Asymptotic Properties of Integrals of Quotients when the Numerator Oscillates and the Denominator Degenerates

Sergei Kuksin

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Asymptotic Properties of Integrals of Quotients when the Numerator Oscillates and the Denominator Degenerates

机译：分子振荡而分母退化时商的积分的渐近性质

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We study asymptotic expansion as ! 0 for integrals over R2d = f(x; y)gof quotients of the form F(x; y) cos( x y) ??(x y)2 + 2 , where 0 andF decays at in nity su ciently fast. Integrals of this kind appear in thetheory of wave turbulence.

机译：我们研究渐近展开为！ R2d = f（x; y）gof商的形式为F（x; y）cos（x y）∑（x y）2 + 2的积分为0，其中0和F在n上的衰减速度足够快。这种积分出现在波湍流理论中。

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《Journal of Mathematical Physics, Analysis, Geometry》 |2018年第4期|共9页
作者
Sergei Kuksin;
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中图分类高等数学;
关键词
asymptotic of integralsoscillating integralsfour-waves interaction.;

机译：积分-振动积分-四波相互作用的渐近性;

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1. Asymptotic expansions for some integrals of quotients with degenerated divisors [J] . Kuksin S. Russian journal of mathematical physics . 2017,第4期

机译：具有退化除数的引用的一些积分的渐近扩展
2. Real canonical cycle and asymptotics of oscillating integrals [J] . Daniel Barlet Nagoya Mathematical Journal . 2003,第5a6期

机译：实典循环和振动积分的渐近性
3. ASYMPTOTICS OF INTEGRALS OF SOME FUNCTIONS RELATED TO THE DEGENERATE THIRD PAINLEVE EQUATION [J] . A. V. Kitaev, A. Vartanian Journal of Mathematical Sciences . 2019,第5期

机译：与退化第三痛苦方程相关的一些功能的积分渐近学
4. Numerator-Denominator Model Based H∞ Robust Control for LCL Filter-Based Grid-Connected Inverters under Weak Grid Conditions [C] . Bo Long, Chu Wang, ZiLin Zhu, 2019 10th International Conference on Power Electronics and ECCE Asia . 2019

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5. Asymptotic expansion of certain n-dimensional Laplace integrals whose phase function has a degenerate critical point. [D] . Kaplan, Mitchell Arthur. 1998

机译：某些n维Laplace积分的渐近展开，其相位函数具有退化的临界点。
6. Exactification of the Poincaré asymptotic expansion of the Hankel integral: spectacularly accurate asymptotic expansions and non-asymptotic scales [O] . Eric A. Galapon, Kay Marie L. Martinez -1

机译：Hankel积分的Poincaré渐近展开的实现：精确的渐近展开和非渐近标度
7. Asymptotic Properties of Integrals of Quotients when the Numerator Oscillates and the Denominator Degenerates [O] . Sergei Kuksin 2018

机译：分子振荡和分母退化时引用积分的渐近性质

Asymptotic Properties of Integrals of Quotients when the Numerator Oscillates and the Denominator Degenerates

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