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Conversely, given any harmonic function in two dimensions, 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

**.**

__Conversely__

**,**

__given__a

**harmonic**

**function**

**,**

**it**

**is**

**the**

**real**

**part**

**of**

**an**

**analytic**

**function**

**,**(

**at**

**least**

**locally**).

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__

**,**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 any

__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__

**the**equilibrium position

**is**said to be " far to

**the**left " if hardly

__any__product

**is**formed from

**the**reactants

**.**

* 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**.**__Conversely__

**,**

__any__surjection between sets determines a partition on its domain

**,**

**the**set

**of**preimages

**of**singletons

**in**

**the**codomain

**.**

__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__

**,**a person may feel like he belongs to one state without having

__any__legal relationship to

**it**

**.**

__Conversely__

**,**

**the**interior

**of**

**the**box has a constant

**,**zero potential energy .< ref > Actually

**,**

__any__constant

**,**finite potential can be specified within

**the**box

**.**

__Conversely__

**,**extremely thin jewelry can cause

**the**same tearing

**in**what

**is**commonly referred to as

**the**" cheese cutter effect ", either during sudden torsion or over a long period

**of**wearing

**,**especially if

**the**thin jewelry bears

__any__weight

**.**

__Conversely__

**,**

__any__Hermitian positive semidefinite matrix M can be written as M = A < sup >*</ sup > A ; this

**is**

**the**Cholesky decomposition

**.**

__Conversely__

**,**if a double sharp were added to

__any__other note not containing a sharp or flat as indicated by

**the**key signature then

**the**note will be raised

**two**semitones or a whole step with respect to

**the**chromatic scale

**.**

__Conversely__

**,**supplementation with L-phenylalanine

**,**L-tyrosine

**,**L-DOPA

**,**or

__any__

**of**

**the**cofactors will increase their respective concentrations

**.**

__Conversely__

**,**

__any__choice

**of**μ

**,**full rank matrix U

**,**and positive diagonal entries Λ < sub > i </ sub > yields a non-singular multivariate normal distribution

**.**

It

**is**a fact that**the**ring**is**a principal ideal ring ; that**is****,**for__any__ideal I**in****,**there exists**an**integer n**in**I such that every element**of**I**is**a multiple**of**n**.**__Conversely__**,****the**set**of**all multiples**of****an**arbitrary integer n**is**necessarily**an**ideal**,**and**is**usually denoted by ( n ).

Conversely and harmonic

__Conversely__

**,**a system which changes

**the**shape

**of**

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

__harmonic__distortion ).

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