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Formally, suppose U is an open subset of the complex plane C, a is an element of U and f: U

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## Some Related Sentences

Formally and U

__Formally__

**,**it

**is**

**a**coalition

**of**

__U__. S.

**and**European CEOs

**,**largely from transnational corporations

**,**launched at

**the**urging

**of**former United States Secretary

**of**Commerce Ron Brown in Seville ( Spain ) in late 1995 at

**a**conference attended by CEOs from more than 100

__U__. S.

**and**EU companies

**and**by top government representatives led by

**the**Commissioners for Trade

**and**Industry

**and**by

**the**

__U__. S. Secretary

**of**Commerce.

__Formally__designated as

**the**Manhattan Engineer District

**,**it refers specifically to

**the**period

**of**

**the**project from 1941 – 1946 under

**the**control

**of**

**the**

__U__. S. Army Corps

**of**Engineers

**,**under

**the**administration

**of**General Leslie R. Groves.

__Formally__dedicated in 1948

**,**it ranks 19th in size among parks within

__U__. S. cities

**,**according to The Trust for Public Land.

__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__

**,**

**a**cumulativity predicate CUM can be defined as follows

**,**where capital X

**is**

**a**variable over sets

**,**

__U__

**is**

**the**universe

**of**discourse

**,**p

**is**

**a**mereological part structure on

__U__

**,**

**and**

**is**

**the**mereological sum operation.

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 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__

**,**

**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__

**,**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.

__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

**:**

Formally and complex

__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__

**,**

**an**elliptic function

**is**

**a**function meromorphic on for which there exist two non-zero

__complex__numbers

**and**with ( in other words

**,**not parallel ), such that

**and**for all.

__Formally__

**,**

**the**singular value decomposition

**of**

**an**m × n real or

__complex__matrix M

**is**

**a**factorization

**of**

**the**form

__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__

**,**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**novel

**is**notable because

**of**its lack

**of**paragraphing

**,**

**a**digressive style

**,**

**the**blending

**of**fact

**and**fiction

**,**very long

**and**

__complex__sentences ( one sentence

**is**about 9 pages long ) as well as

**the**inclusion

**of**

**a**set

**of**mysterious

**and**evocative photographs

**,**scattered throughout

**the**book

**,**which enhance

**the**melancholy message

**of**

**the**text.

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