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Formally, given a vector field v, a vector potential is a vector field A such that

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## Some Related Sentences

Formally and given

__Formally__

__given__to bishop Philip of Senj

**,**the permission to use the Glagolitic liturgy ( the Roman Rite conducted in Slavic language instead of Latin

**,**not the Byzantine rite ), actually extended to all Croatian lands

**,**mostly along the Adriatic coast.

__Formally__

**,**we are

__given__

**a**set of hypotheses and

**a**set of manifestations ; they are related by the domain knowledge

**,**represented by

**a**function

**that**takes as an argument

**a**set of hypotheses and gives as

**a**result the corresponding set of manifestations.

__Formally__

**,**the statement

**that**" value decreases over time "

**is**

__given__by defining the linear differential operator as:

__Formally__

**,**it

**is**

**a**norm defined on the space of bounded linear operators between two

__given__normed

**vector**spaces.

__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__

**,**

__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__

**,**an absolute coequalizer of

**a**pair in

**a**category C

**is**

**a**coequalizer as defined above but with the added property

**that**

__given__any functor F ( Q ) together with F ( q )

**is**the coequalizer of F ( f ) and F ( g ) in the category D. Split coequalizers are examples of absolute coequalizers.

__Formally__

**,**

__given__

**a**partially ordered set ( P

**,**≤), then an element g of

**a**subset S of P

**is**the greatest element of S if

__Formally__

**,**

**a**deterministic algorithm computes

**a**mathematical function ;

**a**function has

**a**unique value for any

__given__input

**,**and the algorithm

**is**

**a**process

**that**produces this particular value as output.

__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__

**,**

__given__

**a**graph G

**,**

**a**vertex labeling

**is**

**a**function mapping vertices of G to

**a**set of labels.

__Formally__this mission was declared to be only in pursuit of the Russian vessels and ammunition taken to Anzali by the White Russian counter-revolutionary General Denikin

**,**who had been

__given__asylum by British forces in Anzali.

__Formally__

**,**

**a**married or widowed woman can be called by the

__given__name of her husband ( Madame (

__given__name of husband ) family name or Madame veuve (

__given__name of husband ) family name ); this

**is**now slightly out of fashion.

Formally and vector

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__

**,**an inner product space

**is**

**a**

__vector__space V over the

**field**together with an inner product

**,**i. e., with

**a**map

__Formally__

**,**in the finite-dimensional case

**,**if the linear map

**is**represented as

**a**multiplication by

**a**matrix

**A**and the translation as the addition of

**a**

__vector__

**,**an affine map acting on

**a**

__vector__can be represented as

__Formally__

**,**

**a**transductive support

__vector__machine

**is**defined by the following primal optimization problem:

__Formally__

**,**Minkowski space

**is**

**a**four-dimensional real

__vector__space equipped with

**a**nondegenerate

**,**symmetric bilinear form with signature < tt >(−,+,+,+)</ tt > ( Some may also prefer the alternative signature < tt >(+,−,−,−)</ tt >; in general

**,**mathematicians and general relativists prefer the former while particle physicists tend to use the latter.

__Formally__

**,**

**a**coalgebra over

**a**

**field**K

**is**

**a**

__vector__space C over K together with K-linear maps Δ: C → C ⊗ C and ε: C → K

**such**

**that**

__Formally__

**,**complexification

**is**

**a**functor Vect < sub > R </ sup > → Vect < sub > C </ sup >, from the category of real

__vector__spaces to the category of complex

__vector__spaces.

__Formally__

**,**

**a**complex projective space

**is**the space of complex lines through the origin of an ( n + 1 )- dimensional complex

__vector__space.

__Formally__

**,**the Mahalanobis distance of

**a**multivariate

__vector__from

**a**group of values with mean and covariance matrix

**is**defined as:

__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 field

__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.

In late 1900s the day

**that**of the City was founded**is**Jakin School**is****a**Private School**is**__Formally__Part of Jakin School Board was Grades One through Twelve there**is**no Football__field__on this school. In 1966 When Jakin School was Closed were Sent to Blakely-Union Elementary**,**Junior High**,**and High School ( which later Became Early County High**,**Middle**,**and Elementary School ). while Carver school was built for African-American students grades One through Twelve. although late 1960s when Carver school was closed along with Kestler School was based in Damascus were sent to Washington High & Elementary at Blakely. In addition to small farm agriculture**,**Jakin's early economic growth resulted from turpentine.__Formally__

**,**an analytic function ƒ ( z ) of the real or complex variables z < sub > 1 </ sub >,…, z < sub > n </ sub >

**is**transcendental if z < sub > 1 </ sub >, …, z < sub > n </ sub >, ƒ ( z ) are algebraically independent

**,**i. e., if ƒ

**is**transcendental over the

__field__C ( z < sub > 1 </ sub >, …, z < sub > n </ sub >).

__Formally__

**,**

**a**Hopf algebra

**is**

**a**( associative and coassociative ) bialgebra H over

**a**

__field__K together with

**a**K-linear map S: H → H ( called the antipode )

**such**

**that**the following diagram commutes:

__Formally__dedicated " as

**a**memorial to the boys

**that**were " on October 30

**,**1915

**,**Alumni Field and its distinctive " maroon goal-posts on

**a**

__field__of green " were hailed in

**that**evening's edition of the Boston Saturday Evening Transcript as " one of the sights in Boston.

__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__

**,**we define

**a**bad

__field__as

**a**structure of the form ( K

**,**T ), where K

**is**an algebraically closed

__field__and T

**is**an infinite

**,**proper

**,**distinguished subgroup of K

**,**

**such**

**that**( K

**,**T )

**is**of finite Morley rank in its full language.

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