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 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 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 controversy relating to the Toltecs include how best to understand reasons behind the perceived similarities in architecture and iconography between the archaeological site of Tula and the Maya site of Chichén Itzá-as of yet no consensus has emerged about the degree or direction of influence between the two sites.

Other problems relating to the ICT infrastructure include poverty and the fact that Mongolia is a landlocked country.

Other controversy relating to the Toltecs include how best to understand reasons behind the perceived similarities in architecture and iconography between the archaeological site of Tula and the Maya site of Chichén Itzá — as of yet no consensus has emerged about the degree or direction of influence between the two sites.

Other, non-pharmacological evidence in support of the dopamine hypothesis relating to the substantia nigra include structural changes in the pars compacta, such as reduction in synaptic terminal size.

Other tourist attractions within the town include five houses relating to Shakespeare's life, which are owned and cared for by the Shakespeare Birthplace Trust.

Other than the new sub-title, all that is added is, a preface to the second edition and a 37-page afterword relating the book's content to the 2000 US presidential election.

Other theories connect the town's name to occupational names relating to mud huts, iron tips for arrows and spears, or the production of tar ( pkielce, a settlement of tar makers ).

Other controversies include a lawsuit relating to the termination of the former City Manager, ( also a defendant in the discrimination suit ) and the suspension and resignation of the City's former Chief of Police.

Other prominent theories relating to intergroup conflict include Social Dominance Theory, and social -/ Self-categorization Theory.

Other correspondence, consisting of letters relating to his mission to Gustavus Adolphus, was edited by SR Gardiner for the Camden Society Miscellany ( 1875 ), vol.

Other parts of the act provided for a greatly expanded federal death penalty, new classes of individuals banned from possessing firearms, and a variety of new crimes defined in statutes relating to immigration law, hate crimes, sex crimes, and gang-related crime.

Other acts dealt with the control of inland waters, and much needed legislation relating to public health, factories, and mining, was also passed.

Other services include directory enquiries, weather forecasts, competitions and voting ( especially relating to television shows ).

* Other provisions to be inserted by the High Contracting Parties relating to the application of any general conditions attached to mandates, which are suitable to the case in Palestine.

Other responsibilities included issues relating to human rights, data protection, and freedom of information.

The Special Subcommittee to Investigate the Administration of the Internal Security Act and Other Internal Security Laws, 1951 – 77, more commonly known as the Senate Internal Security Subcommittee ( SISS ) and sometimes the McCarran Committee, was authorized under S. 366, approved December 21, 1950, to study and investigate ( 1 ) the administration, operation, and enforcement of the Internal Security Act of 1950 (, also known as the McCarran Act ) and other laws relating to espionage, sabotage, and the protection of the internal security of the United States and ( 2 ) the extent, nature, and effects of subversive activities in the United States " including, but not limited to, espionage, sabotage, and infiltration of persons who are or may be under the domination of the foreign government or organization controlling the world Communist movement or any movement seeking to overthrow the Government of the United States by force and violence.

Other names by which they are sometimes identified are Dunkers, Dunkards, Tunkers, and Täufer, all relating to their practice of baptism by immersion.

Other times, issues relating to government relations and agencies are featured, as are stories about the Iraq War.

Other problems relating to several incompatible email systems made HRDC a scapegoat for attacks on the government by opposition parties.

Other major changes include the impact of managed care on mental health care ; an increasing realization of the importance of knowledge relating to multicultural and diverse populations ; and emerging privileges to prescribe psychotropic medication.

Other local street names relating to the Duke of Bedford include Bedford Square, Bedford Place, Bedford Avenue, Bedford Row and Bedford Way ; Woburn Square and Woburn Place ( from Woburn Abbey ); Tavistock Square, Tavistock Place and Tavistock Street ( Marquess of Tavistock ), and Thornhaugh Street ( after a subsidiary title Baron of Thornhaugh ).

Other areas include aspects of local history including the school and shops, a forge, carpenter's shop and exhibits relating to agriculture.

Other composers influenced by Maoism include the Americans Christian Wolff and Frederic Rzewski and the Japanese composer-pianist Yuji Takahashi, all of whom also incorporated political song material into their compositions, though without wholly surrendering the other more abstract musical concerns of their earlier work, whilst the British composer Dave Smith continued to some extent in the tradition established by Cardew, as well as frequently making use of the medium of the nineteenth-century melodrama for speaker and piano, with a wide variety of texts relating to issues in Ireland, Palestine, and elsewhere.

Other materials either never were accepted as canon ( e. g. the novels by Jack McKinney and the Palladium Books role-playing games ) or have been decanonized ( including the Robotech II: The Sentinels footage released a single-issue compilation and most of the comics relating to the series ).

Other problems may ask specific questions relating to the history of the position such as " is the bishop on c1 promoted ?".