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RESEARCH ANNOUNCEMENTS Limit of Bernstein- Bezier Curves for Periodic Control Nets

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数学进展 1993年第5期 454-455页

作者：齐东旭 ,Robert Schaback institut far unmerische and angewandte mathematik der Universitat Gottingen Lotzestrase 16-18 D-3400 Gottingen Germany

Let n≥1 control points .b0, b1,…,bn-1∈ Rdbe given. These control points arerepeated by bj+kn: =bjfor 0≤j≤n - 1, and all k∈Zto form an infinite periodic sequence. The centrold of the points is denoted by

关键词： Bezier Curves for Periodic Control Nets RESEARCH ANNOUNCEMENTS Limit of Bernstein

EXPLICIT ERROR ESTIMATES FOR COURANT, CROUZEIX-RAVIART AND RAVIART-THOMAS FINITE ELEMENT METHODS

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Journal of Computational Mathematics 2012年第4期30卷 337-353页

作者： Carsten Carstensen Joscha Gedicke Donsub Rim institut fur mathematik Humboldt-Universitiit zu Berlin Unter den Linden 6 10099 Berlin Germany Department of Computational Science and Engineering Yonsei University 120-749 Seoul Korea institut fur mathematik Humboldt-Universitat zu Berlin Unter den Linden 6 10099 Berlin Germany Yonsei School of Business and Department of Computational Science and Engineering Yonsei University 120-749 Seoul Korea

The elementary analysis of this paper presents explicit expressions of the constants in the a priori error estimates for the lowest-order Courant, Crouzeix-Raviart nonconforming and P^viart-Thomas mixed finite element methods in the Poisson model problem. The three constants and their dependences on some maximal angle in the triangulation are indeed all comparable and allow accurate a priori error control.

关键词： Error estimates Conforming Nonconforming Mixed Finite element method.

Deciphering the mechanobiology of microglia in traumatic brain injury with advanced microsystems

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Neural Regeneration Research 2025年第8期20卷 2304-2306页

作者： Anthony Procès Sylvain Gabriele Univ.Grenoble Alpes InsermU1216Grenoble Institut des NeurosciencesGrenobleFrance Mechanobiology&Biomaterials Group CIRMAPResearch Institute for BiosciencesUniversity of MonsMonsBelgium

Advanced microsystems in traumatic brain injury research:Traumatic brain injury(TBI)results from a mechanical insult to the brain,leading to neuronal and axonal damage and subsequently causing a secondary *** minutes ... 详细信息

关键词： traumatic injury damage

EFFECT OF FINE GRINDING ACTIVATION ON LEACHING BEHAVIOUR OF SCHEELITE CONCENTRATE

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Acta Metallurgica Sinica(English Letters) 1992年第9期5卷 153-157页

作者： R.KAMMEL institut fr Metallurgie Technische University BerlinGermany

The influence of mechanical activation on the leaching behaviour of scheelite was studied by means of fine grinding in an attritor and subsequently HCl leaching in presence of PO_4^(3-). Results showed that after fine grinding in the attritor,the reaction rate of scheelite with HCl-Na_3PO_4 solution was remarkably increased,the extraction of W increased from about 8 to 99%.The IR spectra and X-ray diffraction analysis indicated that in addition to an enlargement of surface area the fine grinding action had made also changes of fine struc- ture and reactivity of solid surface,hence the leaching process of scheelite can be carried out under mild leaching conditions.

关键词： scheelite fine grinding acid leaching mechanical activation

Structure Polynomials and Subgraphs of Rooted Regular Trees

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Algebra Colloquium 2018年第1期25卷 45-70页

作者： Daniele D'Angeli Alfredo Donno institut ffir Diskrete mathematik Technische Universitat Graz Steyrergasse 30 8010 Graz Austria Universitg degli Studi Niccolo Cusano - Via Don Carlo Gnocchi 300166 Roma Italia

We introduce an algebraic structure allowing us to describe subgraphs of a regular rooted tree. Its elements are called structure polynomials, and they are in a one- to-one correspondence with the set of all subgraphs of the tree. We define two operations, the sum and the product of structure polynomials, giving a graph interpretation of them. Then we introduce an equivalence relation between polynomials, using the action of the full automorphism group of the tree, and we count equivalence classes of subgraphs modulo this equivalence. We also prove that this action gives rise to symmetric Gelfand pairs. Finally, when the regularity degree of the tree is a prime p, we regard each level of the tree as a finite dimensional vector space over the finite field Fp, and we are able to completely characterize structure polynomials corresponding to subgraphs whose leaf set is a vector subspace.

关键词： rooted tree structure polynomial rooted subtree automorphism group of a tree Gelfand pair

Finite Volume Evolution Galerkin Methods for the Shallow Water Equations with Dry Beds

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Communications in Computational Physics 2011年第7期10卷 371-404页

作者： Andreas Bollermann Sebastian Noelle Maria Lukacova-Medvid’ova IGPM RWTH AachenTemplergraben 5552062 AachenGermany institut fur mathematik Universitat MainzStaudingerweg 955099 MainzGermany.

We present a new Finite Volume Evolution Galerkin(FVEG)scheme for the solution of the shallow water equations(SWE)with the bottom topography as a source *** new scheme will be based on the FVEG methods presented in(Noelle and Kraft,***.,221(2007)),but adds the possibility to handle dry *** most important aspect is to preserve the positivity of the water *** present a general approach to ensure this for arbitrary finite volume *** main idea is to limit the outgoing fluxes of a cell whenever they would create negative water ***,this corresponds to the absence of fluxes in the presence of *** is then re-established by splitting gravitational and gravity driven parts of the ***,a new entropy fix is introduced that improves the reproduction of sonic rarefaction waves.

关键词： Well-balanced schemes dry boundaries shallow water equations evolution Galerkin schemes source terms

HANGING NODES IN THE UNIFYING THEORY OF A POSTERIORI FINITE ELEMENT ERROR CONTROL

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Journal of Computational Mathematics 2009年第2期27卷 215-236页

作者： C. Carstensen Jun Hu institut für mathematik Humboldt Universitaet zu Berlin Rudower Chaussee 25 D -12489 Berlin Germany LMAM and School of Mathematical Sciences Peking University Beijing 100871 China

A unified a posteriori error analysis has been developed in [18, 21-23] to analyze the finite element error a posteriori under a universal roof. This paper contributes to the finite element meshes with hanging nodes which are required for local mesh-refining. The twodimensional 1-irregular triangulations into triangles and parallelograms and their combinations are considered with conforming and nonconforming finite element methods named after or by Courant, Q1, Crouzeix-Raviart, Poisson, Stokes and Navier-Lamé equations Han, Rannacher-Turek, and others for the The paper provides a unified a priori and a posteriori error analysis for triangulations with hanging nodes of degree ≤ 1 which are fundamental for local mesh refinement in self-adaptive finite element discretisations.

关键词： A posteriori A priori Finite element Hanging node Adaptive algorithm.

Multilevel Preconditioners for the Interior Penalty Discontinuous Galerkin Method II-Quantitative Studies

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Communications in Computational Physics 2009年第2期5卷 296-325页

作者： Kolja Brix Martin Campos Pinto Wolfgang Dahmen Ralf Massjung institut fur Geometrie und Praktische mathematik RWTH Aachen52056 AachenGermany Universite Louis Pasteur Institut de Recherche Mathematique AvanceeCNRS UMR 750167084 StrasbourgFrance

This paper is concerned with preconditioners for interior penalty discontinuous Galerkin discretizations of second-order elliptic boundary value *** extend earlier related results in[7]in the following *** concrete realizations of splitting the nonconforming trial spaces into a conforming and(remaining)nonconforming part are identified and shown to give rise to uniformly bounded condition *** asymptotic results are complemented by numerical tests that shed some light on their respective quantitative behavior.

关键词： Interior penalty method energy-stable splittings admissible averaging operators frames multilevel Schwarz preconditioners discontinuous Galerkin methods

A NEW APPROACH TO RECOVERY OF DISCONTINUOUS GALERKIN

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Journal of Computational Mathematics 2009年第6期27卷 697-712页

作者： Sebastian franz Lutz Tobiska Helena Zarin institut für Numerische MathematikTechnische Universitt Dresden institut für Analysis und NumerikOtto-von-Guericke Universitt Magdeburg Department of Mathematics and Informatics University of Novi SadTrg Dositeja Obradovica 421 000 Novi Sad

A new recovery operator P ：Qn^disc（T）→Qn＋1^disc（M） for discontinuous Galerkin is derived. It is based on the idea of projecting a discontinuous, piecewise polynomial solution on a given mesh T into a higher order polynomial space on a macro mesh M. In order to do so, we define local degrees of freedom using polynomial moments and provide global degrees of freedom on the macro mesh. We prove consistency with respect to the local L2-projection, stability results in several norms and optimal anisotropic error estimates. As an example, we apply this new recovery technique to a stabilized solution of a singularly perturbed convection-diffusion problem using bilinear elements.

关键词： Discontinuous Galerkin Postprocessing Recovery.