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We establish improved uniform error bounds for the time-splitting methods for the long-time dynamics of the nonlinear Schr\"odinger equation (NLSE) with weak nonlinearity. By a new technique of regula...
In this talk, we are interested in designing some efficient numerical methods for Maxwell-Debye equations in metamaterials with negative refractive index. Dimensional splitting method is used to reduc...
The Borel conjecture considers the obstruction from homotopy equivalence to homeomorphism for aspherical manifolds. The torus is the first computed case of Borel conjecture with the idea of splitting ...
In this talk, we will introduce a novel overlapping domain decomposition splitting algorithm based on a Crank--Nisolson method is developed for the stochastic NLS equation driven by a multiplicative n...
We report iron-containing mixed-oxide nanocomposites as highly effective redox materials for thermochemical CO2-splitting and methane partial oxidation in a cyclic redox scheme, where methane was intr...
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 ...
We discuss rather systematically the principle, implicit in earlier works, that for a “random” element in an arithmetic subgroup of a (split, say) reductive algebraic group over a number field, the sp...
THE SPLITTING OF REDUCTIONS OF AN ABELIAN VARIETY     SPLITTING OF REDUCTIONS  ABELIAN VARIETY       font style='font-size:12px;'> 2015/8/26
Consider an absolutely simple abelian variety A defined over a number field K. For most places v of K, we study how the reduction Av of A modulo v splits up to isogeny. Assumingthe Mumford–Tate conjec...
On June 8, 2008, at 12:25 GMT, a Mw 6.4 earthquake, the Movri Mountain earthquake, occurred in the area of northwest Peloponnese, western Greece. The epicenter was located in the municipality of Movri...
A splitting method for optimal control     Operator splitting algorithm  the secondary control  operation       font style='font-size:12px;'> 2015/8/7
We apply an operator splitting technique to a generic linear-convex optimal control problem, which results in an algorithm that alternates between solving a quadratic control problem, for which there ...
We develop a simple operator splitting method for solving a primal conic optimization problem; we show that the iterates also solve the dual problem. The resulting algorithm is very simple to describe...
Block splitting for distributed optimization     Distributed computing  convex optimization  data  large linear operator  matrix  machine       font style='font-size:12px;'> 2015/8/7
This paper describes a general purpose method for solving convex optimization problems in a distributed computing environment. In particular, if the problem data includes a large linear operator or ma...
Recently, several convergence rate results for Douglas-Rachford splitting and the alternating direction method of multipliers (ADMM) have been presented in the literature. In this paper, we show linea...
Time splitting for wave equations in random media     Time splitting  wave equations  random media       font style='font-size:12px;'> 2015/7/14
Numerical simulation of high frequency waves in highly heterogeneous media is a challenging problem. Resolving the fine structure of the wave field typically requires extremely small time steps and sp...
Time splitting for the Liouville equation in a random medium     Time splitting  Liouville equation  random medium       font style='font-size:12px;'> 2015/7/14
We consider the Liouville equations with highly heterogeneous Hamiltonians and their numerical solution by a time splitting algorithm. Such equations model the density of particles evolving according ...

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