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Logarithm function Summary Logarithmus The natural logarithm has the number e ≈ 2.718 as its base; its use is widespread in mathematics and physics, because of its very simple derivative. The binary logarithm uses base 2 and is frequently used in computer science. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Logarithm function Summary Logarithmus Logarithms were introduced by John Napier in 1614 as a means of simplifying calculations. They were rapidly adopted by navigators, scientists, engineers, surveyors and others to perform high-accuracy computations more easily. Using logarithm tables, tedious multi-digit multiplicat... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Logarithm function Summary Logarithmus This is possible because the logarithm of a product is the sum of the logarithms of the factors: provided that b, x and y are all positive and b ≠ 1. The slide rule, also based on logarithms, allows quick calculations without tables, but at lower precision. The present-day notion ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Logarithm function Summary Logarithmus For example, the decibel (dB) is a unit used to express ratio as logarithms, mostly for signal power and amplitude (of which sound pressure is a common example). In chemistry, pH is a logarithmic measure for the acidity of an aqueous solution. Logarithms are commonplace in scienti... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Logarithm function Summary Logarithmus They help to describe frequency ratios of musical intervals, appear in formulas counting prime numbers or approximating factorials, inform some models in psychophysics, and can aid in forensic accounting. The concept of logarithm as the inverse of exponentiation extends to other m... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Offset logarithmic integral Summary Offset_logarithmic_integral In mathematics, the logarithmic integral function or integral logarithm li(x) is a special function. It is relevant in problems of physics and has number theoretic significance. In particular, according to the prime number theorem, it is a very good approx... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Logarithmic average Summary Logarithmic_average In mathematics, the logarithmic mean is a function of two non-negative numbers which is equal to their difference divided by the logarithm of their quotient. This calculation is applicable in engineering problems involving heat and mass transfer. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Logarithmic norm Summary Logarithmic_norm In mathematics, the logarithmic norm is a real-valued functional on operators, and is derived from either an inner product, a vector norm, or its induced operator norm. The logarithmic norm was independently introduced by Germund Dahlquist and Sergei Lozinskiĭ in 1958, for squa... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Longest element of a Coxeter group Summary Longest_element_of_a_Coxeter_group In mathematics, the longest element of a Coxeter group is the unique element of maximal length in a finite Coxeter group with respect to the chosen generating set consisting of simple reflections. It is often denoted by w0. See (Humphreys 199... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Look-and-say sequence Summary Audioactive_decay In mathematics, the look-and-say sequence is the sequence of integers beginning as follows: 1, 11, 21, 1211, 111221, 312211, 13112221, 1113213211, 31131211131221, ... (sequence A005150 in the OEIS).To generate a member of the sequence from the previous member, read off th... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Look-and-say sequence Summary Audioactive_decay 1211 is read off as "one 1, one 2, two 1s" or 111221. 111221 is read off as "three 1s, two 2s, one 1" or 312211.The look-and-say sequence was analyzed by John Conway after he was introduced to it by one of his students at a party.The idea of the look-and-say sequence is s... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Look-and-say sequence Summary Audioactive_decay If started with any digit d from 0 to 9 then d will remain indefinitely as the last digit of the sequence. For any d other than 1, the sequence starts as follows: d, 1d, 111d, 311d, 13211d, 111312211d, 31131122211d, …Ilan Vardi has called this sequence, starting with d = ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Lower convex envelope Summary Lower_convex_envelope In mathematics, the lower convex envelope f ˘ {\displaystyle {\breve {f}}} of a function f {\displaystyle f} defined on an interval {\displaystyle } is defined at each point of the interval as the supremum of all convex functions that lie under that function, i.e. f ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Pointwise maximum Summary Lower_envelope In mathematics, the lower envelope or pointwise minimum of a finite set of functions is the pointwise minimum of the functions, the function whose value at every point is the minimum of the values of the functions in the given set. The concept of a lower envelope can also be ext... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Pointwise maximum Summary Lower_envelope For functions of a single real variable whose graphs have a bounded number of intersection points, the complexity of the lower or upper envelope can be bounded using Davenport–Schinzel sequences, and these envelopes can be computed efficiently by a divide-and-conquer algorithm t... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Pointwise maximum Summary Lower_envelope The upper and lower envelopes of Lipschitz functions preserve the property of being Lipschitz. However, the lower and upper envelope operations do not necessarily preserve the property of being a continuous function. == References == | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Sorgenfrey line Summary Sorgenfrey_line In mathematics, the lower limit topology or right half-open interval topology is a topology defined on the set R {\displaystyle \mathbb {R} } of real numbers; it is different from the standard topology on R {\displaystyle \mathbb {R} } (generated by the open intervals) and has a ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Sorgenfrey line Summary Sorgenfrey_line Like the Cantor set and the long line, the Sorgenfrey line often serves as a useful counterexample to many otherwise plausible-sounding conjectures in general topology. The product of R l {\displaystyle \mathbb {R} _{l}} with itself is also a useful counterexample, known as the S... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Common denominator Summary Common_denominator In mathematics, the lowest common denominator or least common denominator (abbreviated LCD) is the lowest common multiple of the denominators of a set of fractions. It simplifies adding, subtracting, and comparing fractions. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Magnitude (mathematics) Summary Magnitude_(mathematics) In mathematics, the magnitude or size of a mathematical object is a property which determines whether the object is larger or smaller than other objects of the same kind. More formally, an object's magnitude is the displayed result of an ordering (or ranking) of t... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Iwasawa main conjecture Summary Main_conjecture_of_Iwasawa_theory In mathematics, the main conjecture of Iwasawa theory is a deep relationship between p-adic L-functions and ideal class groups of cyclotomic fields, proved by Kenkichi Iwasawa for primes satisfying the Kummer–Vandiver conjecture and proved for all primes... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Representation theory of SL2(R) Summary Representation_theory_of_SL2(R) In mathematics, the main results concerning irreducible unitary representations of the Lie group SL(2,R) are due to Gelfand and Naimark (1946), V. Bargmann (1947), and Harish-Chandra (1952). | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Mandelbox Summary Mandelbox In mathematics, the mandelbox is a fractal with a boxlike shape found by Tom Lowe in 2010. It is defined in a similar way to the famous Mandelbrot set as the values of a parameter such that the origin does not escape to infinity under iteration of certain geometrical transformations. The man... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Map segmentation Summary Map_segmentation In mathematics, the map segmentation problem is a kind of optimization problem. It involves a certain geographic region that has to be partitioned into smaller sub-regions in order to achieve a certain goal. Typical optimization objectives include: Minimizing the workload of a ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Mapping torus Summary Mapping_torus In mathematics, the mapping torus in topology of a homeomorphism f of some topological space X to itself is a particular geometric construction with f. Take the cartesian product of X with a closed interval I, and glue the boundary components together by the static homeomorphism: M f... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Master stability function Summary Master_stability_function In mathematics, the master stability function is a tool used to analyse the stability of the synchronous state in a dynamical system consisting of many identical oscillators which are coupled together, such as the Kuramoto model. The setting is as follows. Con... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Master stability function Summary Master_stability_function A synchronous state of the system of oscillators is where all the oscillators are in the same state. The coupling is defined by a coupling strength σ {\displaystyle \sigma } , a matrix A i j {\displaystyle A_{ij}} which describes how the oscillators are couple... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Master stability function Summary Master_stability_function {\displaystyle {\dot {x}}_{i}=f(x_{i})+\sigma \sum _{j=1}^{N}A_{ij}g(x_{j}).} It is assumed that the row sums ∑ j A i j {\displaystyle \sum _{j}A_{ij}} vanish so that the manifold of synchronous states is neutrally stable. The master stability function is now ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Matching distance Summary Matching_distance In mathematics, the matching distance is a metric on the space of size functions. The core of the definition of matching distance is the observation that the information contained in a size function can be combinatorially stored in a formal series of lines and points of the p... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Matching distance Summary Matching_distance ℓ 2 {\displaystyle \ell _{2}} ) counted with their multiplicities, augmented by adding a countable infinity of points of the diagonal { ( x , y ) ∈ R 2: x = y } {\displaystyle \{(x,y)\in \mathbb {R} ^{2}:x=y\}} . The matching distance between ℓ 1 {\displaystyle \ell _{1}} and... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Matching distance Summary Matching_distance {\displaystyle \delta \left((x,y),(x',y')\right)=\min \left\{\max\{|x-x'|,|y-y'|\},\max \left\{{\frac {y-x}{2}},{\frac {y'-x'}{2}}\right\}\right\}.} Roughly speaking, the matching distance d match {\displaystyle d_{\text{match}}} between two size functions is the minimum, ove... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Lie theory Summary Lie_theory In mathematics, the mathematician Sophus Lie ( LEE) initiated lines of study involving integration of differential equations, transformation groups, and contact of spheres that have come to be called Lie theory. For instance, the latter subject is Lie sphere geometry. This article addresse... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Lie theory Summary Lie_theory The subject is part of differential geometry since Lie groups are differentiable manifolds. Lie groups evolve out of the identity (1) and the tangent vectors to one-parameter subgroups generate the Lie algebra. The structure of a Lie group is implicit in its algebra, and the structure of t... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Quincunx matrix Summary Quincunx_matrix In mathematics, the matrix ( 1 − 1 1 1 ) {\displaystyle {\begin{pmatrix}1&-1\\1&1\end{pmatrix}}} is sometimes called the quincunx matrix. It is a 2×2 Hadamard matrix, and its rows form the basis of a diagonal square lattice consisting of the integer points whose coordinates both ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Exponential of a matrix Summary Exponential_of_a_matrix In mathematics, the matrix exponential is a matrix function on square matrices analogous to the ordinary exponential function. It is used to solve systems of linear differential equations. In the theory of Lie groups, the matrix exponential gives the exponential m... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Exponential of a matrix Summary Exponential_of_a_matrix Let X be an n×n real or complex matrix. The exponential of X, denoted by eX or exp(X), is the n×n matrix given by the power series where X 0 {\displaystyle X^{0}} is defined to be the identity matrix I {\displaystyle I} with the same dimensions as X {\displaystyle... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Matrix representation of conic sections Summary Matrix_representation_of_conic_sections In mathematics, the matrix representation of conic sections permits the tools of linear algebra to be used in the study of conic sections. It provides easy ways to calculate a conic section's axis, vertices, tangents and the pole an... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Matrix representation of conic sections Summary Matrix_representation_of_conic_sections This equation can be written in matrix notation, in terms of a symmetric matrix to simplify some subsequent formulae, as The sum of the first three terms of this equation, namely is the quadratic form associated with the equation, a... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Matrix sign function Summary Matrix_sign_function In mathematics, the matrix sign function is a matrix function on square matrices analogous to the complex sign function.It was introduced by J.D. Roberts in 1971 as a tool for model reduction and for solving Lyapunov and Algebraic Riccatia equation in a technical report... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Maximum modulus principle Summary Maximum-modulus_theorem In mathematics, the maximum modulus principle in complex analysis states that if f {\displaystyle f} is a holomorphic function, then the modulus | f | {\displaystyle |f|} cannot exhibit a strict local maximum that is properly within the domain of f {\displaystyl... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Maximum-minimums identity Summary Maximum-minimums_identity In mathematics, the maximum-minimums identity is a relation between the maximum element of a set S of n numbers and the minima of the 2n − 1 non-empty subsets of S. Let S = {x1, x2, ..., xn}. The identity states that max { x 1 , x 2 , … , x n } = ∑ i = 1 n x i... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Max–min inequality Summary Max–min_inequality In mathematics, the max–min inequality is as follows: For any function f: Z × W → R , {\displaystyle \ f:Z\times W\to \mathbb {R} \ ,} sup z ∈ Z inf w ∈ W f ( z , w ) ≤ inf w ∈ W sup z ∈ Z f ( z , w ) . {\displaystyle \sup _{z\in Z}\inf _{w\in W}f(z,w)\leq \inf _{w\in W}\su... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Mean dimension Summary Mean_dimension In mathematics, the mean (topological) dimension of a topological dynamical system is a non-negative extended real number that is a measure of the complexity of the system. Mean dimension was first introduced in 1999 by Gromov. Shortly after it was developed and studied systematica... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Mean dimension Summary Mean_dimension For various topological dynamical systems with infinite topological entropy, the mean dimension can be calculated or at least bounded from below and above. This allows mean dimension to be used to distinguish between systems with infinite topological entropy. Mean dimension is also... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Mean curvature Summary Mean_curvature In mathematics, the mean curvature H {\displaystyle H} of a surface S {\displaystyle S} is an extrinsic measure of curvature that comes from differential geometry and that locally describes the curvature of an embedded surface in some ambient space such as Euclidean space. The conc... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Mean value problem Summary Mean_value_problem In mathematics, the mean value problem was posed by Stephen Smale in 1981. This problem is still open in full generality. The problem asks: For a given complex polynomial f {\displaystyle f} of degree d ≥ 2 {\displaystyle d\geq 2} A and a complex number z {\displaystyle z} ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Mean-value theorem Summary Mean_value_theorems_for_definite_integrals In mathematics, the mean value theorem (or Lagrange theorem) states, roughly, that for a given planar arc between two endpoints, there is at least one point at which the tangent to the arc is parallel to the secant through its endpoints. It is one of... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Measurable Riemann mapping theorem Summary Measurable_Riemann_mapping_theorem In mathematics, the measurable Riemann mapping theorem is a theorem proved in 1960 by Lars Ahlfors and Lipman Bers in complex analysis and geometric function theory. Contrary to its name, it is not a direct generalization of the Riemann mappi... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Mediant (mathematics) Summary Mediant_(mathematics) In mathematics, the mediant of two fractions, generally made up of four positive integers a c {\displaystyle {\frac {a}{c}}\quad } and b d {\displaystyle \quad {\frac {b}{d}}\quad } is defined as a + b c + d . {\displaystyle \quad {\frac {a+b}{c+d}}.} That is to say, ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Mediant (mathematics) Summary Mediant_(mathematics) It is sometimes called the freshman sum, as it is a common mistake in the early stages of learning about addition of fractions. Technically, this is a binary operation on valid fractions (nonzero denominator), considered as ordered pairs of appropriate integers, a pri... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Mediant (mathematics) Summary Mediant_(mathematics) However, if the fraction 1/1 is replaced by the fraction 2/2, which is an equivalent fraction denoting the same rational number 1, the mediant of the fractions 2/2 and 1/2 is 3/4. For a stronger connection to rational numbers the fractions may be required to be reduce... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Fuzzy membership Summary Membership_function_(mathematics) In mathematics, the membership function of a fuzzy set is a generalization of the indicator function for classical sets. In fuzzy logic, it represents the degree of truth as an extension of valuation. Degrees of truth are often confused with probabilities, alth... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Metaplectic group Summary Metaplectic_group In mathematics, the metaplectic group Mp2n is a double cover of the symplectic group Sp2n. It can be defined over either real or p-adic numbers. The construction covers more generally the case of an arbitrary local or finite field, and even the ring of adeles. The metaplectic... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Indicial equation Summary Indicial_equation In mathematics, the method of Frobenius, named after Ferdinand Georg Frobenius, is a way to find an infinite series solution for a second-order ordinary differential equation of the form with u ′ ≡ d u d z {\textstyle u'\equiv {\frac {du}{dz}}} and u ″ ≡ d 2 u d z 2 {\textsty... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Charpit method Summary Method_of_characteristics In mathematics, the method of characteristics is a technique for solving partial differential equations. Typically, it applies to first-order equations, although more generally the method of characteristics is valid for any hyperbolic partial differential equation. The m... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Clearing denominators Summary Clearing_fractions In mathematics, the method of clearing denominators, also called clearing fractions, is a technique for simplifying an equation equating two expressions that each are a sum of rational expressions – which includes simple fractions. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hadamard's method of descent Summary Method_of_descent In mathematics, the method of descent is the term coined by the French mathematician Jacques Hadamard as a method for solving a partial differential equation in several real or complex variables, by regarding it as the specialisation of an equation in more variable... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Method of dominant balance Summary Method_of_dominant_balance In mathematics, the method of dominant balance is used to determine the asymptotic behavior of solutions to an ordinary differential equation without fully solving the equation. The process is iterative, in that the result obtained by performing the method o... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Method of dominant balance Summary Method_of_dominant_balance Drop these terms and solve the resulting simpler ODE. Check that the solution is consistent with step 2. If this is the case, then one has the controlling factor of the asymptotic behavior; otherwise, one needs try dropping different terms in step 2, instead... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Equating coefficients Summary Equating_the_coefficients In mathematics, the method of equating the coefficients is a way of solving a functional equation of two expressions such as polynomials for a number of unknown parameters. It relies on the fact that two expressions are identical precisely when corresponding coeff... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Method of matched asymptotic expansions Summary Method_of_matched_asymptotic_expansions In mathematics, the method of matched asymptotic expansions is a common approach to finding an accurate approximation to the solution to an equation, or system of equations. It is particularly used when solving singularly perturbed ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Saddle-point method Summary Saddle-point_method In mathematics, the method of steepest descent or saddle-point method is an extension of Laplace's method for approximating an integral, where one deforms a contour integral in the complex plane to pass near a stationary point (saddle point), in roughly the direction of s... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Saddle-point method Summary Saddle-point_method One version of the method of steepest descent deforms the contour of integration C into a new path integration C′ so that the following conditions hold: C′ passes through one or more zeros of the derivative g′(z), the imaginary part of g(z) is constant on C′.The method of... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Method of undetermined coefficients Summary Method_of_undetermined_coefficients In mathematics, the method of undetermined coefficients is an approach to finding a particular solution to certain nonhomogeneous ordinary differential equations and recurrence relations. It is closely related to the annihilator method, but... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Metric derivative Summary Metric_derivative In mathematics, the metric derivative is a notion of derivative appropriate to parametrized paths in metric spaces. It generalizes the notion of "speed" or "absolute velocity" to spaces which have a notion of distance (i.e. metric spaces) but not direction (such as vector spa... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Mex (mathematics) Summary Mex_(mathematics) In mathematics, the mex ("minimum excluded value") of a subset of a well-ordered set is the smallest value from the whole set that does not belong to the subset. That is, it is the minimum value of the complement set. Beyond sets, subclasses of well-ordered classes have minim... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Mex (mathematics) Summary Mex_(mathematics) Minimum excluded values of subclasses of the ordinal numbers are used in combinatorial game theory to assign nim-values to impartial games. According to the Sprague–Grundy theorem, the nim-value of a game position is the minimum excluded value of the class of values of the po... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Mice problem Summary Mice_problem In mathematics, the mice problem is a continuous pursuit–evasion problem in which a number of mice (or insects, dogs, missiles, etc.) are considered to be placed at the corners of a regular polygon. In the classic setup, each then begins to move towards its immediate neighbour (clockwi... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Mice problem Summary Mice_problem The most common version has the mice starting at the corners of a unit square, moving at unit speed. In this case they meet after a time of one unit, because the distance between two neighboring mice always decreases at a speed of one unit. More generally, for a regular polygon of n {\... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Minimum k-cut Summary Minimum_k-cut In mathematics, the minimum k-cut is a combinatorial optimization problem that requires finding a set of edges whose removal would partition the graph to at least k connected components. These edges are referred to as k-cut. The goal is to find the minimum-weight k-cut. This partitio... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Minimum rank of a graph Summary Minimum_rank_of_a_graph In mathematics, the minimum rank is a graph parameter mr ( G ) {\displaystyle \operatorname {mr} (G)} for a graph G. It was motivated by the Colin de Verdière graph invariant. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tensor (intrinsic definition) Summary Rank_of_a_tensor In mathematics, the modern component-free approach to the theory of a tensor views a tensor as an abstract object, expressing some definite type of multilinear concept. Their properties can be derived from their definitions, as linear maps or more generally; and th... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tensor (intrinsic definition) Summary Rank_of_a_tensor The same is true in general relativity, of tensor fields describing a physical property. The component-free approach is also used extensively in abstract algebra and homological algebra, where tensors arise naturally. Note: This article assumes an understanding of ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hecke group Summary Modular_group In mathematics, the modular group is the projective special linear group PSL ( 2 , Z ) {\textstyle \operatorname {PSL} (2,\mathbb {Z} )} of 2 × 2 matrices with integer coefficients and determinant 1. The matrices A and −A are identified. The modular group acts on the upper-half of th... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Elliptic modulus Summary Elliptic_modulus In mathematics, the modular lambda function λ(τ) is a highly symmetric Holomorphic function on the complex upper half-plane. It is invariant under the fractional linear action of the congruence group Γ(2), and generates the function field of the corresponding quotient, i.e., it... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Moduli stack of elliptic curves Summary Moduli_stack_of_elliptic_curves In mathematics, the moduli stack of elliptic curves, denoted as M 1 , 1 {\displaystyle {\mathcal {M}}_{1,1}} or M ell {\displaystyle {\mathcal {M}}_{\textrm {ell}}} , is an algebraic stack over Spec ( Z ) {\displaystyle {\text{Spec}}(\mathbb {Z} )}... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Modulus and characteristic of convexity Summary Modulus_and_characteristic_of_convexity In mathematics, the modulus of convexity and the characteristic of convexity are measures of "how convex" the unit ball in a Banach space is. In some sense, the modulus of convexity has the same relationship to the ε-δ definition of... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Moment (statistics) Summary Raw_moment In mathematics, the moments of a function are certain quantitative measures related to the shape of the function's graph. If the function represents mass density, then the zeroth moment is the total mass, the first moment (normalized by total mass) is the center of mass, and the s... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Moment (statistics) Summary Raw_moment For a distribution of mass or probability on a bounded interval, the collection of all the moments (of all orders, from 0 to ∞) uniquely determines the distribution (Hausdorff moment problem). The same is not true on unbounded intervals (Hamburger moment problem). In the mid-ninet... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Monkey saddle Summary Monkey_saddle In mathematics, the monkey saddle is the surface defined by the equation z = x 3 − 3 x y 2 , {\displaystyle z=x^{3}-3xy^{2},\,} or in cylindrical coordinates z = ρ 3 cos ( 3 φ ) . {\displaystyle z=\rho ^{3}\cos(3\varphi ).} It belongs to the class of saddle surfaces, and its name d... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Monkey saddle Summary Monkey_saddle The point ( 0 , 0 , 0 ) {\displaystyle (0,0,0)} on the monkey saddle corresponds to a degenerate critical point of the function z ( x , y ) {\displaystyle z(x,y)} at ( 0 , 0 ) {\displaystyle (0,0)} . The monkey saddle has an isolated umbilical point with zero Gaussian curvature at th... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Monkey saddle Summary Monkey_saddle {\displaystyle z=x^{3}-3xy^{2}=\operatorname {Re} =\operatorname {Re} =r^{3}\cos(3\varphi ).} By replacing 3 in the cylindrical equation with any integer k ≥ 1 , {\displaystyle k\geq 1,} one can create a saddle with k {\displaystyle k} depressions. Another orientation of the monkey s... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Monopole moduli space Summary Monopole_moduli_space In mathematics, the monopole moduli space is a space parametrizing monopoles (solutions of the Bogomolny equations). Atiyah and Hitchin (1988) studied the moduli space for 2 monopoles in detail and used it to describe the scattering of monopoles. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Monster Lie algebra Summary Monster_Lie_algebra In mathematics, the monster Lie algebra is an infinite-dimensional generalized Kac–Moody algebra acted on by the monster group, which was used to prove the monstrous moonshine conjectures. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Mountain climbing problem Summary Mountain_climbing_problem In mathematics, the mountain climbing problem is a mathematical problem that considers a two-dimensional mountain range (represented as a continuous function), and asks whether it is possible for two mountain climbers starting at sea level on the left and righ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Moving sofa problem Summary Moving_sofa_problem In mathematics, the moving sofa problem or sofa problem is a two-dimensional idealisation of real-life furniture-moving problems and asks for the rigid two-dimensional shape of largest area that can be maneuvered through an L-shaped planar region with legs of unit width. ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Multicomplex number Summary Multicomplex_number In mathematics, the multicomplex number systems C n {\displaystyle \mathbb {C} _{n}} are defined inductively as follows: Let C0 be the real number system. For every n > 0 let in be a square root of −1, that is, an imaginary unit. Then C n + 1 = { z = x + y i n + 1: x , y ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Multicomplex number Summary Multicomplex_number In the multicomplex number systems one also requires that i n i m = i m i n {\displaystyle i_{n}i_{m}=i_{m}i_{n}} (commutativity). Then C 1 {\displaystyle \mathbb {C} _{1}} is the complex number system, C 2 {\displaystyle \mathbb {C} _{2}} is the bicomplex number system, ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Multicomplex number Summary Multicomplex_number {\displaystyle \mathbb {C} _{n}.} The multicomplex number systems are not to be confused with Clifford numbers (elements of a Clifford algebra), since Clifford's square roots of −1 anti-commute ( i n i m + i m i n = 0 {\displaystyle i_{n}i_{m}+i_{m}i_{n}=0} when m ≠ n for... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Multicomplex number Summary Multicomplex_number Any product i n i m {\displaystyle i_{n}i_{m}} of two distinct multicomplex units behaves as the j {\displaystyle j} of the split-complex numbers, and therefore the multicomplex numbers contain a number of copies of the split-complex number plane. With respect to subalgeb... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Multinomial formula Summary Multinomial_coefficient In mathematics, the multinomial theorem describes how to expand a power of a sum in terms of powers of the terms in that sum. It is the generalization of the binomial theorem from binomials to multinomials. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Multiple gamma function Summary Multiple_gamma_function In mathematics, the multiple gamma function Γ N {\displaystyle \Gamma _{N}} is a generalization of the Euler gamma function and the Barnes G-function. The double gamma function was studied by Barnes (1901). At the end of this paper he mentioned the existence of mu... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Multiple orthogonal polynomials Summary Multiple_orthogonal_polynomials In mathematics, the multiple orthogonal polynomials (MOPs) are orthogonal polynomials in one variable that are orthogonal with respect to a finite family of measures. The polynomials are divided into two classes named type 1 and type 2.In the liter... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Multiple zeta values Summary Multiple_zeta_function In mathematics, the multiple zeta functions are generalizations of the Riemann zeta function, defined by ζ ( s 1 , … , s k ) = ∑ n 1 > n 2 > ⋯ > n k > 0 1 n 1 s 1 ⋯ n k s k = ∑ n 1 > n 2 > ⋯ > n k > 0 ∏ i = 1 k 1 n i s i , {\displaystyle \zeta (s_{1},\ldots ,s_{k})=\s... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Multiplication theorem Summary Multiplication_formula In mathematics, the multiplication theorem is a certain type of identity obeyed by many special functions related to the gamma function. For the explicit case of the gamma function, the identity is a product of values; thus the name. The various relations all stem f... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Oseledets theorem Summary Multiplicative_ergodic_theorem 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... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Wild number Real wild numbers Wild_number > Real wild numbers In mathematics, the multiplicative semigroup, denoted by W0, generated by the set { 3 n + 2 2 n + 1: n ≥ 0 } {\displaystyle \left\{{\frac {3n+2}{2n+1}}:n\geq 0\right\}} is called the Wooley semigroup in honour of the American mathematician Trevor D. Wooley. ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Wild number Real wild numbers Wild_number > Real wild numbers It is called the Wooley integer semigroup and members of this semigroup are called Wooley integers. Similarly, the set of integers in W is itself a multiplicative semigroup. It is called the wild integer semigroup and members of this semigroup are called wil... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Multiple roots of a polynomial Summary Multiplicity_of_a_root_of_a_polynomial In mathematics, the multiplicity of a member of a multiset is the number of times it appears in the multiset. For example, the number of times a given polynomial has a root at a given point is the multiplicity of that root. The notion of mult... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Multiple roots of a polynomial Summary Multiplicity_of_a_root_of_a_polynomial Hence the expression, "counted with multiplicity". If multiplicity is ignored, this may be emphasized by counting the number of distinct elements, as in "the number of distinct roots". However, whenever a set (as opposed to multiset) is forme... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
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