基于刚（粘）塑性流动理论的自然单元法研究

将自然单元法与刚（粘）塑性流动理论相结合,对自然单元法在金属塑性成形过程数值模拟中的应用进行了研究。采用基于Voronoi图和Delaunay三角化结构的Non-Sibsonian插值方法构造近似速度场向量,实现无网格方法中速度边界条件的直接精确施加,提出了基于刚（粘）塑性流动理论的无网格自然单元法。运用不完全广义变分...     

Acceleration of self‐consistent field convergence in ab initio molecular dynamics simulation with multiconfigurational wave function

The Lagrange interpolation of molecular orbital (LIMO) method, which reduces the number of self‐consistent field iterations in ab initio molecular dynamics simulations with the Hartree–Fock method and the Kohn–Sham density functional theories, is extended to the theory of multiconfigurational wave functions. We examine two types of treatments for the active orbitals that are partially occupied. The first treatment, as denoted by LIMO(C), is a simple application of the conventional LIMO method to the union of the inactive core and the active orbitals. The second, as denoted by LIMO(S), separately treats the inactive core and the active orbitals. Numerical tests to compare the two treatments clarify that LIMO(S) is superior to LIMO(C). Further applications of LIMO(S) to various systems demonstrate its effectiveness and robustness. © 2014 Wiley Periodicals, Inc.     

On an extreme class of real interpolation spaces

We investigate the limit class of interpolation spaces that comes up by the choice θ=0 in the definition of the real method. These spaces arise naturally interpolating by the J-method associated to the unit square. Their duals coincide with the other extreme spaces obtained by the choice θ=1. We also study the behavior of compact operators under these two extreme interpolation methods. Moreover, we establish some interpolation formulae for function spaces and for spaces of operators.     

Interpolation problems on the spectrum of <Emphasis Type="Italic">H</Emphasis><Superscript>∞</Superscript>

We characterize those sequences (x _n ) in the spectrum of H ^∞ whose Nevanlinna–Pick interpolation problems admit thin Blaschke products as solutions. We also study under which conditions there is a Blaschke product B with prescribed zero-set distribution and solving problems of the form B(x) = f _n (x) for every x ∈ P(x _n ), where P(x _n ) is the Gleason part associated with the point x _n and where (f _n ) is an arbitrary sequence of functions in the unit ball of H ^∞. As a corollary we get a new characterization of Carleson–Newman Blaschke products in terms of bounded universal functions, a result first proved by Gallardo and Gorkin.      

Good Banach spaces for piecewise hyperbolic maps via interpolation

We introduce a weak transversality condition for piecewise C^1+α and piecewise hyperbolic maps which admit a C^1+α stable distribution. We show bounds on the essential spectral radius of the associated transfer operators acting on classical anisotropic Sobolev spaces of Triebel–Lizorkin type which are better than previously known estimates (when our assumption on the stable distribution holds). In many cases, we obtain a spectral gap from which we deduce the existence of finitely many physical measures with basin of total measure. The analysis relies on standard techniques (in particular complex interpolation) but gives a new result on bounded multipliers. Our method applies also to piecewise expanding maps and to Anosov diffeomorphisms, giving a unifying picture of several previous results on a simpler scale of Banach spaces.     

凸四边形上一类具有C~2-连续的插值问题的样条解及其应用

本文讨论了一类凸四边形上的插值问题.指出这类插值问题是可解的,其解是分片二元三次多项式,且在凸四边形上是C~2-连续的.我们证明了这类插值问题的解的存在性和唯一性,给出了解样条的分片表达式及其逼近度的估计.最后还给出了一个应用实例和图形显示来说明本方法是可行的.     

Representation for the Lagrangian numerical differentiation formula involving elementary symmetric functions

By using elementary symmetric functions, this paper presents an explicit representation for the Lagrangian numerical differentiation formula as well as the error estimate for local approximation. And we also point out that the numerical differentiation formula constructed by Li [J.P. Li, General explicit difference formulas for numerical differentiation, J. Comput. Appl. Math. 183 (2005) 29-52] is actually a special case of the Lagrangian numerical differentiation formula to approximate the values of the derivatives at the nodes.     

Superconvergence estimates of finite element methods for American options

In this paper we are concerned with finite element approximations to the evaluation of American options. First, following W. Allegretto etc., SIAM J. Numer. Anal. 39 (2001), 834–857, we introduce a novel practical approach to the discussed problem, which involves the exact reformulation of the original problem and the implementation of the numerical solution over a very small region so that this algorithm is very rapid and highly accurate. Secondly by means of a superapproximation and interpolation postprocessing analysis technique, we present sharp L ²-, L ^∞-norm error estimates and an H ¹-norm superconvergence estimate for this finite element method. As a by-product, the global superconvergence result can be used to generate an efficient a posteriori error estimator. This work was supported in part by the National Natural Science Foundation of China (10471103 and 10771158), the National Basic Research Program (2007CB814906), Social Science Foundation of the Ministry of Education of China (Numerical Methods for Convertible Bonds, 06JA630047), Tianjin Natural Science Foundation (07JCY-BJC14300), and Tianjin University of Finance and Economics.     

Improving Schwarz inequality in inner product spaces

Some improvements of the celebrated Schwarz inequality in complex inner product spaces are given. Applications for n-tuples of complex numbers are provided.     

Some equivalent definitions of Besov spaces of generalized smoothness

In this paper, we present some alternative definitions of Besov spaces of generalized smoothness, defined via Littlewood–Paley‐type decomposition, involving weak derivatives, polynomials, convolutions and generalized interpolation spaces.