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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：与Lamé函数相关的tau函数与顶点算子: KP及其约化
Lamé函数 tau函数 顶点算子 KP约化
2023/5/5
Lamé函数可以视为当势函数取Weierstrass的p函数时Schr?dinger谱问题的解。KdV/KP型的可积系统存在以Lamé函数为平面波因子的精确解。 该报告将介绍KP方程的相关结果、周期退化、色散关系约化、公开问题、等等。
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：与Lamé函数相关的tau函数与顶点算子: KdV
Lamé函数 tau函数 顶点算子 KdV
2023/5/5
Lamé函数可以视为当势函数取Weierstrass的p函数时Schr?dinger谱问题的解。KdV/KP型的可积系统存在以Lamé函数为平面波因子的精确解。报告将以KdV方程为例，介绍基于Lamé函数的双线性方法框架，包括：椭圆色散关系、双线性方程的拟规范性质、tau函数、顶点算子的椭圆形变、双线性等式。
Optimal Control of dams using P(M,Lambda,tau) policies when the input process is an inverse Gaussian process
Optimal Control of dams P(M,Lambda,tau) policies When the input process inverse Gaussian process
2012/11/23
We consider the P(M,lambda,tau) maintenance policy of a dam using the total discounted and long-run average costs, when the input process is inverse Gaussian.
Schur function expansions of KP tau functions associated to algebraic curves
Schur function expansions of KP tau functions algebraic curves
2010/12/28
The Schur function expansion of Sato-Segal-Wilson KP τ -functions is reviewed. The case of
τ -functions related to algebraic curves of arbitrary genus is studied in detail. Explicit expressions for t...
The Inversion Symmetry of the WDVV Equations and Tau Functions
Inversion Symmetry WDVV Equations Tau Functions
2011/2/28
For two solutions of the WDVV equations that are related by the inversion symmetry, we show that the associated principal hierarchies of integrable systems are related by a reciprocal transformation, ...
Schur function expansions of KP tau functions associated to algebraic curves
Schur function expansions of KP tau functions algebraic curves
2011/2/21
The Schur function expansion of Sato-Segal-Wilson KP τ -functions is reviewed. The case of
τ -functions related to algebraic curves of arbitrary genus is studied in detail.
The symmetric property tau for the Gaussian measure
The symmetric property tau the Gaussian measure
2010/11/15
We give a proof based on the Poincar\'e inequality of the symmetric property tau for the Gaussian measure. This property turns out to be equivalent to a certain functional form of the Blaschke-Santal\...
Comparison of Spearman's rho and Kendall's tau in Normal and Contaminated Normal Models
Spearman's rho Kendall's tau in Normal Contaminated Normal Models
2010/11/15
This paper analyzes the performances of the Spearman's rho (SR) and Kendall's tau (KT) with respect to samples drawn from bivariate normal and bivariate contaminated normal populations. The exact ana...
Cut-and-Join operator representation for Kontsewich-Witten tau-function
Cut-and-Join operator representation Kontsewich-Witten tau-function
2010/12/16
In this short note we construct a simple cut-and-join operator representation for Kontsevich-Witten tau-function that is the partition function of the two-dimensional topological gravity. Our derivati...
Canonical and grand canonical partition functions of Dyson gases as tau-functions of integrable hierarchies and their fermionic realization
partition functions integrable hierarchies Dyson gases
2010/4/2
The partition function for a canonical ensemble of 2D Coulomb charges in a background potential (the Dyson gas) is realized as a vacuum expectation value of a group-like element constructed in terms o...
Isomonodromic tau function on the space of admissible covers
Isomonodromic tau function admissible covers
2010/4/7
The isomonodromic tau function of the Fuchsian differential equations associated to Frobenius structures on Hurwitz spaces can be viewed as a section of a line bundle on the space of admissible covers...
主要考虑用Legendre tau方法求解二维Poisson方程的Dirichlet问题.通过选取带有广义Jacobi权的函数作为检验函数,得到Legendre tau方法对于二维Poisson方程Dirichlet问题的H1模的最优误差估计;然后,通过对偶技巧,得到L2模的最优误差估计;最后,通过数值算例，进一步比较说明理论分析的结果.