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Longer titles found: Hereditarily finite set (view), Dedekind-infinite set (view), Infinite set (view), Hyperfinite set (view), Extremal Problems For Finite Sets (view)

searching for Finite set 397 found (1174 total)

alternate case: finite set

Parametric statistics (363 words) [view diff] no match in snippet view article find links to article

statistics is a branch of statistics which leverages models based on a fixed (finite) set of parameters. Conversely nonparametric statistics does not assume explicit

that can be recursively performed to generate new symbol sequences. A finite set of productions P {\displaystyle P} is the main component in the specification

median, and the mode. A middle tendency can be calculated for either a finite set of values or for a theoretical distribution, such as the normal distribution

every family of graphs that is closed under minors can be defined by a finite set of forbidden minors, in the same way that Wagner's theorem characterizes

real constants ε i {\displaystyle \varepsilon _{i}} indexed by the same finite set I {\displaystyle I} . An operator S {\displaystyle S} lies in the neighborhood

deterministic finite state automaton is acyclic if and only if it recognizes a finite set of strings. By allowing the same vertices to be reached by multiple paths

partition and by Theodore Motzkin a list of sets. An ordered partition of a finite set may be written as a finite sequence of the sets in the partition: for

one can achieve a considerable level of accuracy. The centroid of a finite set of k {\displaystyle k} points x 1 , x 2 , … , x k {\displaystyle \mathbf

criterion (also SIC, SBC, SBIC) is a criterion for model selection among a finite set of models; models with lower BIC are generally preferred. It is based

in 1980 after completing his dissertation titled Duality Properties of Finite Set Systems under his advisor Daniel J. Kleitman. A list of his publications

distributive lattice. For the partially ordered system of all subsets of a finite set, ordered by set inclusion, the antichains are called Sperner families

subgroups H1 and H2. More generally, G is called the direct sum of a finite set of subgroups {Hi} if each Hi is a normal subgroup of G, each Hi has trivial

(typically binary operations such as addition and multiplication), and a finite set of identities, known as axioms, that these operations must satisfy. An

digital processing. The digital signal is a sequence of codes drawn from a finite set of values. The digital signal may be stored, processed or transmitted

Dickson's conjecture is the conjecture stated by Dickson (1904) that for a finite set of linear forms a1 + b1n, a2 + b2n, ..., ak + bkn with bi ≥ 1, there are

called parameters. The state of the system is generally determined by a finite set of coordinates, and the parametrization thus consists of one function

is a kind of dictionary-matching algorithm that locates elements of a finite set of strings (the "dictionary") within an input text. It matches all strings

following components: A finite set N of nonterminal symbols. A finite set Σ of terminal symbols that is disjoint from N. A finite set P of production rules

c_{\Lambda }(\eta ,\xi )>0} where Λ ⊂ G {\displaystyle \Lambda \subset G} is a finite set of sites and η , ξ ∈ Ω {\displaystyle \eta ,\xi \in \Omega } with η i

most five persons can attend such a party. Or, suppose we are given a finite set of nonzero integers, and are asked to mark as large a subset as possible

can be done in a periodic pattern. In 1961, Wang conjectured that if a finite set of Wang tiles can tile the plane, then there also exists a periodic tiling

most five persons can attend such a party. Or, suppose we are given a finite set of nonzero integers, and are asked to mark as large a subset as possible

where Q {\displaystyle \,Q} is a finite set of states; Σ ⊂ Γ {\displaystyle \,\Sigma \subset \Gamma } is the finite set of the input alphabet; Γ {\displaystyle

be applied in a more general setting than Euclidean space. Let K be a finite set of k points in some geometric setting. A line will be called an n-secant

{\displaystyle A} , and thus is 1 if and only if the events are independent. A finite set of events { A i } i = 1 n {\displaystyle \{A_{i}\}_{i=1}^{n}} is pairwise

defining a bounded convex polytope as the convex hull of a finite set of points, where the finite set must contain the set of extreme points of the polytope

where a local model space is an open subset of the vanishing locus of a finite set of holomorphic functions. Denote the constant sheaf on a topological space

of all subsets of a finite set (partially ordered by set inclusion) has this property. The lattice of partitions of a finite set typically lacks the Sperner

Bowyer–Watson algorithm is a method for computing the Delaunay triangulation of a finite set of points in any number of dimensions. The algorithm can be also used

Σ {\displaystyle \Sigma \,\!} is a finite set of symbols, Prim {\displaystyle {\text{Prim}}\,\!} is a finite set of primitive types, and S ∈ Tp ( Prim

a stochastic game are: a finite set of players I {\displaystyle I} ; a state space S {\displaystyle S} (either a finite set or a measurable space ( S

components, a partial function δ: N → U⊥, where U⊥ = U ∪ {⊥} for ⊥ ∉ U, a finite set Θ of transitions. A path u1...un ∈ U* is a string of path components ui

defined by a finite vocabulary (alphabet) Vp, and a finite set Σ of initial strings in Vp, and a finite set F of rules of the form: X → Y, where X and Y are

is given by the riffle shuffle permutation. The shuffle algebra on a finite set is the graded dual of the universal enveloping algebra of the free Lie

{\displaystyle Q\,} is a finite set of states Σ {\displaystyle \Sigma \,} is a finite set of input symbols Γ {\displaystyle \Gamma \,} is a finite set of stack symbols

mathematics, many important families of graphs can be described by a finite set of individual graphs that do not belong to the family and further exclude

specifically projective geometry, a configuration in the plane consists of a finite set of points, and a finite arrangement of lines, such that each point is

honor of Emanuel Sperner), or clutter, is a family F of subsets of a finite set E in which none of the sets contains another. Equivalently, a Sperner

In mathematics, a permutation group G acting on a non-empty finite set X is called primitive if G acts transitively on X and the only partitions the G-action

numerous algorithms are proposed for computing the convex hull of a finite set of points, with various computational complexities. Computing the convex

and Simon B. Kochen, states that for each positive integer d there is a finite set Yd of prime numbers, such that if p is any prime not in Yd then every

indeterminates. More generally, an algebraic curve is the zero set of a finite set of polynomials, which satisfies the further condition of being an algebraic

for the topology of subgroups of finite index. A finite G-set is then a finite set X on which G acts through a quotient finite cyclic group, so that it is

with finitely-many strings and repeatedly transforms them by applying a finite set j of specified rules of a certain form, thus generating a formal language

that can be computed by a mathematician with a pen and paper using a finite set of simple algorithms, can be computed by a Turing machine. Hypercomputers

x_{i}\in A\ \forall i\in \mathbb {Z} \}} , where A {\displaystyle A} is a finite set, which is closed for the Tychonov topology and invariant by translations

polyhedra are the sets of polygons and polyhedra which can be obtained from a finite set of halfplanes (halfspaces) by Boolean operations of set intersection and

music and language feature rhythmic and melodic structure. Both employ a finite set of basic elements (such as tones or words) that are combined in ordered

three-dimensional case depicted to the right). An attractor can be a point, a finite set of points, a curve, a manifold, or even a complicated set with a fractal

partitions of a finite set in the theory of ordinary cumulants is replaced by the set of all noncrossing partitions of a finite set. Just as the cumulants

systems with a finite set of rectangular reflective or refractive objects is undecidable. Ray tracing in 3-D optical systems with a finite set of reflective

{\displaystyle r_{0}} and r 1 {\displaystyle r_{1}} are equivalent if there is no finite set X {\displaystyle X} of vertices that separates infinitely many vertices

non-empty finite set of places of k, then we write AS for the ring of S-adeles and AS for the product of the completions ks, for s in the finite set S. For

isomorphic, as Borel spaces, to either the reals, the integers, or a finite set. Maharam, Dorothy (1942). "On homogeneous measure algebras". Proceedings

words differ by a generator. More precisely, let G be a group and A be a finite set of generators. Then an automatic structure of G with respect to A is a

automaton M is a 5-tuple, (Q, Σ, δ, q0, F), consisting of a finite set of states Q a finite set of input symbols called the alphabet Σ a transition function

the set of non-negative integers and the set of finite strings using a finite set of symbols (the "digits"). Most ordinary numeral systems, such as the

physical processes. A hybrid automaton is a finite state machine with a finite set of continuous variables whose values are described by a set of ordinary

theory, a group A   {\displaystyle A\ } is algebraically closed if any finite set of equations and inequations that are applicable to A   {\displaystyle

) {\displaystyle (V,{\mathcal {I}})} , where V {\displaystyle V} is a finite set and I {\displaystyle {\mathcal {I}}} is a collection of subsets of V {\displaystyle

{\displaystyle Q} is a finite set of states; Σ ⊆ Γ ∖ { b } {\displaystyle \Sigma \subseteq \Gamma \setminus \{b\}} is a finite set of input symbols, that

propositional proof system whose proofs are sequences of formulas derived using a finite set of sound and implicationally complete inference rules. Frege systems (more

Consider the group action of Z / 2 {\displaystyle \mathbb {Z} /2} on the finite set X = { − 2 , − 1 , 0 , 1 , 2 } {\displaystyle X=\{-2,-1,0,1,2\}} which

Graham's scan is a method of finding the convex hull of a finite set of points in the plane with time complexity O(n log n). It is named after Ronald Graham

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

of the utilities of each item separately. Let S {\displaystyle S} be a finite set of items. A cardinal utility function u : 2 S → R {\displaystyle u:2^{S}\to

Jerome Schaefer, states necessary and sufficient conditions under which a finite set S of relations over the Boolean domain yields polynomial-time or NP-complete

{|h|^{2}}{\sum |f_{i}^{2}|^{c}}}} is locally integrable, where the fi are a finite set of local generators of the ideal. Multiplier ideals were independently

syntax posits a finite set of syntactic categories and rules for combining them, so, too, does Conceptual Semantics posit 'a finite set of mental primitives

objects that obey a system of constraints with limited dependence. Given a finite set of bad events {A1, ..., An} in a probability space with limited dependence

check the simultaneously block triangularization and diagonalization of a finite set of matrices under the assumption that each matrix is diagonalizable over

on a surface, meeting the following conditions: The curves meet at a finite set of vertices called switches. Away from the switches, the curves are smooth

and combinatorics, an arrangement of hyperplanes is an arrangement of a finite set A of hyperplanes in a linear, affine, or projective space S. Questions

when the set of two fixed points is replaced by an arbitrary, but fixed, finite set of points in the plane is called an n–ellipse and can be thought of as

irreducibility theorem, conceived by David Hilbert in 1892, states that every finite set of irreducible polynomials in a finite number of variables and having

lattice (AGFL) formalism is a notation for context-free grammars with finite set-valued features, acceptable to linguists of many different schools. The

geometric mean is a mean or average which indicates a central tendency of a finite set of real numbers by using the product of their values (as opposed to the

of its formulae can pick out any given subset of an arbitrarily large finite set. Let T be a complete L-theory. An L-formula φ(x,y) is said to have the

commutative associative algebra A over a field K where there exists a finite set of elements a1,...,an of A such that every element of A can be expressed

involution on a finite set and its number of elements have the same parity. Thus the number of fixed points of all the involutions on a given finite set have the

\delta )} , where Q {\displaystyle Q} is a finite set of states Σ {\displaystyle \Sigma } is a finite set of symbols (the tape alphabet) ι ∈ Q {\displaystyle

usually infinite, a machine learning ensemble consists of only a concrete finite set of alternative models, but typically allows for much more flexible structure

spherical design, part of combinatorial design theory in mathematics, is a finite set of N points on the d-dimensional unit d-sphere Sd such that the average

control systems and video games. They describe switchings between a finite set of tasks in a modular fashion. Their strength comes from their ability

where (random) outcomes of experiments can be described by number or a finite set of numbers, to schemes where outcomes of experiments represent, for example

uncertainty, introduced by Ralph Hartley in 1928. If a sample from a finite set A uniformly at random is picked, the information revealed after the outcome

Gallai concerned incidences of a finite set of points in the Euclidean plane. Theorem (Sylvester-Gallai): A finite set of points in the Euclidean plane

— that is, whether there exists an algorithm for deciding if a given finite set of prototiles admits a tiling of the plane. Wang found algorithms to enumerate

producing and allocating public and private goods and choosing over a finite set of alternatives. In the case of producing and allocating public/private

Turing machines, because the latter are by definition restricted to a finite set of symbols. A Turing machine can represent a countable set (such as the

ensures that only a finite number of features will be present in any finite set of observations but more features may appear as more data points are observed

linear simple curves in the Euclidean plane associated with the shape of a finite set of points. They were first defined by Edelsbrunner, Kirkpatrick & Seidel

can be constructed as the convex hull of its vertices, and for every finite set of points, not all on the same plane, the convex hull is a convex polyhedron

following sense. Unipotent representations should form a small (preferably finite) set of irreducible representations for each reductive group, such that all

symbolically represent a Boolean function whose codomain is an arbitrary finite set S. An ADD is an extension of a reduced ordered binary decision diagram

Cheeger inequalities in expander graphs. Let X {\displaystyle X} be a finite set and let K ( x , y ) {\displaystyle K(x,y)} be the transition probability

multiplication operation × {\displaystyle \times } . The automaton consists of a finite set of states, a finite input alphabet of characters Σ {\displaystyle \Sigma

salesman problem asks for the shortest way to visit every vertex in a finite set with a discrete path, this analytical version may require the curve to

Quickhull is a method of computing the convex hull of a finite set of points in n-dimensional space. It uses a divide and conquer approach similar to that

In mathematics, a system of differential equations is a finite set of differential equations. Such a system can be either linear or non-linear. Also, such

and reflexive;: 6  i.e. a finite tolerance relation. That is, it is a finite set of ordered pairs D {\displaystyle D} , such that If ( a , b ) ∈ D {\displaystyle

either a singleton or the whole l. Finite polar spaces (where P is a finite set) are also studied as combinatorial objects. A polar space of rank two

divisors of x {\displaystyle x} and y {\displaystyle y} lying in a given finite set and that they may be effectively computed. He & Togbé (2008) showed that

where the sets A and B are disjoint, is Card (A ∪ B). The definition of a finite set is given independently of natural numbers: Definition: A set is finite

multicriteria classification (or sorting) involves problems where a finite set of alternative actions should be assigned into a predefined set of preferentially

automaton can also be described by a cellular automaton. An alphabet is any finite set of symbols, which may be thought of as the states of the cells in a cellular

sieving is a phenomenon by which evaluating a generating function for a finite set at roots of unity counts symmetry classes of objects acted on by a cyclic

three, or one of a finite set of 3-smooth numbers, then it is a winning first move, and otherwise it is losing. However, the finite set is not known. Non-constructive

an element of S {\displaystyle S} A finite set called the input alphabet Σ {\displaystyle \Sigma } A finite set called the output alphabet O {\displaystyle

(Σ, S, P), where Σ is a finite alphabet S is a finite set of base strings over Σ P is a finite set of production rules of the form u → v where u and

{\displaystyle f\colon \mathbb {R} ^{n}\rightarrow \mathbb {R} } , there exists a finite set of polynomials g i j ∈ R [ x 1 , … , x n ] {\displaystyle g_{ij}\in \mathbb

(Q,\Sigma ,\delta ,q_{0},F)} , consisting of a finite set of states Q {\displaystyle Q} , a finite set of input symbols Σ {\displaystyle \Sigma } , a

problem is the following decision problem: given a family F of subsets of a finite set S, decide whether there exists a partition of S into two subsets S1, S2

future or past of T. In a multiply non-Archimedean time, there exists a finite set of moments S (where the cardinality of S is greater than two) such that

so-called index symbols, or indices, S ∈ N is the start symbol, and P is a finite set of productions. In productions as well as in derivations of indexed grammars

Kirby, is a method for modifying framed links in the 3-sphere using a finite set of moves, the Kirby moves. Using four-dimensional Cerf theory, he proved

its fiber f−1(f(x)). In other words, every fiber is a discrete (hence finite) set. For every point x of X, the scheme f−1(f(x)) = X ×YSpec κ(f(x)) is a

algorithm is a computer algorithm for generating all permutations of a finite set of objects. Let P and c be arrays of length n with 1-based indexing (i

= 0 {\displaystyle E[z(x)(y-f(x,\theta ))]=0} . That is, z defines a finite set of orthogonality conditions. A natural question to ask, then, is whether

together with function composition, forms a regular semigroup. For a finite set of cardinality n, there are nn transformations and (n+1)n partial transformations

letter occurs in the string. More precisely, let A {\displaystyle A} be a finite set (called the alphabet), a ∈ A {\displaystyle a\in A} a letter of A {\displaystyle

extends the notion of a discrete game, where the players choose from a finite set of pure strategies. The continuous game concepts allows games to include

{\displaystyle M\in X'} , R is the field of fractions of M. There is a finite set of noetherian subrings A i {\displaystyle A_{i}} of R so that X ′ = ∪

valuations are called infinite. Infinite places of a global field form a finite set, which is denoted by P ∞ . {\displaystyle P_{\infty }.} Define O ^ :=

phrase translation, which is where the system only translates a fixed and finite set of phrases that have been manually entered into the system. Speech translation

elementary operations, and proving these results. A finite set of linear equations in a finite set of variables, for example, x1, x2, ..., xn, or x, y

three-dimensional hyperbolic space. It can be defined as the convex hull of a finite set of ideal points. An ideal polyhedron has ideal polygons as its faces,

_{0})} where Q {\displaystyle \,Q} is a finite set of states; Σ {\displaystyle \,\Sigma } is the finite set of the input alphabet; Γ {\displaystyle \

where  E  is a finite set, and card( E ) = n {\displaystyle \sum _{A\ \in \ {\mathcal {P}}(E)}1=2^{n}{\text{, where }}E{\text{ is a finite set, and card(}}E{\text{)

compositions can be decided. More precisely, if A {\displaystyle A} is a finite set of generators for G {\displaystyle G} then the word problem is the membership

asymmetric trade execution model. In this method, a customer queries a finite set of participant market makers who quote a bid/offer ("a market") to the

f(−x) = f(x) for all x even and odd permutations, a permutation of a finite set is even if it is composed of an even number of transpositions Singly even

configuration file for DOS and OS/2 operating systems Configuration (geometry), a finite set of points and lines with certain properties Configuration (polytope),

over all fields. A matroid is defined to be a family of subsets of a finite set, satisfying certain axioms. The sets in the family are called "independent

In mathematics, the cycles of a permutation π of a finite set S correspond bijectively to the orbits of the subgroup generated by π acting on S. These

for the other. A cellular automaton is defined by a grid of cells, a finite set of states that can be assigned to each cell, and an update rule. Often

that map each group element to one of the symbols in the alphabet. As a finite set, the alphabet has a discrete topology, and the collection of states can

Simple polygon which is not convex Convex polytope – Convex hull of a finite set of points in a Euclidean space Cyclic polygon – Points on a common circlePages

let S {\displaystyle S} be a semigroup and A {\displaystyle A} be a finite set of generators. Then an automatic structure for S {\displaystyle S} with

average length of the largest cycle of any function from a finite set to itself. If X is a finite set, if we repeatedly apply a function f: X → X to any element

irreducible, no two of which have the same equational theory. Hence no finite set of finite Heyting algebras can supply all the counterexamples to non-laws

can be assumed to be empty. In this case, for each finite set Xi of vertices there is a finite set Xi+1 with the property that Xi is disjoint from X i

negative value, increase until they reach zero, then cycle through a finite set of positive numbers indefinitely. When a system is rebooted, the sequence

refer to any topology on the semigroup. Let S be a semigroup and X a finite set of letters. A system of equations is a subset E of the Cartesian product

not admit a simple classification; there are continuum-many clones on a finite set of size at least three,: 39  and 22κ (even just maximal,: 39  i.e. precomplete)

the ordered set is also given by an ordinal number. In the case of a finite set, the basic operation of counting, to find the ordinal number of a particular

/ V ) {\displaystyle (\forall v/V)} , where V {\displaystyle V} is a finite set of variables. The intended reading of ( ∃ v / V ) {\displaystyle (\exists

number, a countable number less than infinity, being the cardinality of a finite set Real number, such as may result from a measurement (of time, length, area

finite set representing possible locations of an 'undesirable' public facility (e.g. garbage dump), and let S {\displaystyle S} denote a finite set of

following components: A finite set N of nonterminal symbols. A finite set Σ of terminal symbols that is disjoint from N. A finite set P of production rules

k-chromatic graph G with clique of size ω {\displaystyle \omega } and every finite set T of nonnegative integers containing 0, s p T ( K ω ) ≤ s p T ( G ) ≤

S-units. Let K be a number field with ring of integers R. Let S be a finite set of prime ideals of R. An element x of K is an S-unit if the principal

{\displaystyle M(u_{1},u_{2},\dots ,u_{n})} is hyperbolic as long as a finite set of exceptional slopes E i {\displaystyle E_{i}} is avoided for the i-th

{\hat {\Sigma }},\Gamma ,\delta ,q_{0},F)} where Q {\displaystyle Q} is a finite set of states, Σ ^ {\displaystyle {\hat {\Sigma }}} is the input alphabet

maps. A combinatorial map is a triplet M = (D, σ, α) such that: D is a finite set of darts; σ is a permutation on D; α is an involution on D with no fixed

maps. A combinatorial map is a triplet M = (D, σ, α) such that: D is a finite set of darts; σ is a permutation on D; α is an involution on D with no fixed

distribution is the discrete uniform distribution, where all elements of a finite set are equally likely. It is the probability model for the outcomes of tossing

is a finite set of states Σ {\displaystyle \Sigma } is a finite set which is called the input alphabet Γ {\displaystyle \Gamma } is a finite set which

number, a countable number less than infinity, being the cardinality of a finite set Real number, such as may result from a measurement (of time, length, area

Galois group of some field K {\displaystyle K} , unramified outside some finite set of primes S ⊂ M K {\displaystyle S\subset M_{K}} . Then the representation

low stretch factor. The Johnson–Lindenstrauss lemma asserts that any finite set with n points in a Euclidean space can be embedded into a Euclidean space

this approach (often abbreviated as FPM) the medium is represented by a finite set of points, each endowed with the relevant local properties of the medium

quotients of subalgebras of ultraproducts of members of C. (If C is a finite set of finite algebras, the ultraproduct operation is redundant.) A necessary

with respect to F {\displaystyle {\mathcal {F}}} if, for every nonempty finite set { i 1 , … , i n } {\displaystyle \{i_{1},\ldots ,i_{n}\}} of indices,

preference ordering to be representable by a utility function. For a finite set of alternatives, these require only that the preference ordering is complete

{\displaystyle \Sigma } is a finite set of symbols, called the input alphabet of the automaton, Γ {\displaystyle \Gamma } is another finite set of symbols, called

members to avoid arithmetic progressions. If S {\displaystyle S} is a finite set of non-negative integers on which no three elements form an arithmetic

of n. The asserted result follows from the fact that every non-empty finite set has an equal number of odd- and even-cardinality subsets. This last fact

be either discrete or continuous, and the range of the function is a finite set of real, usually nonnegative numbers. In continuous tomography when a

f(−x) = −f(x) for all x Even and odd permutations, a permutation of a finite set is odd if it is composed of an odd number of transpositions Odd Della

assumption that the set of all primes is finite. Rather, he said: consider any finite set of primes (he did not assume that it contained only the first n primes

and b2 is recognised by finite automata if and only if S differs by a finite set from a finite union of arithmetic progressions. The theorem was proved

group, and X {\displaystyle X} be its Cayley graph with respect to some finite set S {\displaystyle S} of generators. The set X {\displaystyle X} is endowed

D~{\textrm {and}}~x\in N\,\}} . Now let C {\displaystyle C} denote the (finite) set of codewords in the given code. The algorithm proceeds in rounds, where

traded only as a whole. For example, in combinatorial auctions there is a finite set of items, and every agent can buy a subset of the items, but an item cannot

a finite set of possible motions including translation, rotation, and vibration. This finite range of possible motions, along with the finite set of

polynomial h (in any number of variables) belongs to the ideal generated by a finite set of polynomials. Fulton, William (2008), "5.5 Max Noether's Fundamental

sequence. This allows defining linear independence for a finite set of vectors: A finite set of vectors is linearly independent if the sequence obtained

property is enough to ensure that the y • α are all different. Any nonempty finite set has a group structure as a cyclic group generated by any element. Under

by an incidence matrix. Another example is a block design. Here X is a finite set of "points" and Y is a class of subsets of X, called "blocks", subject

due to Seppo Rickman: A K-quasiregular map Rn → Rn can omit at most a finite set. When n = 2, this omitted set can contain at most two points (this is

separability. The two-dimensional version of the theorem states that, if a finite set of red and blue points in the Euclidean plane has the property that, for

Geert-Jan van Houtum. It can be characterized by saying that all values of a finite set of possible values are equally probable, except for the smallest and largest

remaining difficult part of the Skolem problem is determining whether the finite set of non-repeating zeros is empty or not. Partial solutions to the Skolem

{\displaystyle A} and the initial symbol in Γ {\displaystyle \Gamma } , the finite set of stack symbols.: 171  Equivalently, a counter automaton is a nondeterministic

interpret + as "choice", · as "sequencing" and * as "iteration". Let Σ be a finite set (an "alphabet") and let A be the set of all regular expressions over Σ

it is a regular grid of cells, each containing a state drawn from a finite set of states, with a rule for updating all cells simultaneously based on

 185: Theorem. Let U be a simple right R-module, D = End(UR), and X ⊂ U a finite set. Write I = annR(X) for the annihilator of X in R. Let u be in U with u

M)} where V N {\displaystyle V_{N}} is a finite set of non-terminals V T {\displaystyle V_{T}} is a finite set of terminals X 0 {\displaystyle X_{0}} is

been proven that already for n = 4 {\displaystyle n=4} variables, no finite set of linear inequalities is sufficient to characterize all entropic vectors

multiplying a member of the cyclic subgroup and a member of a certain finite set. Every cyclic group is virtually cyclic, as is every finite group. An

as the multiset analogue of the matroid. Let E {\displaystyle E} be a finite set and f : 2 E → R + {\displaystyle f:2^{E}\rightarrow \mathbb {R} _{+}}

( x ) {\displaystyle f(x),{\tilde {f}}(x)=V(x)f(x)} are expanded in a finite set of basis functions (this is the spectral method). For a given set of basis

cardinality, known as the transcendence degree of the extension. For every finite set S of elements of L, the algebraically independent subsets of S satisfy

graph that corresponds to a triangular grid. A Hanan grid graph for a finite set of points in the plane is produced by the grid obtained by intersections

as the multiset analogue of the matroid. Let E {\displaystyle E} be a finite set and f : 2 E → R + {\displaystyle f:2^{E}\rightarrow \mathbb {R} _{+}}

following ingredients: A finite set of state descriptions of the world S, the components of which are weakly ordered in time; A finite set of actors/agents (individual

separability. The two-dimensional version of the theorem states that, if a finite set of red and blue points in the Euclidean plane has the property that, for

defined as a 5-tuple, (Q, Σ, δ, q0, F), consisting of a finite set of states Q a finite set of input symbols Σ a set of labeled edges δ, referred to

units: A rng R is said to be a ring with local units in case for every finite set r1, r2, ..., rt in R we can find e in R such that e2 = e and eri = ri

Gordan's lemma, the set of solutions is generated by a finite set of solutions, i.e., there is a finite set M {\displaystyle M} of multi-hypergraphs, such that

model, but where the waypoints are restricted to fall within one of a finite set of sub-domains. It was originally introduced by Blaževic et al. in order

been proven that already for n = 4 {\displaystyle n=4} variables, no finite set of linear inequalities is sufficient to characterize all entropic vectors

equivalently formulated as follows: Theorem — Given a finite set V {\displaystyle V} and a finite set S {\displaystyle S} of real numbers, assume that f

For example, 3 divides 9, but 9 does not divide 3. A relation R on a finite set X may be represented as: Directed graph: Each member of X corresponds

given event. The model used in Aumann to prove the theorem consists of a finite set of states S {\displaystyle S} with a prior probability p {\displaystyle

– that is, whether there exists an algorithm for deciding if a given finite set of prototiles admits a tiling of the plane. Wang found algorithms to enumerate

multiplying a member of the cyclic subgroup and a member of a certain finite set. Every cyclic group is virtually cyclic, as is every finite group. An

of a denumerably infinite series of axioms and variables, but also a finite set of primitive symbols, denoting abstraction and scope, as well as four

of little consequence, because C[−π,π] is infinite-dimensional, and a finite set of vectors cannot span it. But, removing the restriction that n be finite

In computational geometry, a polygonalization of a finite set of points in the Euclidean plane is a simple polygon with the given points as its vertices

provability predicate of Peano arithmetic; With Alexei Kitaev, proving that a finite set of quantum gates can efficiently approximate an arbitrary unitary operator

be in normal form, we are provided with the following data: There is a finite set I of players, each player is denoted by i. Each player i has a finite

(1992), an n-player extensive-form game thus consists of the following: A finite set of n (rational) players A rooted tree, called the game tree Each terminal

one can specify its collection of facet directions and measures by a finite set of d {\displaystyle d} -dimensional nonzero vectors, one per facet, pointing

\delta ,s,t,r)} where Q {\displaystyle Q} is a finite set of states; Σ {\displaystyle \Sigma } is the finite set of the input alphabet; Γ {\displaystyle \Gamma

Some basic properties follow immediately from the definition. Every finite set of continuous functions is equicontinuous. The closure of an equicontinuous

size). Categorical distribution: for discrete random variables with a finite set of values. Absolutely continuous probability distribution: for many random

ordered list of elements either finite or infinite Systems of equations – finite set of equations Vectors – element of a vector space Matrix – two dimensional

isomorphic to the group itself. Since the only Hausdorff topology on a finite set is the discrete one, a finite Hausdorff topological group must necessarily

anonymous mathematician with the observation that, when each x is mapped to a finite set of values, F is necessarily finite. However, as Erdős showed, the situation

{\displaystyle (O_{1},O_{2},...,O_{n})} , the count number of samples from a finite set of given categories. They satisfy ∑ i O i = N {\displaystyle \sum _{i}O_{i}=N}

resources are divisible. Chores can be infinitely divisible, because the finite set of chores can be partitioned by chore or by time. For example, a load

whole residue (amino acid) is modeled as a single "bead" or "point" of a finite set of types (usually only two), and each residue is restricted to be placed

models theoretically or empirically model choices made by people among a finite set of alternatives. The models have been used to examine, e.g., the choice

mixed-strategy Nash equilibrium will exist for any zero-sum game with a finite set of actions. The contribution of Nash in his 1951 article "Non-Cooperative

variable, the target Y is generally a discrete variable consisting of a finite set of labels, and the conditional probability P ( Y ∣ X ) {\displaystyle

{\displaystyle {\mathcal {P}}(X)} is principal if and only if it contains a finite set. If X {\displaystyle X} is infinite, an ultrafilter U {\displaystyle U}

person's syntactic knowledge can be modelled with two formal mechanisms: A finite set of fundamental principles that are common to all languages; e.g., that

)=m<\infty } , then for any finite set F {\displaystyle F} of edges of Γ {\displaystyle \Gamma } there exists a finite set K {\displaystyle K} of edges

of its dynamics may immediately be seen. First, in Rule 184, for any finite set of cells with periodic boundary conditions, the number of 1s and the number

J U j ≠ ∅ , J  finite set } . {\displaystyle N(C):={\bigg \{}J\subseteq I:\bigcap _{j\in J}U_{j}\neq \varnothing ,J{\text{ finite set}}{\bigg \}}.} In

product topology are cylinder sets. These can be characterized as: If any finite set of natural number coordinates I={i} is selected, and for each i a particular

function, also known as the signum function Sign of a permutation of a finite set Project Sign, a project by the U.S. Air Force to investigate unidentified

of a module M, denoted u.dim(M), is defined to be n if there exists a finite set of uniform submodules Ui such that ⊕ i = 1 n U i {\displaystyle \oplus

conjectured that if G {\displaystyle G} is a primitive permutation group on a finite set S {\displaystyle S} and G α {\displaystyle G_{\alpha }} denotes the stabilizer

of Paretian utility · Neighboring economic agents · Economies with a finite set of equilibria · Smooth preferences · Excess demand functions · The rate

because any genotype encodes a finite set of unique phenotypes, but any given phenotype is not produced by a finite set of genotypes. Innumerable examples

directed or undirected. A state xv for each vertex i of Y taken from a finite set K. The system state is the n-tuple x = (x1, x2, ... , xn), and x[i] is

self-similar fractal nature. Formally, an iterated function system is a finite set of contraction mappings on a complete metric space. Symbolically, { f

because any genotype encodes a finite set of unique phenotypes, but any given phenotype is not produced by a finite set of genotypes. Innumerable examples

algorithms for the efficient construction of arrangements. Intuitively, any finite set of lines in the plane cuts the plane into two-dimensional polygons (cells)

\Gamma ,q_{0},A,\delta _{1},\delta _{2})} , where Q {\displaystyle Q} is a finite set of states Σ {\displaystyle \Sigma } is the input alphabet Γ {\displaystyle

as a reference to measure fairness." In multilevel processor sharing a finite set of thresholds are defined and jobs partitioned according to how much service

that for every ε > 0 , {\displaystyle \varepsilon >0,} there exists a finite set B 0 {\displaystyle B_{0}} in A such that ‖ x − ∑ y ∈ B ⟨ x , y ⟩ y ‖ <

generators are the (isomorphism classes of) orbit types of G. If G acts on a finite set X, then one can write X = ⋃ i X i {\textstyle X=\bigcup _{i}X_{i}} (disjoint

theory. For a finitely generated group, this is independent of choice of finite set of generators, hence an intrinsic property of the group. This is only

strings required for a particular purpose. A simple way to specify a finite set of strings is to list its elements or members. However, there are often

number of Kneser graphs. Every hyperplane intersects the moment curve in a finite set of at most d points. If a hyperplane intersects the curve in exactly d

of a harmonious set is harmonious. If Λ is a harmonious set and F is a finite set then the set Λ + F is also harmonious. The next two properties show that

complete or partial Herbrand structures, each of which are themselves a finite set of ground literals. Such a structure e is said to be a model of the set

set of points Graham scan - a method of finding the convex hull of a finite set of points in the plane with time complexity O(n log n) Hadwiger conjecture

tree grammar G is defined by the tuple G = (N, Σ, Z, P), where N is a finite set of nonterminals, Σ is a ranked alphabet (i.e., an alphabet whose symbols

dynamically in memory. In computing, lists are easier to implement than sets. A finite set in the mathematical sense can be realized as a list with additional restrictions;

{\displaystyle f(K)} are constants depending only on K {\displaystyle K} . For a finite set A {\displaystyle A} of integers, it is always true that | A + A | ≥ 2

{\displaystyle T(N)} . The simplest example is when X {\displaystyle X} is a finite set and μ {\displaystyle \mu } the counting measure. Then a self-map of X

collection of points can have a finite distance set. A Golomb ruler is a finite set of points on a line such that no two pairs of points have the same distance

the number of successes is one. Discrete uniform distribution, for a finite set of values (e.g. the outcome of a fair die) Continuous uniform distribution

simplicity. Characters pause before they make decisions. The small and finite set of contexts and causes impinging on them is clearly delineated. Consequences

determination of cases in which the intersections of cells results in a finite set of points. A key result is that the Schubert cells (or rather, the classes

also of "baboon eating a kebab").[citation needed] A superstring of a finite set P {\displaystyle P} of strings is a single string that contains every

y ≤ 10 {\displaystyle cx+dy\leq 10} . If P {\displaystyle P} is not a finite set, then this problem is a linear semi-infinite programming problem, namely

error correction is used, the usable gates are further restricted to a finite set.: ch. 10 : ch. 14  Later in this article, this is ignored as the focus

{\displaystyle s_{i}\in S} and k i {\displaystyle k_{i}} are integers. The finite set S generates G, so a boundedly generated group is finitely generated. An

to a probability distribution that is characterized only in terms of a finite set of statistics. The most common use of the unscented transform is in the

Netpbm – Toolkit for manipulation of images CLUT – In computer graphics, a finite set of available colorsPages displaying short descriptions of redirect targets

G = ( V , Σ , R , S ) {\displaystyle G=(V,\Sigma ,R,S)} where V is a finite set; each element v ∈ V {\displaystyle v\in V} is called a nonterminal symbol

that are not semisimple, a Cartan matrix is defined by considering a (finite) set of principal indecomposable modules and writing composition series for

degree over a fixed number field with good reduction outside a fixed finite set of places. Aleksei Parshin showed that Shafarevich's finiteness conjecture

recursive function. The Identity Correspondence Problem (ICP) asks whether a finite set of pairs of words (over a group alphabet) can generate an identity pair

data. However, in this most general form, determining a model from a finite set of samples without prior knowledge is an ill-posed problem, in the sense

groups of Lie type. A Zassenhaus group is a permutation group G on a finite set X with the following three properties: G is doubly transitive. Non-trivial

defined as a 5-tuple, (Q, Σ, δ, q0, F), consisting of a finite set of states Q a finite set of input symbols Σ a set of labeled edges δ, referred to

deducible from the latter. But it came to be realized that there is no finite set of statements about actual and possible sense-data from which we can deduce

\delta )} , where Q {\displaystyle Q} is a finite set of states; Σ {\displaystyle \Sigma } is a finite set of input symbols; q 0 ∈ Q {\displaystyle q_{0}\in

A finite set of points (in red) in the Euclidean plane.

data that is the original input for any grand tour visualization is a (finite) set of points in some high-dimensional Euclidean space. This kind of set

Ackermann-complete (and hence nonelementary). A vector addition system consists of a finite set of integer vectors. An initial vector is seen as the initial values of

automaton is a tuple ⟨Q,Σ,Γ,δ,q0,Z0,F,[,],]⟩ where Q, Σ, and Γ is a nonempty finite set of states, input symbols, and stack symbols, respectively, [, ], and ]

conjecture using a finite set of reducible configurations. Every reducible configuration contains a cycle, so for every finite set S of reducible configurations

\delta )} , where Q {\displaystyle Q} is a finite set of states; Σ {\displaystyle \Sigma } is a finite set of input symbols; q 0 ∈ Q {\displaystyle q_{0}\in

No general formula that counts the number of transitive relations on a finite set (sequence A006905 in the OEIS) is known. However, there is a formula for

A)=-D_{\mathrm {KL} }(p^{*}||q).} Define: Σ {\textstyle \Sigma } is a finite set with size ≥ 2 {\textstyle \geq 2} . Understood as “alphabet”. Δ ( Σ )

data that is the original input for any grand tour visualization is a (finite) set of points in some high-dimensional Euclidean space. This kind of set

C\sqsubseteq D} and D ⊑ C {\displaystyle D\sqsubseteq C} . A TBox is any finite set of GCIs. A concept assertion is a statement of the form a : C {\displaystyle

Andreas Dress (1992). "A canonical decomposition theory for metrics on a finite set". Advances in Mathematics. 92 (1): 47–105. doi:10.1016/0001-8708(92)90061-O

over which group they belong to. A hedonic game is specified by giving a finite set of players, and, for each player, a preference ranking over all coalitions

topological methods he proved that if H {\displaystyle {\mathcal {H}}} is a finite set system consisting of the unions of intervals on two disjoint lines, then

property of minors) among the graphs that do not belong to F there is a finite set X of minor-minimal graphs. These graphs are forbidden minors for F: a

An interpolation of a finite set of points on an epitrochoid. The points in red are connected by blue interpolated spline curves deduced only from the

Hilbert basis may refer to In Invariant theory, a finite set of invariant polynomials, such that every invariant polynomial may be written as a polynomial

(as opposed to vector images).[citation needed] Raster images have a finite set of digital values, called picture elements or pixels. The digital image

Following the classical finite volume method framework, we seek to track a finite set of discrete unknowns, Q i n = 1 Δ x ∫ x i − 1 / 2 x i + 1 / 2 q ( t n

all elements of any ideal can be written as a linear combinations of a finite set of elements, with coefficients in the ring. Many commonly considered commutative

one can specify its collection of facet directions and measures by a finite set of d {\displaystyle d} -dimensional nonzero vectors, one per facet, pointing

some functional of the distribution of x {\displaystyle x} . Based on a finite set of observations x 1 , . . . , x n {\displaystyle x_{1},...,x_{n}} , which

infinite field of prime characteristic p > 0 {\displaystyle p>0} there is no finite set of identities that characterizes power-associativity, but there are infinite

the group generated by the symmetric difference on a (not necessarily finite) set, every element has order 2. Any such group is necessarily abelian because

Gaussian Mean-Shift is an Expectation–maximization algorithm. Let data be a finite set S {\displaystyle S} embedded in the n {\displaystyle n} -dimensional Euclidean

Quantization means each amplitude measurement is approximated by a value from a finite set. Rounding real numbers to integers is an example. The Nyquist–Shannon

small acting roles, in 1987 Troisi directed Le vie del Signore sono finite, set during the Fascist era. The film won a Silver Ribbon for best screenplay

is interval finite if every interval of the form {x in P | x ≤ a} is a finite set. Inverse. See converse. Irreflexive. A relation R on a set X is irreflexive

Finite game is a game with finitely many players, each of which has a finite set of strategies. Grand coalition refers to the coalition containing all

{\displaystyle {\mathcal {S}}=\{S_{1},\ldots ,S_{n}\}} of subsets of a finite set U {\displaystyle {\mathcal {U}}} , a set basis for S {\displaystyle {\mathcal

short a block design) is a collection B of b subsets (called blocks) of a finite set X of v elements, such that any element of X is contained in the same number

ordinary non-deterministic finite automaton, one has a finite set of states Q {\displaystyle Q} a finite set of input symbols Σ {\displaystyle \Sigma } a transition

the item are not known. A general outcome set: there is an arbitrary finite set of possible outcomes, each of which yields a different payment to each

consider the real numbers with the counting measure; the measure of any finite set is the number of elements in the set, and the measure of any infinite

\operatorname {Spec} (Q(A))} is the Artinian scheme consisting (as a finite set) of the generic points of the irreducible components of Spec ⁡ ( A ) {\displaystyle

{\displaystyle M=(Q,\Gamma ,\delta ,q_{0},g)} where Q {\displaystyle Q} is the finite set of states Γ {\displaystyle \Gamma } is the finite tape alphabet δ : Q

extension L / K that is unramified outside a finite set S of primes of K (i.e. if there is a finite set S of primes of K such that any prime of K not

in the discussion on the origins of the inverse semigroup. When X is a finite set {1, ..., n}, the inverse semigroup of one-to-one partial transformations

" Ann. of Math. (2) 76 1962 531—540. MR0151948 W. B. R. Lickorish, "A finite set of generators for the homotopy group of a 2-manifold", Proc. Cambridge

s_{T})} be a sequence of states s i {\displaystyle s_{i}} belonging to a finite set of possible states. Let us denote S {\displaystyle {\mathbf {S} }} the

{\displaystyle I\subset \mathbb {K} [x_{1},x_{2},\dotsc ,x_{n}]} is a finite set of generators { g 1 , g 2 , … , g s } {\displaystyle {\{g_{1},g_{2},\dotsc

with at most 7 pages. By the Robertson–Seymour theorem, there exists a finite set H of minimal non-toroidal graphs, such that a graph is toroidal if and

nodes of an input tree. D ⊂ N {\displaystyle D\subset \mathbb {N} } is a finite set of allowed branching degrees in an input tree. For example, if D = { 2

The collection of all squared distances between pairs of points from a finite set may be stored in a Euclidean distance matrix, and is used in this form

rank α, then φ is said to have Morley degree n. A formula defining a finite set has Morley rank 0. A formula with Morley rank 1 and Morley degree 1 is

nodes of an input tree. D ⊂ N {\displaystyle D\subset \mathbb {N} } is a finite set of allowed branching degrees in an input tree. For example, if D = { 2

{\displaystyle I\subset \mathbb {K} [x_{1},x_{2},\dotsc ,x_{n}]} is a finite set of generators { g 1 , g 2 , … , g s } {\displaystyle {\{g_{1},g_{2},\dotsc

its finite subsets, which is a filtered system) and moreover, that any finite set is compact when regarded as an object of Set. Like other categorical notions

referred to as the definition of the function f {\displaystyle f} . On a finite set a function may be defined by listing the elements of the codomain that

Military. Holographic weapon sights use a holographic image of a reticle at finite set range built into the viewing window and a collimated laser diode to illuminate

in a number of ways. Let T {\displaystyle T} be a triangulation of a finite set of points A ⊂ R d {\displaystyle {\mathcal {A}}\subset \mathbb {R} ^{d}}

S2CID 207520945 Bailey, Ralph W. (1998), "The number of weak orderings of a finite set", Social Choice and Welfare, 15 (4): 559–562, doi:10.1007/s003550050123

1 , m 2 , . . . , m n {\displaystyle M={m_{1},m_{2},...,m_{n}}} is a finite set of matrices, which are non-empty sequences m i = [ p i 1 , . . . , p i

degree over a fixed number field with good reduction outside a given finite set of places, now proved as Faltings's theorem The conjecture that the absolute

that the set of natural numbers that do not satisfy this property is a finite set; that is, the set is empty or has a maximum element. As a result, the

morphism π : C′ → C. Geometrically, the assertion that π is ramified at a finite set S of points on C means that π restricted to the complement of S in C is

collection of c fuzzy clusters with respect to some given criterion. Given a finite set of data, the algorithm returns a list of c {\displaystyle c} cluster centres

local height function λ D , v {\displaystyle \lambda _{D,v}} . Fix a finite set of absolute values S {\displaystyle S} of F {\displaystyle F} , and let

finite union of finite sets, which makes Γ {\displaystyle \Gamma } a finite set. Now it follows that f − 1 ( K ) ⊆ f − 1 ( ∪ i = 1 s V k i ) ⊆ ∪ a ∈ Γ

S}p_{ij}V(j)\leq V(i)-\varepsilon } for all i ∉ F {\displaystyle i\notin F} for some finite set F {\displaystyle F} and strictly positive ε {\displaystyle \varepsilon

the polynomial ring F[u] for a finite field F, one can ask how often a finite set of polynomials fi(x) in F[u][x] simultaneously takes irreducible values

{L}}} is represented by its signature which assigns kinds and types to a finite set of constants that represents its syntax, its judgements and its rule schemes

its points contains a third point. But in the Euclidean plane, every finite set of points is either collinear, or includes a pair of points whose line

In computer graphics, a finite set of available colors

{\displaystyle \Sigma } is a finite set of symbols (alphabet) T {\displaystyle T} is a finite set of tags S {\displaystyle S} is a finite set of states with initial

well-quasi-order ( A , ≤ ) {\displaystyle (A,\leq )} , any upward closed set has a finite set of minima, and any sequence S 1 ⊆ S 2 ⊆ . . . {\displaystyle S_{1}\subseteq

= ( V , Σ , R , S ) {\displaystyle G=(V,\Sigma ,R,S)} , where V is a finite set; each element v ∈ V {\displaystyle v\in V} is called a nonterminal character

Gordan's lemma, this monoid is finitely generated, i.e., there exists a finite set of lattice points { x 1 , … , x m } ⊂ C ∩ L {\displaystyle \{x_{1},\ldots

"Angel V" of Mikołaj Jakub Kosmalski - A cubic curve formed on a finite set of points generated by a parametric formula using trigonometric functions and

the probability of a biased coin. A finite Markov chain consists of a finite set of states, and a transition probability p i , j {\displaystyle p_{i,j}}

in application programs: Arithmetic constraints over finite domains, finite set constraints, generalized propagation, interval reasoning over non-linear

Trans. Amer. Math. Soc. 247 (1979), 87-124. D. R. J. Chillingworth, A finite set of generators for the homeotopy group of a non-orientable surface, Proc

of a programming language enables the construction of programs using a finite set of constructs known as instructions. Most abstract machines share a program

Jarvis, R. A. (1973). "On the identification of the convex hull of a finite set of points in the plane". Information Processing Letters. 2: 18–21. doi:10

and only if it admits a subnormal series with cyclic factors, that is a finite set of subgroups, let's say G0, ..., Gn such that Gn coincides with G G0 is

scientific literature. A formal language is a set L for which there exists a finite set of abstract symbols Σ such that L ⊆ Σ ∗ {\displaystyle L\subseteq \Sigma

devised by Gilles Brassard, Peter Høyer and Alain Tapp in 1998. Consider a finite set { 0 , 1 } n {\displaystyle \{0,1\}^{n}} of size N = 2 n {\displaystyle

… , a m } {\displaystyle \textstyle A=\{a_{1},\ldots ,a_{m}\}} be a finite set of m {\displaystyle \textstyle m} possible actions and let Ω = { w 1

sequence of nested topological spaces derived from the covering of a finite set in a metric space by growing metric balls. It is a multidimensional extension

formalism. The discrete uniform distribution, where all elements of a finite set are equally likely. This is the theoretical distribution model for a balanced

to keep count, and verify that n is the same on both sides, unless a finite set of permissible values exists for n. It takes a full parser to recognize

belief states over the POMDP states, A {\displaystyle A} is the same finite set of action as for the original POMDP, τ {\displaystyle \tau } is the belief

element that is above every element in S. If O is any finite set of objects, and A is any finite set of unary attributes for the objects in O, then one may

\kappa ,Q_{I},F)} where Q {\displaystyle Q} is a finite set of states, K {\displaystyle K} is a finite set of keys, Σ {\displaystyle \Sigma } is a finite

cubes. Let S = { 1 , 2 , … , n } {\displaystyle S=\{1,2,\ldots ,n\}} be a finite set, containing n objects or letters. The collection of all bi-infinite strings

all documents, or the set of all images), while the class labels form a finite set Y defined prior to training. Probabilistic classifiers generalize this

{\displaystyle \left\{f_{i}\circ \pi _{i}\right\}_{i}.} A category where every finite set of objects has a product is sometimes called a Cartesian category (although

cubes. Let S = { 1 , 2 , … , n } {\displaystyle S=\{1,2,\ldots ,n\}} be a finite set, containing n objects or letters. The collection of all bi-infinite strings

intersection graph of the segments. For every two parallel lines, and every finite set of line segments with endpoints on both lines, the intersection graph

elements lying in the same orbit of a diagonal action of a finite group on a finite set is a coherent algebra, i.e. W := span ⁡ { A ( u , v ) : u , v ∈ V } {\displaystyle

embedded, called its metric envelope or tight span. The product of a finite set of metric spaces in Met is a metric space that has the cartesian product

(the Hamiltonian) associated to the interaction among all the points of finite set A. Then H Λ Φ ( ω ) {\displaystyle H_{\Lambda }^{\Phi }(\omega )} as the

is extended to a total order, the extension defines a choice from each finite set, its minimum element in the total order. Although finite choice is a weak

{\displaystyle \mathbb {R} ^{n}} is the set of the common zeros of a finite set of differentiable functions in n {\displaystyle n} variables f 1 ( x 1

\kappa ,Q_{I},F)} where Q {\displaystyle Q} is a finite set of states, K {\displaystyle K} is a finite set of keys, Σ {\displaystyle \Sigma } is a finite

be axiomatized by Σ13 sentences even if we add induction schema and a finite set of other sentences (this follows from its connection to Π12-CA0). For

{n}{k}}A_{k}(t)\cdot (t-1)^{n-1-k},{\text{ for }}n>1.} For any property partitioning a finite set into finitely many smaller sets, the sum of the cardinalities of the smaller

every finite Boolean lattice is isomorphic to the lattice of subsets of a finite set, and (less trivially) Birkhoff's representation theorem according to which

constructible sheaf over a genus g smooth projective curve C, of rank n outside a finite set X of points where it has stalk 0. Then χ ( C , F ) = n ( 2 − 2 g ) − ∑

may represent all possible allocations. Let I {\displaystyle I} be a finite set, representing a collection of individuals. For each i ∈ I {\displaystyle

generalization applies to any logical system for which the consistency of a finite set of sentences can be established. The central concept in the theory of

encodes the payoff for two players, depending on which out of a given (finite) set of strategies the players choose. Text mining and automated thesaurus

(1963), "Generalization of Sperner's theorem on the number of subsets of a finite set", Theory of Probability and Its Applications, 8 (2): 203–204, doi:10.1137/1108023

} ( # S {\displaystyle \#S} denotes the number of elements in the finite set S {\displaystyle S} .) It can be shown that if f {\displaystyle f} is

{\mathcal {C}}(X)} is only weakly complete for X {\displaystyle X} a finite set. The vague topology is the weak* topology on the dual of C ( X ) . {\displaystyle

objects; but in order to terminate, a pointer analysis can only use a finite set of names. A typical approximation is to give all the objects allocated

get an approximation to the integral. The integrand is evaluated at a finite set of points called integration points and a weighted sum of these values

overview of the subject can be found in the main tensor article. Given a finite set { V1, ..., Vn } of vector spaces over a common field F, one may form their

problem (or mortal matrix problem) is a decision problem that asks, given a finite set of n×n matrices with integer coefficients, whether the zero matrix can

is also a deformation retract of the full diffeomorphism group. For a finite set of points, the diffeomorphism group is simply the symmetric group. Similarly

{\displaystyle {\mathcal {U}}_{1}} of X {\displaystyle X} . Bob chooses a finite set F 1 ⊂ U 1 {\displaystyle {\mathcal {F}}_{1}\subset {\mathcal {U}}_{1}}

perturbation, U has only a countable spectrum, containing 1 and possibly, a finite set or a sequence tending to 1 on the unit circle. More precisely, suppose

structure of an indexed family.) Let n {\displaystyle \mathbf {n} } be the finite set { 1 , 2 , … n } , {\displaystyle \{1,2,\ldots n\},} where n {\displaystyle

centered at a point x 0 {\displaystyle x_{0}} . Consider the map from the finite set { x 1 , … , x k } {\displaystyle \{x_{1},\dots ,x_{k}\}} into { a 1 ,

the context in which they are used Safety: every expression returns a finite set of results. RDF query languages can be grouped into language families

{\displaystyle (\cdot ,\cdot )} . A root system Φ {\displaystyle \Phi } in E is a finite set of non-zero vectors (called roots) that satisfy the following conditions:

extended number line) the entities which can be represented in the format (a finite set of numbers, together with −0, infinities, and NaN) the particular representations

{\displaystyle C} can be of various types: C {\displaystyle C} may be a finite set of indivisible items, for example: C = { piano , car , apartment } {\displaystyle

labels y = y 1 , … , y n {\displaystyle y_{1},\dots ,y_{n}} from one finite set of labels Y. Instead of directly modeling P(y|x) as an ordinary linear-chain

proved the Erdős–Szemerédi theorem on the number of sums and products in a finite set. With Wolfgang Paul, Nick Pippenger, and William Trotter, he established

alternating sum is finite. In particular, the Euler characteristic of a finite set is simply its cardinality, and the Euler characteristic of a graph is

a ∈ A ⊂ X {\displaystyle a\in A\subset X} with A {\displaystyle A} a finite set, the selector selects a {\displaystyle a} from A {\displaystyle A} with

_{i}\ln(u_{i})} Risch developed a method that allows one to consider only a finite set of functions of Liouville's form. The intuition for the Risch algorithm