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On the Estimation of Solutions for Some Linear Systems of Differential Equations

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Acta Mathematica Sinica,English Series 1998年第1期14卷 41-46页

作者： L. R. Awad E. M. El-Kholy Sh. El-Bendary Universitat Hamburg institut fur Angewandte mathematik Bundesstraβe 55 20146 Hamburg Germany

In this paper we estimate the solutions of homogeneous linear system of differential equations with unbounded coefficients on the real line R. We also give a necessary and sufficient condition in order that the linear... 详细信息

关键词： Homogeneous linear Unbounded coefficient

Almost nonnegative curvature operator and cohomology rings

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Frontiers of Mathematics in China 2016年第5期11卷 1259-1274页

作者： Martin HERRMANN Fakultat fur mathematik Karlsruher Institut fur Technologie Kaiserstraβe 89-93 76133 Karlsruhe Germany

We give a survey of results on the construction of and obstructions to metrics of almost nonnegative curvature operator on closed manifolds and results on the cohomology rings of closed, simply-connected manifolds with a lower curvature and upper diameter bound. The latter is motivated by a question of Grove whether these condition imply finiteness of rational homotopy types. This question has answers by F. Fang-X. Rong, B. Totaro and recently A. Dessai and the present author.

关键词： Nonnegative curvature homogeneous spaces curvature operator almost nonnegative curvature

Finite Groups Whose Character Graphs Associated with Codegrees Have No Triangles

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Algebra Colloquium 2016年第1期23卷 15-22页

作者： Huan Xiong institut fur mathematik Universitat Zurich Winterthurerstrasse 190 CH-8057 Zurich Switzerland

Motivated by Problem 164 proposed by Y. Berkovich and E. Zhmud＇ in their book ＂Characters of Finite Groups＂, we give a characterization of finite groups whose irreducible character codegrees are prime powers. This is based on a new kind of character graphs of finite groups associated with codegrees. Such graphs have close and obvious connections with character codegree graphs. For example, they have the same number of connected components. By analogy with the work of finite groups whose character graphs （associated with degrees） have no triangles, we conduct a result of classifying finite groups whose character graphs associated with codegrees have no triangles in the latter part of this paper.

关键词： finite group character graph codegree

ON ENERGY CONSERVATION BY TRIGONOMETRIC INTEGRATORS IN THE LINEAR CASE WITH APPLICATION TO WAVE EQUATIONS

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Journal of Computational Mathematics 2020年第5期38卷 705-714页

作者： Ludwig Gauckler institut fur mathematik Freie Universitat BerlinArnimallee 9D-14195 BerlinGermany

Trigonometric integrators for oscillatory linear Hamiltonian differential equations are *** a condition of Hairer&Lubich on the filter functions in the method,a modified energy is derived that is exactly preserved by trigonometric *** implies and extends a known result on all-time near-conservation of *** extension can be applied to linear wave equations.

关键词： Oscillatory Hamiltonian systems Trigonometric integrators Energy conservation Long-time behaviour Modified energy

Spaces and moduli spaces of Riemannian metrics

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Frontiers of Mathematics in China 2016年第5期11卷 1335-1343页

作者： Wilderich TUSCHMANN Karlsruher institut fur Technologie (KIT) Fakultat fur Mathematik Institut fiir Algebra und Geometrie Arbeitsgruppe Differentialgeometrie Englerstraβe 2 D-76131 Karlsruhe Germany

These notes present and survey results about spaces and moduli spaces of complete Riemannian metrics with curvature bounds on open and closed manifolds, here focussing mainly on connectedness and disconnectedness prop... 详细信息

关键词： Riemannian metrics moduli spaces sectional curvature positive Ricci curvature positive scalar curvature

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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

Positive curvature, symmetry, and topology

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Frontiers of Mathematics in China 2016年第5期11卷 1099-1122页

作者： Manuel AMANN Fakultat fur mathematik Institut fiir Algebra und Geometrie Karlsruher Institut fiir Technologie Englerstraβe 2 76131 Karlsruhe Germany

We depict recent developments in the field of positive sectional curvature, mainly, but not exclusively, under the assumption of isometric torus actions. After an elaborate introduction to the field, we shall discuss various classification results, before we provide results on the computation of Euler characteristics. This will be the starting point for an examination of more involved invariants and further techniques. In particular, we shall discuss the Hopf conjectures, related decomposition results like the Wilhelm conjecture, results in differential topology and index theory as well as in rational homotopy theory, geometrically formal metrics in positive curvature and much more. The results we present will be discussed for arbitrary dimensions, but also specified to small dimensions. This survey article features mainly depictions of our own work interest in this area and cites results obtained in different collaborations; full statements and proofs can be found in the respective original research articles.

关键词： Positive sectional curvature torus actions Euler characteristic Hopf conjecture index theory Wilhelm conjecture geometric formality

Statistics for Surface Modes of Nanoparticles with Shape Fluctuations

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Communications in Computational Physics 2010年第10期8卷 1224-1241页

作者： Felix Ruting Hannes Uecker institut fur Physik Carl von Ossietzky UniversitatOldenburg D-26111Germany institut fur mathematik Carl von Ossietzky UniversitatOldenburg D-26111Germany

We develop a numerical method for approximating the surface modes of sphere-like nanoparticles in the quasi-static limit,based on an expansion of(the angular part of)the potentials into spherical *** of the results obtained in this manner with exact solutions and with a perturbation ansatz prove that the scheme is accurate if the shape deviations from a sphere are not too *** method allows fast calculations for large numbers of particles,and thus to obtain statistics for nanoparticles with random shape *** an application we present some statistics for the distribution of resonances,polariziabilities,and dipole axes for particles with random perturbations.

关键词： Electrostatic(boundary-value problems) collective excitations(plasmons) shape fluctuations numerical scheme spherical harmonics projection method

Good deal hedging and valuation under combined uncertainty about drift and volatility

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Probability, Uncertainty and Quantitative Risk 2017年第1期2卷 294-333页

作者： Dirk Becherer Klebert Kentia institut fur mathematik Humboldt UniversitatUnter den Linden 610099 BerlinGermany institut fur mathematik Goethe-UniversitatD-60054 Frankfurt am MainGermany

We study robust notions of good-deal hedging and valuation under combined uncertainty about the drifts and volatilities of asset ***-deal bounds are determined by a subset of risk-neutral pricing measures such that not only opportunities for arbitrage are excluded but also deals that are too good,by restricting instantaneous Sharpe ratios.A non-dominated multiple priors approach to model uncertainty(ambiguity)leads to worst-case good-deal *** hedging strategies arise as minimizers of a suitable coherent risk ***-deal bounds and hedges for measurable claims are characterized by solutions to secondorder backward stochastic differential equations whose generators are non-convex in the *** hedging strategies are robust with respect to uncertainty in the sense that their tracking errors satisfy a supermartingale property under all a-priori valuation measures,uniformly over all priors.

关键词： Combined drift and volatility uncertainty Good-deal bounds Robust hedging Hedging to acceptability Second-order BSDE Stochastic control