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alternate case: tuple

Wieferich pair (773 words) [view diff] exact match in snippet view article find links to article

OEIS: A253684 and OEIS: A253685 in OEIS) Barker sequence or Wieferich n-tuple is a generalization of Wieferich pair and Wieferich triple. It is primes

In mathematics, especially order theory, a partial order on a set is an arrangement such that, for certain pairs of elements, one precedes the other. The

that admit ordered tuples, extension by multiple constants as shown here can be accomplished by addition of a new constant tuple and the new constant

a result, TUPLE [A, B, C] conforms to (may be assigned to) TUPLE [A, B], to TUPLE [A] and to TUPLE (without parameters), the topmost tuple type to which

the scientific literature with locations in texts being identified as a tuple within square brackets, for example [54.5798, −3.5820]. The appropriate

minimum tuple size of 4 characters and a maximum tuple length of 10 characters, then the following sub-strings will be indexed: Even though tuple indexes

subset of the Cartesian product X1 × ... × Xn; that is, it is a set of n-tuples (x1, ..., xn), each being a sequence of elements xi in the corresponding

is a Pythagorean n-tuple for any tuple of positive integers (m1, ..., mn) with m2 1 > m2 2 + ... + m2 n. The Pythagorean n-tuple can be made primitive

and tuple type: The depth attribute defines the number of channels in the image, such as 1 for greyscale images and 3 for RGB images. The tuple type

existence of a tuple in the database, then the database could be in two different states with respect to that tuple—the first state contains the tuple, while

The relational calculus consists of two calculi, the tuple relational calculus and the domain relational calculus, that is part of the relational model

Line 1, Address Line 2, City, and Postal Code. More formally, a row is a tuple containing a specific value for each column, for example: (1234, 'Big Company

Such a tensor can be defined as a linear function which maps an (M + N)-tuple of M one-forms and N vectors to a scalar. Consider the following octet of

the C++11 standard (e.g. smart pointers, thread, regex, random, ratio, tuple) and the C++17 standard (e.g. filesystem, any, optional, variant, string_view)

QUEL is a relational database query language, based on tuple relational calculus, with some similarities to SQL. It was created as a part of the Ingres

specific choice of a minimal set of attributes that uniquely specify a tuple (row) in a relation (table). A primary key is a choice[clarification needed]

compound data types: Tuples Tuples are containers for a fixed number of Erlang data types. The syntax {D1,D2,...,Dn} denotes a tuple whose arguments are

fetching from a tuple by type instead of by index. If the tuple has more than one element of the type, a compile-time error results: tuple<string, string

conjecture on prime k-tuples, and the first violation is expected to likely occur for very large values of x. For example, an admissible k-tuple (or prime constellation)

In relational database theory, a tuple-generating dependency (TGD) is a certain kind of constraint on a relational database. It is a subclass of the class

. Args> struct concatenator<cnt, std::tuple<Args...>> { using type = typename concatenator<cnt - 1, std::tuple< typename res< number<cnt> >::result, Args

x0 (assuming x0 is a positive integer), then the distribution of the m-tuple {X1,...,Xm} is negative multinomial. These variables are not multinomially

identified with an MCC/MNC tuple as well. For WiMAX networks, a globally unique Broadband Operator ID can be derived from the MCC/MNC tuple. TETRA networks use

nested_loop_join is for each tuple r in R do for each tuple s in S do if r and s satisfy the join condition then yield tuple <r,s> This algorithm will involve

Stream[Char]) = in match { case cur #:: tail => { def loop(tuple: Result): Result = { val (res, goto) = tuple if (goto == 0) { loop(res match { case NTexpr(v, in)

"Trillian"} 2> Msg. "Trillian" LFE: lfe> (set (tuple len status msg) #(8 ok "Trillian")) lfe> ;; or with LFE literal tuple syntax: lfe> (set `#(,len ,status ,msg)

corresponds to a tuple of Java files [c1…cn], and documentation df is a tuple of HTML files [h1…hk]. A GenVoca value (nested tuples) can be depicted as

systems where the various components interact with each other by exchanging tuples or entries via one or more shared spaces. This is contrasted with the more

required by an axiom, the axiom of pairing. More generally, an unordered n-tuple is a set of the form {a1, a2,... an}. Düntsch, Ivo; Gediga, Günther (2000)

PROCEDURE [ANY, TUPLE [STRING, STRING]] -- Drawing agent of Current. feature {NONE} -- Implementation draw (a_data_agent: FUNCTION [ANY, TUPLE, TUPLE [name, color:

The Pseudo K-tuple nucleotide composition or PseKNC, is a method for converting a nucleotide sequence (DNA or RNA) into a numerical vector so as to be

In number theory, a diophantine m-tuple is a set of m positive integers { a 1 , a 2 , a 3 , a 4 , … , a m } {\displaystyle \{a_{1},a_{2},a_{3},a_{4},\ldots

rewriting systems). For a finite and non-empty set Γ, a tree stack over Γ is a tuple (t, p) where t is a partial function from strings of positive integers to

\Sigma \ ^{-i}=\prod _{j\in \mathrm {N} ,j\neq i}\Sigma \ ^{j}} , is a tuple of strategies for all players other than i. Outcome space Γ {\displaystyle

storage the basic unit is a tuple. Tuples in tuple sets handle the same role as rows in tables for relational databases. Tuples have an arbitrary number

with or without an index. Originally based upon relational algebra and tuple relational calculus, SQL consists of many types of statements, which may

minimum degree k − 1 admit a k-tuple dominating set. However, even if the graph admits k-tuple dominating set, a minimum k-tuple dominating set can be nearly

geometry, the mixed volume is a way to associate a non-negative number to a tuple of convex bodies in R n {\displaystyle \mathbb {R} ^{n}} . This number depends

observation in demography that the approximate rate of multiple births is one n-tuple birth per 89n-1 singleton births: twin births occur about once per 89 singleton

states: Every relation must have at least one index. A transaction can access tuples only after finding them through one or more indices on the relation A transaction

In particular, it is 3-independent: every 3-tuple of keys is equally likely to be mapped to any 3-tuple of hash values. However, it is not 4-independent

of the query is the set of tuples X1 to Xn that make the DRC formula true. This language uses the same operators as tuple calculus, the logical connectives

string tuple, then takes in a function (like foo) that maps from an integer to an integer and string tuple. Its output is an integer and string tuple, which

and Ai → Ai+1 into the morphism Ai−1 → Ai+1, yielding a (k − 1)-tuple for every k-tuple. Similarly, the degeneracy maps s i : N ( C ) k → N ( C ) k + 1

decomposition can be recovered by rejoining the projections. Let t be a tuple in π S 1 ( R ) ⋈ π S 2 ( R ) ⋈ . . . ⋈ π S k ( R ) {\displaystyle \pi _{S_{1}}(R)\bowtie

double sph_neumannl( unsigned n, long double x ) ; new <tuple> header file – tuple based on Boost Tuple library vaguely an extension of the standard std::pair

list_of_lists for elem in lst] def catmull_rom_spline( P0: tuple, P1: tuple, P2: tuple, P3: tuple, num_points: int, alpha: float = 0.5, ): """ Compute the

an integer tuple. In the other direction, the discontinuous function that rounds every tuple of real numbers to the nearest integer tuple is also a quasi-isometry:

→ q {\displaystyle p\rightarrow q} . A labelled transition system is a tuple ( S , Λ , T ) {\displaystyle (S,\Lambda ,T)} where S {\displaystyle S} is

argument, which must be a tuple. In ToonTalk's presentation, a rule appears as a robot, a program as a team of robots, and a tuple as a box that can have

is either a single string tuple, or some use of a (potentially different) composition function which reduces to a string tuple. Rewrite rules look like

form a friendly pair; n numbers with the same abundancy form a friendly n-tuple. Being mutually friendly is an equivalence relation, and thus induces a

mathematics, the Lindström–Gessel–Viennot lemma provides a way to count the tuples of non-intersecting lattice paths, or, more generally, paths on a directed

store a (channel, node, quality) tuple. As ionospheric conditions and mobile-node locations change, these quality tuples will shift. The stored data can

languages, such as Go, F# and Python, combine parallel assignment, tuples, and automatic tuple unpacking to allow multiple return values from a single function

(n+1)-tuple by applying the step 1 difference, p i = p ^ i − p ^ i − 1 . {\displaystyle p_{i}={\hat {p}}_{i}-{\hat {p}}_{i-1}.} Moreover, the (n+1)-tuples associated

paradigm for software generation, where a model of a product line is a tuple of 0-ary and 1-ary functions (program transformations). This page discusses

(unital) ring, described in the language of universal algebra, is an ordered tuple ( R , + , × , a , 0 , 1 ) {\displaystyle (R,+,\times ,a,0,1)} satisfying

coordinated in sets and tuples (see below). Tuple. Tuple is an ordered collection of one or more members from different dimensions. Tuples can be specified by

protocol, source address, destination address, layer-4 protocol, layer-4 key) tuple. The layer-4 key depends on the transport protocol; for TCP/UDP it is the

(PseAAC), used in computational biology for proteomics analysis and pseudo K-tuple nucleotide composition (PseKNC) for genome analysis.[citation needed] He

type. template<typename... Values> class tuple; // takes zero or more arguments The above template class tuple will take any number of typenames as its

[Games in Satisfaction Form] A game in satisfaction form is described by a tuple ( K , { A k } k ∈ K , { f k } k ∈ K ) , {\displaystyle \left({\mathcal {K}}

tuples of values appearing in columns A 1 , . . . , A n {\displaystyle A_{1},...,A_{n}} for facts of R {\displaystyle R} must also appear as a tuple of

continuous; The coalition consistency property: there exists a weight-vector-tuple w, assigning a weight-vector wS to each possible coalition S, such that

is the most general type of constraint used in practice, including both tuple-generating dependencies and equality-generating dependencies. Embedded dependencies

closed manifold in codimension 0 (if the original manifold is closed). A k-tuple point (double, triple, etc.) of an immersion f : M → N is an unordered set

channels in an in tuple and specifying all possible outputs in an out tuple. Every join-pattern in the set must conform to the box input tuple type specifying

symbols { A, C, D, R, L, N, ; } to encode each 5-tuple; as described in the article Turing machine, his 5-tuples are only of types N1, N2, and N3. The number

^{n}} can be represented as a vector-valued function that associates an n-tuple of real numbers to each point of the domain. This representation of a vector

charge on D creates the same electrostatic field outside D as does a k-tuple of point charges at the points z1, …, zk. Quadrature domains and numerous

states. Formally, a deterministic finite automaton A may be defined by the tuple (Q, Σ, δ, q0, F), where Q is the set of states of the automaton, Σ is the

an initial tuple of particles p 1 ∈ P ∗ {\displaystyle \mathbf {p} ^{1}\in P^{*}} . In a specific particle method, the elements of the tuple ( P , G ,

<gpl:GPL_CoordinateTuple xmlns:gpl="http://www.isotc211.org/gpl"> <gpl:tuple srsName="urn:ogc:def:crs:EPSG:6.6:4326"> 35.89421911 139.94637467 </gpl:tuple>

the subject of an optimization problem and computes the Pareto optimum on tuples with multiple dimensions. This operator is an extension to SQL proposed

primes. An equivalent definition of Skewes's number exists for prime k-tuples (Tóth (2019)). Let P = ( p , p + i 1 , p + i 2 , . . . , p + i k ) {\displaystyle

are infinitely many prime sextuplets. A prime sextuple is the largest k-tuple with spacing no greater than 4 between primes. The Skewes number for the

std::unreachable: a function to mark unreachable code made std::tuple compatible with other tuple-like objects std::basic_common_reference specialization for

This type is called the color set of the place. Definition 1. A net is a tuple N = (P, T, A, Σ, C, N, E, G, I ) where: P is a set of places. T is a set

are the n-tuples. The restriction of a pattern to an n-tuple can be regarded as an n-bit number which, together with the identity of the n-tuple, constitutes

variable X {\displaystyle X} is denoted H ( X ) {\displaystyle H(X)} . For a tuple of random variables X 1 , X 2 , … , X n {\displaystyle X_{1},X_{2},\ldots

typing import List, NamedTuple, Tuple class PVQEntry(NamedTuple): codeword: int point: Tuple[int, ...] normalizedPoint: Tuple[float, ...] def create_pvq_codebook(n:

calculus, a calculus for the relational data model Domain relational calculus Tuple calculus, inspired the SQL language Refinement calculus, a way of refining

s := − r mod ( p − 1 ) {\displaystyle s:=-r{\bmod {(p-1)}}} . Then the tuple ( r , s ) {\displaystyle (r,s)} is a valid signature for the message m =

container. UBJSON uses a single binary tuple to represent all JSON value types: type [length] [data] Each element in the tuple is defined as: The type is a 1-byte

extension of some predicates, where the extension of a predicate is the set of tuples of values the predicate is true on. This minimization is similar to the

of an interval. The intersection algorithm begins by creating a table of tuples <offset, type>. For each interval there are three entries: the lower endpoint

The set of all x {\displaystyle x} -tuples is denoted by E x {\displaystyle E_{x}} . For an x {\displaystyle x} -tuple f {\displaystyle f} and a subset y

atomic formula or atom is commonly defined as a predicate applied to a tuple of terms; a ground atom is then a predicate in which only ground terms appear

L-model) in a language L, φ an L-formula, and a ¯ {\displaystyle {\bar {a}}} a tuple of elements of the domain dom(A) of A.[clarification needed] In other words

H. If the degree of every (r – 1)-tuple in V⁄V1 is strictly larger than n⁄2, and the degree of every (r – 1)-tuple in V⁄Vr is at least n⁄2, then H admits

Essential tuple normal form (ETNF) is a normal form used in database normalization. It lies strictly between fourth normal form (4NF) and fifth normal

perfect matchings on n {\displaystyle n} nodes). Their goal is to output a tuple ⟨ i , j , b ⟩ {\displaystyle \langle i,j,b\rangle } such that the edge (

every constraint (every tuple of every relation of the first structure) into a tuple in the relation of the constraint (a tuple in the corresponding relation

platform group. Alice's public/private information: Alice's public key is a tuple of elements a = ( a 1 , … , a n ) {\displaystyle {\bf {a}}=(a_{1},\ldots

{\displaystyle F_{S}:I\to O} . Therefore, the ideal software generates the tuple ( I k , O k ) {\displaystyle (I_{k},O_{k})} which is the input-output set

the tuple. A tuple is a relationship between things. If the concept under analysis is neither a type nor an individual, then it must be a tuple. We identify

n-dimensional vector bundles over a projective line as corresponding to unordered n-tuples of integers. This phenomenon cannot be generalized to higher dimensional

in M. In other words: If there is a tuple a1,…,an in N such that φ(a1,…,an,b1,…,bn) holds in N, then such a tuple also exists in M. This notion is often

Universal Plug and Play (UPnP) Devices Profile for Web Services (DPWS) Tuple space CORBA "Releases". Retrieved 12 June 2017. Reiss, Kevin Kelly, Spencer

and the following is the end of the quote (penultimate 4-tuple): As however the final 4-tuple is incomplete after the period, it must be padded with three

In twelve-tone equal temperament, one can start off with an ordered 12-tuple (tone row) of integers: (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11) representing

Result of FISH analysis using LSI probe (TUPLE 1) from DiGeorge/velocardiofacial syndrome critical region. TUPLE 1 (HIRA) probe was labeled in Spectrum

programming page is recommended, it explains how an FOSD model of a domain is a tuple of 0-ary functions (called values) and a set of 1-ary (unary) functions

one constructor, then the ADT corresponds to a product type similar to a tuple or record. A constructor with no fields corresponds to the empty product

definitions; here is one. A (nondeterministic) infinite-tree automaton is a tuple A = ( Σ , D , Q , q 0 , δ , F ) {\displaystyle A=(\Sigma ,D,Q,q_{0},\delta

same class of formal languages. A queue machine can be defined as a six-tuple M = ( Q , Σ , Γ , $ , s , δ ) {\displaystyle M=(Q,\Sigma ,\Gamma ,\$,s,\delta

Diophantine m-tuples. Dujella has shown that there exists no Diophantine 6-tuple and that there exist at most a finite number of Diophantine 5-tuples. He applied

contain struct and tuple variants. enum Message { Quit, Move { x: i32, y: i32 }, // struct Write(String), // single-element tuple ChangeColor(i32, i32

size n {\displaystyle n} . Tuple W = ( w 1 , w 2 , … , w n ) {\displaystyle W=(w_{1},w_{2},\dots ,w_{n})} , which is the tuple of the (positive) symbol

cardinality among all k-dominating and k-tuple dominating sets are the k-domination number and the k-tuple domination number, respectively. On the square

This result implies the existence of an infinitely repeatable prime 2-tuple, thus establishing a theorem akin to the twin prime conjecture. Zhang's

straight-three engine A semi-truck with three trailers Triple (mathematics) (3-tuple), a list or sequence with three elements Triple (category theory), a construction

here, so AC is not needed); it merely consists of N-tuples. Let a = (a1, ..., aN) be such an N-tuple. We extend a to the whole index set: take a to the

> n {\displaystyle m>n} sending an m {\displaystyle m} -tuple to an n {\displaystyle n} -tuple by forgetting the last coordinates. On a connected variety

taken from a finite set K. The system state is the n-tuple x = (x1, x2, ... , xn), and x[v] is the tuple consisting of the states associated to the vertices

We say that a 5-tuple ( ϕ 1 , … , ϕ 5 ) ∈ C [ I ] 5 {\textstyle (\phi _{1},\dots ,\phi _{5})\in C[I]^{5}} is a Kolmogorov–Arnold tuple if and only if for

σ-algebra F {\displaystyle {\mathcal {F}}} on X . {\displaystyle X.} Then the tuple ( X , F ) {\displaystyle (X,{\mathcal {F}})} is called a measurable space

We say that a 5-tuple ( ϕ 1 , … , ϕ 5 ) ∈ C [ I ] 5 {\textstyle (\phi _{1},\dots ,\phi _{5})\in C[I]^{5}} is a Kolmogorov–Arnold tuple if and only if for

σ-algebra F {\displaystyle {\mathcal {F}}} on X . {\displaystyle X.} Then the tuple ( X , F ) {\displaystyle (X,{\mathcal {F}})} is called a measurable space

introduced by Poizat (1983). M is a model of some theory. x and y stand for n-tuples of variables, for some natural number n. An equivalence formula is a formula

which is no more than the lowest-cost path to the goal Admissible prime k-tuple, in number theory regarding possible constellations of prime numbers Admissible

105 {\displaystyle n=105} , n ± 2, ± 4, and ± 8 must be prime (a prime k-tuple). In contrast, n ± 6, ± 10, ± 12, and ± 14 must be composite, making a prime

M} that is identically equal to m . {\displaystyle m.} This constant map/tuple is an element of the Cartesian product M I = ∏ i ∈ I M {\displaystyle M^{I}={\textstyle

an ℓ {\displaystyle \ell } -tuple of variables and x ¯ {\displaystyle {\overline {x}}} is an n {\displaystyle n} -tuple of variables. The (right) Ziegler

the product operates on n I-tuples by applying operation nfj of Bi to the n elements in the i-th coordinate of the n tuples, for all i in I. When all the

denotes an input that encodes the Turing machine M. Let m be the size of the tuple ([M], x). We know that we can decide membership of Hf by way of a deterministic

form BCNF: Boyce–Codd normal form 4NF: Fourth normal form ETNF: Essential tuple normal form 5NF: Fifth normal form DKNF: Domain-key normal form 6NF: Sixth

variables. A solution of such an equation is a n-tuple such that substituting each element of the tuple for the corresponding variable transforms the equation

\varepsilon } denotes the empty string. A PDA is formally defined as a 7-tuple: M = ( Q , Σ , Γ , δ , q 0 , Z , F ) {\displaystyle M=(Q,\Sigma ,\Gamma

hyperparameter choices than others. Hyperparameter optimization finds a tuple of hyperparameters that yields an optimal model which minimizes a predefined

an m-tuple (x1, ..., xm) where each xi is either equal to 0 (patient does not show symptom i) or 1 (patient does show symptom i). Each such m-tuple is called

mathematics, Dickson's lemma states that every set of n {\displaystyle n} -tuples of natural numbers has finitely many minimal elements. This simple fact

derivative has an integer tuple, and a monomial order ranks the derivative by ranking the derivative's integer tuple. The integer tuple identifies the differential

the projection from Rn to Rk is the function that maps every n-tuple to the k-tuple of the components corresponding to the subset of variables. The projection

uniquely determined by any k-tuple of argument-value pairs with distinct arguments, from which it follows that any k-tuple of distinct arguments is equally

target's control-flow graph; the documentation refers to these edges as tuples and the counts as hitcounts. At the end of the execution, the hitcounts

an m {\displaystyle m} -tuple of real numbers x {\displaystyle x} ) into some codomain (e.g. an n {\displaystyle n} -tuple of real numbers f ( x ) {\displaystyle

Points. In that article, a motive is a "system of realisations" – that is, a tuple ( M B , M D R , M A f , M cris , p , comp D R , B , comp A f , B , comp

to live 87,360 = unitary perfect number 88,789 = the start of a prime 9-tuple, along with 88793, 88799, 88801, 88807, 88811, 88813, 88817, and 88819.

first digits are all distinct, for each of the qq possible choices of the q-tuple (a, b, c, ...). The illustration shows a larger example of the same construction

element, are however slower on lists than on arrays. A record (also called tuple or struct) is an aggregate data structure. A record is a value that contains

{\displaystyle r^{i}\in \mathbb {R} _{+}^{N}} . Each household begins with a tuple of ownerships of the producers α i , j ≥ 0 {\displaystyle \alpha ^{i,j}\geq

Hopcroft and Ullman (1979), an indexed grammar is formally defined a 5-tuple G = ⟨N,T,F,P,S⟩ where N is a set of variables or nonterminal symbols, T

parenthetical expression or tuple (... | ...) (proofs | values) .<...>. termination metric @(...) flat tuple or variadic function parameters tuple (see example's printf)

internally on a 'tuple space', while the Maps are not actually stored but are helpers, each representing nothing more than an immutable tuple prefix. Maps

for any n-ary relation R {\displaystyle R} in our signature and for any n-tuple of terms ( t 1 , … , t n ) {\displaystyle (t_{1},\ldots ,t_{n})} ; An equality

{\displaystyle A=(\Sigma _{1},\Sigma _{2},\ldots ,\Sigma _{n})} denote an n-tuple of (not necessarily pairwise disjoint) alphabets Σ k {\displaystyle \Sigma

two new columns of type DATETIME: StartDate and EndDate. This is known as tuple versioning. These two additional columns define a period of time of "validity"

set in A (in B). iii) A tuple (b_1, ..., b_n) ∈ B^n is guarded in B if {b_1, ..., b_n} ⊆ X for some guarded set X ⊆ B. iv) A tuple (b_1, ..., b_k) ∈ B^k

such that for every (n + 1)-tuple (x0, x1, ... ,xn) of self-adjoint elements of A and every ε > 0, there exists an (n + 1)-tuple (y0, y1, ... ,yn) of self-adjoint

r 2 {\displaystyle q=r_{2}} . The RSA public key is represented as the tuple ( n , e ) {\displaystyle (n,e)} , where the integer e is the public exponent

treatments of logic. Formally, a (single-sorted) signature can be defined as a 4-tuple σ = ( S func , S rel , S const , ar ) , {\displaystyle \sigma =\left(S_{\operatorname

to take. A probabilistic Turing machine can be formally defined as the 7-tuple M = ( Q , Σ , Γ , q 0 , A , δ 1 , δ 2 ) {\displaystyle M=(Q,\Sigma ,\Gamma

languages, enum variants in Rust can contain additional data in the form of a tuple or struct, making them tagged unions rather than simple enumerated types

Smith brothers there are. The starting elements of the smallest Smith n-tuple (meaning n consecutive Smith numbers) in base 10 for n = 1, 2, ... are 4

generated by two group members: one that swaps the first two elements of a five-tuple, and one that performs a circular shift operation on the last four elements

Expressions of the tuple and array types can be written through listing the values, and can be accessed with .index or [index]: let tuple: (u32, bool) = (3

the whole construction is kept finite. A basic categorial grammar is a tuple ( Σ , Prim , S , ◃ ) {\displaystyle (\Sigma ,{\text{Prim}},S,\triangleleft

variables; its domain contains tuples of values for the variables in the associated set; in particular, these are the tuples that satisfy a set of constraints

(an evidence or a confidence) about trust can be represented as a four-tuple (trust, distrust, uncertainty, base rate), where trust, distrust and uncertainty

objects are natural numbers 0, 1, 2,..., and which, for each n, has an n-tuple of morphisms: proji: n → 1, i = 1, ..., n This allows interpreting n as

quintuple-wise intersections. Continue, until the cardinality of the n-tuple-wise intersection is included (if n is odd) or excluded (n even). The name

more rugged to long sequences of errors. Byte/m-tuple conversion: data bytes are encoded into bit m-tuples (m = 4, 5, 6, 7, or 8). Differential coding: In

endofunctor of C {\displaystyle C} , then an F {\displaystyle F} -algebra is a tuple ( A , α ) {\displaystyle (A,\alpha )} , where A {\displaystyle A} is an

intend to figure out about the dirty data: figuring out if some database tuple is certain (i.e., is in every repaired database), figuring out if some query

strategy, it ensures uniform data distribution. With n partitions, the ith tuple in insertion order is assigned to partition (i mod n). This strategy enables

property of the Proj construction; geometrically it corresponds to the d-tuple Veronese embedding. So without loss of generality one may assume that the

similarly to what is dubbed RDBMS, Tuple Stores, also known as Triple Store or Quad Store but also Generic Tuple Store, Document database, that mimics

 list {\displaystyle \tau {}{\text{ list}}} is any k {\displaystyle k} -tuple of values of type τ {\displaystyle \tau } for any k ≥ 0 {\displaystyle k\geq

5, the majority are divisible by 10. Conversion from RAL Design number tuple to CIELAB RAL Design = ( h a b ∘ , L ∗ , C a b ∗ ) a ∗ = C a b ∗ ⋅ cos ⁡

transformation can take any given distinct points Qi for i = 1, 2, 3 to any other 3-tuple Ri of distinct points (triple transitivity). This amount of specification

Distributed data store Document-oriented database Multi-model database Tuple space Ordered Key-Value Store Name–value pair Corbellini, Alejandro; Mateos

and D values of the last tuple. For r1 the following sets have the uniqueness property, i.e., there are no two distinct tuples in the instance with the

definition of equilibrium. According to Nash, "an equilibrium point is an n-tuple such that each player's mixed strategy maximizes [their] payoff if the strategies

given angle and a full turn of 2π radians Circular shift, an operation on a tuple Bitwise rotation, a mathematical operator on bit patterns Curl (mathematics)

definitions of both the differentials from step 2. It is trivial to see that the tuple ( S 0 , C 0 , K [ 0 , 0 ] ) {\displaystyle (S_{0},C_{0},K[0,0])} from the

[citation needed] A (nondeterministic two-way) nested stack automaton is a tuple ⟨Q,Σ,Γ,δ,q0,Z0,F,[,],]⟩ where Q, Σ, and Γ is a nonempty finite set of states

(y,z,x)\in X\}} which permute the entries of an ordered tuple is that, for example, the tuple ( x 1 , x 2 , x 3 , x 4 ) {\displaystyle (x_{1},x_{2},x_{3}

of the previous row. The null End_Date in row two indicates the current tuple version. A standardized surrogate high date (e.g. 9999-12-31) may instead

most prominent ones. This approach presents a framework based on the LINDA tuple space concept to meet these requirements. The implemented TUIpist framework

machine with n {\displaystyle n} -tapes can be formally defined as a 6-tuple M = ⟨ Q , Σ , Γ , δ , q 0 , F ⟩ {\displaystyle M=\langle Q,\Sigma ,\Gamma

L an element of M, and to each n-ary function symbol f of L and each n-tuple ⟨a0,...,an-1⟩ of elements of M, the model must assign an element of M to

elevation: float = 0.0, *, debugtz: tzinfo | None = None, ) -> tuple[float, float, None] | tuple[None, None, bool]: log.debug(f"Latitude f = {_deg2human(f)}")

choose a strategy profile described by the ( N − 1 ) {\displaystyle (N-1)} -tuple a − i {\displaystyle a_{-i}} , then player i {\displaystyle i} 's utility

timed-automaton contains a transition function, which associates to a 3-tuple ( ℓ , a , c ) {\displaystyle (\ell ,a,c)} , with c ∈ B a , ℓ {\displaystyle

0.2))) ;; Generate graphics Scheme] (stree->tree ‘(with "gr-geometry" (tuple "geometry" "400px" "300px" "center") (graphics (with "color" "blue" (text-at

representation for a given ω-language. Formally, a deterministic ω-automaton is a tuple A = (Q,Σ,δ,Q0,Acc) that consists of the following components: Q is a finite

types are: Functional dependency Join dependency Multivalued dependency Tuple-generating dependency Transitive dependency Equality-generating dependency

tree". A nondeterministic Turing machine can be formally defined as a six-tuple M = ( Q , Σ , ι , ⊔ , A , δ ) {\displaystyle M=(Q,\Sigma ,\iota ,\sqcup

produce (k -1) n GF(q) keystream values at each iteration. Compute the kn-tuple of GF(q) values S(x) = (Q1(x),..., Qkn(x)) where x is the current value

calculus, a calculus for the relational data model Domain relational calculus Tuple calculus Refinement calculus, a way of refining models of programs into

P=\{P_{i}\}} gets ordered too. Let the sorted set be a N {\displaystyle N} tuple :- P s =< P i > ; i < j ⟹ | R ( P i ) | < | R ( P j ) | {\displaystyle

punctuation and a rich set of data types (such as URL, email, date and time, tuple, string, tag) that respect common standards. It is designed to not need

reformulated as follows: ω1, ω2, ... , ωn are rationally independent if the only n-tuple of integers k1, k2, ... , kn such that k 1 ω 1 + k 2 ω 2 + ⋯ + k n ω n =

of Lie algebras. An r-component multipartition of an integer n is an r-tuple of partitions λ(1), ..., λ(r) where each λ(i) is a partition of some ai

specifically for this translation. Formally, a generalized Büchi automaton is a tuple A = (Q,Σ,Δ,Q0, F {\displaystyle {\cal {F}}} ) that consists of the following

the number of strokes, or strokes relative to par, rather than as a "n-tuple bogey". It is considered an achievement to complete a bogey-free round.

necessarily deterministic) PDA M {\displaystyle M} can be defined as a 7-tuple: M = ( Q , Σ , Γ , q 0 , Z 0 , A , δ ) {\displaystyle M=(Q\,,\Sigma \,,\Gamma

group G(K) embeds diagonally in the group G(A) by sending g in G(K) to the tuple (gp)p in G(A) with g = gp for all (finite and infinite) primes p. Let Z

on the indices of coordinates. That is, an ordered n {\displaystyle n} -tuple is in the same orbit as any other that is a re-ordered version of it. A

a tuple is stably in an extension at a limit, just in case there's a stage after which the tuple is in the extension up until the limit, and a tuple is

{\displaystyle K} . Furthermore, when those vectors are considered as a tuple of clocks, both vectors have the same set of possible futures. Intuitively

Operators in the orthogonal group that also preserve the orientation of vector tuples form the special orthogonal group, or the group of rotations. Operators

=(\lambda ^{1},\dots ,\lambda ^{q})} be an arbitrary q {\textstyle q} -tuple of functions, the formal adjoint of the operator D a {\textstyle {\mathcal

side-effects: Find a minimal number of tuples to delete in the database in order to delete a particular tuple in the output. Deletion propagation with

Included in the Windows 10 Fall Creators Update. Improved accessibility Value tuple types serialization SHA-2 support April 30, 2018 Supported: 4.7.2 August

Rank Operator MCC / MNC Tuple Number Prefix Technology Services Ownership Total Subscribers as of June 2025 Mainland Pakistan AJ&K/Gilgit-Baltistan 1

Let ( λ 0 , x 0 ) {\displaystyle (\lambda _{0},x_{0})} be an eigenpair. A tuple of vectors ( x 0 , x 1 , … , x r − 1 ) ∈ C n × C n × ⋯ × C n {\displaystyle

project infrastructure. Stream processing Flow-based programming (FBP) Tuple space Functional reactive programming (FRP) Linda (coordination language)

relational databases Relational concept, a set of mathematically defined tuples in tuple relational calculus Relational model, a database model based on first-order

store a file into the local OFFS storage, resp. block cache, choose the tuple size t {\displaystyle t} (default 3), split the source file s {\displaystyle

G^{p}:x_{1}x_{2}\cdots x_{p}=e\,\}} of p-tuples of elements of G whose product (in order) gives the identity. Such a p-tuple is uniquely determined by all its

and design. For example, the state of a typical 2D robot may consist of a tuple ( x , y , θ ) {\displaystyle (x,y,\theta )} for position x , y {\displaystyle

}}\mathbb {R} } (by identifying a function f {\displaystyle f} with the tuple ( f ( x ) ) x ∈ R , {\displaystyle (f(x))_{x\in \mathbb {R} },} and conversely)

and right child r {\displaystyle r} of node v {\displaystyle v} into a tuple ( l , k , r ) {\displaystyle (l,k,r)} . Node ( l , k , r ) {\displaystyle

gn) is an n-tuple of elements of G = A∗B such that M generates G, <g1, g2, ..., gn> = G, then M is Nielsen equivalent in G to an n-tuple of the form M'

Smart-M3 computing platform allows to store and retrieve information based on tuple space mechanisms. Like in Linda (coordination language), a small defined

Repeat for each value, v: Repeat for each (k − 1)-tuple of variables Repeat for each (k − 1)-tuple of values w, which together with v constitute a solution

same agent can also use shared dynamic relations acting as Linda-style tuple stores." The authors also propose that the language is suitable for representing

one has an n‑tuple of bounded self‐adjoint operators x 1 , … , x n {\displaystyle x_{1},\dots ,x_{n}} with spectra in I and an n‑tuple of operators a

Maris–McGwire–Sosa 7-tuples, 8-tuples, & 9-tuples OEIS sequence A045759 (Maris-McGwire numbers) OEIS sequence A045760 (Smallest Maris-McGwire k-tuple (k>1)) OEIS

How-to guide; contains common wisdom on how to make pair programming work. Tuple:Pair Programming Guide Pair programming guide that covers paring styles

matrices, while a weight of this algebra is simply a k {\displaystyle k} -tuple of scalars λ = ( λ 1 , … , λ k ) {\displaystyle \lambda =(\lambda _{1},\dots

^{+})^{*}} .[clarification needed] We define an EPDA by the septuple (7-tuple) M = ( Q , Σ , Γ , δ , q 0 , Q F , σ 0 ) {\displaystyle \,M=(Q,\Sigma ,\Gamma

variable, x → {\displaystyle {\vec {x}}} a tuple of first-order variables, t → {\displaystyle {\vec {t}}} a tuple of terms and the lengths of x → {\displaystyle

relationship between an agent and its environment. Formally, a POMDP is a 7-tuple ( S , A , T , R , Ω , O , γ ) {\displaystyle (S,A,T,R,\Omega ,O,\gamma )}

relationship between an agent and its environment. Formally, a POMDP is a 7-tuple ( S , A , T , R , Ω , O , γ ) {\displaystyle (S,A,T,R,\Omega ,O,\gamma )}

(abstract families of languages) theory. An AFA Schema is an ordered 4-tuple ( Γ , I , f , g ) {\displaystyle (\Gamma ,I,f,g)} , where Γ {\displaystyle

becomes a projection function (function to access the field of a record or tuple); also, # prefixes a string literal to turn it into a character literal

Voldemort Key–value store (ordered) FoundationDB, InfinityDB, LMDB, MemcacheDB Tuple store Apache River, GigaSpaces, Tarantool, TIBCO ActiveSpaces, OpenLink

\Sigma _{k}} as acting on k-tuple n = ( 1 , ⋯ , k ) {\displaystyle n=(1,\cdots ,k)} of positive integers. A given k-tuple n = ( n 1 , ⋯ , n k ) {\displaystyle

Description Sequence type* Authors Year BLAST Local search with fast k-tuple heuristic (Basic Local Alignment Search Tool) Both Altschul SF, Gish W,

DE) for exchanging typed, attributed, ordered, directed graphs (TGraphs), Tuple Attribute Language (TA: University of Waterloo, CA), and the graph format

coordinate system that allows for the measurement of each location as a tuple (x, y), which are also called the easting and northing in many systems such

dimension is given in and: A nD generalized map (or nG-map) is an (n + 2)-tuple G = (D, α0, ..., αn) such that: D is a finite set of darts; α0, ..., αn

small random seed and that are equally likely to map any k-tuple of distinct keys to any k-tuple of indexes. The parameter k can be thought of as a measure

composition operator (defined below). Formally, a finite transducer T is a 6-tuple (Q, Σ, Γ, I, F, δ) such that: Q is a finite set, the set of states; Σ is

visit machine j but not k and vice versa. Group together in cell k the tuple (i*,j*) with higher similarity coefficient, with k being the algorithm iteration

difference of these values. Formally, a value-based argumentation framework is a tuple V A F = ⟨ A , R , V , val , valprefs ⟩ {\displaystyle VAF=\langle A,R,V

bundle over U, which is sometimes also called a moving frame. This is a n-tuple of smooth 1-forms θ1, θ2, …, θn which are linearly independent at each point

import std/locks var thr: array[0..4, Thread[tuple[a,b: int]]] L: Lock proc threadFunc(interval: tuple[a,b: int]) {.thread.} = for i in interval.a..interval

\dotsc ,(t_{m1},\dotsc ,t_{mk})} from R, it holds that the tuple obtained from these m tuples by applying f coordinate-wise, i.e. ( f ( t 11 , … , t m 1

vertices and expressing an oriented simplex σ {\displaystyle \sigma } as an n-tuple ( σ [ 0 ] , σ [ 1 ] , … , σ [ n ] ) {\displaystyle (\sigma [0],\sigma [1]

Stratovarius. The vocal duties will be handled by the incredible- sounding TOMMI 'TUPLE' SALMELA who in recent years has shared the vocals with Marco Hietala in

yields the alternative presentation by order, namely as nondecreasing n-tuples between 0 and 1: Δ ∗ n = { ( s 1 , … , s n ) ∈ R n ∣ 0 = s 0 ≤ s 1 ≤ s 2

subtraction, and comparisons: def divide(number: int, divisor: int) -> tuple[int, int]: """Division by subtraction.""" if divisor == 0: raise ZeroDivisionError

operations. These redundancies can be reduced by using techniques such as tuple id propagation. There are a number of open-source libraries and tools that

arrays of bytes. The final type declared here is a STRUCT, specifically a tuple containing two integers. The program continues by declaring external procedures

Relationships and their attributes Candidate keys for each entity set Attribute and Tuple based constraints Relational Schema, including following information: Tables

IEnumerable<decimal> { private List<Tuple<DateTime, decimal>> credits; // assumed all negative private List<Tuple<DateTime, decimal>> debits; // assumed

U n ( p ) {\displaystyle U_{n}(p)} , where p is really p(x), and x is a tuple of variables of length n. This subscript is typically omitted when no confusion

tree automata.) A bottom-up finite tree automaton over F is defined as a tuple (Q, F, Qf, Δ), where Q is a set of states, F is a ranked alphabet (i.e.

membership in the language. A Positive Range Concatenation Grammar (PRCG) is a tuple G = ( N ,   T ,   V ,   S ,   P ) {\displaystyle G=(N,~T,~V,~S,~P)} , where:

⁠ above. The fully general first Hardy–Littlewood conjecture on prime k-tuples (not given here) implies that the second Hardy–Littlewood conjecture is

choice of a line L {\textstyle L} , and hence it is an invariant of the 4-tuple of lines L i . {\textstyle L_{i}.} This can be understood as follows: if

delay determined by a random variable. A stochastic Petri net is a five-tuple SPN = (P, T, F, M0, Λ) where: P is a set of states, called places. T is

Hausdorff space, a (continuous) Banach bundle over X {\displaystyle X} is a tuple B = ( B , π ) {\displaystyle {\mathfrak {B}}=(B,\pi )} , where B {\displaystyle

two items a and b such that f(a) = f(b). Let x be a mapping, and y a 2-tuple of items in its domain. The binary relation in question P(x,y) has the meaning

quadruples listed above. import math def get_primitive_bends(n: int) -> tuple[int, int, int, int]: if n == 0: yield 0, 0, 1, 1 return for m in range(math

the data volume so early on, both by representing large blocks as small tuples, and by eliminating many blocks, BRIN substantially reduce the amount of

the data volume so early on, both by representing large blocks as small tuples, and by eliminating many blocks, BRIN substantially reduce the amount of

organized on key field or primary key field). One index entry for every tuple in the data file (dense index) contains the value of the indexed attribute

There are similar efforts in other languages, such as the distributed tuple space used in the Impromptu language. Additionally Overtone, Impromptu and

{D}}_{{\mathcal {A}}_{1}},\dots ,{\mathcal {D}}_{{\mathcal {A}}_{k}}\}} is the tuple of the values taken by the assigned variables. Assignment is the association

by fertilization. This transition rule may further be defined as the 4-tuple ( E l , E u , F l , F u ) {\displaystyle (E_{l},E_{u},F_{l},F_{u})} . For

A_{i}\subseteq \mathbb {R} } ; write a {\displaystyle \mathbf {a} } for an N-tuple of actions (i.e. a ∈ ∏ j = 1 N A j {\displaystyle \mathbf {a} \in \prod

of modal logic using models defined as follows. A relational model is a tuple M = ⟨ W , R , V ⟩ {\displaystyle {\mathfrak {M}}=\langle W,R,V\rangle }

inherits from multiple classes, they are kept in the order specified in the tuple of base classes (however in this case, some classes high in the inheritance

Séances de l'Académie des Sciences (1849) Weisstein, Eric W. "de Polignac's Conjecture". MathWorld. Weisstein, Eric W. "k-Tuple Conjecture". MathWorld.

as its content. Tuples are facts holding multiple values. They are represented by a single XML element containing nested Items or Tuples. In the design

integer. Now we define the Gromov–Witten invariants associated to the 4-tuple: ( X , A , g , n ) {\displaystyle (X,A,g,n)} . Let M ¯ g , n {\displaystyle

in linear temporal logic. Formally, a deterministic Büchi automaton is a tuple A = (Q,Σ,δ,q0,F) that consists of the following components: Q is a finite

supports using a custom URI. ResultSet.config's "distinct" argument accepts a tuple of columns. Provide wrapped cursor objects in Django integration layer.

power of the set X, which is a one-element set that contains the empty tuple. Mac Lane 1998. Grégory Berhuy (2010). An Introduction to Galois Cohomology

invented them in 1963. Formally, a deterministic Muller-automaton is a tuple A = (Q,Σ,δ,q0,F) that consists of the following information: Q is a finite

structure is a "tuple consisting of latitude and longitude represents 2-dimensional geographic position", and each number in the tuple is a real number

specify a random variable, so we can identify the random variable X with the tuple ( p 0 , p 1 , p 2 ) ∈ R 3 {\displaystyle (p_{0},p_{1},p_{2})\in \mathbb

formally, a (nondeterministic) tree-walking automaton over an alphabet Σ is a tuple A = (Q, Σ, I, F, R, δ) where Q is a finite set of states, its subsets I

{\displaystyle \mathbb {A} ^{n}} is equivalently an n {\displaystyle n} -tuple of G m {\displaystyle \mathbb {G} _{m}} -equivariant maps to A 1 {\displaystyle

Littlewood in 1923 conjectured (as part of their Hardy–Littlewood prime tuple conjecture) that for any fixed c ≥ 2, the number of representations of a

dimensions. I.e., it assigns a value to each cell, which is identified by an n-tuple of dimension elements; thus the name "functional". The model retains the

{\displaystyle P} . That is, suppose that for every n {\displaystyle n} -tuple of non-negative integers p = ( p 1 , … , p n ) {\displaystyle p=\left(p_{1}

{\displaystyle m} -tuple—over the harmonic series, advancing the window by m {\displaystyle m} positions to select the next m {\displaystyle m} -tuple, and offsetting

R n {\displaystyle \mathbb {R} ^{n}} , then it can be expressed as an n-tuple of sequences in R {\displaystyle \mathbb {R} } by writing x m = ( x m 1