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Formally, it is a norm defined on the space of bounded linear operators between two given normed vector spaces.

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## Some Related Sentences

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

Formally and norm

__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 ).

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 ).

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__

**,**

**a**transductive support

**vector**machine

**is**

__defined__by

**the**following primal optimization problem:

__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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