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asymptotic equation

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  • Asymptotic theory — is the branch of mathematics which studies properties of asymptotic expansions.The most known result of this field is the prime number theorem:Let pi;( x ) be the number of prime numbers that are smaller than or equal to x .The limit:lim {x… …   Wikipedia

  • Asymptotic gain model — The asymptotic gain model [Middlebrook, RD: Design oriented analysis of feedback amplifiers ; Proc. of National Electronics Conference, Vol. XX, Oct. 1964, pp. 1 4] G {infin} T} . while in classical feedback theory, in terms of the open loop gain …   Wikipedia

  • Asymptotic analysis — This article is about the comparison of functions as inputs approach infinite. For asymptotes in geometry, see asymptotic curve. In mathematical analysis, asymptotic analysis is a method of describing limiting behavior. The methodology has… …   Wikipedia

  • Lippmann-Schwinger equation — The Lippmann Schwinger equation (named after Bernard A. Lippmann and Julian Schwinger) is of importance to scattering theory. The equation is: | psi^{(pm)} angle = | phi angle + frac{1}{E H 0 pm i epsilon} V |psi^{(pm)} angle. ,DerivationWe will… …   Wikipedia

  • Sine-Gordon equation — The sine Gordon equation is a nonlinear hyperbolic partial differential equation in 1+1 dimensions involving the d Alembert operator and the sine of the unknown function. It was originally considered in the nineteenth century in the course of… …   Wikipedia

  • Method of matched asymptotic expansions — In mathematics, particularly in solving singularly perturbed differential equations, the method of matched asymptotic expansions is a common approach to finding an accurate approximation to a problem s solution. Contents 1 Method overview 2… …   Wikipedia

  • Hunter–Saxton equation — In mathematical physics, the Hunter–Saxton equationHunter Saxton 1991] :(u t + u u x) x = frac{1}{2} , u x^2is an integrable PDE that arises in the theoretical study of nematic liquid crystals. If the molecules in the liquid crystal are initially …   Wikipedia

  • Orr–Sommerfeld equation — The Orr–Sommerfeld equation, in fluid dynamics, is an eigenvalue equation describing the linear two dimensional modes of disturbance to a viscous parallel flow. The solution to the Navier–Stokes equations for a parallel, laminar flow can become… …   Wikipedia

  • Acoustic wave equation — In physics, the acoustic wave equation governs the propagation of acoustic waves through a material medium. The form of the equation is a second order partial differential equation. The equation describes the evolution of acoustic pressure p or… …   Wikipedia

  • Degasperis-Procesi equation — In mathematical physics, the Degasperis Procesi equation: displaystyle u t u {xxt} + 2kappa u x + 4u u x = 3 u x u {xx} + u u {xxx}is one of only two exactly solvable equations in the following family of third order, non linear, dispersive… …   Wikipedia

  • Degasperis–Procesi equation — In mathematical physics, the Degasperis–Procesi equation is one of only two exactly solvable equations in the following family of third order, non linear, dispersive PDEs: where κ and b are real parameters (b=3 for the Degasperis–Procesi… …   Wikipedia


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