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Science China Mathematics 2005年第Z1期48卷 225-237页

作者： Guy roos Nevski Prospekt 113/4-53 191024 St Petersburg Russian Federation

We introduce the notion of virtual Bergman kernel and study some of its applications.

关键词： Bergman kernel, weighted Bergman kernel, virtual Bergman kernel.

New classes of domains with explicit Bergman kernel

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Science China Mathematics 2004年第3期47卷 352-371页

作者： roos GUY Henan University Kaifeng 475001 China Nevski Prospekt 113/4-53 191024 St Petersburg Russian Federation

We introduce two classes of egg type domains, built on general boundedsymmetric domains, for which we obtain the Bergman kernel inexplicit formulas. As an auxiliary tool, we compute the integralof complex powers of the generic norm on a bounded symmetricdomains using the well-known integral of Selberg. Thisgeneralizes matrix integrals of Hua and leads to a specialpolynomial with integer or half-integer coefficients attached toeach irreducible bounded symmetric domain.

关键词： Cartan domain, Bergman kernel, holomorphic automorphism group, boundedsymmetric domain, Hua integral.

STABILIZED FEM FOR CONVECTION-DIFFUSION PROBLEMS ON LAYER-ADAPTED MESHES

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Journal of Computational Mathematics 2009年第2期27卷 266-279页

作者： Hans-Grg roos TU Dresden Germany

The application of a standard Galerkin finite element method for convection-diffusion problems leads to oscillations in the discrete solution, therefore stabilization seems to be necessary. We discuss several recent stabilization methods, especially its combination with a Galerkin method on layer-adapted meshes. Supercloseness results obtained allow an improvement of the discrete solution using recovery techniques.

关键词： Singular perturbations Convection-diffusion Finite element method Stabi-lization Layer-adapted mesh Superconvergenee Recovery

A New Kernel Function Yielding the Best Known Iteration Bounds for Primal-Dual Interior-Point Algorithms

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Acta Mathematica Sinica,English Series 2009年第12期25卷 2169-2178页

作者： Yan Qin BAI Jin LiGUO Cornelis roos Department of Mathematics Shanghai University Shanghai 200436 P. R. China Business School University of Shanghai for Science and Technology Shanghai 200093 P. R. China Faculty of Electrical Engineering Mathematics and Computer Science Delft University of Technology P.O. Box 5031 2600 GA Delft The Netherlands

Kernel functions play an important role in defining new search directions for primal-dual interior-point algorithm for solving linear optimization problems. In this paper we present a new kernel function which yields ... 详细信息

关键词： linear optimization interior-point method primal-dual method large-update method polynomial complexity

GRADED MESHES FOR HIGHER ORDER FEM

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Journal of Computational Mathematics 2015年第1期33卷 1-16页

作者： Hans-Gorg roos Ljiljana Teofanov Zorica Uzelac Institute of Numerical Mathematics Technical University of Dresden Dresden D-01062 Germany Department for Fundamental Disciplines Faculty of Technical Sciences University of Novi Sad Trg D. Obradovida 6 21000 Novi Sad Serbia

A singularly perturbed one-dimensional convection-diffusion problem is solved numeri- cMly by the finite element method based on higher order polynomials. Numerical solutions are obtained using S-type meshes with special emphasis on meshes which are graded （based on a mesh generating function） in the fine mesh region. Error estimates in the s-weighted energy norm are proved. We derive an ＇optimal＇ mesh generating function in order to min- imize the constant in the error estimate. Two layer-adapted meshes defined by a recursive formulae in the fine mesh region are also considered and a new technique for proving er- ror estimates for these meshes is presented. The aim of the paper is to emphasize the importance of using optimal meshes for higher order finite element methods. Numerical experiments support all theoretical results.

关键词： Singular perturbation Boundary value problem Layer-adapted meshes Gradedmeshes Finite element method.

Nicotinamide mononucleotide:a potential effective natural compound against insulin resistance

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Signal Transduction and Targeted Therapy 2021年第9期6卷 2609-2610页

作者： Julian roos Julia Zinngrebe Pamela Fischer-Posovszky Department of Pediatrics and Adolescent Medicine Ulm University Medical CenterUlmGermany

Recently,a study published in Science by Yoshino et al.1 reported on a randomized,placebo-controlled,double-blind clinical trial to examine the effects of a 10-week nicotinamide mononucleotide(NMN)administration on human metabolism in 25 postmenopausal overweight or obese women with *** revealed positive effects of NMN on insulin sensitivity,insulin signalling,and tissue remodelling in skeletal muscle.

关键词： metabolism clinical

Numerical Analysis of a System of Singularly Perturbed Convection-Diffusion Equations Related to Optimal Control

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Numerical Mathematics(Theory,Methods and Applications) 2011年第4期4卷 562-575页

作者： Hans-Görg roos Christian Reibiger Technische Universität Dresden Institut für Numerische Mathematik01062 DresdenGermany

We consider an optimal control problem with an 1D singularly perturbed differential state *** solving such problems one uses the enhanced system of the state equation and its adjoint ***,we obtain a system of two convectiondiffusion *** linear finite elements on adapted grids we treat the effects of two layers arising at different boundaries of the *** proof uniform error estimates for this method on meshes of Shishkin *** present numerical results supporting our analysis.

关键词： Convection-diffusion linear finite elements a priori analysis layer-adapted meshes singular perturbed optimal control

Anionic Polymerization of Butadiene Using Lithium/Potassium Multi-metallic Systems:Influence on Polymerization Control and Polybutadiene Microstructure

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Chinese Journal of Polymer Science 2020年第4期38卷 357-362,I0006页

作者： Antoine Forens Kevin roos Charlotte Dire Benoit Gadenne Stephane Carlotti Univ.Bordeaux CNRSBordeaux INPLCPOUMR 5629F-33600PessacFrance MFP Michelin Centre de Technologie/Ladoux23 Place des Carmes Dechaux63040 Clermont-Ferrand cedex 9France

Thermal,mechanical,and viscoelastic properties of polybutadiene-based rubber materials are highly dependent on polybutadiene *** use of polar modifier in association with alkyllithium is a well-known method to obtain polybutadiene with a high vinyl con *** approach is to use bimetallic initiating species such as alkyllithium combined to heavier alkali metal alkoxide(RONa,ROK...).The polymerization control is n evertheless not achieved and several parameters were found to influe nee *** bimetallic in itiating systems based on alkyllithium and a potassium alkoxide,alkyllithium structure,initiator preformation time,and initiator composition were identified as parameters influencing the anionic polymerization process of butadiene and/or polybutadiene *** addition,the use of trimetallic systems based on alkyllithium,potassium alkoxide,and alkylaluminum was investigated in order to prevent side reactions regardless of the[K]/[Li]ratio and of the initiator preformation time.

关键词： Polybutadiene Anionic polymerization Microstructure (Multi)metallic systems Lithium/potassium-based systems

Superconvergence of a Galerkin FEM for Higher-Order Elements in Convection-Diffusion Problems

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Numerical Mathematics(Theory,Methods and Applications) 2014年第3期7卷 356-373页

作者： Sebastian Franz H.-G.roos Institut für Numerische Mathematik Technische Universit¨at Dresden01062 DresdenGermany

In this paper we present a first supercloseness analysis for higher-order Galerkin FEM applied to a singularly perturbed convection-diffusion *** a solution decomposition and a special representation of our finite element space,we are able to prove a supercloseness property of p+1/4 in the energy norm where the polynomial order p≥3 is odd.

关键词： Singular perturbation layer-adapted meshes superconvergence postprocessing

UNIFORM SUPERCONVERGENCE OF A FINITE ELEMENT METHOD WITH EDGE STABILIZATION FOR CONVECTION-DIFFUSION PROBLEMS

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Journal of Computational Mathematics 2010年第1期28卷 32-44页

作者： Sebastian Franz Torsten Linβ Hans-Grg roos Sebastian Schiller Department of Mathematics and Statistics University of Limerick Institut für Numerische Mathematik Technische Universitt Dresden

In the present paper the edge stabilization technique is applied to a convection-diffusion problem with exponential boundary layers on the unit square, using a Shishkin mesh with bilinear finite elements in the layer regions and linear elements on the coarse part of the mesh. An error bound is proved for ‖πu-u^h‖Е, where πu is some interpolant of the solution u and uh the discrete solution. This supercloseness result implies an optimal error estimate with respect to the L2 norm and opens the door to the application of postprocessing for improving the discrete solution.

关键词： Convection-diffusion problems Edge stabilization FEM Uniform convergence Shishkin mesh.