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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Algebraic Structures from Integral Equations
积分方程 代数结构 代数分析
2023/11/29
Even though the research style of algebra and analysis are quite different, many algebraic structures naturally arose from analysis, differential equations and integral equations, inspiring further ap...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Higher-order Hamiltonian generalization evolution equations
高阶 哈密顿 广义演化方程
2023/11/13
In this talk, I will review several classes of higher-order generalizations of the integrable Camassa-Holm equation in the Hamiltonian forms. Then, I talk about some new results for one generalized Ca...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Integral equations with bubble-type kernel via the method of moving spheres
运动球体 气泡型核 积分方程
2023/4/27
In this talk, I will describe a moving sphere approach to a class of integral equations with bubble-type kernel. This class of equations comes from higher-order elliptic equations on the standard sphe...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：A second order accurate, decoupled numerical scheme for magnetohydrodynamic equations
磁流体 动力学方程 二阶精确解 耦数值方案
2023/4/27
A temporally second-order accurate, fully discrete finite element method is proposed and analyzed for the magnetohydrodynamic (MHD) equations. A modified Crank-Nicolson method is used to discretize th...
EQUATIONS SOLVABLE BY RADICALS IN A UNIQUELY DIVISIBLE GROUP
EQUATIONS SOLVABLE RADICALS UNIQUELY DIVISIBLE GROUP
2015/8/14
We study equations in groups G with unique m-th roots for each positive integer m. A word equation in two letters is an expression of the form w(X, A) = B, where w is a finite word in the alphabet {X,...
Fast Algorithms for Boundary Integral Equations
Boundary integral equations Laplace equation Helmholtz equation fast algorithms fast multipole method hierarchical matrices wavelets multiscale methods multidirectional methods
2015/7/15
This article reviews several fast algorithms for boundary integral equations. After a brief introduction of the boundary integral equations for the Laplace and Helmholtz equations, we discuss in order...
A fast solver for the Stokes equations with distributed forces in complex geometries
Stokes equations Fast solvers Integral equations Double-layer potential Fast multipole methods Embedded domain methods Immersed interface methods Fictitious domain methods Cartesian grid methods Moving boundaries
2015/7/14
We present a new method for the solution of the Stokes equations. The main features of our method are: (1) it can be applied to arbitrary geometries in a black-box fashion; (2) it is second-order accu...
ABSENCE OF ANOMALOUS DISSIPATION OF ENERGY IN FORCED TWO DIMENSIONAL FLUID EQUATIONS
ABSENCE OF ANOMALOUS DISSIPATION OF ENERGY FORCED TWO DIMENSIONAL FLUID EQUATIONS
2014/4/3
Anomalous dissipation of energy in three dimensional turbulence is one of the basic statements of physical theory [55]. It has been veri ed experimentally to a large degree [75], but not mathematicall...
Families of integrable equations
Integrable lattice equations Yang-Baxter maps Consistency around the cube
2011/7/5
We present a method to obtain families of lattice equations. Specifically we focus on two of such
families, which include 3-parameters and their members are connected through B¨acklund transformation...
Homogenizations of integro-differential equations with L{é}vy operators with asymmetric and degenerate densities
Homogenizations of integro-differential equations L{é}vy operators asymmetric degenerate densities
2011/1/21
We consider periodic homogenization problems for the L´evy operators with asymmetric L´evy densities. The formal asymptotic expansion used for the -stable (symmetric) L´evy operator...
A pseudospectral quadrature method for Navier-Stokes equations on rotating spheres
Navier-Stokes equations unit sphere vector spherical harmonics
2010/12/8
In this work, we describe, analyze, and implement a pseudospec-tral quadrature method for a global computer modeling of the incompressible surface Navier-Stokes equations on the rotating unit sphere. ...
On integral equations related to weighted Toepitz operators
Toeplitz operators Lipschitz spaces holomorphic Besov spaces Hardy spaces
2010/12/7
For weighted Toeplitz operators T N ' defined on spaces of holomorphic functions in the unit ball, we derive regularity prop-erties of the solutions f to the integral equation T N ' (f) = h in terms o...
Lax equations and Knizhnik-Zamolodchikov connection
Current algebra Lax operator algebra Lax integrable system
2010/12/10
Given a Lax system of equations with the spectral parameter on a Riemann surface we construct a projective unitary representation of the Lie algebra of Hamiltonian vector fields by Knizhnik-Zamolodchi...
Operational methods and Lorentz-type equations of motion
Operational methods Lorentz-type equations of motion
2010/12/9
We propose an operational method for the solution of di erential equations involv-ing vector products. The technique we propose is based on the use of the evolution operator, de ned in such a way that...
Intrinsic Equations for a Relaxed Elastic Line on an Oriented Hypersurface in the Minkowski Space Rn1
Elastic line Minkowski space
2010/3/1
We gived the intrinsic equations for a relaxed elastic line on an oriented surface in {\Bbb {R}}13 ([1],[2]). In this paper, we derived the intrinsic equations for a relaxed elastic line on an oriente...