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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.

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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

**.**

**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 X

__Formally__

**,**

**the**convex hull may be defined

**as**

**the**intersection of all convex sets containing

__X__or

**as**

**the**

**set**of all convex combinations of points in

__X__

**.**

If R

**is****a**ring**,**let R denote**the**ring of polynomials in**the**indeterminate__X__over R**.**Hilbert proved that if R**is**" not too large ", in**the**sense that if R**is**Noetherian**,****the**same must be true for R**.**__Formally__**,**__Formally__

**,**

**the**sequence of partial sums of some infinite summation converges if for every fixed power of

__X__

**the**coefficient stabilizes

**:**there

**is**

**a**point beyond which all further partial sums

**have**

**the**same coefficient

**.**

__Formally__styled

**as**" Excelentísimo e Ilustrísimo Señor Profesor Doctor Don N

**,**Rector Magnífico de la Universidad de

__X__" ( Most Excellent

**and**Illustrious Lord Professor Doctor Don N

**,**Rector Magnificus of

**the**University of

__X__), it

**is**

**an**office of high dignity within Spanish society

**,**usually being highly respected

**.**

__Formally__

**,**

**a**statistic s

**is**

**a**measurable function of

__X__; thus

**,**

**a**statistic s

**is**evaluated

**on**

**a**random variable

__X__

**,**taking

**the**value s (

__X__), which

**is**itself

**a**random variable

**.**

__Formally__

**,**

**a**ringed space (

__X__

**,**O < sub >

__X__</ sub >)

**is**

**a**topological space

__X__together with

**a**sheaf of rings O < sub >

__X__</ sub >

**on**

__X__

**.**

__Formally__

**,**

**we**begin by considering some family of distributions for

**a**random variable

__X__

**,**that

**is**indexed by some θ

**.**

__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 and Y

__Formally__

**,**cl ( S ) denotes

**the**smallest subset

__Y__of M that contains S such that for each reaction ( A

**,**B )

__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__

**,**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__it can be seen just

**as**

**an**ordinary function from

**X**to

**the**power

**set**of

__Y__

**,**written

**as**φ

**:**

**X**→ 2 < sup >

__Y__</ sup >.

Formally and is

__Formally__organized vocational programs supported by federal funds allow high school students to gain experience in

**a**field of work which

__is__likely to lead to

**a**full-time job

**on**graduation

**.**

__Formally__

**,**

**the**

**set**of all context-free languages

__is__identical to

**the**

**set**of languages accepted by pushdown automata ( PDA ).

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__

**,**

**the**base

__is__known

**as**Naval Support Facility Diego Garcia (

**the**US activity ) or Permanent Joint Operating Base ( PJOB ) Diego Garcia (

**the**UK's term ).

__Formally__

**,**there

__is__

**a**clear distinction

**:**" DFT " refers to

**a**mathematical transformation or function

**,**regardless of how it

__is__computed

**,**whereas " FFT " refers to

**a**specific family of algorithms for computing DFTs

**.**

__Formally__

**,**oxidation state

__is__

**the**hypothetical charge that

**an**atom would

**have**if all bonds to atoms of different elements were 100 % ionic

**.**

__Formally__

**,**

**an**inner product space

__is__

**a**vector space V over

**the**field together with

**an**inner product

**,**i

**.**e., with

**a**map

__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__**,**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__

**,**

**a**profinite group

__is__

**a**Hausdorff

**,**compact

**,**

**and**totally disconnected topological group

**:**that

__is__

**,**

**a**topological group that

__is__also

**a**Stone space

**.**

__Formally__

**,**this sharing of dynamics

__is__referred to

**as**universality

**,**

**and**systems with precisely

**the**same critical exponents are said to belong to

**the**same universality class

**.**

__Formally__

**,**

**a**frame

__is__defined to be

**a**lattice L in which finite meets distribute over arbitrary joins

**,**i

**.**e

**.**every ( even infinite ) subset

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