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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...
Studies of the Electronic Structure of Metallocene-based Second-order Non-linear Optical Dyes
Electronic Structure Metallocene Second-order Non linear Optical Dyes
2016/5/23
This paper describes a simple orbital picture for understanding the optical transitions and the second-order nonlinear optical response of metallocene-based chromophores of the form metallocene-(pi-br...
Second Order Hadamard Differentiability in Statistical Applications
Cramer-von Mises statistic goodness of fit test Hadamard differentiability limiting distribution linear models M-estimator statistical functionals uniform asymptotic linearity weighted empirical processes
2015/12/11
A formulation of the second-order Hadamard differentiability of (extended) statistical functionals and some related theoretical results are established. These results are applied to derive the limitin...
Second-Order Corrections to Mean Field Evolution of Weakly Interacting Bosons.I.
Second-Order Corrections Mean Field Evolution Weakly Interacting Bosons
2015/10/16
Inspired by the works of Rodnianski and Schlein [31] and Wu [34,35], we derive a new nonlinear Schrödinger equation that describes a second-order correction to the usual tensor product (mean-fiel...
Second-order corrections to mean field evolution of weakly interacting Bosons.II
Second-order corrections Mean field evolution Weakly interacting bosons
2015/10/16
We study the evolution of an N-body weakly interacting system of Bosons. Our work forms an extension of our previous paper Grillakis, Machedon, and Margetis (2010) [13], in which we derived a second-o...
SECOND ORDER CORRECTIONS TO MEAN FIELD EVOLUTION FOR WEAKLY INTERACTING BOSONS, I
SECOND ORDER equation
2015/10/15
Inspired by the works of Rodnianski and Schlein [31]
and Wu [34, 35], we derive a new nonlinear Schr¨odinger equation
that describes a second-order correction to the usual tensor product (mean-ʂ...
SECOND-ORDER CORRECTIONS TO MEAN FIELD EVOLUTION OF WEAKLY INTERACTING BOSONS. II
SECOND-ORDER WEAKLY INTERACTING BOSONS
2015/10/15
We study the evolution of a N-body weakly interacting system of Bosons. Our work forms an extension of our previous paper I [13], in which we derived a second-order correction
to a mean-field e...
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...
Applications of second-order cone programming
Second-order cone programming linear function affine sets linear nonlinear convex problem quadratic program
2015/8/11
In a second-order cone program (SOCP) a linear function is minimized over the intersection of an affine set and the product of second-order (quadratic) cones. SOCPs are nonlinear convex problems that ...
Array signal processing with robust rejection constraints via second-order cone programming
Vector and array signal processing noise the ellipsoid array robust optimization
2015/8/10
We consider the array signal processing problem of choosing the weight vector to minimize noise power, subject to a unit array gain for the desired wave, and subject to rejection constraints on interf...
The Harnack inequality for second-order elliptic equations with divergence-free drifts
Harnack inequality second-order elliptic equations divergence-free drifts
2015/7/14
We consider an elliptic equation with a divergence-free drift b. We prove that an inequality of Harnack type holds under the assumption b ∈ Ln/2+δ ∩ L2 where δ > 0. As an application we provide a one ...
The Harnack inequality for second-order parabolic equations with divergence-free drifts of low regularity
Harnack inequality second-order parabolic equations divergence-free drifts low regularity
2015/7/14
We establish the Harnack inequality for advection-diffusion equations with divergencefree drifts of low regularity.While our previous work [IKR] considered the elliptic case, here we treat the more ch...
On the spectral analysis of second-order Markov chains
second order Markov chains trajectorial reversibility spectrum of non-reversible Markov kernels spectral gap improvement of speed of convergence discrete position-speed Markov chains homogeneous and Abelian second order Markov chains
2015/7/7
Second order Markov chains which are trajectorially reversible are considered. Contrary to the reversibility notion for usual Markov chains, no symmetry property can be deduced for the corresponding t...
First-order SODE: OU processdX+aX(t)dt= dW(t)
Three options:a >0, a= 0, a <0.
First-order SPDE:du= au
xx dt+dW(t, x)
One option:a >0(Infinite-dimensional stable OU process.)
Second-order SODE:X¨ ...
MODIFIED SECOND ORDER SLOPE ROTATABLE DESIGNS USING BIBD
Response surface designs modified slope rotatable central composite designs
2015/3/18
In this paper, a new method of modified second order slope rotatable designs
(SOSRD) using balanced incomplete block designs (BIBD) for 4≤v≤16 is presented. In
this method the number of design point...