period
(0.001 seconds)
21—30 of 72 matching pages
21: 25.11 Hurwitz Zeta Function
22: 25.16 Mathematical Applications
23: 21.9 Integrable Equations
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►The KP equation has a class of quasi-periodic solutions described by Riemann theta functions, given by
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24: 23.2 Definitions and Periodic Properties
§23.2 Definitions and Periodic Properties
… ►§23.2(iii) Periodicity
… ►Hence is an elliptic function, that is, is meromorphic and periodic on a lattice; equivalently, is meromorphic and has two periods whose ratio is not real. … ►The function is quasi-periodic: for , … ►For further quasi-periodic properties of the -function see Lawden (1989, §6.2).25: 27.19 Methods of Computation: Factorization
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►Deterministic algorithms are slow but are guaranteed to find the factorization within a known period of time.
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26: 28.5 Second Solutions ,
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§28.5(i) Definitions
… ►If a nontrivial solution of Mathieu’s equation with has period or , then any linearly independent solution cannot have either period. … ►
28.5.3
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28.5.4
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►As a consequence of the factor on the right-hand sides of (28.5.1), (28.5.2), all solutions of Mathieu’s equation that are linearly independent of the periodic solutions are unbounded as on .
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27: 20.13 Physical Applications
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►The functions , , provide periodic solutions of the partial differential equation
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►Thus the classical theta functions are “periodized”, or “anti-periodized”, Gaussians; see Bellman (1961, pp. 18, 19).
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28: 28.33 Physical Applications
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►The separated solutions must be -periodic in , and have the form
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►If the parameters of a physical system vary periodically with time, then the question of stability arises, for example, a mathematical pendulum whose length varies as .
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►For points that are at intersections of with the characteristic curves or , a periodic solution is possible.
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29: 29.17 Other Solutions
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►They are algebraic functions of , , and , and have primitive period
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