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Page "Homotopy" ¶ 5
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Formally and between
Formally, as per the 2002 Memorandum of Understanding between the BSI and the United Kingdom Government, British Standards are defined as:
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, it is a norm defined on the space of bounded linear operators between two given normed vector spaces.
Formally, assuming the axiom of choice, cardinality of a set X is the least ordinal α such that there is a bijection between X and α.
Formally, the situation has the characteristics of a prisoner's dilemma game that is played repeatedly between the same partners, and in this case " defection "-jumping the queue-would not be advantageous.
Formally, Chrétien and Martin have remained publicly respectful of each other ; while much of the verbal sparring was between their supporters.
Formally, an antihomomorphism between X and Y is a homomorphism, where equals Y as a set, but has multiplication reversed: denoting the multiplication on Y as and the multiplication on as, we have.
a < sub > i </ sub >, a < sub > i + 1 </ sub >,..., which is a suffix of w. Formally, the satisfaction relation between a word and an LTL formula is defined as follows:
Formally called " the Wigwam ", this immense edifice was located on Girard Avenue between 19th and 20th Streets, across from Philadelphia's Girard College.
Formally, for received words, let denote the Hamming distance between and, that is, the number of positions in which and differ.
Formally dedicated with Governor Mike Easley and U. S. Representative Mike McIntyre in attendance, the segment was located between I-40 and NC 133 ( Castle Hayne Road ).
Formally, these failed when they were rejected by the Church of England's General Synod in 1972, however conversations and co-operation continued leading in 2003 to the signing of a covenant between the two churches.
Formally, the equation above defines the macroscopic neutron cross-section ( for reaction x ) as the proportionality constant between a neutron flux incident on a ( thin ) piece of material and the number of reactions that occur ( per unit volume ) in that material.
Formally ( see quote from Lewis, below ), it can also occur between nonallelic regions of the genome as well as regions of the genome that are not transcribed.
Formally known as the Federal Reserve Wire Network, Fedwire is a Real Time Gross Settlement Funds Transfer system operated by the United States Federal Reserve Banks that enables financial institutions to electronically transfer funds between its more than 9, 289 participants ( as of March 19, 2009 ).

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, 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 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, 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, 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, a monad consists of a type constructor M and two operations, bind and return.
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, 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, 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.

Formally and continuous
Formally, a strongly continuous semigroup is a representation of the semigroup ( R < sub >+</ sub >,+) on some Banach space X that is continuous in the strong operator topology.

Formally and functions
Formally, this means that the probability density functions or probability mass functions in this class have the form
Formally, given complex-valued functions f and g of a natural number variable n, one writes
Formally, the bounded Borel functional calculus of a self adjoint operator T on Hilbert space H is a mapping defined on the space of bounded complex-valued Borel functions f on the real line,
Formally, an algebraic function in n variables over the field K is an element of the algebraic closure of the field of rational functions K ( x < sub > 1 </ sub >,..., x < sub > n </ sub >).
Formally, if we denote the set of stable functions by S ( D ) and the stability radius by r ( f, D ), then:

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