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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：An algebraic framework for geometrically continuous splines
几何 连续样条 代数框架
2023/11/6
Geometrically continuous splines are piecewise polynomials defined on a collection of patches stitched together through transition maps. In this talk, we introduce an algebraic framework to study geom...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：A New Framework for SIMD Bootstrapping in Polynomial Modulus
多项式 模数 SIMD自举 新框架
2023/4/28
In this series of work, we aim at improving the bootstrapping paradigm for fully homomorphic encryption (FHE). Our main goal is to show that the amortized cost of bootstrapping within a polynomial mod...
Adaptive local basis set for Kohn–Sham density functional theory in a discontinuous Galerkin framework I: Total energy calculation
Electronic structure Kohn–Sham density functional theory Discontinuous Galerkin Adaptive local basis set Enrichment functions Eigenvalue problem
2015/7/14
Kohn–Sham density functional theory is one of the most widely used electronic structure theories. In the pseudopotential framework, uniform discretization of the Kohn–Sham Hamiltonian generally result...
Homogenization of a stochastic nonlinear reaction-diffusion equation with a large reaction term: the almost periodic framework
Stochastic Homogenization Almost Periodic Stochastic Reaction-Diffusion Equations Wiener Process
2011/9/21
Abstract: Homogenization of a stochastic nonlinear reaction-diffusion equation with a large non- linear term is considered. Under a general Besicovitch almost periodicity assumption on the coefficient...
Integrating strong and weak discontinuities without integration subcells and example applications in an XFEM/GFEM framework
Schwarz Christoffel conformal mapping numerical integration extended finite element method quadrature generalized finite element method
2011/9/20
Abstract: Partition of unity methods, such as the extended finite element method (XFEM) allow discontinuities to be simulated independently of the mesh [1]. This eliminates the need for the mesh to be...
A new algebraic and arithmetic framework for interval computations
algebraic arithmetic framework interval computations Numerical Analysis
2011/10/9
Abstract: In this paper we propose some very promissing results in interval arithmetics which permit to build well-defined arithmetics including distributivity of multiplication and division according...
Convolution powers in the operator-valued framework
Convolution powers the operator-valued framework Operator Algebras
2011/9/9
Abstract: We consider the framework of an operator-valued noncommutative probability space over a unital C*-algebra B. We show how for a B-valued distribution \mu one can define convolution powers wit...
Abstract: We prove that a sequence of averaged quantities $\int_{\R^m}h_n(x,p)\rho(p)dp$, $n\in \N$, is strongly precompact in $L^1_{loc}(\R^d)$, where $\rho\in C_0(\R^m)$, and $h_n\in L^p(\R^d\times ...
Methods of Approximation in hpk Framework for ODEs in Time Resulting from Decoupling of Space and Time in IVPs
Finite Element Approximations Numerical Studies Time Approximation Variationally Consis- tent Integral Forms
2013/1/30
The present study considers mathematical classification of the time differential operators and then applies methods of approximation in time such as Galerkin method (GM ), Galerkin method with weak fo...
The non-autonomous chiral model and the Ernst equation of General Relativity in the bidifferential calculus framework
non-autonomous chiral model bidifferential calculus framework Ernst equation General Relativity
2011/7/7
We generate exact solutions of the non-autonomous chiral model, which in particular arises in General Relativity, using a general result of the bidifferential calculus approach to integrable PDDEs. In...
The non-autonomous chiral model and the Ernst equation of General Relativity in the bidifferential calculus framework
non-autonomous chiral model bidifferential calculus framework Ernst equation General Relativity
2011/7/7
We generate exact solutions of the non-autonomous chiral model, which in particular arises in General Relativity, using a general result of the bidifferential calculus approach to integrable PDDEs. In...
Fixed-Point Approaches to Computing Bertrand-Nash Equilibrium Prices Under Mixed Logit Demand: A Technical Framework for Analysis and Efficient Computational Methods
Mixed Logit Demand Technical Framework Analysis Efficient Computational Methods
2011/2/28
Bertrand competiton has been a prominent paradigm for the empirical study of differentiated
product markets for at least twenty years. Firms engaged in Bertrand competition maximize profits by choosi...
A mathematical framework for reducing the domain in the mechanical analysis of periodic structures
A mathematical framework mechanical analysis of periodic structures
2011/1/21
A theoretical framework is developped leading to a sound derivation of Periodic Boundary Conditions (PBCs) for the analysis of domains smaller then the Unit Cells (UCs), named reduced Unit Cells (rUCs...
A framework is a graph and a map from its vertices to R^d. A framework is called universally rigid if there is no other framework with the same graph and edge lengths in R^d' for any d'. A framework a...
Late-time relaxation limits of nonlinear hyperbolic systems. A general framework
nonlinear hyperbolic systems A general framework
2010/11/19
We investigate the late-time asymptotic behavior of solutions to nonlinear hyperbolic systems of conservation laws containing stiff source term. On one hand, we determine the relevant asymptotic expa...