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In this talk, I will review several classes of higher-order generalizations of the integrable Camassa-Holm equation in the Hamiltonian forms. Then, I talk about some new results for one generalized Ca...
We develop and compare two algorithms for computing first-order right-hand factors in the ring of linear Mahler operators l_r M^r+?+l_1 M+l_0 where l_0,…,l_r are polynomials in x and Mx=x^b M for some...
We propose two families of nonconforming finite elements on $n$-rectangle meshes of any dimension to solve the sixth-order elliptic equations. The unisolvent property and the approximation ability of ...
A new class of high-order maximum principle preserving numerical methods is proposed for solving the semilinear Allen-Cahn equation. We start with the method consists of a $k$th-order multistep expone...
We get a priori estimates for the fifth-order modified KdV equations in Besov spaces with low regularity which cover the full subcritical range. These estimates are obtained from the power series expa...
The regularity estimates have well-established for second-order elliptic and parabolic equations, as well as for equations with stable-like non-local operators. Whether similar results hold for non-lo...
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...
Since the work of Sela, and Kharlampovich & Myasnikov on Tarski’s problem for non-abelian free groups, the model theoretic analysis of classes of groups arising from combinatorial and geometric group ...
In this talk, we first consider convex optimization whose smooth components have a locally Lipschitz continuous gradient and propose a first-order method for finding an epsilon-KKT solution. We then c...
Model Order Reduction techniques represent an advanced simulation tool for a large variety of problems of practical and fundamental interest in both industrial and research applications. Indeed, despi...
Big data problems present great challenges to statisti-cal analyses, especially from the computational side. In this paper, we consider regression estimation of high-order mo-ments in big data problem...
We develop preconditioners for systems arising from finite element discretizations of parabolic problems which are fourth order in space. We consider boundary conditions which yield a natural ...
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...
We derive a posteriori error estimates, which exhibit optimal global order, for a class of time stepping methods of any order that include Runge{Kutta Collocation (RK-C) methods and the continuous ...
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...

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