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Conversely, for real-valued functions f ( t ), the Hartley transform is given from the Fourier transform's real and imaginary parts:

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## Some Related Sentences

Conversely and for

__Conversely__

**,**if he gives a heavy rating to his own reading

**,**

**and**finds more accurate facts in it than in

**the**others

**,**a point

**is**chalked up

__for__

**the**intrinsic

**,**objective meaningfulness of this type of mediumistic material.

__Conversely__

**,**some elements do not maintain distinct allotropes in different phases –

__for__example phosphorus has numerous solid allotropes

**,**which all revert to

**the**same P < sub > 4 </ sub > form when melted to

**the**liquid state.

__Conversely__

**,**British English favours fitted as

**the**past tense of fit generally

**,**whereas

**the**preference of American English

**is**more complex

**:**AmEng prefers fitted

__for__

**the**metaphorical sense of having made an object " fit "

**(**i. e., suited )

__for__a purpose ; in spatial transitive contexts

**,**AmEng uses fitted

__for__

**the**sense of having made an object conform to an unchanged object that it surrounds

**(**e. g., " fitted X around Y ") but fit

__for__

**the**sense of having made an object conform to an unchanged object that surrounds it

**(**e. g., " fit X into Y ");

**and**

__for__

**the**spatial senses

**(**both intransitive

**and**transitive ) of having been matching with respect to contour

**,**with no alteration of either object implied

**,**AmEng prefers fit (" The clothes fit.

__Conversely__

**the**use of true brass seems to have declined in Western Europe during this period in favour of gunmetals

**and**other mixed alloys but by

**the**end of

**the**first Millennium AD brass artefacts are found in Scandinavian graves in Scotland

**,**brass was being used in

**the**manufacture of coins in Northumbria

**and**there

**is**archaeological

**and**historical evidence

__for__

**the**production of brass in Germany

**and**The Low Countries areas rich in calamine ore which would remain important centres of brass making throughout

**the**medieval period

**,**especially Dinant – brass objects are still collectively known as dinanterie in French.

__Conversely__

**,**many fighter aircraft

**,**such as

**the**F-16

**,**are often used as ' bomb trucks ,' despite being designed

__for__aerial combat.

__Conversely__

**,**a subset R defines a binary function if

**and**only if

**,**

__for__any x in X

**and**y in Y

**,**there exists a unique z in Z such that

**(**x

**,**y

**,**z ) belongs to R.

__Conversely__

**,**certain general principles

**(**

__for__example

**,**neighbourliness

**,**or charity ) are seen to be universal

**and**consistent.

__Conversely__

**,**in more recent times

**,**Russian existentialist philosopher Lev Shestov viewed Job as

**the**embodiment of

**the**battle between reason

**(**which offers general

**and**seemingly comforting explanations

__for__complex events )

**and**faith in a personal god

**,**

**and**one man's desperate cry

__for__him.

__Conversely__

**,**

**the**vast majority of early attempts at proper excavation techniques failed to accurately measure or record stratigraphy

**,**thereby failing to provide a secure context

__for__artefact finds making interpretations extremely limited in scope.

__Conversely__

**,**in

**the**English language as a whole

**,**singular verb forms can often be used with nouns ending in "- s " that were once considered plural

**(**

__for__example

**:**" Physics

**is**my favorite academic subject ").

__Conversely__

**,**Derek Bickerton

**and**others argue that

**the**advent of abstract words provided a mental basis

__for__analyzing higher-order relations

**,**

**and**that any communication system that remotely resembles human language utterly relies on cognitive architecture that co-evolved alongside language.

__Conversely__

**,**

**the**tiny meson mass mass differences responsible

__for__meson oscillations are often expressed in

**the**more convenient inverse picoseconds.

__Conversely__

**,**in functional code

**,**

**the**output value of a function depends only on

**the**arguments that are input to

**the**function

**,**so calling a function

**f**twice with

**the**same value

__for__an argument x will produce

**the**same result

**f**

**(**x ) both times.

__Conversely__

**,**

**the**bodies of people who had certain medical conditions are useful

__for__research into those conditions.

__Conversely__

**,**if

**the**data are sparse — that

**is**

**,**if only K out of N

**Fourier**coefficients are nonzero — then

**the**complexity can be reduced to O

**(**K log N log

**(**N / K )),

**and**this has been demonstrated to lead to practical speedups compared to an ordinary FFT

__for__N / K > 32 in a large-N example

**(**N = 2 < sup > 22 </ sup >) using a probabilistic approximate algorithm

**(**which estimates

**the**largest K coefficients to several decimal places ).

__Conversely__

**,**one might expect that inertial motions

**,**once identified by observing

**the**actual motions of bodies

**and**making allowances

__for__

**the**external forces

**(**such as electromagnetism or friction

**),**can be used to define

**the**geometry of space

**,**as well as a time coordinate.

__Conversely__

**,**

__for__many deductive systems

**,**it

**is**possible to prove

**the**completeness theorem as an effective consequence of

**the**compactness theorem.

Conversely and real-valued

**for**some

__real-valued__

**functions**a

**and**b depending

**,**respectively

**,**on x

**and**y.

__Conversely__

**,**

**given**any such pair of

__real-valued__

**functions**

**,**there exists a vector field X satisfying 1.

**and**2.

A sublinear modulus of continuity can easily found

**for**any uniformly function which**is**a bounded perturbations of a Lipschitz function**:**if**is**a uniformly continuous function with modulus of continuity**,****and****is**a Lipschitz function with uniform distance**from****,**then admits**the**sublinear module of continuity__Conversely__**,**at least**for**__real-valued__**functions****,**any bounded**,**uniformly continuous perturbation of a Lipschitz function**is**a special uniformly continuous function ; indeed more**is**true as shown below.**:**

__Conversely__

**,**suppose that φ

**is**a smooth

__real-valued__function on M in a neighborhood of p. Since every smooth function has a local coordinate expression

**,**we may express φ as a function in

**the**coordinates.

Conversely and functions

#

__Conversely__if u**is**a solution of Laplace's equation**,**then there exist__functions__v which solve**the**Cauchy – Riemann equations together with u.__Conversely__

**,**such a rational parameterization induces a field homomorphism of

**the**field of

__functions__of V into.

__Conversely__

**,**a rural area

**(**or a suburban area flanked mostly by rural areas ) in which county

**and**municipal

__functions__are consolidated in one government

**is**not a metropolitan municipality but a regional municipality.

**for**all compactly supported

__functions__ƒ

**and**h.

__Conversely__

**,**() characterizes Δ completely

**,**in

**the**sense that it

**is**

**the**only operator with this property.

Conversely and f

__Conversely__

**,**

**given**a groupoid G in

**the**algebraic sense

**,**let G < sub > 0 </ sub > be

**the**set of all elements of

**the**form x * x < sup >− 1 </ sup > with x varying through G

**and**define G

**(**x * x < sup >-1 </ sup >, y * y < sup >-1 </ sup >) as

**the**set of all elements

__f__such that y * y < sup >-1 </ sup > *

__f__* x * x < sup >-1 </ sup > exists.

)

__Conversely__**,**a critical point x of__f__can be analysed by considering**the**second derivative of__f__at x**:**__Conversely__

**,**any equation can take

**the**canonical form

__f__

**(**x ) = 0

**,**so equation solving

**is**

**the**same thing as computing

**(**or finding ) a root of a function.

__Conversely__

**,**if X

**is**a Hausdorff space

**and**ker

__f__

**is**a closed set

**,**then

**the**coimage of

__f__

**,**if

**given**

**the**quotient space topology

**,**must also be a Hausdorff space.

If

__f__**is**flat**,**then .< ref > EGA IV < sub > 2 </ sub >, Corollaire 6. 1. 2 .</ ref >__Conversely__**,**if this equality holds**for**all x**,**X**is**Cohen-Macaulay**,****and**Y**is**regular**,**then__f__**is**flat .< ref > EGA IV < sub > 2 </ sub >, Proposition 6. 1. 5.
If X

**is**reduced or normal at x**,**then Y**is**reduced or normal**,**respectively**,**at__f__**(**x ).< ref > EGA IV < sub > 2 </ sub >, Proposition 2. 1. 13 .</ ref >__Conversely__**,**if__f__**is**also of finite presentation**and**__f__< sup >− 1 </ sup >( y )**is**reduced or normal**,**respectively**,**at x**,**then X**is**reduced or normal**,**respectively**,**at x .< ref > EGA IV < sub > 3 </ sub >, Proposition 11. 3. 13 .</ ref >__Conversely__

**,**if Y

**is**regular at

__f__

**(**x )

**and**

__f__< sup >− 1 </ sup >(

__f__

**(**x ))

**is**regular at x

**,**then X

**is**regular at x .< ref > EGA IV < sub > 2 </ sub >, Corollaire 6. 5. 2 .</ ref >

__Conversely__

**,**if Y

**is**normal at

__f__

**(**x )

**and**

__f__< sup >− 1 </ sup >(

__f__

**(**x ))

**is**normal at x

**,**then X

**is**normal at x .< ref > EGA IV < sub > 2 </ sub >, Corollaire 6. 5. 4 .</ ref >

__Conversely__if

__f__

**is**a homomorphism

**from**G to K < sub > k </ sub >, then one can color G by using

**the**same color

**for**two vertices in G whenever they are both mapped to

**the**same vertex in K < sub > k </ sub >.

Conversely and t

__Conversely__

**,**

**given**two one-parameter unitary groups U

**(**

__t__)

**and**V

**(**s ) satisfying

**the**braiding relation

__Conversely__

**,**if B

**(**

__t__)

**is**a Brownian bridge

**and**Z

**is**a standard normal random variable

**,**then

**the**process

0.211 seconds.