.wikipedia.org/wiki/False_%28logic%29 |
The intercept theorem, also known as Thales's theorem, basic proportionality theorem or side splitter theorem, is an important theorem in elementary geometry about the ratios of various line segments that are created if two rays with a common starting point are intercepted by a pair of parallels. It is equivalent to th... | https://en.wikipedia.org/wiki/Intercept_theorem |
In mathematics, a submanifold of a manifold
$$
M
$$
is a subset
$$
S
$$
which itself has the structure of a manifold, and for which the inclusion map
$$
S \rightarrow M
$$
satisfies certain properties. There are different types of submanifolds depending on exactly which properties are required. Different authors ... | https://en.wikipedia.org/wiki/Submanifold |
Secret sharing (also called secret splitting) refers to methods for distributing a secret among a group, in such a way that no individual holds any intelligible information about the secret, but when a sufficient number of individuals combine their 'shares', the secret may be reconstructed. Whereas insecure secret shar... | https://en.wikipedia.org/wiki/Secret_sharing |
A counterexample is any exception to a generalization. In logic a counterexample disproves the generalization, and does so rigorously in the fields of mathematics and philosophy. For example, the fact that "student John Smith is not lazy" is a counterexample to the generalization "students are lazy", and both a counte... | https://en.wikipedia.org/wiki/Counterexample |
In mathematics and computer science, a string metric (also known as a string similarity metric or string distance function) is a metric that measures distance ("inverse similarity") between two text strings for approximate string matching or comparison and in fuzzy string searching. A requirement for a string metric (e... | https://en.wikipedia.org/wiki/String_metric |
Code-excited linear prediction (CELP) is a linear predictive speech coding algorithm originally proposed by Manfred R. Schroeder and Bishnu S. Atal in 1985. At the time, it provided significantly better quality than existing low bit-rate algorithms, such as residual-excited linear prediction (RELP) and linear predictiv... | https://en.wikipedia.org/wiki/Code-excited_linear_prediction |
In probability theory, the continuous mapping theorem states that continuous functions preserve limits even if their arguments are sequences of random variables. A continuous function, in Heine's definition, is such a function that maps convergent sequences into convergent sequences: if xn → x then g(xn) → g(x). The co... | https://en.wikipedia.org/wiki/Continuous_mapping_theorem |
Cosmic background radiation is electromagnetic radiation that fills all space. The origin of this radiation depends on the region of the spectrum that is observed. One component is the cosmic microwave background. This component is redshifted photons that have freely streamed from an epoch when the Universe became tran... | https://en.wikipedia.org/wiki/Cosmic_background_radiation |
In mathematics, Grothendieck's six operations, named after Alexander Grothendieck, is a formalism in homological algebra, also known as the six-functor formalism. It originally sprang from the relations in étale cohomology that arise from a morphism of schemes . The basic insight was that many of the elementary facts ... | https://en.wikipedia.org/wiki/Six_operations |
In mathematics, a pseudometric space is a generalization of a metric space in which the distance between two distinct points can be zero. Pseudometric spaces were introduced by Đuro Kurepa in 1934. In the same way as every normed space is a metric space, every seminormed space is a pseudometric space. Because of this a... | https://en.wikipedia.org/wiki/Pseudometric_space |
Liquid is a state of matter with a definite volume but no fixed shape. Liquids adapt to the shape of their container and are nearly incompressible, maintaining their volume even under pressure. The density of a liquid is usually close to that of a solid, and much higher than that of a gas. Therefore, liquid and solid a... | https://en.wikipedia.org/wiki/Liquid |
In probability theory and statistics, the Gumbel distribution (also known as the type-I generalized extreme value distribution) is used to model the distribution of the maximum (or the minimum) of a number of samples of various distributions.
This distribution might be used to represent the distribution of the maximum ... | https://en.wikipedia.org/wiki/Gumbel_distribution |
In operator theory, Atkinson's theorem (named for Frederick Valentine Atkinson) gives a characterization of Fredholm operators.
## The theorem
Let H be a Hilbert space and L(H) the set of bounded operators on H. The following is the classical definition of a Fredholm operator: an operator T ∈ L(H) is said to be a Fredh... | https://en.wikipedia.org/wiki/Atkinson%27s_theorem |
In logic and mathematics, a truth value, sometimes called a logical value, is a value indicating the relation of a proposition to truth, which in classical logic has only two possible values (true or false). Truth values are used in computing as well as various types of logic.
## Computing
In some programming languages... | https://en.wikipedia.org/wiki/Truth_value |
In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine and standardize the position of the points or other geometric elements on a manifold such as Euclidean space. The order of the coordinates is significant, and they are sometimes identified by their position... | https://en.wikipedia.org/wiki/Coordinate_system |
Energy () is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat and light. Energy is a conserved quantity—the law of conservation of energy states that energy can be converted in form, but not created or destroyed. The unit of... | https://en.wikipedia.org/wiki/Energy |
In functional analysis, a branch of mathematics, two methods of constructing normed spaces from disks were systematically employed by Alexander Grothendieck to define nuclear operators and nuclear spaces.
One method is used if the disk
$$
D
$$
is bounded: in this case, the auxiliary normed space is
$$
\operatorname... | https://en.wikipedia.org/wiki/Auxiliary_normed_space |
A wave disk engine or wave disk generator is a type of pistonless rotary engine being developed at Michigan State University and Warsaw Institute of Technology. The engine has a spinning disk with curved blades. Once fuel and air enter the engine, the rotation of the disk creates shockwaves that compress the mixture. W... | https://en.wikipedia.org/wiki/Wave_disk_engine |
The visual cortex of the brain is the area of the cerebral cortex that processes visual information. It is located in the occipital lobe. Sensory input originating from the eyes travels through the lateral geniculate nucleus in the thalamus and then reaches the visual cortex. The area of the visual cortex that receives... | https://en.wikipedia.org/wiki/Visual_cortex |
SipHash is an add–rotate–xor (ARX) based family of pseudorandom functions created by Jean-Philippe Aumasson and Daniel J. Bernstein in 2012, in response to a spate of "hash flooding" denial-of-service attacks (HashDoS) in late 2011.
SipHash is designed as a secure pseudorandom function and can also be used as a secure ... | https://en.wikipedia.org/wiki/SipHash |
In geometry, Poncelet's closure theorem, also known as Poncelet's porism, states that whenever a polygon is inscribed in one conic section and circumscribes another one, the polygon must be part of an infinite family of polygons that are all inscribed in and circumscribe the same two conics. It is named after French en... | https://en.wikipedia.org/wiki/Poncelet%27s_closure_theorem |
The critical path method (CPM), or critical path analysis (CPA), is an algorithm for scheduling a set of project activities. A critical path is determined by identifying the longest stretch of dependent activities and measuring the time required to complete them from start to finish. It is commonly used in conjunction ... | https://en.wikipedia.org/wiki/Critical_path_method |
An ion source is a device that creates atomic and molecular ions. Ion sources are used to form ions for mass spectrometers, optical emission spectrometers, particle accelerators, ion implanters and ion engines.
## Electron ionization
Electron ionization is widely used in mass spectrometry, particularly for organic mole... | https://en.wikipedia.org/wiki/Ion_source |
A database index is a data structure that improves the speed of data retrieval operations on a database table at the cost of additional writes and storage space to maintain the index data structure. Indexes are used to quickly locate data without having to search every row in a database table every time said table is ... | https://en.wikipedia.org/wiki/Database_index |
In mathematics, an extreme point of a convex set
$$
S
$$
in a real or complex vector space is a point in
$$
S
$$
that does not lie in any open line segment joining two points of
$$
S.
$$
The extreme points of a line segment are called its endpoints. In linear programming problems, an extreme point is also called ... | https://en.wikipedia.org/wiki/Extreme_point |
In mathematics, Mostow's rigidity theorem, or strong rigidity theorem, or Mostow–Prasad rigidity theorem, essentially states that the geometry of a complete, finite-volume hyperbolic manifold of dimension greater than two is determined by the fundamental group and hence unique.
## The theorem
was proven for closed m... | https://en.wikipedia.org/wiki/Mostow_rigidity_theorem |
In geometry, Radon's theorem on convex sets, published by Johann Radon in 1921, states that:Any set of d + 2 points in Rd can be partitioned into two sets whose convex hulls intersect. A point in the intersection of these convex hulls is called a Radon point of the set.For example, in the case d = 2, any set of four po... | https://en.wikipedia.org/wiki/Radon%27s_theorem |
The order in probability notation is used in probability theory and statistical theory in direct parallel to the big O notation that is standard in mathematics. Where the big O notation deals with the convergence of sequences or sets of ordinary numbers, the order in probability notation deals with convergence of sets... | https://en.wikipedia.org/wiki/Big_O_in_probability_notation |
A calendar queue (CQ) is a priority queue (queue in which every element has associated priority and the dequeue operation removes the highest priority element). It is analogous to desk calendar, which is used by humans for ordering future events by date. Discrete event simulations require a future event list (FEL) stru... | https://en.wikipedia.org/wiki/Calendar_queue |
A gravitational singularity, spacetime singularity, or simply singularity, is a theoretical condition in which gravity is predicted to be so intense that spacetime itself would break down catastrophically. As such, a singularity is by definition no longer part of the regular spacetime and cannot be determined by "where... | https://en.wikipedia.org/wiki/Gravitational_singularity |
In probability theory, a random measure is a measure-valued random element. Random measures are for example used in the theory of random processes, where they form many important point processes such as Poisson point processes and Cox processes.
## Definition
Random measures can be defined as transition kernels or as r... | https://en.wikipedia.org/wiki/Random_measure |
The adiabatic theorem is a concept in quantum mechanics. Its original form, due to Max Born and Vladimir Fock (1928), was stated as follows:
A physical system remains in its instantaneous eigenstate if a given perturbation is acting on it slowly enough and if there is a gap between the eigenvalue and the rest of the Ha... | https://en.wikipedia.org/wiki/Adiabatic_theorem |
In portfolio theory, a mutual fund separation theorem, mutual fund theorem, or separation theorem is a theorem stating that, under certain conditions, any investor's optimal portfolio can be constructed by holding each of certain mutual funds in appropriate ratios, where the number of mutual funds is smaller than the n... | https://en.wikipedia.org/wiki/Mutual_fund_separation_theorem |
In mathematics, particularly in number theory, Hillel
## Furstenberg's proof
of the infinitude of primes is a topological proof that the integers contain infinitely many prime numbers. When examined closely, the proof is less a statement about topology than a statement about certain properties of arithmetic sequence... | https://en.wikipedia.org/wiki/Furstenberg%27s_proof_of_the_infinitude_of_primes |
In physics, canonical quantization is a procedure for quantizing a classical theory, while attempting to preserve the formal structure, such as symmetries, of the classical theory to the greatest extent possible.
Historically, this was not quite Werner Heisenberg's route to obtaining quantum mechanics, but Paul Dirac ... | https://en.wikipedia.org/wiki/Canonical_quantization |
In the mathematical field of differential geometry, the Calabi conjecture was a conjecture about the existence of certain kinds of Riemannian metrics on certain complex manifolds, made by . It was proved by , who received the Fields Medal and Oswald Veblen Prize in part for his proof. His work, principally an analysis ... | https://en.wikipedia.org/wiki/Calabi_conjecture |
In computing, a group of parallel arrays (also known as structure of arrays or SoA) is a form of implicit data structure that uses multiple arrays to represent a singular array of records. It keeps a separate, homogeneous data array for each field of the record, each having the same number of elements. Then, objects lo... | https://en.wikipedia.org/wiki/Parallel_array |
In complex geometry, an Inoue surface is any of several complex surfaces of Kodaira class VII. They are named after Masahisa Inoue, who gave the first non-trivial examples of Kodaira class VII surfaces in 1974.
The Inoue surfaces are not Kähler manifolds.
## Inoue surfaces with b2 = 0
Inoue introduced three families of... | https://en.wikipedia.org/wiki/Inoue_surface |
In physics, a wave packet (also known as a wave train or wave group) is a short burst of localized wave action that travels as a unit, outlined by an envelope. A wave packet can be analyzed into, or can be synthesized from, a potentially-infinite set of component sinusoidal waves of different wavenumbers, with phases a... | https://en.wikipedia.org/wiki/Wave_packet |
A birthday attack is a bruteforce collision attack that exploits the mathematics behind the birthday problem in probability theory. This attack can be used to abuse communication between two or more parties. The attack depends on the higher likelihood of collisions found between random attack attempts and a fixed degre... | https://en.wikipedia.org/wiki/Birthday_attack |
An American flag sort is an efficient, in-place variant of radix sort that distributes items into buckets. Non-comparative sorting algorithms such as radix sort and American flag sort are typically used to sort large objects such as strings, for which comparison is not a unit-time operation.
American flag sort iterate... | https://en.wikipedia.org/wiki/American_flag_sort |
Alpha–beta pruning is a search algorithm that seeks to decrease the number of nodes that are evaluated by the minimax algorithm in its search tree. It is an adversarial search algorithm used commonly for machine playing of two-player combinatorial games (Tic-tac-toe, Chess, Connect 4, etc.). It stops evaluating a move ... | https://en.wikipedia.org/wiki/Alpha%E2%80%93beta_pruning |
In compiler design, static single assignment form (often abbreviated as SSA form or simply SSA) is a type of intermediate representation (IR) where each variable is assigned exactly once. SSA is used in most high-quality optimizing compilers for imperative languages, including LLVM, the GNU Compiler Collection, and man... | https://en.wikipedia.org/wiki/Static_single-assignment_form |
The survival function is a function that gives the probability that a patient, device, or other object of interest will survive past a certain time.
The survival function is also known as the survivor function or reliability function.
The term reliability function is common in engineering while the term survival functi... | https://en.wikipedia.org/wiki/Survival_function |
In number theory, Lagrange's theorem is a statement named after Joseph-Louis Lagrange about how frequently a polynomial over the integers may evaluate to a multiple of a fixed prime p. More precisely, it states that for all integer polynomials
$$
\textstyle f \in \mathbb{Z}[x]
$$
, either:
- every coefficient of is d... | https://en.wikipedia.org/wiki/Lagrange%27s_theorem_%28number_theory%29 |
In probability and statistics, the Tweedie distributions are a family of probability distributions which include the purely continuous normal, gamma and inverse Gaussian distributions, the purely discrete scaled Poisson distribution, and the class of compound Poisson–gamma distributions which have positive mass at zero... | https://en.wikipedia.org/wiki/Tweedie_distribution |
In mathematics, a periodic travelling wave (or wavetrain) is a periodic function of one-dimensional space that moves with constant speed. Consequently, it is a special type of spatiotemporal oscillation that is a periodic function of both space and time.
Periodic travelling waves play a fundamental role in many mathema... | https://en.wikipedia.org/wiki/Periodic_travelling_wave |
In set theory, the Baire space is the set of all infinite sequences of natural numbers with a certain topology, called the product topology. This space is commonly used in descriptive set theory, to the extent that its elements are often called "reals". It is denoted by
$$
\N^{\N}
$$
, or ωω, or by the symbol
$$
\... | https://en.wikipedia.org/wiki/Baire_space_%28set_theory%29 |
Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form, since to do so would require writing out an inconveniently long string of digits. It may be referred to as scientific form or standard index form, or standard form in the United Kingdom. This b... | https://en.wikipedia.org/wiki/Scientific_notation |
Spread betting is any of various types of wagering on the outcome of an event where the pay-off is based on the accuracy of the wager, rather than a simple "win or lose" outcome, such as fixed-odds (or money-line) betting or parimutuel betting.
A point spread is a range of outcomes and the bet is whether the outcome wi... | https://en.wikipedia.org/wiki/Spread_betting |
In Euclidean geometry, the British flag theorem says that if a point P is chosen inside a rectangle ABCD then the sum of the squares of the Euclidean distances from P to two opposite corners of the rectangle equals the sum to the other two opposite corners..
As an equation:
$$
AP^2 + CP^2 = BP^2 + DP^2.
$$
The theorem ... | https://en.wikipedia.org/wiki/British_flag_theorem |
A Byzantine fault is a condition of a system, particularly a distributed computing system, where a fault occurs such that different symptoms are presented to different observers, including imperfect information on whether a system component has failed. The term takes its name from an allegory, the "Byzantine generals p... | https://en.wikipedia.org/wiki/Byzantine_fault |
A two-dimensional space is a mathematical space with two dimensions, meaning points have two degrees of freedom: their locations can be locally described with two coordinates or they can move in two independent directions. Common two-dimensional spaces are often called planes, or, more generally, surfaces. These includ... | https://en.wikipedia.org/wiki/Two-dimensional_space |
A coordination game is a type of simultaneous game found in game theory. It describes the situation where a player will earn a higher payoff when they select the same course of action as another player. The game is not one of pure conflict, which results in multiple pure strategy Nash equilibria in which players choos... | https://en.wikipedia.org/wiki/Coordination_game |
In computational geometry, the gift wrapping algorithm is an algorithm for computing the convex hull of a given set of points.
## Planar case
In the two-dimensional case the algorithm is also known as Jarvis march, after R. A. Jarvis, who published it in 1973; it has O(nh) time complexity, where n is the number of poin... | https://en.wikipedia.org/wiki/Gift_wrapping_algorithm |
In data mining, k-means++http://theory.stanford.edu/~sergei/slides/BATS-Means.pdf Slides for presentation of method by Arthur, D. and Vassilvitskii, S. is an algorithm for choosing the initial values (or "seeds") for the k-means clustering algorithm. It was proposed in 2007 by David Arthur and Sergei Vassilvitskii, as... | https://en.wikipedia.org/wiki/K-means%2B%2B |
The kelvin (symbol: K) is the base unit for temperature in the International System of Units (SI). The Kelvin scale is an absolute temperature scale that starts at the lowest possible temperature (absolute zero), taken to be 0 K. By definition, the Celsius scale (symbol °C) and the Kelvin scale have the exact same magn... | https://en.wikipedia.org/wiki/Kelvin |
The shallow-water equations (SWE) are a set of hyperbolic partial differential equations (or parabolic if viscous shear is considered) that describe the flow below a pressure surface in a fluid (sometimes, but not necessarily, a free surface). The shallow-water equations in unidirectional form are also called (de) Sai... | https://en.wikipedia.org/wiki/Shallow_water_equations |
A cold wave (known in some regions as a cold snap, cold spell or Arctic Snap) is a weather phenomenon that is distinguished by a cooling of the air. Specifically, as used by the U.S. National Weather Service, a cold wave is a rapid fall in temperature within a 24-hour period requiring substantially increased protection... | https://en.wikipedia.org/wiki/Cold_wave |
In the theory of stochastic processes, a part of the mathematical theory of probability, the variance gamma (VG) process, also known as Laplace motion, is a Lévy process determined by a random time change. The process has finite moments, distinguishing it from many Lévy processes. There is no diffusion component in th... | https://en.wikipedia.org/wiki/Variance_gamma_process |
Booth's multiplication algorithm is a multiplication algorithm that multiplies two signed binary numbers in two's complement notation.
## The algorithm
was invented by Andrew Donald Booth in 1950 while doing research on crystallography at Birkbeck College in Bloomsbury, London. Booth's algorithm is of interest in the... | https://en.wikipedia.org/wiki/Booth%27s_multiplication_algorithm |
The hydrogen line, 21 centimeter line, or H I line is a spectral line that is created by a change in the energy state of solitary, electrically neutral hydrogen atoms. It is produced by a spin-flip transition, which means the direction of the electron's spin is reversed relative to the spin of the proton. This is a qua... | https://en.wikipedia.org/wiki/Hydrogen_line |
A Venn diagram is a widely used diagram style that shows the logical relation between sets, popularized by John Venn (1834–1923) in the 1880s. The diagrams are used to teach elementary set theory, and to illustrate simple set relationships in probability, logic, statistics, linguistics and computer science. A Venn diag... | https://en.wikipedia.org/wiki/Venn_diagram |
The ground state of a quantum-mechanical system is its stationary state of lowest energy; the energy of the ground state is known as the zero-point energy of the system. An excited state is any state with energy greater than the ground state. In quantum field theory, the ground state is usually called the vacuum.
If mo... | https://en.wikipedia.org/wiki/Ground_state |
An industry standard data model, or simply standard data model, is a data model that is widely used in a particular industry. The use of standard data models makes the exchange of information easier and faster because it allows heterogeneous organizations to share an agreed vocabulary, semantics, format, and quality s... | https://en.wikipedia.org/wiki/Industry_standard_data_model |
The median of a set of numbers is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as the “middle" value. The basic feature of the median in describing data compared to the mean (often simply described as the "av... | https://en.wikipedia.org/wiki/Median |
The pirate game is a simple mathematical game. It is a multi-player version of the ultimatum game.
## The game
There are five rational pirates (in strict decreasing order of seniority A, B, C, D and E) who found 100 gold coins. They must decide how to distribute them.
The pirate world's rules of distribution say that t... | https://en.wikipedia.org/wiki/Pirate_game |
In physics, Wien's displacement law states that the black-body radiation curve for different temperatures will peak at different wavelengths that are inversely proportional to the temperature. The shift of that peak is a direct consequence of the Planck radiation law, which describes the spectral brightness or intensit... | https://en.wikipedia.org/wiki/Wien%27s_displacement_law |
In category theory, a branch of mathematics, Beck's monadicity theorem gives a criterion that characterises monadic functors, introduced by in about 1964. It is often stated in dual form for comonads. It is sometimes called the Beck tripleability theorem because of the older term triple for a monad.
Beck's monadicity... | https://en.wikipedia.org/wiki/Beck%27s_monadicity_theorem |
In graph theory, a connected graph is said to be -vertex-connected (or -connected) if it has more than vertices and remains connected whenever fewer than vertices are removed.
The vertex-connectivity, or just connectivity, of a graph is the largest for which the graph is -vertex-connected.
## Definitions
A graph (o... | https://en.wikipedia.org/wiki/K-vertex-connected_graph |
In cryptography, key stretching techniques are used to make a possibly weak key, typically a password or passphrase, more secure against a brute-force attack by increasing the resources (time and possibly space) it takes to test each possible key. Passwords or passphrases created by humans are often short or predictab... | https://en.wikipedia.org/wiki/Key_stretching |
In Boolean algebra, Petrick's method (also known as Petrick function or branch-and-bound method) is a technique described by Stanley R. Petrick (1931–2006) in 1956 for determining all minimum sum-of-products solutions from a prime implicant chart. Petrick's method is very tedious for large charts, but it is easy to imp... | https://en.wikipedia.org/wiki/Petrick%27s_method |
In computer science, a monotone priority queue is a variant of the priority queue abstract data type in which the priorities of extracted items are required to form a monotonic sequence. That is, for a priority queue in which each successively extracted item is the one with the minimum priority (a min-heap), the minimu... | https://en.wikipedia.org/wiki/Monotone_priority_queue |
In mathematics, Minkowski's second theorem is a result in the geometry of numbers about the values taken by a norm on a lattice and the volume of its fundamental cell.
## Setting
Let be a closed convex centrally symmetric body of positive finite volume in -dimensional Euclidean space . The gauge or distanceCassels (1... | https://en.wikipedia.org/wiki/Minkowski%27s_second_theorem |
In mathematics, the soul theorem is a theorem of Riemannian geometry that largely reduces the study of complete manifolds of non-negative sectional curvature to that of the compact case. Jeff Cheeger and Detlef Gromoll proved the theorem in 1972 by generalizing a 1969 result of Gromoll and Wolfgang Meyer. The related s... | https://en.wikipedia.org/wiki/Soul_theorem |
The ultraviolet catastrophe, also called the Rayleigh–Jeans catastrophe, was the prediction of late 19th century and early 20th century classical physics that an ideal black body at thermal equilibrium would emit an unbounded quantity of energy as wavelength decreased into the ultraviolet range. The term "ultraviolet c... | https://en.wikipedia.org/wiki/Ultraviolet_catastrophe |
A marginal likelihood is a likelihood function that has been integrated over the parameter space. In Bayesian statistics, it represents the probability of generating the observed sample for all possible values of the parameters; it can be understood as the probability of the model itself and is therefore often referred... | https://en.wikipedia.org/wiki/Marginal_likelihood |
In computer vision and image processing, a feature is a piece of information about the content of an image; typically about whether a certain region of the image has certain properties. Features may be specific structures in the image such as points, edges or objects. Features may also be the result of a general neighb... | https://en.wikipedia.org/wiki/Feature_%28computer_vision%29 |
In probability theory and statistics, the skew normal distribution is a continuous probability distribution that generalises the normal distribution to allow for non-zero skewness.
## Definition
Let
$$
\phi(x)
$$
denote the standard normal probability density function
$$
\phi(x)=\frac{1}{\sqrt{2\pi}}e^{-\frac{x^2}{2}... | https://en.wikipedia.org/wiki/Skew_normal_distribution |
In the platonia dilemma introduced in Douglas Hofstadter's book Metamagical Themas, an eccentric trillionaire gathers 20 people together, and tells them that if one and only one of them sends them a telegram (reverse charges) by noon the next day, that person will receive a billion dollars. If they receive more than on... | https://en.wikipedia.org/wiki/Platonia_dilemma |
In applied mechanics, bending (also known as flexure) characterizes the behavior of a slender structural element subjected to an external load applied perpendicularly to a longitudinal axis of the element.
The structural element is assumed to be such that at least one of its dimensions is a small fraction, typically 1/... | https://en.wikipedia.org/wiki/Bending |
In mathematics, the lexicographic or lexicographical order (also known as lexical order, or dictionary order) is a generalization of the alphabetical order of the dictionaries to sequences of ordered symbols or, more generally, of elements of a totally ordered set.
There are several variants and generalizations of the ... | https://en.wikipedia.org/wiki/Lexicographic_order |
A heat wave or heatwave, sometimes described as extreme heat, is a period of abnormally hot weather generally considered to be at least five consecutive days. A heat wave is usually measured relative to the usual climate in the area and to normal temperatures for the season. The main difficulties with this broad defin... | https://en.wikipedia.org/wiki/Heat_wave |
A prefix code is a type of code system distinguished by its possession of the prefix property, which requires that there is no whole code word in the system that is a prefix (initial segment) of any other code word in the system. It is trivially true for fixed-length codes, so only a point of consideration for variable... | https://en.wikipedia.org/wiki/Prefix_code |
Basic research, also called pure research, fundamental research, basic science, or pure science, is a type of scientific research with the aim of improving scientific theories for better understanding and prediction of natural or other phenomena. In contrast, applied research uses scientific theories to develop techno... | https://en.wikipedia.org/wiki/Basic_research |
In information theory, the limiting density of discrete points is an adjustment to the formula of Claude Shannon for differential entropy.
It was formulated by Edwin Thompson Jaynes to address defects in the initial definition of differential entropy.
## Definition
Shannon originally wrote down the following formula fo... | https://en.wikipedia.org/wiki/Limiting_density_of_discrete_points |
In mathematics, a pullback is either of two different, but related processes: precomposition and fiber-product. Its dual is a pushforward.
## Precomposition
Precomposition with a function probably provides the most elementary notion of pullback: in simple terms, a function
$$
f
$$
of a variable
$$
y,
$$
where
$$
... | https://en.wikipedia.org/wiki/Pullback |
In mathematics, the Arens square is a topological space, named for Richard Friederich Arens. Its role is mainly to serve as a counterexample.
## Definition
The Arens square is the topological space
$$
(X,\tau),
$$
where
$$
X=((0,1)^2\cap\mathbb{Q}^2)\cup\{(0,0)\}\cup\{(1,0)\}\cup\{(1/2,r\sqrt{2})|\ r\in\mathbb{Q},\ 0... | https://en.wikipedia.org/wiki/Arens_square |
A material is brittle if, when subjected to stress, it fractures with little elastic deformation and without significant plastic deformation. Brittle materials absorb relatively little energy prior to fracture, even those of high strength. Breaking is often accompanied by a sharp snapping sound.
When used in materials ... | https://en.wikipedia.org/wiki/Brittleness |
In mathematics, a topological space X is uniformizable if there exists a uniform structure on X that induces the topology of X. Equivalently, X is uniformizable if and only if it is homeomorphic to a uniform space (equipped with the topology induced by the uniform structure).
Any (pseudo)metrizable space is uniformizab... | https://en.wikipedia.org/wiki/Uniformizable_space |
In mathematics, the diameter of a set of points in a metric space is the largest distance between points in the set. As an important special case, the diameter of a metric space is the largest distance between any two points in the space. This generalizes the diameter of a circle, the largest distance between two point... | https://en.wikipedia.org/wiki/Diameter_of_a_set |
A nozzle is a device designed to control the direction or characteristics of a fluid flow (specially to increase velocity) as it exits (or enters) an enclosed chamber or pipe.
A nozzle is often a pipe or tube of varying cross sectional area, and it can be used to direct or modify the flow of a fluid (liquid or gas). No... | https://en.wikipedia.org/wiki/Nozzle |
Density (volumetric mass density or specific mass) is the ratio of a substance's mass to its volume. The symbol most often used for density is ρ (the lower case Greek letter rho), although the Latin letter D can also be used:
$$
\rho = \frac{m}{V},
$$
where ρ is the density, m is the mass, and V is the volume. In some... | https://en.wikipedia.org/wiki/Density |
In information theory, linguistics, and computer science, the Levenshtein distance is a string metric for measuring the difference between two sequences. The Levenshtein distance between two words is the minimum number of single-character edits (insertions, deletions or substitutions) required to change one word into t... | https://en.wikipedia.org/wiki/Levenshtein_distance |
In mathematical optimization and decision theory, a loss function or cost function (sometimes also called an error function) is a function that maps an event or values of one or more variables onto a real number intuitively representing some "cost" associated with the event. An optimization problem seeks to minimize a ... | https://en.wikipedia.org/wiki/Loss_function |
In mathematics, the sign of a real number is its property of being either positive, negative, or 0. Depending on local conventions, zero may be considered as having its own unique sign, having no sign, or having both positive and negative sign. In some contexts, it makes sense to distinguish between a positive and a ne... | https://en.wikipedia.org/wiki/Sign_%28mathematics%29 |
In mathematics, a scattered space is a topological space X that contains no nonempty dense-in-itself subset.Engelking, p. 59 Equivalently, every nonempty subset A of X contains a point isolated in A.
A subset of a topological space is called a scattered set if it is a scattered space with the subspace topology.
## E... | https://en.wikipedia.org/wiki/Scattered_space |
A tropical cyclone is a rapidly rotating storm system with a low-pressure area, a closed low-level atmospheric circulation, strong winds, and a spiral arrangement of thunderstorms that produce heavy rain and squalls. Depending on its location and strength, a tropical cyclone is called a hurricane (), typhoon (), tropic... | https://en.wikipedia.org/wiki/Tropical_cyclone |
Pulse wave velocity (PWV) is the velocity at which the blood pressure pulse propagates through the circulatory system, usually an artery or a combined length of arteries. PWV is used clinically as a measure of arterial stiffness and can be readily measured non-invasively in humans, with measurement of carotid to femor... | https://en.wikipedia.org/wiki/Pulse_wave_velocity |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.