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Formally, if is an open subset of the complex plane, a point of, and is a holomorphic function, then is called a removable singularity for if there exists a holomorphic function which coincides with on.

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## Some Related Sentences

Formally and if

__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__

**,**

__if__d

**is**

**the**dimension

**of**

**the**parameter

**,**

**and**n

**is**

**the**number

**of**samples

**,**

__if__as

**and**as

**,**

**then**

**the**model

**is**semi-parametric

**.**

__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**decision problem

**is**P-complete ( complete

**for**

**the**complexity class P )

__if__it

**is**in P

**and**that every problem in P can be reduced to it by using

**an**appropriate reduction

**.**

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__

**,**

**a**hypothesis

**is**compared against its opposite or null hypothesis ("

__if__I release this ball

**,**it will not fall to

**the**floor ").

__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__

**,**

**a**

**function**ƒ

**is**real analytic

**on**

**an**

**open**set D in

**the**real line

__if__

**for**any x < sub > 0 </ sub > in D one can write

__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

**.**

Informally

**,**G has**the**above presentation__if__it**is****the**" freest group " generated by S subject only to**the**relations R**.**__Formally__**,****the**group G**is**said to have**the**above presentation__if__it**is**isomorphic to**the**quotient**of****a**free group**on**S by**the**normal subgroup generated by**the**relations R**.**__Formally__

**,**

__if__we write F < sub > Δ </ sub >( x ) to mean

**the**f-polynomial

**of**Δ

**,**

**then**

**the**h-polynomial

**of**Δ

**is**

__Formally__

**,**

**a**cardinal κ

**is**defined to be weakly compact

__if__it

**is**uncountable

**and**

**for**every

**function**f: < sup > 2 </ 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__

**,**

**an**inner product space

__is__

**a**vector space V over

**the**field together

**with**

**an**inner product

**,**i

**.**e.,

**with**

**a**map

*

__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 open

__Formally__inaugurated in March 2004

**,**

**the**Global Leadership Foundation works to " promote good governance – democratic institutions

**,**

__open__markets

**,**human rights

**and**

**the**rule

**of**law –

**and**to contribute to

**the**prevention

**and**resolution

**of**conflict through mediation

**.**

__Formally__

**,**in Euclidean space

**,**

**the**wave front set

**of**ƒ

**is**defined as

**the**complement

**of**

**the**set

**of**all pairs ( x < sub > 0 </ sub >, v ) such that

**there**

**exists**

**a**test

**function**

**with**φ ( x < sub > 0 </ sub >) ≠ 0

**and**

**an**

__open__cone Γ containing v such that

**the**estimate

Formally and subset

__Formally__

**,**cl ( S ) denotes

**the**smallest

__subset__Y

**of**M that contains S such that

**for**each reaction ( A

**,**B )

__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__

**,**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**partially ordered set ( P

**,**≤)

**is**bounded complete

**if**

**the**following holds

**for**any

__subset__S

**of**P:

__Formally__

**,**let P be

**a**poset ( partially ordered set ),

**and**let F be

**a**filter

**on**P ; that

**is**

**,**F

**is**

**a**

__subset__

**of**P such that:

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