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Operator Equations and Duality Mappings in Sobolev Spaces with Variable Exponents

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Chinese Annals of Mathematics,Series B 2013年第5期34卷 639-666页

作者： philippe g.CIARLET george DINCA Pavel MATEI Department of Mathematics City University of Hong Kong83 Tat Chee AvenueKowloonHong KongChina Faculty of Mathematics and Computer Science University of Bucharest14 Academiei Street010014 BucharestRomania. Technical University of Civil Engineering Department of Mathematics and Computer Science124 Lacul Tei Blvd.020396 BucharestRomania.

After studying in a previous work the smoothness of the space UΓ0={u∈W1,p(·)(Ω);u=0 on Γ0 Γ=Ω},where dΓ-measΓ0>0,with p(·)∈C(Ω)and p(x)>1 for all x∈Ω,the authors study in this paper the strict and uniform convexity as well as some special properties of duality mappings defined on the same *** results obtained in this direction are used for proving existence results for operator equations having the form Ju=Nfu,where J is a duality mapping on UΓ0 corresponding to the gauge function,and Nf is the Nemytskij operator generated by a Carath′eodory function f satisfying an appropriate growth condition ensuring that Nf may be viewed as acting from UΓ0 into its dual.

关键词： Sobolev空间对偶映射算子方程规范函数生长条件操作者平滑性一致凸

Hyperbolic Conservation Laws on *** Error Estimate for Finite Volume Schemes

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Acta Mathematica Sinica,English Series 2009年第7期25卷 1041-1066页

作者： philippe g.LeFLOCH Baver OKUTMUSTUR Wladimir NEVES Laboratoire Jacques-Louis Lions Centre National de la Recherche ScientifiqueUniversité de Paris 6 Instituto de Matemática Universidade Federal do Rio de Janeiro C.P. 68530Cidade Universitária 21945-970

Following Ben-Artzi and LeFloch, we consider nonlinear hyperbolic conservation laws posed on a Riemannian manifold, and we establish an L1-error estimate for a class of finite volume schemes allowing for the approximation of entropy solutions to the initial value problem. The error in the L1 norm is of order h1/4 at most, where h represents the maximal diameter of elements in the family of geodesic triangulations. The proof relies on a suitable generalization of Cockburn, Coquel, and LeFloch＇s theory which was originally developed in the Euclidian setting. We extend the arguments to curved manifolds, by taking into account the effects to the geometry and overcoming several new technical difficulties.

关键词： Hyperbolic conservation law entropy solution finite volume scheme error estimate discrete entropy inequality convergence rate

Recovery of Immersions from Their Metric Tensors and Nonlinear Korn Inequalities:A Brief Survey

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Chinese Annals of Mathematics,Series B 2017年第1期38卷 253-280页

作者： philippe g.CIARLET Cristinel MARDARE Sorin MARDARE Department of Mathematics City University of Hong Kong83 Tat Chee AvenueKowloonHong Kong. Sorbonne Universites Universite Pierre et Marie CurieLaboratoire Jacques-Louis LionsCNRS-UMR7598F-7.5005 Laboratoire de Mathematiques Raphael Salem UMR 6085 CNRS-Universite de Rouen Avenue de l'Universite BP.12 Technopole du Madrillet F76801

The authors discuss the existence and uniqueness up to isometries of Enof immersions φ : Ω  R^n→ E^n with prescribed metric tensor field(g ij) : Ω→ S^n>, and discuss the continuity of the mapping(gij) →φ defined in this fashion with respect to various topologies. In particular, the case where the function spaces have little regularity is considered. How, in some cases, the continuity of the mapping(gij) →φ can be obtained by means of nonlinear Korn inequalities is shown.

关键词： Isometric immersions Nonlinear Korn inequalities Metric tensor

On a Vector Version of a Fundamental Lemma of ***

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Chinese Annals of Mathematics,Series B 2018年第1期39卷 33-46页

作者： philippe g. CIARLET Maria MALIN Cristinel MARDARE Department of Mathematics City University of Hong Kong 83 Tat Chee Avenue Kowloon Hong Kong. Sorbonne Universites Universite Pierre et Marie Curie Laboratoire Jacques-Louis Lions 4 Place Jussieu 75005 Paris France

Let ? be a bounded and connected open subset of R^N with a Lipschitzcontinuous boundary,the set ? being locally on the same side of ??.A vector version of a fundamental lemma of ***,due to ***,the first author,*** and ***,asserts that any vector field v =(vi) ∈(D′(?))~N,such that all the components 1/2(?_jv_i + ?_iv_j),1 ≤ i,j ≤ N,of its symmetrized gradient matrix field are in the space H^(-1)(?),is in effect in the space(L^2(?))~*** objective of this paper is to show that this vector version of *** lemma is equivalent to a certain number of other properties of interest by *** include in particular a vector version of a well-known inequality due to ***ˇcas,weak versions of the classical Donati and Saint-Venant compatibility conditions for a matrix field to be the symmetrized gradient matrix field of a vector field,or a natural vector version of a fundamental surjectivity property of the divergence operator.

关键词： J.L.Lions lemma Neˇcas inequality Donati compatibility conditions Saint-Venant compatibility conditions

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On Korn's Inequality

Chinese Annals of Mathematics,Series B 2010年第5期31卷 607-618页

作者： philippe g.CIARLET Department of Mathematics City University of Hong Kong

The author first reviews the classical Korn inequality and its *** recent works of ***,***,Jr.,and the author,it is shown how the Korn inequality can be recovered by an entirely different *** new proof hinges on appropriate weak versions of the classical Poincar'e and Saint-Venant *** fine,both proofs essentially depend on a crucial lemma of ***,recalled at the beginning of this paper.

关键词： Korn不等式证明庞加莱作者引理

In-process failure analysis of thin-wall structures made by laser powder bed fusion additive manufacturing

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Journal of Materials Science & Technology 2022年第3期98卷 233-243页

作者： Apratim Chakraborty Reza Tangestani Rasim Batmaz Waqas Muhammad philippe Plamondon Andrew Wessman Lang Yuan Étienne Martin University of Waterloo 200 University Avenue WestWaterlooON N2L 3G1Canada Polytechnique Montréal 2500 Chemin de PolytechniqueMontréalQC H3T 1J4Canada University of Arizona 1235 E.James E.Rogers WayTucsonAZ 85721-0012United States University of South Carolina 301 Main StreetColumbiaSC 29208United States

Fabrication of thin-wall components using the laser powder bed fusion(LPBF)additive manufacturing(AM)technology was investigated for two“hard-to-weld”high gamma prime Ni-based superalloys RENé65(R65)and RENé108(R108).Simple block parts with wall thicknesses of 0.25 mm,1.00 mm,and5.00 mm are printed using a bidirectional laser scanning strategy without layer-wise *** with walls thinner than 5 mm fail before reaching the designated build *** indicate that reduction of limiting build height(LBH)corresponds to the reduction of part thickness and is unaffected by alloy *** the contrary,the number of internal micro-cracks along columnar grain boundaries in the build direction(BD)increases with part thickness and is significantly higher in R108 than *** findings suggest that reduced LBH in parts with thinner walls is not caused by internal micro-crack *** and finite element analysis(FEA)of the in-process thermal stresses show that the LBH trend is not explained by the conventional cracking *** suggest that part thickness affects stress distribution leading to more substantial distortion and consequent failure to add layers for continued fabrication of thinner parts.

关键词： Laser powder bed fusion Superalloys Thin-wall Residual stress Additive manufacturing

Advantages and Drawbacks of Quantum Mechanical Static and Dynamic Approaches to Modelling Infrared Spectra

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Chinese Journal of Chemical Physics 2009年第2期22卷 123-128页

作者： Claude Pouchan philippe Carbonniere groupe Chimie Théorique et Réactivité ECP IPREM UMR CNRS 5254 Université de Pau et des Pays de I'Adour 2 Rue Jules Ferry F-54000 Pau France

我们在从有效的秒顺序 perturbative 和变化不安处理的泛音近似以外的机械震动的计算定义为静态的途径的现在的量，以及从密度的震动的分析功能的理论在 300 和 600 K 的分子的动力学轨道。四个计划用 B3LYP/6 31+g 在理论的一样的水平... 详细信息

我们在从有效的秒顺序 perturbative 和变化不安处理的泛音近似以外的机械震动的计算定义为静态的途径的现在的量，以及从密度的震动的分析功能的理论在 300 和 600 K 的分子的动力学轨道。四个计划用 B3LYP/6 31+g 在理论的一样的水平以相应中等红外线的光谱的基本转变，和模拟的预言被比较(d， p ) 对电子结构的描述。我们关于这二条途径的优点和缺点总结结论并且报导为半硬、灵活的分子获得的主要结果。

关键词：量子力学非谐振动振动组态互相作用微扰方法从头计算

Animal phylogeny and large-scale sequencing： progress and pitfalls

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植物分类学报 2008年第3期46卷 274-286页

作者： Henner BRINKMANN Herve philippe Centre Robert Cedergren Departement de Biochimie Universite de Montreal 2900 Boulevard Edouard-Montpetit Montreal Quebec H3TIJ4 Canada

Phylogenomics, the inference of phylogenetic trees using genome-scale data, is becoming the rule for resolving difficult parts of the tree of life. Its promise resides in the large amount of information available, which should eliminate stochastic error. However, systematic error, which is due to limitations of reconstruction meth-ods, is becoming more apparent. We will illustrate, using animal phylogeny as a case study, the three most effi-cient approaches to avoid the pitfalls of phylogenomics: (1) using a dense taxon sampling, (2) using probabilistic methods with complex models of sequence evolution that more accurately detect multiple substitutions, and (3) removing the fastest evolving part of the data (e.g., species and positions). The analysis of a dataset of 55 animal species and 102 proteins (25712 amino acid positions) shows that standard site-homogeneous model inference is sensitive to long-branch attraction artifact, whereas the site-heterogeneous CAT model is less so. The latter model correctly locates three very fast evolving species, the appendicularian tunicate Oikopleura, the acoel Convoluta and the myxozoan Buddenbrockia. Overall, the resulting tree is in excellent agreement with the new animal phylogeny, confirming that "simple" organisms like platyhelminths and nematodes are not necessarily of basal emergence. This further emphasizes the importance of secondary simplification in animals, and for organismal evolution in general.

关键词：动物发展史测序方法缺陷改进措施

On the Stability of Racing Sailing Boats with Foils

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Chinese Annals of Mathematics,Series B 2018年第3期39卷 427-450页

作者： philippe DESTUYNDER Caroline FABRE Département d'ingénierie Mathématique Laboratoire M2N Conservatoire National des Arts et Métiers 292rue saint Martin75003 ParisFrance Laboratoire de Mathématiques d'Orsay Univ.Paris-SudCNRSUniversitéParis-Saclay 91405 OrsayFrance

The development of foils for racing boats has changed the strategy of ***,the America's cup held in San Francisco,has been the theatre of a tragicomic history due to the foils. During the last round,the New-Zealand boat was winning by 8 to1 against the defender USA. The winner is the first with 9 victories. USA team understood suddenly(may be) how to use the control of the pitching of the main foils by adjusting the rake in order to stabilize the ship. And USA won by 9 victories against 8 to the challenger NZ. The goal in this paper is to point out few aspects which could be taken into account in order to improve this mysterious control law which is known as the key of the victory of the USA team. There are certainly many reasons and in particular the cleverness of the sailors and of all the engineering team behind this project. But it appears interesting to have a mathematical discussion,even if it is a partial one,on the mechanical behaviour of these extraordinary sailing boats. The numerical examples given here are not the true *** have just been invented in order to explain the theoretical developments concerning three points: The possibility of tacking on the foils for sailing upwind,the nature of foiling instabilities,if there are,when the boat is flying and the control laws.

关键词：不稳定性航行控制轮船旧金山美国法律水手