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Other representations of the Cauchy – Riemann equations occasionally arise in other coordinate systems.

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## Some Related Sentences

Other and representations

__Other__states with large

__representations__

**in**

**the**student body are Michigan, Pennsylvania, Illinois, and Ohio

**.**

__Other__knowledge

__representations__are trees, graphs and hypergraphs, by means

**of**which

**the**connections among fundamental concepts and derivative concepts can be shown

**.**

__Other__numbers have standard

__representations__

**in**base-φ, with rational numbers having recurring

__representations__

**.**

__Other__

__representations__may show her holding a golden arrow, reminding one

**of**

**the**" eros ",

**the**feeling that she inspires

**in**everybody, and at times she is accompanied by

**the**god Eros, holding a torch

**.**

In both these

__representations__, Jane was shown as being a political tool**in****the**hands**of**her husband's uncle,**the**Duke**of**Norfolk, although**the**presentation**of**her**in**The__Other__Boleyn Girl was more sympathetic**.**__Other__pro bono initiatives include asylum, Violence Against Women Act petitions, criminal appeals and art law

__representations__

**.**

__Other__

__representations__attracting wide exposure have included Jeb Stuart Magruder during

**the**Watergate period ; President Richard Nixon ’ s close confidant Bebe Rebozo ; Oscar Wyatt ; Clifford Irving ; and on an international level, among others, Philippines General Fabian Ver

**.**

(

__Other__columns at**the**same level also feed into a given column, and serve mostly to inhibit**the**activiation exclusive__representations__**.**__Other__leading figures

**of**

**the**Amarna period, both royal and otherwise, are also shown with some

**of**these features, suggesting a possible religious connotation, especially as some sources suggest that private

__representations__

**of**Akhenaten, as opposed to official art, show him as quite normal

**.**

__Other__projects that have functionality related to ( or competing with ) binary

__representations__include:

__Other__displays show data at varying levels

**of**resolution, from whole karyotypes down to text-based

__representations__

**of**DNA and amino acid sequences, or present

**other**types

**of**display such as trees

**of**similar genes ( homologues ) across a range

**of**species

**.**

__Other__important developments have been made by Caroline Howarth

**in**linking Social identity theory with

**the**theory

**of**social

__representations__, by Gerard Duveen

**in**elaborating developmental aspects

**in**relation to

**the**micro-genesis

**of**social

__representations__

**of**gender, and by Wolfgang Wagner

**in**fathoming

**the**relationship between discursive processes, collective behaviour patterns and

**the**construction

**of**social

__representations__

**.**

Other and Cauchy

__Other__examples

**of**distributions that are not exponential families are

**the**F-distribution,

__Cauchy__distribution, hypergeometric distribution and logistic distribution

**.**

__Other__examples

**of**unimodal distributions include

__Cauchy__distribution, Student's t-distribution and chi-squared distribution

**.**

Other and –

* 1904

__–__The first international rugby league match is played between England and an__Other__Nationalities team ( Welsh & Scottish players )**in**Central Park, Wigan, England**.**__Other__well-known Berg compositions include

**the**Lyric Suite ( 1926 ), which was later shown to employ elaborate cyphers to document a secret love affair ;

**the**extraordinarily elaborate post-Mahlerian Three Pieces for Orchestra ( completed

**in**1915 but not performed until after Wozzeck ); and

**the**Chamber Concerto ( Kammerkonzert, 1923

__–__25 ) for violin, piano and 13 wind instruments: this latter is written so conscientiously that Pierre Boulez has called it " Berg's strictest composition " and it, too, is permeated by cyphers and posthumously disclosed hidden programs

**.**

__Other__specialized cycloadditions include multicomponent reactions such as alkyne trimerisation to give aromatic compounds and

**the**cycloaddition

**of**an alkyne, alkene and carbon monoxide

**in**

**the**Pauson

__–__Khand reaction

**.**

__Other__Arab mathematicians who studied amicable numbers are al-Majriti ( died 1007 ), al-Baghdadi ( 980-1037 ), and al-Fārisī ( 1260

__–__1320 ).

(

__Other__scholars suggest that chapters 55__–__66 were written by Deutero-Isaiah after**the**fall**of**Babylon**.**__Other__notable 17th-century outbreaks were

**the**Italian Plague ( 1629

__–__1631 );

**the**Great Plague

**of**Seville ( 1647

__–__1652 );

**the**Great Plague

**of**London ( 1665

__–__1666 ); and

**the**Great Plague

**of**Vienna ( 1679 ).

__Other__areas damaged during World War II bombing included:

**in**September 1940 two unexploded bombs hit

**the**Edward VII galleries,

**the**King's Library received a direct hit from a high explosive bomb, incendiaries fell on

**the**dome

**of**

**the**Round Reading Room but did little damage ; on

**the**night

**of**10 to 11 May 1941 several incendiaries fell on

**the**south west corner

**of**

**the**Museum, destroying

**the**book stack and 150, 000 books

**in**

**the**courtyard and

**the**galleries around

**the**top

**of**

**the**Great Staircase

__–__this damage was not fully repaired until

**the**early 1960s

**.**

Some

**of**these configurations lead to inflation …__Other__configurations lead to a uniform, flat universe directly__–__without inflation**.**__Other__claimants included

**the**United States, whose American Guano Mining Company claimed it under

**the**Guano Islands Act

**of**1856 ; Mexico also claimed Clipperton due to activities undertaken there as early as 1848

__–__1849

**.**

__Other__complications continued to stall

**the**EU negotiating process, most notably Slovenia's blockade

**of**Croatia's EU accession

**in**2008

__–__2009

**.**

__Other__prion diseases include Gerstmann

__–__Sträussler

__–__Scheinker syndrome ( GSS ), fatal familial insomnia ( FFI ) and kuru

**in**humans, as well as bovine spongiform encephalopathy ( BSE, commonly known as mad cow disease )

**in**cattle, chronic wasting disease ( CWD )

**in**elk and deer, and scrapie

**in**sheep

**.**

__Other__invertebrate groups, including rudists ( reef-building clams ) and inoceramids ( giant relatives

**of**modern scallops ), also became extinct at

**the**K

__–__T boundary

**.**

__Other__Biblical passages that some interpret as addressing

**the**issue

**of**homosexual behavior include Romans 1, I Corinthians 6: 8

__–__10, and Jude 1: 7 ;

**the**relevant portion

**of**Romans 1 reads as follows:

* 1976

__–__The United Nations General Assembly adopts**the**Convention on**the**Prohibition**of**Military or Any__Other__Hostile Use**of**Environmental Modification Techniques**.**__Other__languages that use

**the**ergative case are Georgian, Chechen, and

**other**Caucasian languages, Mayan languages, Mixe

__–__Zoque languages, Wagiman and

**other**Australian Aboriginal languages as well as Basque, Burushaski, Hindi, Yaghnobi and Tibetan

**.**

__Other__examples include ⟨ ph ⟩ pronounced ( which is usually spelt ⟨ f ⟩), and ⟨ ch ⟩ pronounced ( which is usually spelt ⟨ c ⟩ or ⟨ k ⟩)

__–__

**the**use

**of**these spellings for these sounds often mark words that have been borrowed from Greek

**.**

__Other__theories existed, including

**the**Greek philosopher Anaxamines ' ( 585

__–__526 BCE ) beliefs that short incline episodes

**of**dryness and wetness caused seismic activity

**.**

Other and Riemann

__Other__theorists, such as Leonhard Euler ( 1739 ), Hermann von Helmholtz ( 1863 / 1885 ), Arthur von Oettingen ( 1866 ), Hugo

__Riemann__( who should not be confused with

**the**famous mathematician Bernhard

__Riemann__), and Christopher Longuet-Higgins ( 1978 ) have modeled pitch relationships using two-dimensional ( or higher-dimensional ) lattices, under

**the**name

**of**Tonnetz

**.**

Other and equations

__Other__famous problems on his list include

**the**Poincaré conjecture,

**the**P = NP problem, and

**the**Navier-Stokes

__equations__, all

**of**which have been designated Millennium Prize Problems by

**the**Clay Mathematics Institute

**.**

__Other__important contributions to mathematics that he made involved discontinuous functions and divergent series, differential

__equations__, interpolation,

**the**gamma function and elliptic functions

**.**

Except for

**the**Dym equation and**the**Ginzburg**–**Landau equation,**the**above__equations__are linear**in****the**sense that they can be written**in****the**form Au = f for a given linear operator A and a given function f**.**__Other__important non-linear__equations__include**the**Navier**–**Stokes__equations__describing**the**flow**of**fluids, and Einstein's field__equations__**of**general relativity**.**__Other__methods include examining

**the**characteristics and using

**the**methods outlined above for ordinary differential

__equations__

**.**

__Other__important mathematical physicists

**of**

**the**seventeenth century included

**the**Dutchman Christiaan Huygens ( famous for having suggested

**the**wave theory

**of**light ), and

**the**German Johannes Kepler ( Tycho Brahe's assistant who discovered

**the**

__equations__for planetary motion ).

__Other__

__equations__

**in**

**the**family are obtained by substituting specific expressions for

**the**three correction factors, P < sub > F </ sub > and λ < sub > Z </ sub > it contains

**.**

__Other__much studied periodic one-dimensional

__equations__are

**the**Kronig

**–**Penney model and Mathieu's equation

**.**

__Other__

__equations__

**in**physics, such as Gauss's law

**of**

**the**electric field and Gauss's law for gravity, have a similar mathematical form to

**the**continuity equation, but are not usually called by

**the**term " continuity equation ", because j

**in**those cases does not represent

**the**flow

**of**a real physical quantity

**.**

__Other__11-dimensional theories are known that are quantum-mechanically inequivalent to

**the**CJS theory, but classically equivalent ( that is, they reduce to

**the**CJS theory when one imposes

**the**classical

__equations__

**of**motion ).

__Other__, self-acknowledged ASTROLOGERS also use mathematical

__equations__

**of**celestial phenomena to make future predictions, using past historical data to guide them

**in**what will happen

**the**next time

**the**same planetary aspects are formed

**.**

__Other__key advances

**in**automatic controls include differential

__equations__, stability theory and system theory ( 1938 ), frequency domain analysis ( 1940 ), ship control ( 1950 ), and stochastic analysis ( 1941 ).

__Other__mathematics included

**in**Śrīpati's work includes,

**in**particular, rules for

**the**solution

**of**simultaneous indeterminate

__equations__

**of**

**the**first degree that are similar to those given by Brahmagupta

__Other__techniques include

**the**path integration that draws on

**the**analogy between statistical physics and quantum mechanics ( for example,

**the**Fokker-Planck equation can be transformed into

**the**Schrödinger equation by rescaling a few variables ) or by writing down ordinary differential

__equations__for

**the**statistical moments

**of**

**the**probability distribution function

**.**

__Other__

__equations__that appear are Euler's identity and P = NP which is a reference to

**the**famous P vs NP problem, and similarly contradicts

**the**general belief that

**in**fact P ≠ NP

**.**

__Other__possible sources are Poincaré's Science and Hypothesis, where he described

**the**Principle

**of**Relativity and which was read by Einstein

**in**1904, and

**the**writings

**of**Max Abraham, from whom he borrowed

**the**terms " Maxwell-Hertz

__equations__" and " longitudinal and transverse mass ".

__Other__

__equations__relating to adsorption exist, such as

**the**Temkin equation or

**the**Freundlich equation

**.**

__Other__techniques include linearization, solving simultaneous

__equations__, reducing dimensions, treating

**the**problem as a time series, converting

**the**problem to a ( hopefully ) linear differential equation, and using mean values

**.**

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