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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On the preservation of second integrals by RK methods
RK方法 保存 第二积分
2023/4/25
One can elucidate integrability properties of ODEs by knowing the existence of second integrals. However, little is known about how they are preserved, if at all, under numerical methods. In this talk...
Let C(t) : I 7! R2 be a simple closed unit-speed C2 curve in R2 with normal ~n(t). The
curve C generates a distribution ¡ which acts on vector ˉelds ~v(x1; x2) : R2 7! R2 by line
integration ac...
FAST DIRECTIONAL COMPUTATION OF HIGH FREQUENCY BOUNDARY INTEGRALS VIA LOCAL FFTs
boundary integral method scattering high frequency waves directional algorithm low-rank approximation Chebyshev interpolation fast Fourier transforms
2015/7/14
The boundary integral method is an efficient approach for solving time-harmonic acoustic obstacle scattering problems. The main computational task is the evaluation of an oscillatory boundary integral...
THE GROMOV-WITTEN POTENTIAL OF A POINT, HURWITZ NUMBERS, AND HODGE INTEGRALS
Hurwitz numbers Gromov-Witten potential moduli space
2015/7/14
It is the Deligne-Mumford compacti cation of the moduli space Mg;n of smooth
n-pointed genus g curves. It has n natural line bundles Li (roughly, the cotangent
space to the ith marked point) and a n...
HODGE INTEGRALS AND HURWITZ NUMBERS VIA VIRTUAL LOCALIZATION
HODGE INTEGRALS HURWITZ NUMBERS
2015/7/14
We give another proof of Ekedahl, Lando, Shapiro, and Vainshtein's remarkable formula expressing Hurwitz numbers (counting covers of
P1 with speci ed simple branch points, and speci ed branching over...
Let C(t) : I 7→ R2 be a simple closed unit-speed C2 curve in R2 with normal ~ n(t). The curve C generates a distribution Γ which acts on vector fields ~ v(x1,x2) : R2 7→ R2 by line integration accordi...
Operads, homotopy algebra and iterated integrals for double loop spaces
Operads homotopy algebra iterated integrals double loop spaces
2015/3/25
This paper provides some background to the theory of operads, used in the first author's papers on 2d topological field theory (hep-th/921204, CMP 159 (1994), 265-285; hep-th/9305013). It is intended ...
Solution of Singular Integrals in Mathematical Model of Mode I Crack near Strength Mismatched Interface
Crack Opening Displacement Singular Integrals Strength Mismatch Weld Interface Cauchy’s Principal Value Theorem
2013/1/30
Characteristics of Mode I crack near the interface of elasticity matched but plasticity and strength mismatched materials differ from those of the crack in a homogenous body. Interface body of differe...
Efficient Discretization of Stochastic Integrals
Efficient Discretization Stochastic Integrals Probability
2012/4/18
Sharp asymptotic lower bounds of the expected quadratic variation of discretization error in stochastic integration are given. The theory relies on inequalities for the kurtosis and skewness of a gene...
Hermite-Hadamard's inequalities for preinvex functions via fractional integrals and related fractional inequalities
Hermite-Hadamard inequalities invex set preinvex function fractional integral
2012/4/17
In this paper, first we have established Hermite- Hadamard's inequalities for preinvex functions via fractional integrals. Second we extend some estimates of the right side of a Hermite- Hadamard type...
Nonexistence of formal first integrals for nonlinear systems under resonance
Non-integrability Resonance First integral Normal form
2011/10/12
In this paper, by using normal form theory we give some criteria of nonexistence of formal first integrals for general nonlinear systems under resonance. As application, we also give a criterion for n...
New inequalities of Ostrowski type for mappings whose derivatives are s-convex in the second sense via fractional integrals
Ostrowski type inequality convex function Riemann-Liouville fractional integral
2011/9/22
Abstract: New identity similar to an identity of [13] for fractional integrals have been defined. Then making use of this identity, some new Ostrowski type inequalities for Riemann-Liouville fractiona...
Predictable projections of conformal stochastic integrals: an application to Hermite series and to Widder's representation
conformal stochastic integrals Widder's representation Hermite series
2011/9/21
Abstract: In this article, we study predictable projections of stochastic integrals with respect to the conformal Brownian motion, extending the connection between powers of the conformal Brownian mot...
Convergence of Wigner integrals to the tetilla law
Contractions Free Brownian motion Free cumulants Free probability Non-central limit theorems Wigner chaos
2011/9/14
Abstract: If x and y are two free semicircular random variables in a non-commutative probability space (A,E) and have variance one, we call the law of 2^{-1/2}(xy+yx) the tetilla law (and we denote it...
Moments on Riemann surfaces and hyperelliptic Abelian integrals
Moments Riemann surfaces hyperelliptic Abelian integrals Dynamical Systems
2011/9/9
Abstract: In the present paper we solve the following different but interrelated problems: (a) the moment problem on Riemann surfaces, (b) the vanishing problem of polynomial Abelian integrals of dime...