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Formally, a transductive support vector machine is defined by the following primal optimization problem:

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## Some Related Sentences

Formally and support

Following

**a**merger with**the**Furnishing Industry Trust (__Formally__The Furnishing Trades Benevolent Association ) in 2011**,****the**Company has become**the**most significant charity in**the**sector**,**supporting**the**needy and promoting welfare and education of those entering and working within**the**industry**,**as well as**the**wider__support__of**the**charitable work of**the**Mayoralty and**the**Corporation of**the**City of London.

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__

**,**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__

**,**it

**is**

**a**norm

**defined**on

**the**space of bounded linear operators between two given normed

__vector__spaces.

__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 machine

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 ).

__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__

**,**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

Formally and defined

__Formally__

**,**as per

**the**2002 Memorandum of Understanding between

**the**BSI and

**the**United Kingdom Government

**,**British Standards are

__defined__as

**:**

__Formally__speaking

**,**

**a**collation method typically defines

**a**total order on

**a**set of possible identifiers

**,**called sort keys

**,**which consequently produces

**a**total preorder on

**the**set of items of information ( items with

**the**same identifier are not placed in any

__defined__order ).

__Formally__

**,**these reside in

**a**complex separable Hilbert space-variously called

**the**" state space " or

**the**" associated Hilbert space " of

**the**system-that

**is**well

__defined__up to

**a**complex number of norm 1 (

**the**phase factor ).

Limits and colimits in

**a**category C are__defined__**by**means of diagrams in C.__Formally__**,****a**diagram of type J in C**is****a**functor from J to C**:**__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.

__Formally__

**,**

**a**unique factorization domain

**is**

__defined__to be an integral domain R in which every non-zero and non-unit x of R can be written as

**a**product ( including an empty product ) of irreducible elements p < sub > i </ sub > of R and

**a**unit u

**:**

__Formally__

**,**bending modulus

**is**

__defined__as

**the**energy required to deform

**a**membrane from its intrinsic curvature to some other curvature.

__Formally__

**,**

**a**constraint satisfaction

**problem**

**is**

__defined__as

**a**triple

**,**where

**is**

**a**set of variables

**,**

**is**

**a**domain of values

**,**and

**is**

**a**set of constraints.

__Formally__

**,**

**the**case where only

**a**subset of parameters

**is**

__defined__

**is**still

**a**composite hypothesis ; nonetheless

**,**

**the**term point hypothesis

**is**often applied in such cases

**,**particularly where

**the**hypothesis test can be structured in such

**a**way that

**the**distribution of

**the**test statistic (

**the**distribution under

**the**null hypothesis ) does not depend on

**the**parameters whose values have not been specified under

**the**point null hypothesis.

__Formally__

**,**

**the**index of H in G

**is**

__defined__as

**the**number of cosets of H in G. ( The number of left cosets of H in G

**is**always equal to

**the**number of right cosets.

__Formally__

**,**

**a**cardinal κ

**is**

__defined__to be weakly compact if it

**is**uncountable and for every function f

**:**< sup > 2 </ sup > →

__Formally__

**,**

**the**sets of free and bound names of

**a**process in π – calculus are

__defined__inductively as follows.

__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.

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