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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Boundary expansion in the Loewner-Nirenberg problem
Loewner-Nirenberg problem 边界展开 利玛窦曲率
2023/4/28
We first review some classical results of the Loewner-Nirenberg problem. Then we discuss the characteristics of boundary expansion and its applications in studying the negativity of Ricci curvatures o...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：A Sparse Expansion of (Deep) Gaussian Processes
深层 高斯过程 稀疏展开
2023/4/18
Conventional inferential methods for (deep) Gaussian Processes models can suffer from high computational complexity as they require large-scale operations with kernel matrices for training and inferen...
Closed-form expansion, conditional expectation, and option valuation
asymptotic expansion diffusion option pricing conditional expectation iterated stochastic integral
2016/1/25
Enlightened by the theory of Watanabe [Watanabe S (1987) Analysis of Wiener functionals (Malliavin calculus) and its applications to heat kernels. Ann. Probab. 15:1–39] for analyzing generalized rando...
Fractional diffusion limit for collisional kinetic equations:a Hilbert expansion approach
Fractional diffusion limit collisional kinetic equations Hilbert expansion
2015/10/15
We develop a Hilbert expansion approach for the derivation of fractional diffusion equations from the linear Boltzmann equation with heavy tail equilibria.
A second order expansion of the separatrix map for trigonometric perturbations of a priori unstable systems
second order expansion separatrix map for trigonometric perturbations priori unstable systems
2015/9/25
In this paper we study a so-called separatrix map introduced by Zaslavskii-Filonenko [ZF68] and studied by Treschev and Piftankin [Tre98, Tre02,Pif06, PT07]. We derive a second order expansion of this...
POLE EXPANSION FOR SOLVING A TYPE OF PARAMETRIZED LINEAR SYSTEMS IN ELECTRONIC STRUCTURE CALCULATIONS
Pole expansion approximation theory parametrized linear systems electronic structure calculation
2015/7/14
We present a new method for solving parametrized linear systems. Under certain assumptions on the parametrization, solutions to the linear systems for all parameters can be accurately approximated by ...
A quasi-tree expansion of the Krushkal polynomial
quasi-tree expansion Krushkal polynomial Combinatorics
2012/5/24
We introduce a generalization of the Krushkal polynomial to nonorientable surfaces, and prove that this polynomial has a natural quasi-tree expansion. This generalized Krushkal polynomial contains the...
The Poisson Rain Tessellation Under Spatial Expansion and Temporal Transformation
The Poisson Rain Tessellation Spatial Expansion Temporal Transformation Probability
2012/4/16
For cell-division processes in a window, Cowan introduced four selection rules and two division rules each of which stands for one cell-division model. One of these is the area-weighted in-cell model....
Asymptotic expansion of smooth interval maps
Asymptotic expansion smooth interval maps Dynamical Systems
2012/4/16
We show that several different ways to quantify the asymptotic expansion of a non-degenerate smooth interval map coincide. A consequence is an extension to multimodal maps of the remarkable result of ...
Real analytic expansion of spectral projection and extension of Hecke-Bochner identity
Coxeter group Hecke-Bochner identity Heisenberg group Laguerre polynomials spherical harmonics twisted convolution
2012/4/16
In this article, we review the Weyl correspondence of bigraded spherical harmonics and use it to extend the Hecke-Bochner identities for the spectral projections $f\times\varphi_k^{n-1}$ for function ...
Embedded Zassenhaus Expansion to Operator Splitting Schemes: Theory and Application in Fluid Dynamics
Operator splitting method Iterative splitting Zassenhaus product Parabolic differential equations Convection-Diffusion-Reaction Equations
2012/4/18
In this paper, we contribute operator-splitting methods improved by the Zassenhaus product for the numerical solution of linear partial differential equations. We address iterative splitting methods, ...
General Solution of Generalized (2+1)–Dimensional Kadomtsev-Petviashvili (KP) Equation by Using the –Expansion Method
(G,/G)-Expansion Method Generalized Kadomtsev-Petviashvili (KP) Equation Hyperbolic Function Solutions Trigonometric Function Solutions
2013/1/30
In this work, the (G,/G)- --expansion method is proposed for constructing more general exact solutions of the (2 + 1)--dimensional Kadomtsev-Petviashvili (KP) equation and its generalized forms. Our w...
Multiplicative white noise functionals and the Krylov-Veretennikov expansion for coalescing stochastic flows
Krylov-Veretennikov expansion coalescing stochastic flows Probability
2011/9/20
Abstract: In this article we consider multiplicative operator-valued white noise functionals related to a stochastic flow. A generalization of the Krylov-Veretennikov expansion is presented. An analog...
Expansion of $k$-Schur functions for maximal $k$-rectangles within the affine nilCoxeter algebra
$k$-Schur functions $k$-rectangles affine nilCoxeter algebra Combinatorics
2011/9/14
Abstract: We give several explicit combinatorial formulas for the expansion of $k$-Schur functions indexed by maximal $k$-rectangles, $s_R^{(k)}$, in terms of the standard basis of the affine nilCoxet...
Estimates on the modulus of expansion for vector fields solving nonlinear equations
Estimates vector fields nonlinear equations Differential Geometry
2011/9/5
Abstract: By adapting methods of \cite{AC} we prove a sharp estimate on the expansion modulus of the gradient of the log of the parabolic kernel to the Sch\"ordinger operator with convex potential, wh...