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

Other types of differential equations can be used to define the evolution rule:

Other modern equations of only slightly greater complexity are much more accurate.

Other important functional equations for the gamma function are Euler's reflection formula

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 useful equations are:

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 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.

Other synapses appear as terminals at the ends of axonal branches.

Other old French games such as thèque, la balle au bâton, and la balle empoisonnée also appear to be related.

Other hybrid creatures appear in Greek mythology, always with some liminal connection that links Hellenic culture with archaic or non-Hellenic cultures:

Other examples include the black tarnish on silver, and red or green corrosion that may appear on copper and its alloys, such as brass.

Other examples of late Biblical Hebrew include the qetAl pattern form nouns, which would have dated after an Aramaic influence, the frequent use of the relative sh (- ש ) alongside asher ( אשר ), the Ut ending ( ות -), the frequent use of the participle for the present ( which is later developed in Rabbinic Hebrew ), using the prefix conjugation in the future ( vs. the older preterite use ), and terms that appear to specifically fit a Persian / Hellenistic context ( e. g. Shallit ).

Other aspects in ASL include the following: stative, inchoative (" to begin to ..."), predisposional (" to tend to ..."), susceptative (" to ... easily "), frequentative (" to ... often "), protractive (" to ... continuously "), incessant (" to ... incessantly "), durative (" to ... for a long time "), iterative (" to ... over and over again "), intensive (" to ... very much "), resultative (" to ... completely "), approximative (" to ... somewhat "), semblitive (" to appear to ..."), increasing (" to ... more and more ").

Other founding horse-associated twin brothers are attested among various other Germanic peoples, and appear in other Indo-European cultures.

Other colors can appear in the presence of light absorbing impurities, where the impurity is dictating the color rather than the ice itself.

Other drawings of interest include numerous studies generally referred to as " caricatures " because, although exaggerated, they appear to be based upon observation of live models.

Other values recognized by one or more search engines can influence how the engine indexes pages, and how those pages appear on the search results.

" Other labels, such as " baroque ," often appear.

Other trees in the towns of Amioun appear to be at least 1, 500 years old.

Other themes began to appear at this time which would later seep into his prose.

Other forms also appear: shara ' u as ( prf.

Other Latin formulations that first appear in his work are " three Persons, one Substance " as the Latin " tres Personae, una Substantia " ( itself from the Koine Greek " treis Hypostases, Homoousios ").

Other songs from this session did not appear until the 1988 bootleg Lion's Share, along with four tracks from their infamous last show at the Starwood.

Other clues appear to place the main settlement farther south, such as the mention of a mild winter and the reports in both sagas of grapes being found nearby.

Other subjects such as animals and human figures also appear.

Other plagues which were less well recorded also appear in the record.

Other diseases such as Guillain-Barré syndrome, stroke, and myasthenia gravis can appear similar to botulism, and special tests may be needed to exclude these other conditions.

Other anxieties about unstable identity appear throughout the novel: Robert's relationship with George has homosexual overtones, especially considered in light of his attraction to Clara, George's sister, who is described as looking identical to George.

Other noncoding sequences have likely, but as-yet undetermined, functions ( this is inferred from high levels of homology and conservation seen in sequences that do not encode proteins but, nonetheless, appear to be under heavy selective pressure ).

Other naked-eye comets may be brighter and more spectacular, but will appear only once in thousands of years.

Other references to these alternate Oerths appear in the Gord the Rogue short story anthology Night Arrant as well as in Gygax's Epic of Aerth campaign setting for the Dangerous Journeys roleplaying game.

Other names, like Adrasteia, Ide, the nymph of Mount Ida, or Adamanthea, which appear in mythology handbooks, are simply duplicates of Amalthea.