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Value creation
In marketing, a company’s value proposition is the full mix of benefits or economic value which it promises to deliver to the current and future customers (i.e., a market segment) who will buy their products and/or services. It is part of a company's overall marketing strategy which differentiates its br... | Wiki-STEM-kaggle |
Value creation
However, often there is a discrepancy between what the company thinks about its value proposition and what the clients think it is.A company's value propositions can evolve, whereby values can add up over time. For example, Apple's value proposition contains a mix of three values.Originally, in the 1980s... | Wiki-STEM-kaggle |
Product model
In marketing, a product is an object, or system, or service made available for consumer use as of the consumer demand; it is anything that can be offered to a market to satisfy the desire or need of a customer. In retailing, products are often referred to as merchandise, and in manufacturing, products are... | Wiki-STEM-kaggle |
Customer segmentation
In marketing, market segmentation is the process of dividing a broad consumer or business market, normally consisting of existing and potential customers, into sub-groups of consumers (known as segments) based on shared characteristics. In dividing or segmenting markets, researchers typically look... | Wiki-STEM-kaggle |
Markup overlap
In markup languages and the digital humanities, overlap occurs when a document has two or more structures that interact in a non-hierarchical manner. A document with overlapping markup cannot be represented as a tree. This is also known as concurrent markup. Overlap happens, for instance, in poetry, wher... | Wiki-STEM-kaggle |
Émery topology
In martingale theory, Émery topology is a topology on the space of semimartingales. The topology is used in financial mathematics. The class of stochastic integrals with general predictable integrands coincides with the closure of the set of all simple integrals.The topology was introduced in 1979 by the... | Wiki-STEM-kaggle |
Fragmentation pattern
In mass spectrometry, fragmentation is the dissociation of energetically unstable molecular ions formed from passing the molecules mass spectrum. These reactions are well documented over the decades and fragmentation patterns are useful to determine the molar weight and structural information of u... | Wiki-STEM-kaggle |
Quadrupole mass analyzer
In mass spectrometry, the quadrupole mass analyzer (or quadrupole mass filter) is a type of mass analyzer originally conceived by Nobel laureate Wolfgang Paul and his student Helmut Steinwedel. As the name implies, it consists of four cylindrical rods, set parallel to each other. In a quadrupol... | Wiki-STEM-kaggle |
Sieving coefficient
In mass transfer, the sieving coefficient is a measure of equilibration between the concentrations of two mass transfer streams. It is defined as the mean pre- and post-contact concentration of the mass receiving stream divided by the pre- and post-contact concentration of the mass donating stream. ... | Wiki-STEM-kaggle |
Binary phase
In materials chemistry, a binary phase or binary compound is a chemical compound containing two different elements. Some binary phase compounds are molecular, e.g. carbon tetrachloride (CCl4). More typically binary phase refers to extended solids. Famous examples zinc sulfide, which contains zinc and sulfu... | Wiki-STEM-kaggle |
Quaternary phase
In materials chemistry, a quaternary phase is a chemical compound containing four elements. Some compounds can be molecular or ionic, examples being chlorodifluoromethane (CHClF2) sodium bicarbonate (NaCO3H). More typically quaternary phase refers to extended solids. A famous example are the yttrium ba... | Wiki-STEM-kaggle |
ABC analysis
In materials management, ABC analysis is an inventory categorisation technique. ABC analysis divides an inventory into three categories—"A items" with very tight control and accurate records, "B items" with less tightly controlled and good records, and "C items" with the simplest controls possible and mini... | Wiki-STEM-kaggle |
Crack growth resistance curve
In materials modeled by linear elastic fracture mechanics (LEFM), crack extension occurs when the applied energy release rate G {\displaystyle G} exceeds G R {\displaystyle G_{R}} , where G R {\displaystyle G_{R}} is the material's resistance to crack extension. Conceptually G {\displaysty... | Wiki-STEM-kaggle |
Radiation length
In materials of high atomic number (e.g. tungsten, uranium, plutonium) the electrons of energies >~10 MeV predominantly lose energy by bremsstrahlung, and high-energy photons by e+e− pair production. The characteristic amount of matter traversed for these related interactions is called the radiation le... | Wiki-STEM-kaggle |
Giant magnetoimpedance
In materials science Giant Magnetoimpedance (GMI) is the effect that occurs in some materials where an external magnetic field causes a large variation in the electrical impedance of the material. It should not be confused with the separate physical phenomenon of Giant Magnetoresistance. | Wiki-STEM-kaggle |
Viscoelasticity
In materials science and continuum mechanics, viscoelasticity is the property of materials that exhibit both viscous and elastic characteristics when undergoing deformation. Viscous materials, like water, resist shear flow and strain linearly with time when a stress is applied. Elastic materials strain ... | Wiki-STEM-kaggle |
Viscous forces
In materials science and engineering, one is often interested in understanding the forces or stresses involved in the deformation of a material. For instance, if the material were a simple spring, the answer would be given by Hooke's law, which says that the force experienced by a spring is proportional ... | Wiki-STEM-kaggle |
Viscous forces
In many fluids, the flow velocity is observed to vary linearly from zero at the bottom to u {\displaystyle u} at the top. Moreover, the magnitude of the force, F {\displaystyle F} , acting on the top plate is found to be proportional to the speed u {\displaystyle u} and the area A {\displaystyle A} of ea... | Wiki-STEM-kaggle |
Viscous forces
In shearing flows with planar symmetry, it is what defines μ {\displaystyle \mu } . It is a special case of the general definition of viscosity (see below), which can be expressed in coordinate-free form. Use of the Greek letter mu ( μ {\displaystyle \mu } ) for the dynamic viscosity (sometimes also call... | Wiki-STEM-kaggle |
Functionally graded element
In materials science and mathematics, functionally graded elements are elements used in finite element analysis. They can be used to describe a functionally graded material. | Wiki-STEM-kaggle |
Thermostability
In materials science and molecular biology, thermostability is the ability of a substance to resist irreversible change in its chemical or physical structure, often by resisting decomposition or polymerization, at a high relative temperature. Thermostable materials may be used industrially as fire retar... | Wiki-STEM-kaggle |
Poisson's Ratio
In materials science and solid mechanics, Poisson's ratio ν {\displaystyle \nu } (nu) is a measure of the Poisson effect, the deformation (expansion or contraction) of a material in directions perpendicular to the specific direction of loading. The value of Poisson's ratio is the negative of the ratio o... | Wiki-STEM-kaggle |
Residual stress
In materials science and solid mechanics, residual stresses are stresses that remain in a solid material after the original cause of the stresses has been removed. Residual stress may be desirable or undesirable. For example, laser peening imparts deep beneficial compressive residual stresses into metal... | Wiki-STEM-kaggle |
Ostwald's step rule
In materials science, Ostwald's rule or Ostwald's step rule, conceived by Wilhelm Ostwald, describes the formation of polymorphs. The rule states that usually the less stable polymorph crystallizes first. Ostwald's rule is not a universal law but a common tendency observed in nature.This can be expl... | Wiki-STEM-kaggle |
Schmid's law
In materials science, Schmid's law (also Schmid factor) describes the slip plane and the slip direction of a stressed material, which can resolve the most shear stress. Schmid's Law states that the critically resolved shear stress (τ) is equal to the stress applied to the material (σ) multiplied by the cos... | Wiki-STEM-kaggle |
Lomer–Cottrell junction
In materials science, a Lomer–Cottrell junction is a particular configuration of dislocations. When two perfect dislocations encounter along a slip plane, each perfect dislocation can split into two Shockley partial dislocations: a leading dislocation and a trailing dislocation. When the two lea... | Wiki-STEM-kaggle |
Rule of mixtures
In materials science, a general rule of mixtures is a weighted mean used to predict various properties of a composite material . It provides a theoretical upper- and lower-bound on properties such as the elastic modulus, ultimate tensile strength, thermal conductivity, and electrical conductivity. In g... | Wiki-STEM-kaggle |
Matrix (composite)
In materials science, a matrix is a constituent of a composite material. | Wiki-STEM-kaggle |
Creep (deformation)
In materials science, creep (sometimes called cold flow) is the tendency of a solid material to undergo slow deformation while subject to persistent mechanical stresses. It can occur as a result of long-term exposure to high levels of stress that are still below the yield strength of the material. C... | Wiki-STEM-kaggle |
Critical resolved shear stress
In materials science, critical resolved shear stress (CRSS) is the component of shear stress, resolved in the direction of slip, necessary to initiate slip in a grain. Resolved shear stress (RSS) is the shear component of an applied tensile or compressive stress resolved along a slip plan... | Wiki-STEM-kaggle |
Friability
In materials science, friability ( FRY-ə-BIL-ə-tee), the condition of being friable, describes the tendency of a solid substance to break into smaller pieces under duress or contact, especially by rubbing. The opposite of friable is indurate. Substances that are designated hazardous, such as asbestos or crys... | Wiki-STEM-kaggle |
Lamellar structure
In materials science, lamellar structures or microstructures are composed of fine, alternating layers of different materials in the form of lamellae. They are often observed in cases where a phase transition front moves quickly, leaving behind two solid products, as in rapid cooling of eutectic (such... | Wiki-STEM-kaggle |
Reinforcement (composite)
In materials science, reinforcement is a constituent of a composite material which increases the composite's stiffness and tensile strength. | Wiki-STEM-kaggle |
Modulus of rigidity
In materials science, shear modulus or modulus of rigidity, denoted by G, or sometimes S or μ, is a measure of the elastic shear stiffness of a material and is defined as the ratio of shear stress to the shear strain: G = d e f τ x y γ x y = F / A Δ x / l = F l A Δ x {\displaystyle G\ {\stackrel {\m... | Wiki-STEM-kaggle |
Superplastic deformation
In materials science, superplasticity is a state in which solid crystalline material is deformed well beyond its usual breaking point, usually over about 400% during tensile deformation. Such a state is usually achieved at high homologous temperature. Examples of superplastic materials are some... | Wiki-STEM-kaggle |
Burgers vector
In materials science, the Burgers vector, named after Dutch physicist Jan Burgers, is a vector, often denoted as b, that represents the magnitude and direction of the lattice distortion resulting from a dislocation in a crystal lattice. The vector's magnitude and direction is best understood when the dis... | Wiki-STEM-kaggle |
Burgers vector
In most metallic materials, the magnitude of the Burgers vector for a dislocation is of a magnitude equal to the interatomic spacing of the material, since a single dislocation will offset the crystal lattice by one close-packed crystallographic spacing unit. In edge dislocations, the Burgers vector and ... | Wiki-STEM-kaggle |
Charpy test
In materials science, the Charpy impact test, also known as the Charpy V-notch test, is a standardized high strain rate test which determines the amount of energy absorbed by a material during fracture. Absorbed energy is a measure of the material's notch toughness. It is widely used in industry, since it i... | Wiki-STEM-kaggle |
Zener–Hollomon parameter
In materials science, the Zener–Hollomon parameter, typically denoted as Z, is used to relate changes in temperature or strain-rate to the stress-strain behavior of a material. It has been most extensively applied to the forming of steels at increased temperature, when creep is active. It is gi... | Wiki-STEM-kaggle |
Threshold displacement energy
In materials science, the threshold displacement energy (Td) is the minimum kinetic energy that an atom in a solid needs to be permanently displaced from its site in the lattice to a defect position. It is also known as "displacement threshold energy" or just "displacement energy". In a cr... | Wiki-STEM-kaggle |
Yield strength anomaly
In materials science, the yield strength anomaly refers to materials wherein the yield strength (i.e., the stress necessary to initiate plastic yielding) increases with temperature. For the majority of materials, the yield strength decreases with increasing temperature. In metals, this decrease i... | Wiki-STEM-kaggle |
Antiferromagnetic interaction
In materials that exhibit antiferromagnetism, the magnetic moments of atoms or molecules, usually related to the spins of electrons, align in a regular pattern with neighboring spins (on different sublattices) pointing in opposite directions. This is, like ferromagnetism and ferrimagnetism... | Wiki-STEM-kaggle |
Pseudo-differential operator
In mathematical analysis a pseudo-differential operator is an extension of the concept of differential operator. Pseudo-differential operators are used extensively in the theory of partial differential equations and quantum field theory, e.g. in mathematical models that include ultrametric ... | Wiki-STEM-kaggle |
Oscillatory integral
In mathematical analysis an oscillatory integral is a type of distribution. Oscillatory integrals make rigorous many arguments that, on a naive level, appear to use divergent integrals. It is possible to represent approximate solution operators for many differential equations as oscillatory integra... | Wiki-STEM-kaggle |
Z-order curve
In mathematical analysis and computer science, functions which are Z-order, Lebesgue curve, Morton space-filling curve, Morton order or Morton code map multidimensional data to one dimension while preserving locality of the data points. It is named in France after Henri Lebesgue, who studied it in 1904, a... | Wiki-STEM-kaggle |
Sigma field
In mathematical analysis and in probability theory, a σ-algebra (also σ-field) on a set X is a nonempty collection Σ of subsets of X closed under complement, countable unions, and countable intersections. The ordered pair ( X , Σ ) {\displaystyle (X,\Sigma )} is called a measurable space. The σ-algebras are... | Wiki-STEM-kaggle |
Sigma field
In general, a finite algebra is always a σ-algebra. If { A 1 , A 2 , A 3 , … } , {\displaystyle \{A_{1},A_{2},A_{3},\ldots \},} is a countable partition of X {\displaystyle X} then the collection of all unions of sets in the partition (including the empty set) is a σ-algebra. A more useful example is the se... | Wiki-STEM-kaggle |
Multi-variable function
In mathematical analysis and its applications, a function of several real variables or real multivariate function is a function with more than one argument, with all arguments being real variables. This concept extends the idea of a function of a real variable to several variables. The "input" v... | Wiki-STEM-kaggle |
Bounded poset
In mathematical analysis and related areas of mathematics, a set is called bounded if it is, in a certain sense, of finite measure. Conversely, a set which is not bounded is called unbounded. The word "bounded" makes no sense in a general topological space without a corresponding metric.Boundary is a dist... | Wiki-STEM-kaggle |
Agmon's inequality
In mathematical analysis, Agmon's inequalities, named after Shmuel Agmon, consist of two closely related interpolation inequalities between the Lebesgue space L ∞ {\displaystyle L^{\infty }} and the Sobolev spaces H s {\displaystyle H^{s}} . It is useful in the study of partial differential equations... | Wiki-STEM-kaggle |
Agmon's inequality
{\displaystyle \displaystyle \|u\|_{L^{\infty }(\Omega )}\leq C\|u\|_{L^{2}(\Omega )}^{1/4}\|u\|_{H^{2}(\Omega )}^{3/4}.} In 2D, the first inequality still holds, but not the second: let u ∈ H 2 ( Ω ) ∩ H 0 1 ( Ω ) {\displaystyle u\in H^{2}(\Omega )\cap H_{0}^{1}(\Omega )} where Ω ⊂ R 2 {\displaystyl... | Wiki-STEM-kaggle |
Cesàro summation
In mathematical analysis, Cesàro summation (also known as the Cesàro mean) assigns values to some infinite sums that are not necessarily convergent in the usual sense. The Cesàro sum is defined as the limit, as n tends to infinity, of the sequence of arithmetic means of the first n partial sums of the ... | Wiki-STEM-kaggle |
Clairaut's equation
In mathematical analysis, Clairaut's equation (or the Clairaut equation) is a differential equation of the form y ( x ) = x d y d x + f ( d y d x ) {\displaystyle y(x)=x{\frac {dy}{dx}}+f\left({\frac {dy}{dx}}\right)} where f {\displaystyle f} is continuously differentiable. It is a particular case ... | Wiki-STEM-kaggle |
Darboux's formula
In mathematical analysis, Darboux's formula is a formula introduced by Gaston Darboux (1876) for summing infinite series by using integrals or evaluating integrals using infinite series. It is a generalization to the complex plane of the Euler–Maclaurin summation formula, which is used for similar pur... | Wiki-STEM-kaggle |
Dini continuity
In mathematical analysis, Dini continuity is a refinement of continuity. Every Dini continuous function is continuous. Every Lipschitz continuous function is Dini continuous. | Wiki-STEM-kaggle |
Ehrenpreis's fundamental principle
In mathematical analysis, Ehrenpreis's fundamental principle, introduced by Leon Ehrenpreis, states: Every solution of a system (in general, overdetermined) of homogeneous partial differential equations with constant coefficients can be represented as the integral with respect to an a... | Wiki-STEM-kaggle |
Ekeland's variational principle
In mathematical analysis, Ekeland's variational principle, discovered by Ivar Ekeland, is a theorem that asserts that there exist nearly optimal solutions to some optimization problems. Ekeland's principle can be used when the lower level set of a minimization problems is not compact, so... | Wiki-STEM-kaggle |
Fourier integral operator
In mathematical analysis, Fourier integral operators have become an important tool in the theory of partial differential equations. The class of Fourier integral operators contains differential operators as well as classical integral operators as special cases. A Fourier integral operator T {\... | Wiki-STEM-kaggle |
Fubini's Theorem
In mathematical analysis, Fubini's theorem is a result that gives conditions under which it is possible to compute a double integral by using an iterated integral, introduced by Guido Fubini in 1907. One may switch the order of integration if the double integral yields a finite answer when the integran... | Wiki-STEM-kaggle |
Fubini's Theorem
Tonelli's theorem, introduced by Leonida Tonelli in 1909, is similar, but applies to a non-negative measurable function rather than one integrable over their domains. A related theorem is often called Fubini's theorem for infinite series, which states that if { a m , n } m = 1 , n = 1 ∞ {\textstyle \{a... | Wiki-STEM-kaggle |
Glaeser's continuity theorem
In mathematical analysis, Glaeser's continuity theorem is a characterization of the continuity of the derivative of the square roots of functions of class C 2 {\displaystyle C^{2}} . It was introduced in 1963 by Georges Glaeser, and was later simplified by Jean Dieudonné.The theorem states:... | Wiki-STEM-kaggle |
Haar's Tauberian theorem
In mathematical analysis, Haar's Tauberian theorem named after Alfréd Haar, relates the asymptotic behaviour of a continuous function to properties of its Laplace transform. It is related to the integral formulation of the Hardy–Littlewood Tauberian theorem. | Wiki-STEM-kaggle |
Heine's Reciprocal Square Root Identity
In mathematical analysis, Heine's identity, named after Heinrich Eduard Heine is a Fourier expansion of a reciprocal square root which Heine presented as where Q m − 1 2 {\displaystyle Q_{m-{\frac {1}{2}}}} is a Legendre function of the second kind, which has degree, m − 1⁄2, a h... | Wiki-STEM-kaggle |
Hölder's inequality
In mathematical analysis, Hölder's inequality, named after Otto Hölder, is a fundamental inequality between integrals and an indispensable tool for the study of Lp spaces. The numbers p and q above are said to be Hölder conjugates of each other. The special case p = q = 2 gives a form of the Cauchy–... | Wiki-STEM-kaggle |
Korn's inequality
In mathematical analysis, Korn's inequality is an inequality concerning the gradient of a vector field that generalizes the following classical theorem: if the gradient of a vector field is skew-symmetric at every point, then the gradient must be equal to a constant skew-symmetric matrix. Korn's theor... | Wiki-STEM-kaggle |
Krein's condition
In mathematical analysis, Krein's condition provides a necessary and sufficient condition for exponential sums { ∑ k = 1 n a k exp ( i λ k x ) , a k ∈ C , λ k ≥ 0 } , {\displaystyle \left\{\sum _{k=1}^{n}a_{k}\exp(i\lambda _{k}x),\quad a_{k}\in \mathbb {C} ,\,\lambda _{k}\geq 0\right\},} to be dense... | Wiki-STEM-kaggle |
Lambert summation
In mathematical analysis, Lambert summation is a summability method for a class of divergent series. | Wiki-STEM-kaggle |
Lipschitz function
In mathematical analysis, Lipschitz continuity, named after German mathematician Rudolf Lipschitz, is a strong form of uniform continuity for functions. Intuitively, a Lipschitz continuous function is limited in how fast it can change: there exists a real number such that, for every pair of points on... | Wiki-STEM-kaggle |
Littlewood's 4/3 inequality
In mathematical analysis, Littlewood's 4/3 inequality, named after John Edensor Littlewood, is an inequality that holds for every complex-valued bilinear form defined on c 0 {\displaystyle c_{0}} , the Banach space of scalar sequences that converge to zero. Precisely, let B: c 0 × c 0 → C {\... | Wiki-STEM-kaggle |
Lorentz space
In mathematical analysis, Lorentz spaces, introduced by George G. Lorentz in the 1950s, are generalisations of the more familiar L p {\displaystyle L^{p}} spaces. The Lorentz spaces are denoted by L p , q {\displaystyle L^{p,q}} . Like the L p {\displaystyle L^{p}} spaces, they are characterized by a norm... | Wiki-STEM-kaggle |
Mosco convergence
In mathematical analysis, Mosco convergence is a notion of convergence for functionals that is used in nonlinear analysis and set-valued analysis. It is a particular case of Γ-convergence. Mosco convergence is sometimes phrased as “weak Γ-liminf and strong Γ-limsup” convergence since it uses both the ... | Wiki-STEM-kaggle |
Netto's theorem
In mathematical analysis, Netto's theorem states that continuous bijections of smooth manifolds preserve dimension. That is, there does not exist a continuous bijection between two smooth manifolds of different dimension. It is named after Eugen Netto.The case for maps from a higher-dimensional manifold... | Wiki-STEM-kaggle |
Netto's theorem
A near-bijection from the unit square to the unit interval can be obtained by interleaving the digits of the decimal representations of the Cartesian coordinates of points in the square. The ambiguities of decimal, exemplified by the two decimal representations of 1 = 0.999..., cause this to be an injec... | Wiki-STEM-kaggle |
Parseval's formula
In mathematical analysis, Parseval's identity, named after Marc-Antoine Parseval, is a fundamental result on the summability of the Fourier series of a function. Geometrically, it is a generalized Pythagorean theorem for inner-product spaces (which can have an uncountable infinity of basis vectors). ... | Wiki-STEM-kaggle |
Rademacher's theorem
In mathematical analysis, Rademacher's theorem, named after Hans Rademacher, states the following: If U is an open subset of Rn and f: U → Rm is Lipschitz continuous, then f is differentiable almost everywhere in U; that is, the points in U at which f is not differentiable form a set of Lebesgue me... | Wiki-STEM-kaggle |
Strichartz estimate
In mathematical analysis, Strichartz estimates are a family of inequalities for linear dispersive partial differential equations. These inequalities establish size and decay of solutions in mixed norm Lebesgue spaces. They were first noted by Robert Strichartz and arose out of connections to the Fou... | Wiki-STEM-kaggle |
Tannery's theorem
In mathematical analysis, Tannery's theorem gives sufficient conditions for the interchanging of the limit and infinite summation operations. It is named after Jules Tannery. | Wiki-STEM-kaggle |
Trudinger's theorem
In mathematical analysis, Trudinger's theorem or the Trudinger inequality (also sometimes called the Moser–Trudinger inequality) is a result of functional analysis on Sobolev spaces. It is named after Neil Trudinger (and Jürgen Moser). It provides an inequality between a certain Sobolev space norm a... | Wiki-STEM-kaggle |
Wiener's Tauberian theorem
In mathematical analysis, Wiener's tauberian theorem is any of several related results proved by Norbert Wiener in 1932. They provide a necessary and sufficient condition under which any function in L 1 {\displaystyle L^{1}} or L 2 {\displaystyle L^{2}} can be approximated by linear combinati... | Wiki-STEM-kaggle |
Zorich's theorem
In mathematical analysis, Zorich's theorem was proved by Vladimir A. Zorich in 1967. The result was conjectured by M. A. Lavrentev in 1938. | Wiki-STEM-kaggle |
Banach limit
In mathematical analysis, a Banach limit is a continuous linear functional ϕ: ℓ ∞ → C {\displaystyle \phi :\ell ^{\infty }\to \mathbb {C} } defined on the Banach space ℓ ∞ {\displaystyle \ell ^{\infty }} of all bounded complex-valued sequences such that for all sequences x = ( x n ) {\displaystyle x=(x_{n}... | Wiki-STEM-kaggle |
Banach limit
As a consequence of the above properties, a real-valued Banach limit also satisfies: lim inf n → ∞ x n ≤ ϕ ( x ) ≤ lim sup n → ∞ x n . {\displaystyle \liminf _{n\to \infty }x_{n}\leq \phi (x)\leq \limsup _{n\to \infty }x_{n}.} The existence of Banach limits is usually proved using the Hahn–Banach theorem (... | Wiki-STEM-kaggle |
Besicovitch covering theorem
In mathematical analysis, a Besicovitch cover, named after Abram Samoilovitch Besicovitch, is an open cover of a subset E of the Euclidean space RN by balls such that each point of E is the center of some ball in the cover. The Besicovitch covering theorem asserts that there exists a consta... | Wiki-STEM-kaggle |
Contraction semigroup
In mathematical analysis, a C0-semigroup Γ(t), t ≥ 0, is called a quasicontraction semigroup if there is a constant ω such that ||Γ(t)|| ≤ exp(ωt) for all t ≥ 0. Γ(t) is called a contraction semigroup if ||Γ(t)|| ≤ 1 for all t ≥ 0. | Wiki-STEM-kaggle |
Carathéodory function
In mathematical analysis, a Carathéodory function (or Carathéodory integrand) is a multivariable function that allows us to solve the following problem effectively: A composition of two Lebesgue-measurable functions does not have to be Lebesgue-measurable as well. Nevertheless, a composition of a ... | Wiki-STEM-kaggle |
Hermitian function
In mathematical analysis, a Hermitian function is a complex function with the property that its complex conjugate is equal to the original function with the variable changed in sign: f ∗ ( x ) = f ( − x ) {\displaystyle f^{*}(x)=f(-x)} (where the ∗ {\displaystyle ^{*}} indicates the complex conjugate... | Wiki-STEM-kaggle |
Young measure
In mathematical analysis, a Young measure is a parameterized measure that is associated with certain subsequences of a given bounded sequence of measurable functions. They are a quantification of the oscillation effect of the sequence in the limit. Young measures have applications in the calculus of varia... | Wiki-STEM-kaggle |
Bounded domain
In mathematical analysis, a domain or region is a non-empty connected open set in a topological space, in particular any non-empty connected open subset of the real coordinate space Rn or the complex coordinate space Cn. A connected open subset of coordinate space is frequently used for the domain of a f... | Wiki-STEM-kaggle |
Equicontinuous linear maps
In mathematical analysis, a family of functions is equicontinuous if all the functions are continuous and they have equal variation over a given neighbourhood, in a precise sense described herein. In particular, the concept applies to countable families, and thus sequences of functions. Equic... | Wiki-STEM-kaggle |
Function of bounded variation
In mathematical analysis, a function of bounded variation, also known as BV function, is a real-valued function whose total variation is bounded (finite): the graph of a function having this property is well behaved in a precise sense. For a continuous function of a single variable, being ... | Wiki-STEM-kaggle |
Metric differential
In mathematical analysis, a metric differential is a generalization of a derivative for a Lipschitz continuous function defined on a Euclidean space and taking values in an arbitrary metric space. With this definition of a derivative, one can generalize Rademacher's theorem to metric space-valued Li... | Wiki-STEM-kaggle |
Complete metric space
In mathematical analysis, a metric space M is called complete (or a Cauchy space) if every Cauchy sequence of points in M has a limit that is also in M. Intuitively, a space is complete if there are no "points missing" from it (inside or at the boundary). For instance, the set of rational numbers ... | Wiki-STEM-kaggle |
Modulus of continuity
In mathematical analysis, a modulus of continuity is a function ω: → used to measure quantitatively the uniform continuity of functions. So, a function f: I → R admits ω as a modulus of continuity if and only if | f ( x ) − f ( y ) | ≤ ω ( | x − y | ) , {\displaystyle |f(x)-f(y)|\leq \omega (|x-... | Wiki-STEM-kaggle |
Modulus of continuity
A special role is played by concave moduli of continuity, especially in connection with extension properties, and with approximation of uniformly continuous functions. For a function between metric spaces, it is equivalent to admit a modulus of continuity that is either concave, or subadditive, or... | Wiki-STEM-kaggle |
Measure zero
In mathematical analysis, a null set is a Lebesgue measurable set of real numbers that has measure zero. This can be characterized as a set that can be covered by a countable union of intervals of arbitrarily small total length. The notion of null set should not be confused with the empty set as defined in... | Wiki-STEM-kaggle |
Positive invariant set
In mathematical analysis, a positively (or positive) invariant set is a set with the following properties: Suppose x ˙ = f ( x ) {\displaystyle {\dot {x}}=f(x)} is a dynamical system, x ( t , x 0 ) {\displaystyle x(t,x_{0})} is a trajectory, and x 0 {\displaystyle x_{0}} is the initial point. Let... | Wiki-STEM-kaggle |
Strong measure zero set
In mathematical analysis, a strong measure zero set is a subset A of the real line with the following property: for every sequence (εn) of positive reals there exists a sequence (In) of intervals such that |In| < εn for all n and A is contained in the union of the In. (Here |In| denotes the leng... | Wiki-STEM-kaggle |
Thin set (analysis)
In mathematical analysis, a thin set is a subset of n-dimensional complex space Cn with the property that each point has a neighbourhood on which some non-zero holomorphic function vanishes. Since the set on which a holomorphic function vanishes is closed and has empty interior (by the Identity theo... | Wiki-STEM-kaggle |
Improper integrals
In mathematical analysis, an improper integral is an extension of the notion of a definite integral to cases that violate the usual assumptions for that kind of integral. In the context of Riemann integrals (or, equivalently, Darboux integrals), this typically involves unboundedness, either of the se... | Wiki-STEM-kaggle |
Improper integrals
Such an integral is sometimes described as being of the "first" type or kind if the integrand otherwise satisfies the assumptions of integration. Integrals in the fourth form that are improper because f ( x ) {\displaystyle f(x)} has a vertical asymptote somewhere on the interval {\displaystyle } ma... | Wiki-STEM-kaggle |
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