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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.

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## Some Related Sentences

Formally and there

However

**,**shortly after this positive result**,**Kurt Gödel published On__Formally__Undecidable Propositions**of**Principia Mathematica and Related Systems ( 1931 ), showing that in any sufficiently strong axiomatic system__there__are true statements which cannot be proved in the system**.**__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__

**,**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__

**,**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

**.**

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__

**,**however

**,**

__there__

**is**an examination board consisting

**of**

**a**candidate's teachers / examiners

**,**the headmaster / headmistress and one external Vorsitzende ( r ) ( head ), usually

**a**high-ranking school official

**or**the head

**of**another school

**.**

__Formally__

**,**

**a**measurable cardinal

**is**an uncountable cardinal number κ such that

__there__exists

**a**κ-additive

**,**non-trivial

**,**0-1-valued measure on the power set

**of**κ

**.**

__Formally__

**,**assuming the axiom

**of**choice

**,**cardinality

**of**

**a**set X

**is**the least ordinal α such that

__there__

**is**

**a**bijection between X and α

**.**

__Formally__

**,**

**a**cardinal number κ

**is**λ-unfoldable if and only if

**for**every transitive model M

**of**cardinality κ

**of**ZFC-minus-power set such that κ

**is**in M and M contains all its sequences

**of**length less than κ

**,**

__there__

**is**

**a**non-trivial elementary embedding j

**of**M into

**a**transitive model with the critical point

**of**j being κ and j ( κ ) ≥ λ

**.**

__Formally__

**,**if

__there__

**is**

**a**utility

**function**that describes preferences over L commodities

**,**the expenditure

**function**

__Formally__

**,**if f

**is**

**a**harmonic

**function**

**,**then f cannot exhibit

**a**true local maximum within the domain

**of**definition

**of**f

**.**In other words

**,**either f

**is**

**a**constant

**function**

**,**

**or**

**,**

**for**any point inside the domain

**of**f

**,**

__there__exist other points arbitrarily close

**to**at which f takes larger values

**.**

__Formally__

**,**however

**,**

__there__

**is**an examination board consisting

**of**

**a**candidate ’ s teachers / examiners

**,**the headmaster / headmistress and

**a**Vorsitzende ( r ) ( head ), usually

**a**high-ranking school official

**or**the head

**of**another school

**.**

__Formally__

**,**

**a**number n

**is**colossally abundant if and only if

__there__

**is**an ε > 0 such that

**for**all k > 1

**,**

__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__

**,**at least

**,**the European Commission has primarily

**a**monitoring role ; in practice

**,**however

**,**

__there__

**is**considerable scope

**for**

**it**

**to**help set the policy agenda and persuade reluctant Member States

**to**implement agreed policies

**.**

__Formally__

**,**

**a**market

**is**complete with respect

**to**

**a**trading strategy

**,**

**,**if

__there__exists

**a**self-financing trading strategy

**,**such that at any time

**,**the returns

**of**the two strategies

**,**and are equal

**.**

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__

**,**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 refers

__Formally__

**,**dependence

__refers__

**to**any situation in which random variables do not satisfy

**a**

**mathematical**condition

**of**probabilistic independence

**.**

__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__

**,**

**it**

__refers__

**to**

**a**set

**of**six verb forms inflected

**for**person and number forming

**a**single paradigm

**.**

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