[permalink] [id link]

Every holomorphic function can be separated into its real and imaginary parts, and each of these is a solution of Laplace's equation on R < sup > 2 </ sup >.

from
Wikipedia

## Some Related Sentences

Every and holomorphic

__Every__meromorphic

**function**

**on**D

**can**

**be**expressed as the ratio between two

__holomorphic__functions ( with the denominator not constant 0 ) defined

**on**D: any pole must coincide with

**a**zero

**of**the denominator.

__Every__Riemann surface

**is**

**a**two-dimensional

**real**analytic manifold ( i. e.,

**a**surface ), but it contains more structure ( specifically

**a**complex structure ) which

**is**needed for the unambiguous definition

**of**

__holomorphic__functions.

__Every__Riemann surface

**is**the quotient

**of**

**a**free

**,**proper

**and**

__holomorphic__action

**of**

**a**discrete group

**on**

**its**universal covering

**and**this universal covering

**is**holomorphically isomorphic ( one also says: " conformally equivalent ") to one

**of**the following:

*

__Every____holomorphic__vector bundle**on****a**projective variety**is**induced by**a**unique algebraic vector bundle.
*

__Every__Stein manifold**is**holomorphically spreadable**,**i. e. for every point**,**there are__holomorphic__functions defined**on**all**of**which form**a**local coordinate system when restricted to some open neighborhood**of**.

Every and function

__Every__such subset has

**a**smallest element

**,**so to specify our choice

__function__we

**can**simply say that it maps

**each**set to the least element

**of**that set.

__Every__contraction mapping

**is**Lipschitz continuous

**and**hence uniformly continuous ( for

**a**Lipschitz continuous

__function__

**,**the constant k

**is**no longer necessarily less than 1 ).

__Every__effectively calculable

__function__( effectively decidable predicate )

**is**general recursive italics

__Every__bijective

__function__g has an inverse g

**<**

**sup**>− 1

**</**

**sup**>, such that gg

**<**

**sup**>− 1

**</**

**sup**

**>**= I ;

__Every__entire

__function__

**can**

**be**represented as

**a**power series that converges uniformly

**on**compact sets.

__Every__completely multiplicative

__function__

**is**

**a**homomorphism

**of**monoids

**and**

**is**completely determined by

**its**restriction to the prime numbers.

__Every__time another object or customer enters the line to wait

**,**they join the end

**of**the line

**and**represent the “ enqueue ”

__function__.

__Every__type that

**is**

**a**member

**of**the type class defines

**a**

__function__that will extract the data from the string representation

**of**the dumped data.

__Every__output

**of**an encoder

**can**

**be**described by

**its**own transfer

__function__

**,**which

**is**closely related to the generator polynomial.

__Every__continuous

__function__in the

__function__space

**can**

**be**represented as

**a**linear combination

**of**basis functions

**,**just as every vector in

**a**vector space

**can**

**be**represented as

**a**linear combination

**of**basis vectors.

Every and can

__Every__information exchange between living organisms — i. e. transmission

**of**signals that involve

**a**living sender

**and**receiver

__can__

**be**considered

**a**form

**of**communication ;

**and**even primitive creatures such as corals are competent to communicate.

__Every__context-sensitive grammar which does not generate the empty string

__can__

**be**transformed

**into**an equivalent one in Kuroda normal form.

__Every__grammar in Chomsky normal form

**is**context-free

**,**

**and**conversely

**,**every context-free grammar

__can__

**be**transformed

**into**an equivalent one which

**is**in Chomsky normal form.

__Every__module over

**a**division ring has

**a**basis ; linear maps between finite-dimensional modules over

**a**division ring

__can__

**be**described by matrices

**,**

**and**the Gaussian elimination algorithm remains applicable.

Group actions / representations:

__Every__group G__can__**be**considered as**a**category with**a**single object whose morphisms are the elements**of**G. A functor from G to Set**is**then nothing but**a**group action**of**G**on****a**particular set**,**i. e.**a**G-set.__Every__sequence

__can__

**,**thus

**,**

**be**read in three reading frames

**,**

**each**

**of**which will produce

**a**different amino acid sequence ( in the given example

**,**Gly-Lys-Pro

**,**Gly-Asn

**,**or Glu-Thr

**,**respectively ).

__Every__hyperbola

**is**congruent to the origin-centered East-West opening hyperbola sharing

**its**same eccentricity ε (

**its**shape

**,**or degree

**of**" spread "),

**and**

**is**also congruent to the origin-centered North-South opening hyperbola with identical eccentricity ε — that

**is**

**,**it

__can__

**be**rotated so that it opens in the desired direction

**and**

__can__

**be**translated ( rigidly moved in the plane ) so that it

**is**centered at the origin.

__Every__species

__can__

**be**given

**a**unique (

**and**

**,**one hopes

**,**stable ) name

**,**as compared with common names that are often neither unique nor consistent from place to place

**and**language to language.

__Every__vector v in determines

**a**linear map from

**R**to taking 1 to v

**,**which

__can__

**be**thought

**of**as

**a**Lie algebra homomorphism.

__Every__use

**of**modus tollens

__can__

**be**converted to

**a**use

**of**modus ponens

**and**one use

**of**transposition to the premise which

**is**

**a**material implication.

__Every__adult

**,**healthy

**,**sane Muslim who has the financial

**and**physical capacity to travel to Mecca

**and**

__can__make arrangements for the care

**of**his / her dependants during the trip

**,**must perform the Hajj once in

**a**lifetime.

*

__Every__finite topological space gives rise to**a**preorder**on****its**points**,**in which x ≤ y if**and**only if x belongs to every neighborhood**of**y**,****and**every finite preorder__can__**be**formed as the specialization preorder**of****a**topological space in this way.
*

__Every__preorder__can__**be**given**a**topology**,**the Alexandrov topology ;**and**indeed**,**every preorder**on****a**set**is**in one-to-one correspondence with an Alexandrov topology**on**that set.__Every__binary relation

**R**

**on**

**a**set S

__can__

**be**extended to

**a**preorder

**on**S by taking the transitive closure

**and**reflexive closure

**,**

**R**

**<**

**sup**>+=</

**sup**

**>.**

0.127 seconds.