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Conversely, given a harmonic function, it is the real part of an analytic function, ( at least locally ).

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## Some Related Sentences

Conversely and given

__Conversely__

**,**if

**a**Boolean ring A

**is**

__given__

**,**we can turn

**it**into

**a**Boolean algebra by defining x ∨ y := x + y +

**(**x · y ) and x ∧ y := x · y.

__Conversely__

**,**there are other stars that never rise above

**the**horizon

**,**as seen from any

__given__point on

**the**Earth's surface

**(**except exactly on

**the**equator

**).**

__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__

**,**

__given__central idempotents

**a**< sub > 1 </ sub >,...,

**a**< sub > n </ sub > in R that are pairwise orthogonal and have sum 1

**,**then R

**is**

**the**direct sum

**of**

**the**rings Ra < sub > 1 </ sub >,…, Ra < sub > n </ sub >.

Given

**a**field ordering ≤ as in Def 1**,****the**elements such that x ≥ 0 forms**a**positive cone**of**F.__Conversely__**,**__given__**a**positive cone P**of**F as in Def 2**,**one can associate**a**total ordering ≤< sub > P </ sub > by setting x ≤ y to mean y − x ∈ P. This total ordering ≤< sub > P </ sub > satisfies**the**properties**of**Def 1.__Conversely__

**,**only

**the**wiki users interested in

**a**

__given__project need look

**at**its associated wiki pages

**,**in contrast to high-traffic mailing lists which may burden subscribers with many messages

**,**regardless

**of**their relevance.

Each convex set containing X must

**(**by**the**assumption that**it****is**convex ) contain all convex combinations**of**points in X**,**so**the**set**of**all convex combinations**is**contained in**the**intersection**of**all convex sets containing X.__Conversely__**,****the**set**of**all convex combinations**is**itself**a**convex set containing X**,**so**it**also contains**the**intersection**of**all convex sets containing X**,**and therefore**the**sets__given__by these two definitions must be equal.__Conversely__

**,**surveys conducted among living donors postoperatively and in

**a**period

**of**five years following

**the**procedure have shown extreme regret in

**a**majority

**of**

**the**donors

**,**who said that

__given__

**the**chance to repeat

**the**procedure

**,**they would not.

__Conversely__

**,**

__given__

**an**ordered tree

**,**and conventionally draw

**the**root

**at**

**the**top

**,**then

**the**child nodes in

**an**ordered tree can be drawn left-to-right

**,**yielding

**an**essentially unique planar embedding

**(**up to embedded homotopy

**,**i. e., moving

**the**edges and nodes without crossing

**).**

__Conversely__

**,**

**the**influence

**of**

**the**data

**at**any

__given__point on

**the**initial line propagates with

**the**finite velocity c: there

**is**no effect outside

**a**triangle through that point whose sides are characteristic curves.

__Conversely__

**,**

__given__any

**harmonic**

**function**in two dimensions

**,**

**it**

**is**

**the**

**real**

**part**

**of**

**an**

**analytic**

**function**

**,**

**at**

**least**

**locally**.

__Conversely__

**,**if

**(**A

**,**m

**,**e

**,**inv )

**is**

**a**group object in one

**of**those categories

**,**then m necessarily coincides with

**the**

__given__operation on A

**,**e

**is**

**the**inclusion

**of**

**the**

__given__identity element on A

**,**inv

**is**

**the**inversion operation and A with

**the**

__given__operation

**is**

**an**abelian group.

__Conversely__

**,**if

**the**Turing Machine

**is**expected polynomial-time

**(**for any

__given__x ), then

**a**considerable fraction

**of**

**the**runs must be polynomial-time bounded

**,**and

**the**coin sequence used in such

**a**run will be

**a**witness.

__Conversely__

**,**

__given__any ring

**,**we can form

**a**category by taking objects A < sub > n </ sub > indexed by

**the**set

**of**natural numbers

**(**including zero ) and letting

**the**hom-set

**of**morphisms from to be

**the**set of-by-matrices over

**,**and where composition

**is**

__given__by matrix multiplication.

__Conversely__

**,**

**it**

**is**hard to believe

**,**

__given__

**the**length and intensity

**of**

**the**struggle between Máel Sechnaill and Brian

**,**that

**the**High King would surrender his title without

**a**fight.

__Conversely__

**,**

**an**algorithm to test for solvability in arbitrary integers could be used to test

**a**

__given__equation for solvability in natural numbers by applying that supposed algorithm to

**the**equation obtained from

**the**

__given__equation by replacing each unknown by

**the**sum

**of**

**the**squares

**of**four new unknowns.

__Conversely__

**,**

**a**disease that

**is**easily transmitted but has

**a**short duration might spread widely during 2002 but

**is**likely to have

**a**low prevalence

**at**any

__given__point in 2003

**(**due to its short duration ) but

**a**high incidence during 2002

**(**as many people develop

**the**disease

**).**

Conversely and harmonic

__Conversely__

**,**

**a**system which changes

**the**shape

**of**

**the**wave

**(**beyond simple scaling or shifting ) creates additional harmonics

**(**

__harmonic__distortion

**).**

Conversely and function

__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__

**,**sociology

**of**law may help comparative law answer questions

**,**such as: How do regulations in different legal systems really

__function__in

**the**respective societies?

__Conversely__

**,**if ƒ: C → C

**is**

**a**

__function__which

**is**differentiable when regarded as

**a**

__function__on R < sup > 2 </ sup >, then ƒ

**is**complex differentiable if and only if

**the**Cauchy – Riemann equations hold.

__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__most

**(**but not all )

**of**

**the**ASCII " control characters " have some control

__function__in isolation

**,**therefore are not escape characters.

__Conversely__

**,**those who wish to

__function__primarily as clinical ED physicians choose

**the**CCFP route

**of**certification.

__Conversely__

**,**warming

**of**

**an**affected extremity may indicate

**a**disruption

**of**

**the**body's normal thermoregulatory vasoconstrictor

__function__

**,**which may sometimes indicate underlying CRPS.

__Conversely__

**,**except in dimension 2

**,**if

**the**curvature

**of**

**a**Riemannian manifold has this form for some

__function__K

**,**then

**the**Bianchi identities imply that K

**is**constant and thus that

**the**manifold

**is**

**(**

**locally**)

**a**space form.

__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__.

Equipped with this notion

**of**length**,****a**Riemannian manifold**is****a**metric space**,**meaning that**it**has**a**distance__function__d**(**p**,**q ) whose value**at****a**pair**of**points p and q**is****the**distance from p to q.__Conversely__**,****the**metric tensor itself**is****the**derivative**of****the**distance__function__**(**taken in**a**suitable manner**).**__Conversely__

**,**by

**the**inverse

__function__theorem

**,**there can be

**at**most one value for σ that

**,**when applied as

**an**input to

**,**will result in

**a**particular value for C.

__Conversely__

**,**culture decline

**is**

**a**

__function__

**of**

**the**feckless mixture

**of**Aryan

**,**with lesser ' animalistic ,' blood ...

__Conversely__

**,**if

**it**

**is**too wet

**,**mud cakes in

**the**machinery and moisture weighs down

**the**material

**,**making

**it**impossible for

**the**equipment to

__function__without picking up large quantities

**of**mud.

__Conversely__

**,**

**a**single email address may be

**an**alias and have

**a**distribution

__function__to many mailboxes.

__Conversely__

**,**there may be levels

**of**production where marginal cost

**is**higher than average cost

**,**and average cost

**is**

**an**increasing

__function__

**of**output.

__Conversely__

**,**

**a**

__function__u: E < sub > 1 </ sub > → E < sub > 2 </ sub > defined on

**a**basis

**of**E < sub > 1 </ sub > can be uniquely extended to

**a**linear

__function__.

Conversely and is

__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__

**,**

**an**adiabatic process that

__is__irreversible and extracts no work

__is__in

**an**isenthalpic process

**,**such as viscous drag

**,**progressing towards

**a**nonnegative change in entropy.

__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__

**,**because space

__is__expanding

**,**and more distant objects are receding ever more quickly

**,**light emitted by us today may never " catch up " to very distant objects.

__Conversely__

**,**modern biological sciences

**(**including even concepts such as molecular ecology ) are intimately entwined and dependent on

**the**methods developed through biotechnology and what

__is__commonly thought

**of**as

**the**life sciences industry.

__Conversely__

**,**if

**the**second theory

__is__correct

**,**then

**the**Athenians were merely reacting to

**the**Persians attacking them.

__Conversely__

**the**equilibrium position

__is__said to be " far to

**the**left " if hardly any product

__is__formed from

**the**reactants.

__Conversely__

**,**

**the**islands do not receive

**the**upwellings

**(**cold streams ) that affect

**the**West African coast

**,**so

**the**air temperature

__is__cooler than in Senegal

**,**but

**the**sea

__is__actually warmer

**,**because

**the**orographic relief

**of**some islands

**,**as Sao Miguel with steep mountains

**,**cover

**it**with rich woods and luxuriant vegetation where

**the**dense moisture condense and soak

**the**plants

**,**rocks

**,**soil

**,**logs

**,**moss etc.

__Conversely__in francophone Canada

**,**one hundredth

**of**

**a**Canadian dollar

__is__informally called

**a**sou

**(**penny ), though cent

__is__official in both English and French.

__Conversely__

**,**

**an**absence

**of**secure cycle-parking

__is__

**a**recurring complaint by cyclists from cities with low modal share

**of**cycling.

* The spectrum

**of**any bounded linear operator on**a**Banach space__is__**a**nonempty compact subset**of****the**complex numbers C.__Conversely__**,**any compact subset**of**C arises in this manner**,**as**the**spectrum**of**some bounded linear operator.0.181 seconds.