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Formally, a homotopy between two continuous functions f and g from a

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## Some Related Sentences

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__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**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__

**,**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__

**,**

**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__

**,**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__

**,**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:

0.288 seconds.