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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, 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, a monad consists of a type constructor M and two operations, bind and return.
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 three
More rigorously, the divergence of a vector field F at a point p is defined as the limit of the net flow of F across the smooth boundary of a three dimensional region V divided by the volume of V as V shrinks to p. Formally,
Formally named " United Press Associations " for incorporation and legal purposes, but publicly known and identified as United Press or UP, it was created by the 1907 uniting of three smaller news syndicates by the Midwest newspaper publisher E. W. Scripps.
Formally classified moons include 176 planetary satellites orbiting six of the eight planets, and eight orbiting three of the five IAU-listed dwarf planets.
Formally, this means symmetry under a sub-group of the Euclidean group of isometries in two or three dimensional Euclidean space.
Formally, the process is one of progressive development, divided into three stages of increasingly complexity.
Formally nominated on July 13, 1867, Blatchford was confirmed by the United States Senate three days later, receiving his commission the same day.

Formally and groups
* Formally, when working over the reals, as here, this is accomplished by considering the limit as ε → 0 ; but the " infinitesimal " language generalizes directly to Lie groups over general rings.
Formally, according to the Constitution, citizens of Turkmenistan have the right to set up political parties and other public associations, acting within the framework of the Constitution and laws, and public associations and groups of citizens have the right to nominate their candidates in accordance with the election law.
Formally, a frieze group is a class of infinite discrete symmetry groups for patterns on a strip ( infinitely wide rectangle ), hence a class of groups of isometries of the plane, or of a strip.
Formally, this means classifying finitely generated groups with their word metric up to quasi-isometry.

Formally and four
Formally known as " Brooks Institute of Photography ," Brooks Institute offers four majors, two certificate programs and two graduate programs.

Formally and measure
Formally, a measurable cardinal is an uncountable cardinal number κ such that there exists a κ-additive, non-trivial, 0-1-valued measure on the power set of κ.
Formally, f < sub > X, Y </ sub >( x, y ) is the probability density function of ( X, Y ) with respect to the product measure on the respective supports of X and Y.
Formally, assuming our intuition from the finite dimensional case carries over into the infinite dimensional setting, the measure should then be equal to

Formally and phrases
Formally, these prepositions are actually prepositional phrases.

Formally and times
Formally, let be a stochastic process and let represent the cumulative distribution function of the joint distribution of at times.
Formally abolished in 1918 after the Russian Revolution, the academy was renamed several times.
Formally, that a wavefront can be regarded as diffraction-limited if its RMS phase error is 14 times less than its wavelength.

Formally and each
Formally, a topological space X is called compact if each of its open covers has a finite subcover.
Formally, cl ( S ) denotes the smallest subset Y of M that contains S such that for each reaction ( A, B )
Formally speaking, the strategy pattern defines a family of algorithms, encapsulates each one, and makes them interchangeable.
Formally, the outcomes Y < sub > i </ sub > are described as being Bernoulli-distributed data, where each outcome is determined by an unobserved probability p < sub > i </ sub > that is specific to the outcome at hand, but related to the explanatory variables.
Formally, this follows from the convolution theorem in mathematics, which relates the Fourier transform of the power spectrum ( the intensity of each frequency ) to its autocorrelation.
Formally, one inserts under the trace for each degree of freedom
Formally said, the intersection of each two of them is empty ( the null event ): A and B
Formally, this means that, for some function f, the image f ( D ) of a directed set D ( i. e. the set of the images of each element of D ) is again directed and has as a least upper bound the image of the least upper bound of D. One could also say that f preserves directed suprema.
Formally, A is reflexive if it is equal to the algebra of bounded operators which leave invariant each subspace left invariant by every operator in A.
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 re-assess priorities and ongoing project viability with each delivered increment
Formally, Chrétien and Martin have remained publicly respectful of each other ; while much of the verbal sparring was between their supporters.
Formally, the work is a rondo, with each return of the theme appearing in varied form.
Formally, the use of a reduction is the function that sends each natural number n to the largest natural number m whose membership in the set B was queried by the reduction while determining the membership of n in A.
Formally described, it alternates slow sections in a modal F with faster sections, " Neue Kraft fühlend " ( with renewed strength ), in D. The slow sections each have two elements, ( 1 ) a passage reminiscent of the opening of the first movement in which the instruments overlap each other with a brief motive ; ( 2 ) a chorale, the actual song.
Formally the tempo increases while the awzan simply within each of five sections, called mizan.
Formally, consider an economic model with different mathematical weightings placed on the utilities of each self.
Formally, a Markov partition is used to provide a finite cover for the smooth system ; each set of the cover is associated with a single symbol, and the sequences of symbols result as a trajectory of the system moves from one of the covering sets to another.
Formally, each of the following definitions defines a concrete category, and every pair of these categories can be shown to be concretely isomorphic.
Formally, the city has designations for each of the eight neighborhoods which are represented by neighborhood councils.
Formally, propositional models can be represented by sets of propositional variables ; namely, each model is represented by the set of propositional variables it assigns to true.
Formally, the quick steps are full strides, with one foot passing the other on each step.

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