On the solution of the triple correlation equation

von Wolfersdorf L.

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On the solution of the triple correlation equation

机译：关于三重相关方程的解

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The paper presents an analytic treatment of the triple correlation equation which occurs in spectroscopy. By means of the Fourier transformation the nonlinear integral equation is reduced to a functional equation in two variables. For the solvability of this functional equation necessary and sufficient conditions are derived and the complex-valued solution of the equation is given in closed form. Thereby the determination of the argument of the solution function (the phase) is carried out with the aid of the bounded solution to a related functional equation in a Single variable. (C) 2003 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. [References: 15]

机译：本文介绍了在光谱学中出现的三重相关方程的解析处理。通过傅立叶变换将非线性积分方程简化为两个变量的泛函。对于该功能方程的可解性，导出了必要和充分的条件，并以封闭形式给出了该方程的复数值解。由此，借助于对单个变量中的相关函数方程的有界解来确定解函数（相）的自变量。（C）2003 WILEY-VCH Verlag GmbH＆Co.KGaA，Weinheim。 [参考：15]

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《Zeitschrift fur Angewandte Mathematik und Mechanik》 |2003年第11期|共7页
作者
von Wolfersdorf L.;
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正文语种 eng
中图分类应用数学;
关键词
Reconstruction of signals; Triple auto-correlation; Cubic integral equation; Functional equations; Ultrashort laser-pulses; Recovery; Phase;

机译：信号重构三重自相关三次积分方程函数方程超短激光脉冲恢复相位;

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1. The elementary solution of triple integral equations and the solution of triple series equations involving associated legendre polynomials and their application [J] . Singh BM, Rokne J, Dhaliwal RS Integral equations and operator theory . 2005,第4期

机译：三重积分方程的初等解和涉及勒让德多项式的三重序列方程的解及其应用
2. On the autocorrelation and the triple correlation equation for complex-valued signals [J] . von Wolfersdorf L Zeitschrift fur Angewandte Mathematik und Mechanik . 2004,第6期

机译：关于复值信号的自相关和三重相关方程
3. Inhomogeneous integral equation approach to pair and triple correlations in a glass-forming simple liquid - art. no. 011203 [J] . Lomba E., Alvarez M., Jorge S. Physical review, E. Statistical physics, plasmas, fluids, and related interdisciplinary topics . 2001,第1aPta1期

机译：非均匀积分方程法在玻璃形成简单液体中的对和三重相关性。没有。 011203
4. Triple Wronskian representation of the multi-soliton solutions for a coupled GMNLS equations [C] . Lei Wang International Conference on Energy, Environment and Sustainable Development . 2014

机译：用于耦合的GmnLS方程的多孤子解决方案的三重装饰表示
5. A high -order finite difference method for solving bioheat transfer equations in three-dimensional triple -layered skin structure [D] . Yu, Haofeng 2004

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6. Correlations of skin fold thickness and validation of prediction equations using DEXA as the gold standard for estimation of body fat composition in Pakistani children [O] . Zainab Hussain, Tazeen Jafar, Maseeh uz Zaman, 2014

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7. A direct integral equation method for the solution of dual-or triple-series equations with applications to heat conduction and diffusion–reaction systems [O] . Mills P.L., Duduković M.P. 1984

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8. Asymptotic Behaviour of the Regular Solution of Three-Particle Integrodifferential Equations in the Vicinity of the Triple Collision Point [R] . Pupyshev, V. V. 1987

机译：三重碰撞点附近三粒子积分微分方程正则解的渐近性态

On the solution of the triple correlation equation

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