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Umberto Zannier
Umberto Zannier (born 25 May 1957, in Spilimbergo, Italy) is an Italian mathematician, specializing in number theory and Diophantine geometry.
Umberto Zannier
Umberto Zannier
Born (1957-05-25) 25 May 1957
Spilimbergo, Italy
NationalityItalian
Alma materScuola Normale Superiore di Pisa
Known forManin–M... |
Umbilical point
In the differential geometry of surfaces in three dimensions, umbilics or umbilical points are points on a surface that are locally spherical. At such points the normal curvatures in all directions are equal, hence, both principal curvatures are equal, and every tangent vector is a principal direction.... |
Umbral calculus
In mathematics before the 1970s, the term umbral calculus referred to the surprising similarity between seemingly unrelated polynomial equations and certain shadowy techniques used to "prove" them. These techniques were introduced by John Blissard and are sometimes called Blissard's symbolic method.[1]... |
Umbral moonshine
In mathematics, umbral moonshine is a mysterious connection between Niemeier lattices and Ramanujan's mock theta functions. It is a generalization of the Mathieu moonshine phenomenon connecting representations of the Mathieu group M24 with K3 surfaces.
Mathieu moonshine
The prehistory of Mathieu moo... |
Umbrella sampling
Umbrella sampling is a technique in computational physics and chemistry, used to improve sampling of a system (or different systems) where ergodicity is hindered by the form of the system's energy landscape. It was first suggested by Torrie and Valleau in 1977.[1] It is a particular physical applicat... |
Unambiguous Turing machine
In theoretical computer science, a Turing machine is a theoretical machine that is used in thought experiments to examine the abilities and limitations of computers. An unambiguous Turing machine is a special kind of non-deterministic Turing machine, which, in some sense, is similar to a det... |
Fair division among groups
Fair division among groups[1] (or families[2]) is a class of fair division problems, in which the resources are allocated among groups of agents, rather than among individual agents. After the division, all members in each group consume the same share, but they may have different preferences... |
Unary operation
In mathematics, a unary operation is an operation with only one operand, i.e. a single input.[1] This is in contrast to binary operations, which use two operands.[2] An example is any function f : A → A, where A is a set. The function f is a unary operation on A.
Common notations are prefix notation (... |
Unary function
A unary function is a function that takes one argument. A unary operator belongs to a subset of unary functions, in that its range coincides with its domain. In contrast, a unary function's domain may or may not coincide with its range.
Examples
The successor function, denoted $\operatorname {succ} $,... |
Unary language
In computational complexity theory, a unary language or tally language is a formal language (a set of strings) where all strings have the form 1k, where "1" can be any fixed symbol. For example, the language {1, 111, 1111} is unary, as is the language {1k | k is prime}. The complexity class of all such ... |
Unary numeral system
The unary numeral system is the simplest numeral system to represent natural numbers:[1] to represent a number N, a symbol representing 1 is repeated N times.[2]
Part of a series on
Numeral systems
Place-value notation
Hindu-Arabic numerals
• Western Arabic
• Eastern Arabic
• Bengali
• D... |
Assignment problem
The assignment problem is a fundamental combinatorial optimization problem. In its most general form, the problem is as follows:
The problem instance has a number of agents and a number of tasks. Any agent can be assigned to perform any task, incurring some cost that may vary depending on the agent... |
Unbiased estimation of standard deviation
In statistics and in particular statistical theory, unbiased estimation of a standard deviation is the calculation from a statistical sample of an estimated value of the standard deviation (a measure of statistical dispersion) of a population of values, in such a way that the ... |
Spectral triple
In noncommutative geometry and related branches of mathematics and mathematical physics, a spectral triple is a set of data which encodes a geometric phenomenon in an analytic way. The definition typically involves a Hilbert space, an algebra of operators on it and an unbounded self-adjoint operator, e... |
Unbounded operator
In mathematics, more specifically functional analysis and operator theory, the notion of unbounded operator provides an abstract framework for dealing with differential operators, unbounded observables in quantum mechanics, and other cases.
The term "unbounded operator" can be misleading, since
... |
O*-algebra
In mathematics, an O*-algebra is an algebra of possibly unbounded operators defined on a dense subspace of a Hilbert space. The original examples were described by Borchers (1962) and Uhlmann (1962), who studied some examples of O*-algebras, called Borchers algebras, arising from the Wightman axioms of quan... |
Fuzzy set
In mathematics, fuzzy sets (a.k.a. uncertain sets) are sets whose elements have degrees of membership. Fuzzy sets were introduced independently by Lotfi A. Zadeh in 1965 as an extension of the classical notion of set.[1][2] At the same time, Salii (1965) defined a more general kind of structure called an L-r... |
Uncertainty theory
Uncertainty theory is a branch of mathematics based on normality, monotonicity, self-duality, countable subadditivity, and product measure axioms.
Mathematical measures of the likelihood of an event being true include probability theory, capacity, fuzzy logic, possibility, and credibility, as well ... |
Schauder basis
In mathematics, a Schauder basis or countable basis is similar to the usual (Hamel) basis of a 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 Schauder bases more suitable for the analysis of in... |
Unconditional convergence
In mathematics, specifically functional analysis, a series is unconditionally convergent if all reorderings of the series converge to the same value. In contrast, a series is conditionally convergent if it converges but different orderings do not all converge to that same value. Unconditional... |
Observational study
In fields such as epidemiology, social sciences, psychology and statistics, an observational study draws inferences from a sample to a population where the independent variable is not under the control of the researcher because of ethical concerns or logistical constraints. One common observational... |
Uncountable set
In mathematics, an uncountable set (or uncountably infinite set)[1] is an infinite set that contains too many elements to be countable. The uncountability of a set is closely related to its cardinal number: a set is uncountable if its cardinal number is larger than that of the set of all natural number... |
Landau set
In voting systems, the Landau set (or uncovered set, or Fishburn set) is the set of candidates $x$ such that for every other candidate $z$, there is some candidate $y$ (possibly the same as $x$ or $z$) such that $y$ is not preferred to $x$ and $z$ is not preferred to $y$. In notation, $x$ is in the Landau s... |
Hendecahedron
A hendecahedron (or undecahedron) is a polyhedron with 11 faces. There are numerous topologically distinct forms of a hendecahedron, for example the decagonal pyramid, and enneagonal prism.
Three forms are Johnson solids: augmented hexagonal prism, biaugmented triangular prism, and elongated pentagonal ... |
Impossible object
An impossible object (also known as an impossible figure or an undecidable figure) is a type of optical illusion that consists of a two-dimensional figure which is instantly and naturally understood as representing a projection of a three-dimensional object but cannot exist as a solid object. Impossi... |
Undefined (mathematics)
In mathematics, the term undefined is often used to refer to an expression which is not assigned an interpretation or a value (such as an indeterminate form, which has the possibility of assuming different values).[1] The term can take on several different meanings depending on the context. For... |
Overcategory
In mathematics, specifically category theory, an overcategory (and undercategory) is a distinguished class of categories used in multiple contexts, such as with covering spaces (espace etale). They were introduced as a mechanism for keeping track of data surrounding a fixed object $X$ in some category ${\... |
Undercut procedure
The undercut procedure is a procedure for fair item assignment between two people. It provably finds a complete envy-free item assignment whenever such assignment exists. It was presented by Brams and Kilgour and Klamler[1] and simplified and extended by Aziz.[2]
Assumptions
The undercut procedure... |
Damping
Damping is an influence within or upon an oscillatory system that has the effect of reducing or preventing its oscillation. In physical systems, damping is produced by processes that dissipate the energy stored in the oscillation.[1] Examples include viscous drag (a liquid's viscosity can hinder an oscillatory... |
Trefoil knot
In knot theory, a branch of mathematics, the trefoil knot is the simplest example of a nontrivial knot. The trefoil can be obtained by joining together the two loose ends of a common overhand knot, resulting in a knotted loop. As the simplest knot, the trefoil is fundamental to the study of mathematical k... |
Multigraph
In mathematics, and more specifically in graph theory, a multigraph is a graph which is permitted to have multiple edges (also called parallel edges[1]), that is, edges that have the same end nodes. Thus two vertices may be connected by more than one edge.
There are 2 distinct notions of multiple edges:
... |
Forgetful functor
In mathematics, in the area of category theory, a forgetful functor (also known as a stripping functor) 'forgets' or drops some or all of the input's structure or properties 'before' mapping to the output. For an algebraic structure of a given signature, this may be expressed by curtailing the signat... |
Overshoot (signal)
In signal processing, control theory, electronics, and mathematics, overshoot is the occurrence of a signal or function exceeding its target. Undershoot is the same phenomenon in the opposite direction. It arises especially in the step response of bandlimited systems such as low-pass filters. It is ... |
Underwood Dudley
Underwood Dudley (born January 6, 1937) is an American mathematician and writer. His popular works include several books describing crank mathematics by pseudomathematicians who incorrectly believe they have squared the circle or done other impossible things.
Career
Dudley was born in New York City.... |
Unduloid
In geometry, an unduloid, or onduloid, is a surface with constant nonzero mean curvature obtained as a surface of revolution of an elliptic catenary: that is, by rolling an ellipse along a fixed line, tracing the focus, and revolving the resulting curve around the line. In 1841 Delaunay proved that the only s... |
Unfoldable cardinal
In mathematics, an unfoldable cardinal is a certain kind of large cardinal number.
Formally, a cardinal number κ is λ-unfoldable if and only if for every transitive model M of cardinality κ of ZFC-minus-power set such that κ is in M and M contains all its sequences of length less than κ, there is ... |
Net (polyhedron)
In geometry, a net of a polyhedron is an arrangement of non-overlapping edge-joined polygons in the plane which can be folded (along edges) to become the faces of the polyhedron. Polyhedral nets are a useful aid to the study of polyhedra and solid geometry in general, as they allow for physical models... |
Ungula
In solid geometry, an ungula is a region of a solid of revolution, cut off by a plane oblique to its base.[1] A common instance is the spherical wedge. The term ungula refers to the hoof of a horse, an anatomical feature that defines a class of mammals called ungulates.
The volume of an ungula of a cylinder wa... |
Mathematical operators and symbols in Unicode
The Unicode Standard encodes almost all standard characters used in mathematics.[1] Unicode Technical Report #25 provides comprehensive information about the character repertoire, their properties, and guidelines for implementation.[1] Mathematical operators and symbols ar... |
Unicoherent space
In mathematics, a unicoherent space is a topological space $X$ that is connected and in which the following property holds:
For any closed, connected $A,B\subset X$ with $X=A\cup B$, the intersection $A\cap B$ is connected.
For example, any closed interval on the real line is unicoherent, but a cir... |
Unified strength theory
The unified strength theory (UST).[1][2][3][4] proposed by Yu Mao-Hong is a series of yield criteria (see yield surface) and failure criteria (see Material failure theory). It is a generalized classical strength theory which can be used to describe the yielding or failure of material begins whe... |
Markov information source
In mathematics, a Markov information source, or simply, a Markov source, is an information source whose underlying dynamics are given by a stationary finite Markov chain.
Formal definition
An information source is a sequence of random variables ranging over a finite alphabet $\Gamma $, havi... |
Discrete uniform distribution
In probability theory and statistics, the discrete uniform distribution is a symmetric probability distribution wherein a finite number of values are equally likely to be observed; every one of n values has equal probability 1/n. Another way of saying "discrete uniform distribution" would... |
Uniform 10-polytope
In ten-dimensional geometry, a 10-polytope is a 10-dimensional polytope whose boundary consists of 9-polytope facets, exactly two such facets meeting at each 8-polytope ridge.
Graphs of three regular and related uniform polytopes.
10-simplex
Truncated 10-simplex
Rectified 10-simplex
Cantellate... |
Uniform 1 k2 polytope
In geometry, 1k2 polytope is a uniform polytope in n-dimensions (n = k+4) constructed from the En Coxeter group. The family was named by their Coxeter symbol 1k2 by its bifurcating Coxeter-Dynkin diagram, with a single ring on the end of the 1-node sequence. It can be named by an extended Schläfl... |
Uniform 2 k1 polytope
In geometry, 2k1 polytope is a uniform polytope in n dimensions (n = k+4) constructed from the En Coxeter group. The family was named by their Coxeter symbol as 2k1 by its bifurcating Coxeter-Dynkin diagram, with a single ring on the end of the 2-node sequence. It can be named by an extended Schl... |
Uniform 6-polytope
In six-dimensional geometry, a uniform 6-polytope is a six-dimensional uniform polytope. A uniform polypeton is vertex-transitive, and all facets are uniform 5-polytopes.
Graphs of three regular and related uniform polytopes
6-simplex
Truncated 6-simplex
Rectified 6-simplex
Cantellated 6-simple... |
Uniform integrability
In mathematics, uniform integrability is an important concept in real analysis, functional analysis and measure theory, and plays a vital role in the theory of martingales.
Measure-theoretic definition
Uniform integrability is an extension to the notion of a family of functions being dominated ... |
Uniform absolute-convergence
In mathematics, uniform absolute-convergence is a type of convergence for series of functions. Like absolute-convergence, it has the useful property that it is preserved when the order of summation is changed.
Motivation
A convergent series of numbers can often be reordered in such a way... |
Uniform algebra
In functional analysis, a uniform algebra A on a compact Hausdorff topological space X is a closed (with respect to the uniform norm) subalgebra of the C*-algebra C(X) (the continuous complex-valued functions on X) with the following properties:[1]
the constant functions are contained in A
for every x... |
Antiprism
In geometry, an n-gonal antiprism or n-antiprism is a polyhedron composed of two parallel direct copies (not mirror images) of an n-sided polygon, connected by an alternating band of 2n triangles. They are represented by the Conway notation An.
Set of uniform n-gonal antiprisms
Uniform hexagonal antiprism (... |
Uniform antiprismatic prism
In 4-dimensional geometry, a uniform antiprismatic prism or antiduoprism is a uniform 4-polytope with two uniform antiprism cells in two parallel 3-space hyperplanes, connected by uniform prisms cells between pairs of faces. The symmetry of a p-gonal antiprismatic prism is [2p,2+,2], order ... |
Minimax approximation algorithm
A minimax approximation algorithm (or L∞ approximation or uniform approximation) is a method to find an approximation of a mathematical function that minimizes maximum error.[1][2]
For example, given a function $f$ defined on the interval $[a,b]$ and a degree bound $n$, a minimax polyn... |
Arithmetic dynamics
Arithmetic dynamics[1] is a field that amalgamates two areas of mathematics, dynamical systems and number theory. Part of the inspiration comes from complex dynamics, the study of the iteration of self-maps of the complex plane or other complex algebraic varieties. Arithmetic dynamics is the study ... |
Uniform boundedness conjecture for rational points
In arithmetic geometry, the uniform boundedness conjecture for rational points asserts that for a given number field $K$ and a positive integer $g\geq 2$ that there exists a number $N(K,g)$ depending only on $K$ and $g$ such that for any algebraic curve $C$ defined ov... |
Compact convergence
In mathematics compact convergence (or uniform convergence on compact sets) is a type of convergence that generalizes the idea of uniform convergence. It is associated with the compact-open topology.
Definition
Let $(X,{\mathcal {T}})$ be a topological space and $(Y,d_{Y})$ be a metric space. A s... |
Uniform convergence
In the mathematical field of analysis, uniform convergence is a mode of convergence of functions stronger than pointwise convergence. A sequence of functions $(f_{n})$ converges uniformly to a limiting function $f$ on a set $E$ as the function domain if, given any arbitrarily small positive number ... |
Uniform convergence in probability
Uniform convergence in probability is a form of convergence in probability in statistical asymptotic theory and probability theory. It means that, under certain conditions, the empirical frequencies of all events in a certain event-family converge to their theoretical probabilities. ... |
Convex uniform honeycomb
In geometry, a convex uniform honeycomb is a uniform tessellation which fills three-dimensional Euclidean space with non-overlapping convex uniform polyhedral cells.
Twenty-eight such honeycombs are known:
• the familiar cubic honeycomb and 7 truncations thereof;
• the alternated cubic h... |
Uniform 4-polytope
In geometry, a uniform 4-polytope (or uniform polychoron)[1] is a 4-dimensional polytope which is vertex-transitive and whose cells are uniform polyhedra, and faces are regular polygons.
There are 47 non-prismatic convex uniform 4-polytopes. There are two infinite sets of convex prismatic forms, al... |
Dijkstra's algorithm
Dijkstra's algorithm (/ˈdaɪkstrəz/ DYKE-strəz) is an algorithm for finding the shortest paths between nodes in a weighted graph, which may represent, for example, road networks. It was conceived by computer scientist Edsger W. Dijkstra in 1956 and published three years later.[4][5][6]
Dijkstra's ... |
Uniform field theory
Uniform field theory is a formula for determining the effective electrical resistance of a parallel wire system. By calculating the mean square field acting throughout a section of coil, formulae are obtained for the effective resistances of single- and multi-layer solenoidal coils of either solid... |
Kernel (statistics)
The term kernel is used in statistical analysis to refer to a window function. The term "kernel" has several distinct meanings in different branches of statistics.
Bayesian statistics
In statistics, especially in Bayesian statistics, the kernel of a probability density function (pdf) or probabili... |
Uniform limit theorem
In mathematics, the uniform limit theorem states that the uniform limit of any sequence of continuous functions is continuous.
Statement
More precisely, let X be a topological space, let Y be a metric space, and let ƒn : X → Y be a sequence of functions converging uniformly to a function ƒ : X ... |
Uniform matroid
In mathematics, a uniform matroid is a matroid in which the independent sets are exactly the sets containing at most r elements, for some fixed integer r. An alternative definition is that every permutation of the elements is a symmetry.
Definition
The uniform matroid $U{}_{n}^{r}$ is defined over a ... |
Uniform norm
In mathematical analysis, the uniform norm (or sup norm) assigns to real- or complex-valued bounded functions $f$ defined on a set $S$ the non-negative number
$\|f\|_{\infty }=\|f\|_{\infty ,S}=\sup \left\{\,|f(s)|:s\in S\,\right\}.$
This article is about the function space norm. For the finite-dimension... |
Uniform module
In abstract algebra, a module is called a uniform module if the intersection of any two nonzero submodules is nonzero. This is equivalent to saying that every nonzero submodule of M is an essential submodule. A ring may be called a right (left) uniform ring if it is uniform as a right (left) module over... |
Uniform polyhedron compound
In geometry, a uniform polyhedron compound is a polyhedral compound whose constituents are identical (although possibly enantiomorphous) uniform polyhedra, in an arrangement that is also uniform, i.e. the symmetry group of the compound acts transitively on the compound's vertices.
The unif... |
Uniform polyhedron
In geometry, a uniform polyhedron has regular polygons as faces and is vertex-transitive (i.e., there is an isometry mapping any vertex onto any other). It follows that all vertices are congruent.
Uniform polyhedra may be regular (if also face- and edge-transitive), quasi-regular (if also edge-tran... |
Focused proof
In mathematical logic, focused proofs are a family of analytic proofs that arise through goal-directed proof-search, and are a topic of study in structural proof theory and reductive logic. They form the most general definition of goal-directed proof-search—in which someone chooses a formula and performs... |
Uniform property
In the mathematical field of topology a uniform property or uniform invariant is a property of a uniform space which is invariant under uniform isomorphisms.
Since uniform spaces come as topological spaces and uniform isomorphisms are homeomorphisms, every topological property of a uniform space is a... |
Scaling (geometry)
In affine geometry, uniform scaling (or isotropic scaling[1]) is a linear transformation that enlarges (increases) or shrinks (diminishes) objects by a scale factor that is the same in all directions. The result of uniform scaling is similar (in the geometric sense) to the original. A scale factor o... |
List of uniform polyhedra by Schwarz triangle
There are many relationships among the uniform polyhedra. The Wythoff construction is able to construct almost all of the uniform polyhedra from the acute and obtuse Schwarz triangles. The numbers that can be used for the sides of a non-dihedral acute or obtuse Schwarz tri... |
Uniform tiling symmetry mutations
In geometry, a symmetry mutation is a mapping of fundamental domains between two symmetry groups.[1] They are compactly expressed in orbifold notation. These mutations can occur from spherical tilings to Euclidean tilings to hyperbolic tilings. Hyperbolic tilings can also be divided b... |
Uniform tree
In mathematics, a uniform tree is a locally finite tree which is the universal cover of a finite graph. Equivalently, the full automorphism group G=Aut(X) of the tree, which is a locally compact topological group, is unimodular and G\X is finite. Also equivalent is the existence of a uniform X-lattice in ... |
Uniformization theorem
In mathematics, the uniformization theorem says that every simply connected Riemann surface is conformally equivalent to one of three Riemann surfaces: the open unit disk, the complex plane, or the Riemann sphere. The theorem is a generalization of the Riemann mapping theorem from simply connect... |
Gowers norm
In mathematics, in the field of additive combinatorics, a Gowers norm or uniformity norm is a class of norms on functions on a finite group or group-like object which quantify the amount of structure present, or conversely, the amount of randomness.[1] They are used in the study of arithmetic progressions ... |
Uniformizable space
In mathematics, a topological space X is uniformizable if there exists a uniform structure on X that induces the topology of X. Equivalently, X is uniformizable if and only if it is homeomorphic to a uniform space (equipped with the topology induced by the uniform structure).
Any (pseudo)metrizabl... |
Uniformization (probability theory)
In probability theory, uniformization method, (also known as Jensen's method[1] or the randomization method[2]) is a method to compute transient solutions of finite state continuous-time Markov chains, by approximating the process by a discrete-time Markov chain.[2] The original cha... |
Uniformization (set theory)
In set theory, a branch of mathematics, the axiom of uniformization is a weak form of the axiom of choice. It states that if $R$ is a subset of $X\times Y$, where $X$ and $Y$ are Polish spaces, then there is a subset $f$ of $R$ that is a partial function from $X$ to $Y$, and whose domain (t... |
Discrete valuation ring
In abstract algebra, a discrete valuation ring (DVR) is a principal ideal domain (PID) with exactly one non-zero maximal ideal.
This means a DVR is an integral domain R which satisfies any one of the following equivalent conditions:
1. R is a local principal ideal domain, and not a field.
... |
Uniformly Cauchy sequence
In mathematics, a sequence of functions $\{f_{n}\}$ from a set S to a metric space M is said to be uniformly Cauchy if:
• For all $\varepsilon >0$, there exists $N>0$ such that for all $x\in S$: $d(f_{n}(x),f_{m}(x))<\varepsilon $ whenever $m,n>N$.
Another way of saying this is that $d_{u... |
Uniform continuity
In mathematics, a real function $f$ of real numbers is said to be uniformly continuous if there is a positive real number $\delta $ such that function values over any function domain interval of the size $\delta $ are as close to each other as we want. In other words, for a uniformly continuous real... |
Uniformly connected space
In topology and related areas of mathematics a uniformly connected space or Cantor connected space is a uniform space U such that every uniformly continuous function from U to a discrete uniform space is constant.
A uniform space U is called uniformly disconnected if it is not uniformly conn... |
Uniformly disconnected space
In mathematics, a uniformly disconnected space is a metric space $(X,d)$ for which there exists $\lambda >0$ such that no pair of distinct points $x,y\in X$ can be connected by a $\lambda $-chain. A $\lambda $-chain between $x$ and $y$ is a sequence of points $x=x_{0},x_{1},\ldots ,x_{n}=y... |
Delone set
In the mathematical theory of metric spaces, ε-nets, ε-packings, ε-coverings, uniformly discrete sets, relatively dense sets, and Delone sets (named after Boris Delone) are several closely related definitions of well-spaced sets of points, and the packing radius and covering radius of these sets measure how... |
Uniformly distributed measure
In mathematics — specifically, in geometric measure theory — a uniformly distributed measure on a metric space is one for which the measure of an open ball depends only on its radius and not on its centre. By convention, the measure is also required to be Borel regular, and to take positi... |
Equidistributed sequence
In mathematics, a sequence (s1, s2, s3, ...) of real numbers is said to be equidistributed, or uniformly distributed, if the proportion of terms falling in a subinterval is proportional to the length of that subinterval. Such sequences are studied in Diophantine approximation theory and have a... |
Equicontinuity
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.
Equicontinuity ... |
Uniform isomorphism
In the mathematical field of topology a uniform isomorphism or uniform homeomorphism is a special isomorphism between uniform spaces that respects uniform properties. Uniform spaces with uniform maps form a category. An isomorphism between uniform spaces is called a uniform isomorphism.
Definition... |
Uniformly hyperfinite algebra
In mathematics, particularly in the theory of C*-algebras, a uniformly hyperfinite, or UHF, algebra is a C*-algebra that can be written as the closure, in the norm topology, of an increasing union of finite-dimensional full matrix algebras.
Definition
A UHF C*-algebra is the direct limi... |
Recurrent word
In mathematics, a recurrent word or sequence is an infinite word over a finite alphabet in which every factor occurs infinitely many times.[1][2][3] An infinite word is recurrent if and only if it is a sesquipower.[4][5]
A uniformly recurrent word is a recurrent word in which for any given factor X in ... |
Uniformly smooth space
In mathematics, a uniformly smooth space is a normed vector space $X$ satisfying the property that for every $\epsilon >0$ there exists $\delta >0$ such that if $x,y\in X$ with $\|x\|=1$ and $\|y\|\leq \delta $ then
$\|x+y\|+\|x-y\|\leq 2+\epsilon \|y\|.$
The modulus of smoothness of a normed ... |
Unimodality
In mathematics, unimodality means possessing a unique mode. More generally, unimodality means there is only a single highest value, somehow defined, of some mathematical object.[1]
Unimodal probability distribution
In statistics, a unimodal probability distribution or unimodal distribution is a probabili... |
Unimodular lattice
In geometry and mathematical group theory, a unimodular lattice is an integral lattice of determinant 1 or −1. For a lattice in n-dimensional Euclidean space, this is equivalent to requiring that the volume of any fundamental domain for the lattice be 1.
Not to be confused with modular lattice.
Th... |
Coherent topology
In topology, a coherent topology is a topology that is uniquely determined by a family of subspaces. Loosely speaking, a topological space is coherent with a family of subspaces if it is a topological union of those subspaces. It is also sometimes called the weak topology generated by the family of s... |
Axiom of union
In axiomatic set theory, the axiom of union is one of the axioms of Zermelo–Fraenkel set theory. This axiom was introduced by Ernst Zermelo.[1]
The axiom states that for each set x there is a set y whose elements are precisely the elements of the elements of x.
Formal statement
In the formal language... |
Unipotent representation
In mathematics, a unipotent representation of a reductive group is a representation that has some similarities with unipotent conjugacy classes of groups.
Informally, Langlands philosophy suggests that there should be a correspondence between representations of a reductive group and conjugacy... |
Fundamental theorem of arithmetic
In mathematics, the fundamental theorem of arithmetic, also called the unique factorization theorem and prime factorization theorem, states that every integer greater than 1 can be represented uniquely as a product of prime numbers, up to the order of the factors.[3][4][5] For example... |
Ergodicity
In mathematics, ergodicity expresses the idea that a point of a moving system, either a dynamical system or a stochastic process, will eventually visit all parts of the space that the system moves in, in a uniform and random sense. This implies that the average behavior of the system can be deduced from the... |
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