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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Singular integral and geometry
奇异积分 几何 谐波分析
2023/5/8
The geometric considerations enter in a decisive way in many questions of harmonic analysis. For example, the estimation of the Fourier transform of surface-carried measure, which played a key role in...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On forward/inverse spectral problems, approximation problems and multiple integral formulae for non-smooth solitons
非光滑孤子 正/逆谱问题 近似问题 多重积分公式
2023/4/28
A class of nonlinear integrable PDEs admit non-smooth solitary wave solutions as certain special weak solutions. These solutions can be used to capture main attributes of solutions of these PDEs, e.g....
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Strong approximation and integral quadratic forms over affine curves
仿射曲线 强近似 积分二次形式
2023/5/9
Let $k$ be a field of characteristic 0 and let $C$ be the a smooth affine curve over $k$. We will first discuss applications of strong approximation to the theory of integral quadratic forms over $C$....
The Embedded Boundary Integral Method (EBI) for the Incompressible Navier-Stokes equations
Embedded Boundary Integral Method (EBI) Incompressible Navier Stokes equations
2015/7/15
We present a new method for the solution of the unsteady incompressible Navier-Stokes equations. Our goal is to achieve a robust and scalable methodology for two and three dimensional incompressible f...
THE INTEGRAL K-THEORETIC NOVIKOV CONJECTURE FOR GROUPS WITH FINITE ASYMPTOTIC DIMENSION
K-THEORETIC integral
2015/7/7
The goal of this paper is to apply the techniques developed by the first author
in [3] to verify the integral Novikov conjecture for groups with finite asymptotic
dimension as defi...
INTEGRAL IDENTITIES AND MINKOWSKI TYPE INEQUALITIES INVOLVING SCHOUTEN TENSOR
INTEGRAL IDENTITIES MINKOWSKI TYPE INEQUALITIES INVOLVING SCHOUTEN TENSOR
2014/4/3
New formulas for the integration of the k-th elementary symmetric functions of the Shouten tensor are derived and applied to deduce some
Minkowski type inequalities.
On Explicit Holmes-Thompson Area Formula in Integral Geometry
Minkowski space Holmes-Thompson Volume symplectic structure
2010/12/13
In this article, we give an exposition on the Holmes-Thompson theory developed by Alvarez. The space of geodesics in Minkowski space has a symplectic structure which is induced by the projection from ...
On Rayleigh-Type Formulas for a Non-local Boundary Value Problem Associated with an Integral Operator Commuting with the Laplacian
Rayleigh functions Laplacian eigenvalue problems non-local boundary conditions
2010/12/9
In this article, we provide two different ways of producing recursive formulas for the Rayleigh functions of eigenvalues of the one-dimensional Laplacian with non-local boundary conditions, which comm...
Compact integral manifolds of differential systems
ordinary differential system total differential system linear system of partial differential equations
2010/12/7
The boundedness tests for the number of compact integral manifolds of autonomous ordi-nary differential systems, of autonomous total differential systems, of linear systems of partial
differential eq...
EXTEND MEAN CURVATURE FLOW WITH FINITE INTEGRAL CURVATURE
EXTEND MEAN CURVATURE FINITE INTEGRAL CURVATURE
2018/4/19
In this note, we first prove that the solution of mean curvature flow on a finite time interval [0, T ) can be extended over time T if the space-time integration of the norm of the second fundamental ...
The Random Integral Representation Conjecture: a quarter of a century later
Class L distributions or selfdecomposable distributions infinite divisibility Lévy-Khintchine formula
2010/12/6
In Jurek 1985 and 1988 the random integral representations conjecture was stated. It claims that (some) limit laws can be written as probability distributions of random integrals of
the form R (a,b] ...
A monopole homology for integral homology 3-spheres
monopole homology integral homology 3-spheres
2010/3/1
To an integral homology 3-sphere Y, we assign a well-defined {\mathbb Z}-graded (monopole) homology MH*(Y, Ih(Q; h0)) whose construction in principle follows from the instanton Floer theory with...
Explicit integrable systems on two dimensional manifolds with a cubic first integral
Explicit integrable systems dimensional manifolds first integral
2010/4/2
A few years ago Selivanova gave an existence proof for some integrable models, in fact geodesic flows on two dimensional manifolds, with a cubic first integral. However the explicit form of these mod...
Volterra Integral and Integrodifferential Equations in Two Variables
Volterra integral and integrodifferential equations Banach fixed point theorem Bielecki type norm integral inequalities existence and uniqueness estimates on the solutions approximate solutions
2010/4/16
The aim of this paper is to study the existence, uniqueness and other properties of solutions of certain Volterra integral and integrodifferential equations in two variables. The tools employed in the...
Some Retarded Nonlinear Integral Inequalities in Two Variables and Applications
Integral inequality Nonlinear Two variables Retarded
2010/1/22
In this paper, some retarded nonlinear integral inequalities in two variables with more than one distinct nonlinear term are established. Our results are also applied to show the boundedness of the so...