## Sasaki metric

Let M, G {\the style property display the value of M,G} be a Riemannian manifold, we denote by τ: t m → m {\the style property display set to \Tau \colon \mathrm {T} M\ \ M} in the tangent bundle over M {\the style property display the value of m ...

## Vector bundle

In mathematics, a vector bundle is a topological construction that makes precise the idea of a family of vector spaces parameterized by another space X: at each point X of the space X we associate a vector space V in Such a way that these vector ...

## Complex vector bundle

In mathematics, a complex vector bundle is a vector bundle whose fibers are complex vector spaces. Any complex vector bundle can be regarded as a real vector bundle via restriction of scalars. Conversely, any real vector bundle E can be made into ...

## Dual bundle

In mathematics, the dual bundle of a vector bundle π: e → X is a vector bundle π ∗ e ∗ → X whose fibers are the conjugate spaces in the fibers, i.e. a double set, you can use related set of works, taking the dual representation of the structure g ...

## Flat vector bundle

Let π: E → X {\the style property display the value of \Pi:E\X} denote the flat vector bundle, and ∇ Γ x, e → Γ x, Ω 1 x ⊗ e {\the style property display set to \nabla:\gamma x,E\K X \gamma,\ omega _{x}^{1}\otimes E} be the covariant derivative a ...

## Tautological bundle

In mathematics, the tautological bundle is a bundle going on for Grossman in a natural tautological way: the fiber of the bundle over a vector space V into itself. In the case of projective space, the package is called tautological line bundle. I ...

## De Rham curve

In mathematics, a de Rham curve is a certain type of fractal curve named in honor of Georges de Rham. The Cantor function, cesàro curve, Minkowskis functions of a question mark, levy C curve, the blancmange curve and the Koch curve are all specia ...

## Levy C curve

In mathematics, the lévy C curve is a self-replicating fractal that was first described and differential properties of which were analysed by Ernesto cesàro in 1906 and Georg Faber in 1910, but now bears the name of French mathematician Paul levy ...

## Multiplier algebra

In mathematics, the multiplier algebra, denoted by m C*-algebra a is a unital C*-algebra, which is the largest unital C*-algebra which contains a as an ideal in "non-degenerate" way. It is the noncommutative generalization of stone–Cech compactif ...

## Approximately finite-dimensional C*-algebra

In mathematics, approximately finite-dimensional C*-algebra is a C*-algebra that is the inductive limit of a sequence of finite-dimensional C*-algebras. Approximate finite-dimensionality was first defined and described combinatorial OLA Bratteli. ...

## Bunce–Deddens algebra

In mathematics, Bunce–Deddens algebra, named in honor of John W. Bunce and James A. Deddens, is a specific type of direct limit of matrix algebras over the continuous functions on the circle. Therefore, they are examples of simple unital at algeb ...

## Completely positive map

In mathematics, a positive map is a map between C*-algebras that sends positive elements to positive elements. Absolutely positive the card is one that satisfies more durable and steady state.

## Cuntz algebra

In mathematics, the Cuntz algebra o n {\the style property display the value of {\mathcal {o}}_{n}}, is named after Joachim Cuntz, is the universal C*-algebra generated by N isometries satisfying certain relations. In the Cuntz algebra introduced ...

## Exact C*-algebra

C*-algebra e precisely if for any short exact sequence, 0 → A → f B → g C → 0 {\displaystyle 0\,{\xrightarrow {}}\,A\,{\xrightarrow {f}}\,B\,{\xrightarrow {g}}\,C\,{\xrightarrow {}}\,0} the sequence 0 → A ⊗ min E → f ⊗ id B ⊗ min E → g ⊗ id C ⊗ m ...

## Graph C*-algebra

## Hereditary C*-subalgebra

In mathematics, a hereditary C*-subalgebra of the C*-algebra of a particular type with a*is the subalgebra whose structure is closely linked to a larger C*-algebra. C*-subalgebra a of B is a hereditary C*-subalgebra if for all A ∈ A and B ∈ B, su ...

## K-graph C*-algebra

In mathematics, a K-graph is a countable category Λ {\the style property display set to \type } with the domain and codomain of the map R {\the style property display the value of R} and S {\the style property display value}, together with a func ...

In mathematics, Kadisha Brosses metric is a metric on the space of C * -algebras on a fixed Hilbert space. This is the Hausdorff distance between the unit balls of two C * -algebras, in accordance with the norm induced by the metric on the space ...

## Nuclear C*-algebra

In Mathematics, a nuclear C*-algebra is a C*-algebra a such that the injective and projective C*-cross norms on a ⊗ B are the same for any C*-algebra B. This property was first studied by takesaki called "the Hotel", which has nothing to Kazhdans ...

## Toeplitz algebra

In operator algebras, in algebra, the greenhouse is a C*-algebra generated by the unilateral transfer on the Hilbert space L 2. Taking L 2 for the hardy space H 2, then Toeplitz algebra consists of elements of the form T f + K {\displaystyle T_{f ...

## Uniformly hyperfinite algebra

In mathematics, especially in the theory of C*-algebras, uniformly giperkineza, or UHF, algebra is a C*-algebra that can be written as the closure in the norm topology, the increasing Union of finite-dimensional full matrix algebras.

## Universal C*-algebra

In mathematics, the universal C*-algebra is a C*-algebra to describe in terms of generators and relations. Unlike rings or algebras which can be viewed free private rings to create generic objects with*-algebras should be realizable as algebras o ...

## Category of elements

In category theory, if c is a category and F: S → E T {\the style property display value F:C\to \mathbf {set} } is a multi-valued functor, the category of elements of f E L ⁡ {\the style property display set to \mathop {\RM {El}} } - a category d ...

## Density theorem (category theory)

In category theory, branch of mathematics, the density theorem says that every presheaf of sets is a colimit of representable presheaves in a canonical way. For example, by definition, complex is a simplicial presheaf on the simplex category Δ, a ...

## Generalized function

In mathematics, generalized functions, or distributions, are objects, extends the concept of a function. There is more than one recognized theory. Generalized functions are especially useful in making discontinuous functions more like smooth func ...

## Boehmians

In mathematics, Boehmians are objects obtained by an abstract algebraic construction of the "private series".The original design was dictated by the regular operators introduced K. T. Boehme. Regular operators are a subclass of operators Mikusins ...

## Multiscale Greens function

The multiscale function of the green is a generalized and extended version of the classical technique, the function of Herbs to solve mathematical equations. The main application of the method MSGF is a simulation of nanomaterials. These material ...

## Singularity function

Singularity functions are a class of discontinuous functions that contain singularities, i.e. they are continuous in their particular points. Function singularity is actively studied in the field of mathematics under the alternative names of gene ...

## White noise analysis

In probability theory, the mathematics of white noise analysis is the basis for the infinite dimensional and stochastic calculus, based on the Gaussian white noise probability space, in comparison with the Malliavin calculus based on the Wiener p ...

## Anti-function

## Local inverse

Local reverse view of the inverse function or the inverse matrix is used in processing images and signals, as well as other General areas of mathematics. The concept of local back out of the reconstruction of the interior of the image of KT. One ...

## Superrigidity

In mathematics, in the theory of discrete groups, superrigidity is a concept designed to show how a linear representation ρ of a discrete group Γ of an algebraic group G may, in some circumstances, can be as good as the view itself, as this pheno ...

## Weight-of-conflict conjecture

The weight of the conflict hypothesis was proposed by Glenn Shafer in his book on the Dempster–Shafer called the mathematical theory of evidence. It says that if Q 1 {\the style property display the value of Q_{1}} and q 2 {\the style property di ...

## Free probability theory

## Conditional dependence

In probability theory, conditional dependence is a relationship between two or more events that depend upon the occurrence of the third event. For example, if A and B are two events that individually increase the likelihood of a third event C, an ...

## Conditional independence

## Subindependence

In probability theory and statistics, subindependence is a weak form of independence. Two random variables X and y are referred to as subindependent if the characteristic function of their sum is equal to the product of their marginal characteris ...

## Polya urn model

In statistics, a model of the urn field, named in honor of George Polya, this type of statistical model used as an idealized mental exercise structure, unifying many treatments. In the model box, the objects of real interest are represented as co ...

## Probabilistic relevance model (BM25)

## Dunford–Pettis property

In functional analysis, the Dunford–Pettis property, named after Nelson Dunford and George. b. Pettis is a Banach space property that all weakly compact operators from this space to another Banach space is completely continuous. Many of the stand ...

## Infinite-dimensional holomorphy

In mathematics, infinite-dimensional of holomorphes is a branch of functional analysis. This is due to the generalization of the notion of holomorphic functions in the given functions and taking values in complex Banach spaces, usually of infinit ...

## List of Banach spaces

In the mathematical field of functional analysis, Banach spaces are one of the most important objects of study. In other areas of mathematical analysis, most of the places that arise in practice, are Banach spaces as well.

## Lorentz space

In mathematical analysis, Lorentz spaces, introduced by George G. Lorentz in the 1950s, the years are generalizations of the more familiar L R {\the style property display the value of L^{P}} spaces. The Lorentz spaces are denoted by L P, Q {\the ...

## Lp sum

In mathematics, particularly in functional analysis, L P the sum of a family of Banach spaces is a way of turning a subset of the product Set of the family members in a Banach space in its own right. Construction is due to the classical L P space.

## Method of continuity

In mathematics, Banach spaces, the method of continuity provides sufficient conditions for deducing the invertibility of one of the restricted linear operator from another associated operator.

## Opial property

In mathematics, the Opial property is an abstract property of Banach spaces that plays an important role in the study of weak convergence of iterations of mappings of Banach spaces, asymptotic behavior of nonlinear semigroups. The hotel is named ...

## Polynomially reflexive space

Polynomials in mathematics, a reflexive space is a Banach space X, where the space of all polynomials in each degree is a reflexive space. Given a multilinear functional M N of degree n, i.e. M n n-linear, we can define a polynomial P as p x = M ...

## Schauder basis

In mathematics, a Schauder basis or countable basis is similar to the usual basis of the vector space, the difference is that Hamel bases use linear combinations that are finite sums, while for Schauder bases they may be infinite sums. This makes ...

## Tsirelson space

In mathematics, especially functional analysis, the Tsirelson space is the first example of Banach spaces containing l P space nor a 0 space can be embedded. In Tsirelson space is reflexive. It was introduced by B. S. Tsirelson in 1974. In the sa ...

## Abel equation of the first kind

In mathematics, Abels equation of the first kind, named after Niels Henrik Abel, is any ordinary differential equation that is cubic in the unknown function. In other words, this equation of the form y ′ = f 3 x y 3 + f 2 x y 2 + f 1 x y + f 0 x ...

## Encyclopedic dictionary

Translation
 аҧсуа Afaraf Afrikaans Akan Shqip አማርኛ العربية Aragonés Հայերեն অসমীয়া авар мацӀ avesta aymar aru azərbaycan dili bamanankan башҡорт теле euskara Беларуская বাংলা भोजपुरी Bislama bosanski jezik brezhoneg български език ဗမာစာ Català Chamoru нохчийн мотт chiCheŵa 中文 чӑваш чӗлхи Kernewek corsu ᓀᐦᐃᔭᐍᐏᐣ hrvatski česky dansk ދިވެހި Nederlands English Esperanto eesti Eʋegbe føroyskt vosa Vakaviti suomi français Fulfulde Galego ქართული Deutsch Ελληνικά Avañeẽ ગુજરાતી Kreyòl ayisyen Hausa עברית עברית Otjiherero हिन्दी Hiri Motu Magyar Interlingua Bahasa Indonesia Originally called Occidental Gaeilge Asụsụ Igbo Iñupiaq Ido Íslenska Italiano ᐃᓄᒃᑎᑐᑦ 日本語 basa Jawa kalaallisut ಕನ್ನಡ Kanuri कश्मीरी Қазақ тілі ភាសាខ្មែរ Gĩkũyũ Ikinyarwanda кыргыз тили коми кыв KiKongo 한국어 كوردی‎ Kuanyama latine Lëtzebuergesch Luganda Limburgs Lingála ພາສາລາວ lietuvių kalba Luba-Katanga latviešu valoda Gaelg македонски јазик Malagasy fiteny بهاس ملايو‎ മലയാളം Malti te reo Māori मराठी Kajin M̧ajeļ монгол Ekakairũ Naoero Dinékʼehǰí Norsk bokmål isiNdebele नेपाली Owambo Norsk nynorsk Norsk ꆈꌠ꒿ Nuosuhxop isiNdebele Occitan ᐊᓂᔑᓈᐯᒧᐎᓐ ѩзыкъ словѣньскъ Afaan Oromoo ଓଡ଼ିଆ ирон æвзаг ਪੰਜਾਬੀ पाऴि فارسی polski پښتو Português Runa Simi rumantsch grischun kiRundi română русский язык संस्कृतम् sardu سنڌي، سندھی‎ Davvisámegiella gagana faa Samoa yângâ tî sängö српски језик Gàidhlig chiShona සිංහල slovenčina slovenščina Soomaaliga Sesotho español Basa Sunda Kiswahili SiSwati svenska தமிழ் తెలుగు تاجیکی‎ ไทย ትግርኛ བོད་ཡིག Türkmen Wikang Tagalog Setswana faka Tonga Türkçe Xitsonga تاتارچا‎ Twi Reo Tahiti ئۇيغۇرچە‎ українська اردو أۇزبېك‎ Tshivenḓa Tiếng Việt Volapük Walon Cymraeg Wollof Frysk isiXhosa ייִדיש Yorùbá Saɯ cueŋƅ аҧсуа Afaraf Afrikaans Akan Shqip አማርኛ العربية Aragonés Հայերեն অসমীয়া авар мацӀ avesta aymar aru azərbaycan dili bamanankan башҡорт теле euskara Беларуская বাংলা भोजपुरी Bislama bosanski jezik brezhoneg български език ဗမာစာ Català Chamoru нохчийн мотт chiCheŵa 中文 чӑваш чӗлхи Kernewek corsu ᓀᐦᐃᔭᐍᐏᐣ hrvatski česky dansk ދިވެހި Nederlands English Esperanto eesti Eʋegbe føroyskt vosa Vakaviti suomi français Fulfulde Galego ქართული Deutsch Ελληνικά Avañeẽ ગુજરાતી Kreyòl ayisyen Hausa עברית עברית Otjiherero हिन्दी Hiri Motu Magyar Interlingua Bahasa Indonesia Originally called Occidental Gaeilge Asụsụ Igbo Iñupiaq Ido Íslenska Italiano ᐃᓄᒃᑎᑐᑦ 日本語 basa Jawa kalaallisut ಕನ್ನಡ Kanuri कश्मीरी Қазақ тілі ភាសាខ្មែរ Gĩkũyũ Ikinyarwanda кыргыз тили коми кыв KiKongo 한국어 كوردی‎ Kuanyama latine Lëtzebuergesch Luganda Limburgs Lingála ພາສາລາວ lietuvių kalba Luba-Katanga latviešu valoda Gaelg македонски јазик Malagasy fiteny بهاس ملايو‎ മലയാളം Malti te reo Māori मराठी Kajin M̧ajeļ монгол Ekakairũ Naoero Dinékʼehǰí Norsk bokmål isiNdebele नेपाली Owambo Norsk nynorsk Norsk ꆈꌠ꒿ Nuosuhxop isiNdebele Occitan ᐊᓂᔑᓈᐯᒧᐎᓐ ѩзыкъ словѣньскъ Afaan Oromoo ଓଡ଼ିଆ ирон æвзаг ਪੰਜਾਬੀ पाऴि فارسی polski پښتو Português Runa Simi rumantsch grischun kiRundi română русский язык संस्कृतम् sardu سنڌي، سندھی‎ Davvisámegiella gagana faa Samoa yângâ tî sängö српски језик Gàidhlig chiShona සිංහල slovenčina slovenščina Soomaaliga Sesotho español Basa Sunda Kiswahili SiSwati svenska தமிழ் తెలుగు تاجیکی‎ ไทย ትግርኛ བོད་ཡིག Türkmen Wikang Tagalog Setswana faka Tonga Türkçe Xitsonga تاتارچا‎ Twi Reo Tahiti ئۇيغۇرچە‎ українська اردو أۇزبېك‎ Tshivenḓa Tiếng Việt Volapük Walon Cymraeg Wollof Frysk isiXhosa ייִדיש Yorùbá Saɯ cueŋƅ
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