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Formally, a monad consists of a type constructor M and two operations, bind and return.
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Formally and consists
Formally it consists of a short lyric composed in a single metre with a single rhyme throughout.
Formally, a generalised self reproducing system consists
Formally it consists of three groups of four measure phrases of three to four chords repeated four times each, ABC :|| ABC, which then merges with the next movement, " Floe " with the entrance of the horns.
Formally, a deterministic Büchi automaton is a tuple A = ( Q, Σ, δ, q < sub > 0 </ sub >, F ) that consists of the following components:
Formally, given two categories C and D, an equivalence of categories consists of a functor F: C → D, a functor G: D → C, and two natural isomorphisms ε: FG → I < sub > D </ sub > and η: I < sub > C </ sub >→ GF.
Formally, a rigged Hilbert space consists of a Hilbert space H, together with a subspace Φ which carries a finer topology, that is one for which the natural inclusion
Formally, a frame on a homogeneous space G / H consists of a point in the tautological bundle G → G / H.
Formally, a semigroupoid consists of:
Formally, a bicategory B consists of:
Formally, Mbenga – Mbuti Pygmy music consists of at most only four parts, and can be described as an, " ostinato with variations ," or similar to a passacaglia, in that it is cyclical.
Formally, the game ( coalitional game ) consists of a finite set of players, called the grand coalition, and a characteristic function denotes the power set of .</ ref > from the set of all possible coalitions of players to a set of payments that satisfies.
Formally, he says, the piece consists of two parts of nearly equal length, the end of the first section being bars 24 – 28 ( p. 77 ).
Formally, a parsing expression grammar consists of:
Formally, a graph rewriting system usually consists of a set of graph rewrite rules of the form, with being called pattern graph ( or left-hand side ) and being called replacement graph ( or right-hand side of the rule ).
Formally, an institution consists of
Formally, a signed graph Σ is a pair ( G, σ ) that consists of a graph G = ( V, E ) and a sign mapping or signature σ from E to the sign group
Formally, the right Kan extension of along consists of a functor and a natural transformation which is couniversal with respect to the specification, in the sense that for any functor and natural transformation, a unique natural transformation is defined and fits into a commutative diagram
Formally and type
Limits and colimits in a category C are defined by means of diagrams in C. Formally, a diagram of type J in C is a functor from J to C:
Formally, type theory studies type systems.
Formally system networks correspond to type lattices in formal lattice theory, although they are occasionally erroneously mistaken for flowcharts or directed decision trees.
Formally and M
Formally, if M is a set, the identity function f on M is defined to be that function with domain and codomain M which satisfies
Formally, the singular value decomposition of an m × n real or complex matrix M is a factorization of the form
Formally, cl ( S ) denotes the smallest subset Y of M that contains S such that for each reaction ( A, B )
Formally, scalar multiplication is a linear map, inducing a map ( send a scalar λ to the corresponding scalar transformation, multiplication by λ ) exhibiting End ( M ) as a R-algebra.
Formally, we start with a metric space M and a subset X.
Formally, the problem can be stated as follows: given a desired property, expressed as a temporal logic formula p, and a structure M with initial state s, decide if.
Formally, a cardinal number κ is λ-unfoldable if and only if for every transitive model M of cardinality κ of ZFC-minus-power set such that κ is in M and M contains all its sequences of length less than κ, there is a non-trivial elementary embedding j of M into a transitive model with the critical point of j being κ and j ( κ ) ≥ λ.
Formally, the definition only requires some invertibility, so we can substitute for Q any matrix M whose eigenvalues do not include − 1.
Formally, the normal bundle to N in M is a quotient bundle of the tangent bundle on M: one has the short exact sequence of vector bundles on N:
Formally and two
Formally, the Congress serves two functions: to approve changes to the Party constitution regarding policy and to elect a Central Committee, about 300 strong.
Formally, these failed when they were rejected by the Church of England's General Synod in 1972 ; conversations and co-operation continued, however, leading in 2003 to the signing of a covenant between the two churches.
Formally, we start with a category C with finite products ( i. e. C has a terminal object 1 and any two objects of C have a product ).
Formally, this means symmetry under a sub-group of the Euclidean group of isometries in two or three dimensional Euclidean space.
Formally, EMF is classified as the external work expended per unit of charge to produce an electric potential difference across two open-circuited terminals.
Formally, an elliptic function is a function meromorphic on for which there exist two non-zero complex numbers and with ( in other words, not parallel ), such that and for all.
Formally, two variables are inversely proportional ( or varying inversely, or in inverse variation, or in inverse proportion or in reciprocal proportion ) if one of the variables is directly proportional with the multiplicative inverse ( reciprocal ) of the other, or equivalently if their product is a constant.
Formally, the two parts are given by the following expression, where is the number being encoded:
( Formally speaking, this then satisfies the premises of an axiom of well-founded induction, which asserts that these two conditions are sufficient for the proposition to hold for all x.
Formally, a homotopy between two continuous functions f and g from a
Formally, it is a norm defined on the space of bounded linear operators between two given normed vector spaces.
Formally known as trilina, the armónico has seven strings, two of which form a doubled string.
Formally, a Lie superalgebra is a ( nonassociative ) Z < sub > 2 </ sub >- graded algebra, or superalgebra, over a commutative ring ( typically R or C ) whose product, called the Lie superbracket or supercommutator, satisfies the two conditions ( analogs of the usual Lie algebra axioms, with grading ):
Formally, this is achieved by mapping the input x to a two dimensional vector u ( x )
Formally said, the intersection of each two of them is empty ( the null event ): A and B
Formally, the poem can be understood as the combination of two sonnets, though the spacing of the stanzas is irregular.
Formally, the mutual information of two discrete random variables X and Y can be defined as:
Formally, a vertex cover of a graph G is a set C of vertices such that each edge of G is incident to at least one vertex in C. The set C is said to cover the edges of G. The following figure shows examples of vertex covers in two graphs ( and the set C is marked with red ).
Formally, given two partially ordered sets ( S, ≤) and ( T, ≤), a function f: S → T is an order-embedding if f is both order-preserving and order-reflecting, i. e. for all x and y in S, one has
Formally, given a finite set X, a collection C of subsets of X, all of size n, has Property B if we can partition X into two disjoint subsets Y and Z such that every set in C meets both Y and Z.
Formally known as " Brooks Institute of Photography ," Brooks Institute offers four majors, two certificate programs and two graduate programs.
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