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Quantum graph Summary Metric_graph In mathematics and physics, a quantum graph is a linear, network-shaped structure of vertices connected on edges (i.e., a graph) in which each edge is given a length and where a differential (or pseudo-differential) equation is posed on each edge. An example would be a power network c... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Recurrent tensor Summary Recurrent_tensor In mathematics and physics, a recurrent tensor, with respect to a connection ∇ {\displaystyle \nabla } on a manifold M, is a tensor T for which there is a one-form ω on M such that ∇ T = ω ⊗ T . {\displaystyle \nabla T=\omega \otimes T.\,} | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Scalar fields Summary Scalar_field_(physics) In mathematics and physics, a scalar field is a function associating a single number to every point in a space – possibly physical space. The scalar may either be a pure mathematical number (dimensionless) or a scalar physical quantity (with units). In a physical context, sc... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Soliton wave Summary Soliton_wave In mathematics and physics, a soliton is a nonlinear, self-reinforcing, localized wave packet that is strongly stable, in that it preserves its shape while propagating freely, at constant velocity, and recovers it even after collisions with other such localized wave packets. Its remark... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Soliton wave Summary Soliton_wave The soliton phenomenon was first described in 1834 by John Scott Russell (1808–1882) who observed a solitary wave in the Union Canal in Scotland. He reproduced the phenomenon in a wave tank and named it the "Wave of Translation". The term soliton was coined by Zabusky and Kruskal to de... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tensor analysis Summary Tensor_analysis In mathematics and physics, a tensor field assigns a tensor to each point of a mathematical space (typically a Euclidean space or manifold). Tensor fields are used in differential geometry, algebraic geometry, general relativity, in the analysis of stress and strain in materials,... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Traveling plane wave Summary Traveling_plane_wave In mathematics and physics, a traveling plane wave is a special case of plane wave, namely a field whose evolution in time can be described as simple translation of its values at a constant wave speed c {\displaystyle c} , along a fixed direction of propagation n → {\di... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Traveling plane wave Summary Traveling_plane_wave This plane too travels along the direction of propagation n → {\displaystyle {\vec {n}}} with velocity c {\displaystyle c} ; and the value of the field is then the same, and constant in time, at every one of its points. The wave F {\displaystyle F} may be a scalar or ve... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Vector space Summary Linear_space In mathematics and physics, a vector space (also called a linear space) is a set whose elements, often called vectors, may be added together and multiplied ("scaled") by numbers called scalars. Scalars are often real numbers, but can be complex numbers or, more generally, elements of a... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Vector space Summary Linear_space The terms real vector space and complex vector space are often used to specify the nature of the scalars: real coordinate space or complex coordinate space. Vector spaces generalize Euclidean vectors, which allow modeling of physical quantities, such as forces and velocity, that have n... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Vector space Summary Linear_space This provides a concise and synthetic way for manipulating and studying systems of linear equations. Vector spaces are characterized by their dimension, which, roughly speaking, specifies the number of independent directions in the space. This means that, for two vector spaces over a g... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Vector space Summary Linear_space A vector space is finite-dimensional if its dimension is a natural number. Otherwise, it is infinite-dimensional, and its dimension is an infinite cardinal. Finite-dimensional vector spaces occur naturally in geometry and related areas. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Vector space Summary Linear_space Infinite-dimensional vector spaces occur in many areas of mathematics. For example, polynomial rings are countably infinite-dimensional vector spaces, and many function spaces have the cardinality of the continuum as a dimension. Many vector spaces that are considered in mathematics ar... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Acceleration vector Summary Acceleration_(differential_geometry) In mathematics and physics, acceleration is the rate of change of velocity of a curve with respect to a given linear connection. This operation provides us with a measure of the rate and direction of the "bend". | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Equipotential Summary Equipotential_surface In mathematics and physics, an equipotential or isopotential refers to a region in space where every point is at the same potential. This usually refers to a scalar potential (in that case it is a level set of the potential), although it can also be applied to vector potentia... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Equipotential Summary Equipotential_surface An equipotential region might be referred as being 'of equipotential' or simply be called 'an equipotential'. An equipotential region of a scalar potential in three-dimensional space is often an equipotential surface (or potential isosurface), but it can also be a three-dimen... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Equipotential Summary Equipotential_surface Electrical conductors offer an intuitive example. If a and b are any two points within or at the surface of a given conductor, and given there is no flow of charge being exchanged between the two points, then the potential difference is zero between the two points. Thus, an e... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Equipotential Summary Equipotential_surface Extending this definition, an isopotential is the locus of all points that are of the same potential. Gravity is perpendicular to the equipotential surfaces of the gravity potential, and in electrostatics and steady electric currents, the electric field (and hence the current... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Equipotential Summary Equipotential_surface In electrostatics, a conductor is a three-dimensional equipotential region. In the case of a hollow conductor (Faraday cage), the equipotential region includes the space inside. A ball will not be accelerated left or right by the force of gravity if it is resting on a flat, h... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
D'Alembert–Euler condition Summary D'Alembert–Euler_condition In mathematics and physics, especially the study of mechanics and fluid dynamics, the d'Alembert-Euler condition is a requirement that the streaklines of a flow are irrotational. Let x = x(X,t) be the coordinates of the point x into which X is carried at tim... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Asymptotic homogenization Summary Asymptotic_homogenization In mathematics and physics, homogenization is a method of studying partial differential equations with rapidly oscillating coefficients, such as ∇ ⋅ ( A ( x → ϵ ) ∇ u ϵ ) = f {\displaystyle \nabla \cdot \left(A\left({\frac {\vec {x}}{\epsilon }}\right)\nabla u... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Asymptotic homogenization Summary Asymptotic_homogenization Under this assumption, materials such as fluids, solids, etc. can be treated as homogeneous materials and associated with these materials are material properties such as shear modulus, elastic moduli, etc. Frequently, inhomogeneous materials (such as composite... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Asymptotic homogenization Summary Asymptotic_homogenization {\displaystyle \nabla _{y}\cdot \left(A({\vec {y}})\nabla w_{j}\right)=-\nabla _{y}\cdot \left(A({\vec {y}}){\vec {e}}_{j}\right).} This process of replacing an equation with a highly oscillatory coefficient with one with a homogeneous (uniform) coefficient is... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Asymptotic homogenization Summary Asymptotic_homogenization This subject is inextricably linked with the subject of micromechanics for this very reason. In homogenization one equation is replaced by another if u ϵ ≈ u {\displaystyle u_{\epsilon }\approx u} for small enough ϵ {\displaystyle \epsilon } , provided u ϵ → u... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Asymptotic homogenization Summary Asymptotic_homogenization The analogue of the differential element in the continuum concept (which contains enough atom, or molecular structure to be representative of that material), is known as the "Representative Volume Element" in homogenization and micromechanics. This element con... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Asymptotic homogenization Summary Asymptotic_homogenization Classical results of homogenization theory were obtained for media with periodic microstructure modeled by partial differential equations with periodic coefficients. These results were later generalized to spatially homogeneous random media modeled by differen... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Warped model Summary Warped_model In mathematics and physics, in particular differential geometry and general relativity, a warped geometry is a Riemannian or Lorentzian manifold whose metric tensor can be written in form d s 2 = g a b ( y ) d y a d y b + f ( y ) g i j ( x ) d x i d x j . {\displaystyle ds^{2}=g_{ab}(y... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Generalizations of Pauli matrices Summary Generalizations_of_Pauli_matrices In mathematics and physics, in particular quantum information, the term generalized Pauli matrices refers to families of matrices which generalize the (linear algebraic) properties of the Pauli matrices. Here, a few classes of such matrices are... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Euler's Equation Summary Euler's_equations In mathematics and physics, many topics are named in honor of Swiss mathematician Leonhard Euler (1707–1783), who made many important discoveries and innovations. Many of these items named after Euler include their own unique function, equation, formula, identity, number (sing... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Multiple-scale analysis Summary Multiple-scale_analysis In mathematics and physics, multiple-scale analysis (also called the method of multiple scales) comprises techniques used to construct uniformly valid approximations to the solutions of perturbation problems, both for small as well as large values of the independe... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Anti-de Sitter space Summary Anti-de_Sitter_space In mathematics and physics, n-dimensional anti-de Sitter space (AdSn) is a maximally symmetric Lorentzian manifold with constant negative scalar curvature. Anti-de Sitter space and de Sitter space are named after Willem de Sitter (1872–1934), professor of astronomy at L... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Anti-de Sitter space Summary Anti-de_Sitter_space Einstein's general theory of relativity places space and time on equal footing, so that one considers the geometry of a unified spacetime instead of considering space and time separately. The cases of spacetime of constant curvature are de Sitter space (positive), Minko... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Toda field theory Summary Toda_field_theory In mathematics and physics, specifically the study of field theory and partial differential equations, a Toda field theory, named after Morikazu Toda, is specified by a choice of Lie algebra and a specific Lagrangian. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Super Minkowski space Summary Super_Minkowski_space In mathematics and physics, super Minkowski space or Minkowski superspace is a supersymmetric extension of Minkowski space, sometimes used as the base manifold (or rather, supermanifold) for superfields. It is acted on by the super Poincaré algebra. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Kinetic Monte Carlo surface growth method Summary Kinetic_Monte_Carlo_surface_growth_method In mathematics and physics, surface growth refers to models used in the dynamical study of the growth of a surface, usually by means of a stochastic differential equation of a field. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Artin billiard Summary Artin_billiard In mathematics and physics, the Artin billiard is a type of a dynamical billiard first studied by Emil Artin in 1924. It describes the geodesic motion of a free particle on the non-compact Riemann surface H / Γ , {\displaystyle \mathbb {H} /\Gamma ,} where H {\displaystyle \mathbb ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Artin billiard Summary Artin_billiard As such, it is an example of an Anosov flow. Artin's paper used symbolic dynamics for analysis of the system. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Artin billiard Summary Artin_billiard The quantum mechanical version of Artin's billiard is also exactly solvable. The eigenvalue spectrum consists of a bound state and a continuous spectrum above the energy E = 1 / 4 {\displaystyle E=1/4} . The wave functions are given by Bessel functions. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Christoffel symbol Summary Connection_coefficient In mathematics and physics, the Christoffel symbols are an array of numbers describing a metric connection. The metric connection is a specialization of the affine connection to surfaces or other manifolds endowed with a metric, allowing distances to be measured on that... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Christoffel symbol Summary Connection_coefficient Abstractly, one would say that the manifold has an associated (orthonormal) frame bundle, with each "frame" being a possible choice of a coordinate frame. An invariant metric implies that the structure group of the frame bundle is the orthogonal group O(p, q). As a resu... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Christoffel symbol Summary Connection_coefficient The Christoffel symbols provide a concrete representation of the connection of (pseudo-)Riemannian geometry in terms of coordinates on the manifold. Additional concepts, such as parallel transport, geodesics, etc. can then be expressed in terms of Christoffel symbols. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Christoffel symbol Summary Connection_coefficient In general, there are an infinite number of metric connections for a given metric tensor; however, there is a unique connection that is free of torsion, the Levi-Civita connection. It is common in physics and general relativity to work almost exclusively with the Levi-C... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Christoffel symbol Summary Connection_coefficient At each point of the underlying n-dimensional manifold, for any local coordinate system around that point, the Christoffel symbols are denoted Γijk for i, j, k = 1, 2, ..., n. Each entry of this n × n × n array is a real number. Under linear coordinate transformations o... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Christoffel symbol Summary Connection_coefficient Christoffel symbols are used for performing practical calculations. For example, the Riemann curvature tensor can be expressed entirely in terms of the Christoffel symbols and their first partial derivatives. In general relativity, the connection plays the role of the g... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Kadomtsev–Petviashvili equation Summary Kadomtsev–Petviashvili_equation In mathematics and physics, the Kadomtsev–Petviashvili equation (often abbreviated as KP equation) is a partial differential equation to describe nonlinear wave motion. Named after Boris Borisovich Kadomtsev and Vladimir Iosifovich Petviashvili, th... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Kadomtsev–Petviashvili equation Summary Kadomtsev–Petviashvili_equation Like the KdV equation, the KP equation is completely integrable. It can also be solved using the inverse scattering transform much like the nonlinear Schrödinger equation.In 2002, the regularized version of the KP equation, naturally referred to as... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Magnus expansion Summary Magnus_expansion In mathematics and physics, the Magnus expansion, named after Wilhelm Magnus (1907–1990), provides an exponential representation of the solution of a first-order homogeneous linear differential equation for a linear operator. In particular, it furnishes the fundamental matrix o... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Poincaré recurrence theorem Summary Recurrence_time In mathematics and physics, the Poincaré recurrence theorem states that certain dynamical systems will, after a sufficiently long but finite time, return to a state arbitrarily close to (for continuous state systems), or exactly the same as (for discrete state systems... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Poincaré recurrence theorem Summary Recurrence_time The theorem is commonly discussed in the context of ergodic theory, dynamical systems and statistical mechanics. Systems to which the Poincaré recurrence theorem applies are called conservative systems. The theorem is named after Henri Poincaré, who discussed it in 18... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Geometric center Summary Centroid In mathematics and physics, the centroid, also known as geometric center or center of figure, of a plane figure or solid figure is the arithmetic mean position of all the points in the surface of the figure. The same definition extends to any object in n-dimensional Euclidean space.In ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Diamagnetic inequality Summary Diamagnetic_inequality In mathematics and physics, the diamagnetic inequality relates the Sobolev norm of the absolute value of a section of a line bundle to its covariant derivative. The diamagnetic inequality has an important physical interpretation, that a charged particle in a magneti... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Heat diffusion Summary Heat_equation In mathematics and physics, the heat equation is a certain partial differential equation. Solutions of the heat equation are sometimes known as caloric functions. The theory of the heat equation was first developed by Joseph Fourier in 1822 for the purpose of modeling how a quantity... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Heat diffusion Summary Heat_equation The heat equation can also be considered on Riemannian manifolds, leading to many geometric applications. Following work of Subbaramiah Minakshisundaram and Åke Pleijel, the heat equation is closely related with spectral geometry. A seminal nonlinear variant of the heat equation was... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Heat diffusion Summary Heat_equation Certain solutions of the heat equation known as heat kernels provide subtle information about the region on which they are defined, as exemplified through their application to the Atiyah–Singer index theorem.The heat equation, along with variants thereof, is also important in many f... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Heat diffusion Summary Heat_equation In image analysis, the heat equation is sometimes used to resolve pixelation and to identify edges. Following Robert Richtmyer and John von Neumann's introduction of "artificial viscosity" methods, solutions of heat equations have been useful in the mathematical formulation of hydro... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Inverse scattering Summary Inverse_scattering In mathematics and physics, the inverse scattering problem is the problem of determining characteristics of an object, based on data of how it scatters incoming radiation or particles. It is the inverse problem to the direct scattering problem, which is to determine how rad... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Inverse scattering Summary Inverse_scattering The nonlinear Schrödinger equation, the Korteweg–de Vries equation and the KP equation are examples of soliton equations. In one space dimension the inverse scattering problem is equivalent to a Riemann-Hilbert problem. Since its early statement for radiolocation, many appl... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Orientation entanglement Summary Orientation_entanglement In mathematics and physics, the notion of orientation entanglement is sometimes used to develop intuition relating to the geometry of spinors or alternatively as a concrete realization of the failure of the special orthogonal groups to be simply connected. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Plate trick Summary Plate_trick In mathematics and physics, the plate trick, also known as Dirac's string trick, the belt trick, or the Balinese cup trick, is any of several demonstrations of the idea that rotating an object with strings attached to it by 360 degrees does not return the system to its original state, wh... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Right hand grip rule Summary Right-hand_screw_rule In mathematics and physics, the right-hand rule is a common mnemonic for understanding the orientation of axes in three-dimensional space. It is also a convenient method for quickly finding the direction of the cross product of two vectors. Rather than a mathematical f... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Right hand grip rule Summary Right-hand_screw_rule One can see this by holding one's hands outward and together, palms up, with the thumbs out-stretched to the right and left, and the fingers making a curling motion from straight outward to pointing upward. If the curling motion of the fingers represents a movement fro... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Right hand grip rule Summary Right-hand_screw_rule The rule can be used to find the direction of the magnetic field, rotation, spirals, electromagnetic fields, mirror images, and enantiomers in mathematics and chemistry. The sequence is often: index finger along the first vector, then middle finger along the second, th... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Spectral asymmetry Summary Spectral_asymmetry In mathematics and physics, the spectral asymmetry is the asymmetry in the distribution of the spectrum of eigenvalues of an operator. In mathematics, the spectral asymmetry arises in the study of elliptic operators on compact manifolds, and is given a deep meaning by the A... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Spectral asymmetry Summary Spectral_asymmetry For example, the vacuum expectation value of the baryon number is given by the spectral asymmetry of the Hamiltonian operator. The spectral asymmetry of the confined quark fields is an important property of the chiral bag model. For fermions, it is known as the Witten index... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Generator (mathematics) Summary Generator_(mathematics) In mathematics and physics, the term generator or generating set may refer to any of a number of related concepts. The underlying concept in each case is that of a smaller set of objects, together with a set of operations that can be applied to it, that result in ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Vector notation Summary Vector_notation In mathematics and physics, vector notation is a commonly used notation for representing vectors, which may be Euclidean vectors, or more generally, members of a vector space. For representing a vector, the common typographic convention is lower case, upright boldface type, as in... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Quota rule Summary Quota_rule In mathematics and political science, the quota rule describes a desired property of a proportional apportionment or election method. It states that the number of seats that should be allocated to a given party should be between the upper or lower roundings (called upper and lower quotas) ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Skorokhod's embedding theorem Summary Skorokhod's_embedding_theorem In mathematics and probability theory, Skorokhod's embedding theorem is either or both of two theorems that allow one to regard any suitable collection of random variables as a Wiener process (Brownian motion) evaluated at a collection of stopping time... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Continuum percolation theory Summary Continuum_percolation_theory In mathematics and probability theory, continuum percolation theory is a branch of mathematics that extends discrete percolation theory to continuous space (often Euclidean space ℝn). More specifically, the underlying points of discrete percolation form ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Continuum percolation theory Summary Continuum_percolation_theory As in discrete percolation, a common research focus of continuum percolation is studying the conditions of occurrence for infinite or giant components. Other shared concepts and analysis techniques exist in these two types of percolation theory as well a... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Borell–TIS inequality Summary Borell–TIS_inequality In mathematics and probability, the Borell–TIS inequality is a result bounding the probability of a deviation of the uniform norm of a centered Gaussian stochastic process above its expected value. The result is named for Christer Borell and its independent discoverer... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Harmonic spinor Summary Harmonic_spinor In mathematics and quantum mechanics, a Dirac operator is a differential operator that is a formal square root, or half-iterate, of a second-order operator such as a Laplacian. The original case which concerned Paul Dirac was to factorise formally an operator for Minkowski space,... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Symbols of grouping Summary Symbols_of_grouping In mathematics and related subjects, understanding a mathematical expression depends on an understanding of symbols of grouping, such as parentheses (), brackets , and braces {}. These same symbols are also used in ways where they are not symbols of grouping. For example,... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Symbols of grouping Summary Symbols_of_grouping For example, to indicate the product of binomials, parentheses are usually used, thus: ( 2 x + 3 ) ( 3 x + 4 ) {\displaystyle (2x+3)(3x+4)} . But if one of the binomials itself contains parentheses, as in ( 2 ( a + b ) + 3 ) {\displaystyle (2(a+b)+3)} one or more pairs of... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Symbols of grouping Summary Symbols_of_grouping The usage of the word "parentheses" varies from country to country. In the United States, the word parentheses (singular "parenthesis") is used for the curved symbol of grouping, but in many other countries the curved symbol of grouping is called a "bracket" and the symbo... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Symbols of grouping Summary Symbols_of_grouping If two of these symbols are used, one on the left and the mirror image of it on the right, it almost always indicates a set, as in { a , b , c } {\displaystyle \{a,b,c\}} , the set containing three members, a {\displaystyle a} , b {\displaystyle b} , and c {\displaystyle ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Symbols of grouping Summary Symbols_of_grouping One is the bar above an expression, as in the square root sign in which the bar is a symbol of grouping. For example √p+q is the square root of the sum. The bar is also a symbol of grouping in repeated decimal digits. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Symbols of grouping Summary Symbols_of_grouping A decimal point followed by one or more digits with a bar over them, for example 0.123, represents the repeating decimal 0.123123123... .A superscript is understood to be grouped as long as it continues in the form of a superscript. For example if an x has a superscript o... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Nonlinear differential equation Summary Nonlinear_equation In mathematics and science, a nonlinear system (or a non-linear system) is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and ma... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Nonlinear differential equation Summary Nonlinear_equation In other words, in a nonlinear system of equations, the equation(s) to be solved cannot be written as a linear combination of the unknown variables or functions that appear in them. Systems can be defined as nonlinear, regardless of whether known linear functio... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Nonlinear differential equation Summary Nonlinear_equation As nonlinear dynamical equations are difficult to solve, nonlinear systems are commonly approximated by linear equations (linearization). This works well up to some accuracy and some range for the input values, but some interesting phenomena such as solitons, c... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Nonlinear differential equation Summary Nonlinear_equation Although such chaotic behavior may resemble random behavior, it is in fact not random. For example, some aspects of the weather are seen to be chaotic, where simple changes in one part of the system produce complex effects throughout. This nonlinearity is one o... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hereditarily finite set Summary Hereditarily_finite_set In mathematics and set theory, hereditarily finite sets are defined as finite sets whose elements are all hereditarily finite sets. In other words, the set itself is finite, and all of its elements are finite sets, recursively all the way down to the empty set. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Analytic representation Summary Analytic_representation In mathematics and signal processing, an analytic signal is a complex-valued function that has no negative frequency components. The real and imaginary parts of an analytic signal are real-valued functions related to each other by the Hilbert transform. The analyt... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Analytic representation Summary Analytic_representation The basic idea is that the negative frequency components of the Fourier transform (or spectrum) of a real-valued function are superfluous, due to the Hermitian symmetry of such a spectrum. These negative frequency components can be discarded with no loss of inform... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hilbert Transform Summary Hilbert_Transform In mathematics and signal processing, the Hilbert transform is a specific singular integral that takes a function, u(t) of a real variable and produces another function of a real variable H(u)(t). The Hilbert transform is given by the Cauchy principal value of the convolution... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Z-transform Summary Z-transform In mathematics and signal processing, the Z-transform converts a discrete-time signal, which is a sequence of real or complex numbers, into a complex frequency-domain (the z-domain or z-plane) representation.It can be considered as a discrete-time equivalent of the Laplace transform (the... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Z-transform Summary Z-transform The s-domain's left half-plane maps to the area inside the z-domain's unit circle, while the s-domain's right half-plane maps to the area outside of the z-domain's unit circle. One of the means of designing digital filters is to take analog designs, subject them to a bilinear transform w... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Advanced Z-transform Summary Advanced_Z-transform In mathematics and signal processing, the advanced z-transform is an extension of the z-transform, to incorporate ideal delays that are not multiples of the sampling time. It takes the form F ( z , m ) = ∑ k = 0 ∞ f ( k T + m ) z − k {\displaystyle F(z,m)=\sum _{k=0}^{\... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Constant-Q transform Summary Variable-Q_transform In mathematics and signal processing, the constant-Q transform and variable-Q transform, simply known as CQT and VQT, transforms a data series to the frequency domain. It is related to the Fourier transform and very closely related to the complex Morlet wavelet transfor... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Collaboration graph Summary Collaboration_graph In mathematics and social science, a collaboration graph is a graph modeling some social network where the vertices represent participants of that network (usually individual people) and where two distinct participants are joined by an edge whenever there is a collaborati... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Constant-energy surface Summary Gamma_point In mathematics and solid state physics, the first Brillouin zone (named after Léon Brillouin) is a uniquely defined primitive cell in reciprocal space. In the same way the Bravais lattice is divided up into Wigner–Seitz cells in the real lattice, the reciprocal lattice is bro... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Constant-energy surface Summary Gamma_point The first Brillouin zone is the locus of points in reciprocal space that are closer to the origin of the reciprocal lattice than they are to any other reciprocal lattice points (see the derivation of the Wigner–Seitz cell). Another definition is as the set of points in k-spac... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Constant-energy surface Summary Gamma_point There are also second, third, etc., Brillouin zones, corresponding to a sequence of disjoint regions (all with the same volume) at increasing distances from the origin, but these are used less frequently. As a result, the first Brillouin zone is often called simply the Brillo... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Constant-energy surface Summary Gamma_point A related concept is that of the irreducible Brillouin zone, which is the first Brillouin zone reduced by all of the symmetries in the point group of the lattice (point group of the crystal). The concept of a Brillouin zone was developed by Léon Brillouin (1889–1969), a Frenc... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Dimension of an algebraic variety Summary Dimension_of_an_algebraic_variety In mathematics and specifically in algebraic geometry, the dimension of an algebraic variety may be defined in various equivalent ways. Some of these definitions are of geometric nature, while some other are purely algebraic and rely on commuta... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Formal space Summary Rational_homotopy_theory In mathematics and specifically in topology, rational homotopy theory is a simplified version of homotopy theory for topological spaces, in which all torsion in the homotopy groups is ignored. It was founded by Dennis Sullivan (1977) and Daniel Quillen (1969). This simplifi... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Formal space Summary Rational_homotopy_theory A geometric application was the theorem of Sullivan and Micheline Vigué-Poirrier (1976): every simply connected closed Riemannian manifold X whose rational cohomology ring is not generated by one element has infinitely many geometrically distinct closed geodesics. The proof... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Skorokhod's representation theorem Summary Skorokhod's_representation_theorem In mathematics and statistics, Skorokhod's representation theorem is a result that shows that a weakly convergent sequence of probability measures whose limit measure is sufficiently well-behaved can be represented as the distribution/law of ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Mean of circular quantities Summary Circular_mean In mathematics and statistics, a circular mean or angular mean is a mean designed for angles and similar cyclic quantities, such as times of day, and fractional parts of real numbers. This is necessary since most of the usual means may not be appropriate on angle-like q... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
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