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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...
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...
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...
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...
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...
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...
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...
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 ...
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 ...
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...
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¨ ...
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...
n this article, we discuss that an initial-irregular oblique derivative problem for non-linear uniformly parabolic complex equation of second order A0 u zˉ z −Re[Quzz+A1 u z ]−A2 u&...
In this article, we discuss that an oblique derivative boundary value problem for nonlinear uniformly elliptic complex equation of second order wz1z=F(z; w; w z ;wz; w zz ;wzz)+G(z; w; ; w z ;...

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