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Chinese Annals of Mathematics,Series B 2002年第2期23卷 165-180页

作者： A.BENSOUSSAN J.FREHSE UniversityParis Institut fur Angewandte Mathematik Dauphineand CNES(CentreNationald’Etudes Spatiales)2PlaceMauriceQuentin75001Pari

The objective of this paper is to consider the theory of regularity of systems of partial differential equations with Neumann boundary conditions. It complements previous works of the authors for the Dirichlet case. This type of problem is motivated by stochastic differential games. The Neumann case corresponds to stochastic differential equations with reflection on boundary of the domain.

关键词： Regularity theory Neumann boundary conditions Dirichlet problem

Berry-Esseen bounds and moderate deviations for the norm, entries and spectral radius of products of positive random matrices

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Science China Mathematics 2024年第3期67卷 627-646页

作者： Hui Xiao Ion Grama Quansheng Liu institut fur mathematik und angewandte informatik Universitat HildesheimHildesheim 31141Germany Academy of Mathematics and Systems Science Chinese Academy of SciencesBeijing 100190China LMBA Universite Bretagne SudCNRS UMR 6205Vannes F-56000France

Let(g_(n))_(n≥1) be a sequence of independent and identically distributed positive random d×d matrices and consider the matrix product G_(n)=g_(n)…g_*** suitable conditions,we establish the Berry-Esseen bounds on the rate of convergence in the central limit theorem and Cramer-type moderate deviation expansions,for any matrix norm ‖G_(n)‖ of G_(n),its entries G_(n)^(i,j) and its spectral radius ρ(G_(n)).Extended versions of their joint law with the direction of the random walk G_(n)x are also established,where x is a starting point in the unit sphere of R~d.

关键词： Berry-Esseen bound Cramér-type moderate deviation product of random matrices operator norm entry spectral radius

Modelling and Numerical Valuation of Power Derivatives in Energy Markets

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Advances in Applied Mathematics and Mechanics 2012年第3期4卷 259-293页

作者： Mai Huong Nguyen Matthias Ehrhardt institut fur mathematik Technische Universitat BerlinStrasse des 17.Juni 13610623 BerlinGermany Lehrstuhl fur angewandte mathematik und Numerische Analysis Fachbereich C-Mathematik und NaturwissenschaftenBergische Universitat WuppertalGaußstr.2042119 WuppertalGermany

In this work we investigate the pricing of swing options in a model where the underlying asset follows a jump diffusion *** focus on the derivation of the partial integro-differential equation(PIDE)which will be applied to swing contracts and construct a novel pay-off function from a tree-based pay-off matrix that can be used as initial condition in the PIDE *** valuing swing type derivatives we develop a theta implicit-explicit finite difference scheme to discretize the PIDE using a Gaussian quadrature method for the integral *** on known results for the classical theta-method the existence and uniqueness of solution to the new implicit-explicit finite difference method is *** numerical examples illustrate the usability of the proposed method and allow us to analyse the sensitivity of swing options with respect to model *** particular the effects of number of exercise rights,jump intensities and dividend yields will be investigated in depth.

关键词： Swing options jump-diffusion process mean-reverting Black-Scholes equation energy market partial integro-differential equation theta-method Implicit-Explicit-Scheme

Matrix Tensor Product Approach to the Equivalence of Multipartite States under Local Unitary Transformations

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Communications in Theoretical Physics 2006年第2期45卷 267-270页

作者： GAO Xiu-Hong S. Alberverio FEI Shao-Ming WANG Zhi-Xi Department of Mathematics Capital Normal University Beijing 100037 China institut fur angewandte mathematik Universitat Bonn D-53115 Bonn Germany

The equivalence of multipartite quantum mixed states under local unitary transformations is studied. A criterion for the equivalence of non-degenerate mixed multipartite quantum states under local unitary transformati... 详细信息

关键词： local unitary transformation multipartite quantum mixed state tensor decomposable

ON SOME MODEL DIFFUSION PROBLEMS WITH A NONLOCAL LOWER ORDER TERM

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Chinese Annals of Mathematics,Series B 2003年第2期24卷 147-166页

作者： N.H.CHANG M.CHIPOT Academia Sinica Institute of MathematicsTaipei 11 529Taiwan China.Institut fur MathematikAbt.Angewandte MathematikUniversitat Zurich Winterthurerstrasse 190CH-8057 ZurichSwitzerland.

The authors consider a class of nonlinear parabolic problems where the lower order term isdepending on a weighted integral of the solution, and address the issues of existence, uniqueness,stationary solutions and in s... 详细信息

关键词： Nonlocal problems Elliptic equations Parabolic equations Asymptotic behaviour Stationary problems

The Dichotomy Between Traces on d-sets Г in R^n and the Density of D(R^n\Г) in Function Spaces

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Acta Mathematica Sinica,English Series 2008年第4期24卷 539-554页

作者： Hans TRIEBEL Mathematisches institut Fakultt fr Mathematik und InformatikFriedrich-Schiller-Universitt JenaD-07737 JenaGermany

A space Apq^s （R^n） with A ： B or A = F and s ∈R, 0 〈 p, q 〈 ∞ either has a trace in Lp（Г）, where Г is a compact d-set in R^n with 0 〈 d 〈 n, or D（R^n／Г） is dense in it. Related dichotomy numbers are ... 详细信息

A space Apq^s （R^n） with A ： B or A = F and s ∈R, 0 〈 p, q 〈 ∞ either has a trace in Lp（Г）, where Г is a compact d-set in R^n with 0 〈 d 〈 n, or D（R^n／Г） is dense in it. Related dichotomy numbers are introduced and calculated.

关键词： function spaces d-sets fractals traces

Periodic Algebras Generated by Groups

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Algebra Colloquium 2015年第4期22卷 541-554页

作者： S. Albeverio B.A. Omirov U.A. Rozikov institut fur angewandte mathematik and HCM Universitat Bonn Bonn Germany institute of Mathematics 29 Do'rmon Yo'li str. 100125 Tashkent Uzbekistan

We consider algebras with basis numerated by elements of a group G. We fix a function f from G × G to a ground field and give a multiplication of the algebra which depends on f. We study the basic properties of such algebras. In particular, we find a condition on f under which the corresponding algebra is a Leibniz algebra. Moreover, for a given subgroup G of G we define a G-periodic algebra, which corresponds to a G-periodic function f, we establish a criterion for the right nilpotency of a G-periodic algebra. In addition, for （7 = Z we describe all 2Z- and 3Z-periodic algebras. Some properties of nZ-periodic algebras are obtained.

关键词： periodic algebra Leibniz algebra group

Symmetry Adapted Block Diagonalisation in Equivariant Steady State Bifurcation Problems and its Numerical Application

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数学进展 1991年第4期 455-487页

作者： Peter Stork,Bodo Werner institut fur angewandte mathematik der Universitat Hamburg Bundesstr.55 D-2000 Hamburg 13 Federal Republic of Germany institut fur angewandte mathematik der Universitat Hamburg Bundesstr.55 D-2000 Hamburg 13 Federal Republic of Germany

Considering steady state bifurcation of single parameter r-equivariant systemswhere Γ is a compact Lie group acting on X via a faithful orthogonal representation, we simultaneously block-diagonalise all jacobians of g along a solution path with respect to symmetry adapted subspaces and apply bifurcation groups to reduce symmetry breaking bifurcation points to simple bifurcation points. In generical situations this algorithm allows for numerically stable use of continuation methods and steady state bifurcation point detection and computation. The large scale decrease of computing efforts is demonstrated at computing the equilibria of a hexagonal lattice dome with 21 degrees of freedom, we present a great variety of solution arcs with symmetry from full D6 down to Z2 symmetry.

关键词： Symmetry Adapted Block Diagonalisation in Equivariant Steady State Bifurcation Problems and its Numerical Application

Optical coatings:trends and challenges

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光学精密工程 2005年第4期13卷 389-396页

作者： Norbert Kaiser Torsten Feigl Olaf Stenzel Ulrike Schulz Fraunhofer institut für angewandte Optik und Feinmechanik Albert-Einstein-Str. 7D-07745 Jena GermanyFraunhofer Institut für Angewandte Optik und Feinmechanik Albert-Einstein-Str. 7D-07745 Jena GermanyFraunhofer Institut für Angewandte Optik und Feinmechanik Albert-Einstein-Str. 7D-07745 Jena GermanyFraunhofer Institut für Angewandte Optik und Feinmechanik Albert-Einstein-Str. 7D-07745 Jena Germany

New applications in optoelectronics, photonics, telecommunication, displays, optical data processing, biomedicine, sensors, energy control, automobile, aerospace, and architecture stimulation are important developments in physics and technology of optical coatings. This paper will focus on the latest advances in the areas of new optical film systems and devices, new optical coating materials and film fabrication techniques, process control and monitoring, and different advanced applications. Particularly, focus is on optical films that combine optical design with microstructural features tailored on the nanometer and micrometer scales. Evaluation of film stability and integrity in harsh industrial environments and their compatibility with organic polymers are important as well.

关键词：光学涂覆技术光电子技术光学仪器光学材料