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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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...
Identification of Second-Order Stochastic Dynamical Systems
Dynamical Systems Second-Order
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2015/4/3
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
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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...