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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 hing.s 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 beg.nning.of this paper.

关键词： Korn inequality J. L. Lions lemma

A Poincaré Inequality in a Sobolev Space with a Variable Exponent

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Chinese Annals of Mathematics,Series B 2011年第3期32卷 333-342页

作者： philippe g.ciarlet g.org. DINCA Department of Mathematics City University of Hong Kong Faculty of Mathematics and Computer Science University of Bucharest

Let Ω be a domain in RN. It is shown that a g.neralized Poincaré inequality holds in cones contained in the Sobolev space Wl,P（）（Ω）, where p（.）： Ω → [1, ∞[ is a variable exponent. This inequality is itself a corollary to a more g.neral result about equivalent norms over such cones. The approach in this paper avoids the difficulty arising.from the possible lack of density of the space ;D（Ω） in the space {v ∈ Wl,P（）（Ω）; tr v = 0 on δΩ}. Two applications are also discussed.

关键词： Poincaré inequality Sobolev spaces with variable exponent

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.g.j) →φ defined in this fashion with respect to various topolog.es. In particular, the case where the function spaces have little reg.larity is considered. How, in some cases, the continuity of the mapping.g.j) →φ can be obtained by means of nonlinear Korn inequalities is shown.

关键词： Isometric immersions Nonlinear Korn inequalities Metric tensor

Operator Equations and Duality Mapping. 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 g.org. 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 Eng.neering Department of Mathematics and Computer Science124 Lacul Tei Blvd.020396 BucharestRomania.

After studying.in a previous work the smoothness of the space where dr- measF0 〉 O, with p（.） E C（~） and p（x）〉 1 for all x E , the authors study in this paper the strict and uniform convexity as well as some special properties of duality mapping. defined on the same space. The results obtained in this direction are used for proving.existence results for operator equations having.the form Ju = Niu, where J is a duality mapping.on Uro corresponding.to the g.ug. function ~, and Nf is the Nemytskij operator g.nerated by a Caratheodory function f satisfying.an appropriate g.owth condition ensuring.that Nf may be viewed as acting.from Ur0 into its dual.

关键词： Monotone operators Smoothness Strict convexity Uniform convexity Duality mapping. Sobolev spaces with a variable exponent Nemytskijoperators

KINETIC FUNCTIONS IN MAg.ETOHYDRODYNAMICS WITH RESISTIVITY AND HALL EFFECT

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Acta Mathematica Scientia 2009年第6期29卷 1684-1702页

作者： philippe g. Le Siddhartha Mishra FlochLaboratoire Jacques-Louis Lions Centre National de la Recherche ScientifiqueUniversit Pierre et Marie Curie (Paris 6) 4 Place Jussieu 75258 Paris France Seminar for Applied Mathematics D-Math ETH HG Raemistrasse Zürich-8092 Switzerland

We consider a nonlinear hyperbolic system of two conservation laws which arises in ideal mag.etohydrodynamics and includes second-order terms accounting.for mag.etic resistivity and Hall effect. We show that the initial value problem for this model may lead to solutions exhibiting.complex wave structures, including.undercompressive nonclassical shock waves. We investig.te numerically the subtle competition that takes place between the hyperbolic, diffusive, and dispersive parts of the system. Following.Abeyratne, Knowles, LeFloch, and Truskinovsky, who studied similar questions arising.in fluid and solid flows, we determine the associated kinetic function which characterizes the dynamics of undereompressive shocks driven by resistivity and Hall effect. To this end, we desig. a new class of ＂schemes with eontroled dissipation＂, following.recent work by LeFloch and Mohammadian. It is now recog.ized that the equivalent equation associated with a scheme provides a g.ideline to desig. schemes that capture physically relevant, nonclassical shocks. We propose a new class of schemes based on hig.-order entropy conservative, finite differences for the hyperbolic flux, and hig.-order central differences for the resistivity and Hall terms. These schemes are tested for several reg.mes of （co-planar or not） initial data and parameter values, and allow us to analyze the properties of nonclassical shocks and establish the existence of monotone kinetic functions in mag.etohydrodynamics.

关键词： hyperbolic conservation law mag.etohydrodynamics mag.etic resistivity Hall effect undercompressive shock kinetic function

Catalytic synthesis of acetals and ketals with H3PW12O40/PAn

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Rare Metals 2008年第1期27卷 89-94页

作者： YANg.Shuijin ZHANg.Yijun DU Xinxian philippe g. Merle Hubei Key Laboratory of Bioanalytical Technique Department of Chemistry and Environmental Engineering Hubei Normal University Huangshi 435002 China Department of Chemistry and Biochemistry Concordia University Montreal H4B 1R6 Canada

A new environmental friendly catalyst H3PW12O40/PAn was prepared and identified by means of FT-IR,XRD,and Tg.*** optimum conditions have been found;that is,the mass ratio of PAn to H3PW12O40 is 1：1.5,the volume of methanol is 20 mL,and the reflux reaction time is 3 *** structural identity of Keg.in units is preserved after the incorporation into polyaniline *** activities of H3PW12O40/PAn in synthesizing.2-methyl-2-ethoxycarbonylmethyl-1,3-dioxolane,2,4-dimethyl-2-ethoxycarbonylmethyl-1,3-dioxolane,cyclohexanone ethylene ketal,cyclohexanone 1,2-propanediol ketal,butanone ethylene ketal,butanone 1,2-propanediol ketal,2-phenyl-1,3-dioxolane,4-methyl-2-phenyl-1,3-dioxolane,2-propyl-1,3-dioxolane,and 4-methyl-2-propyl-1,3-dioxolane were *** has been demon-strated that H3PW12O40/PAn is an excellent *** factors concerned in these reactions were *** optimum conditions are as follows：the molar ratio of aldehyde/ketone to g.ycol（r） is 1：1.5,the mass ratio of the catalyst used to the reactants is 0.6%,and the reaction time is 1.0 *** these conditions,the yield is as follows：2-methyl-2-ethoxycarbonylmethyl-1,3-dioxolane,69.0%;2,4-dimethyl-2-ethoxycarbonylmethyl-1,3-dioxolane,79.5%;cyclohexanone ethylene ketal,78.9%;cyclohexanone 1,2-propanediol ketal,85.3%;butanone ethylene ketal,56.9%;butanone 1,2-propanediol ketal,78.1%;2-phenyl-1,3-dioxolane,76.3%;4-methyl-2-phenyl-1,3-dioxolane,94.2%;2-propyl-1,3-dioxolane,70.7%;and 4-methyl-2-propyl-1,3-dioxolane,79.2%.

关键词： phosphotung.tic acid acetal ketal polyaniline catalysis

Effects of Polypropylene Fibers on the Physical and Mechanical Properties of Recycled Ag.reg.te Concrete

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Journal of Wuhan University of Technolog.(Materials Science) 2019年第6期34卷 1327-1344页

作者： Pierre Matar g.rard-philippe Zéhil Lebanese University Faculty of EngineeringBranch 2RoumiehLebanon Notre Dame University-Louaize Faculty of EngineeringZouk MosbehLebanon

The viability of using.polypropylene fibers(PPF) in concrete was larg.ly studied. Yet, few of the existing.research studies investig.ted the effects of PPF on the properties of concrete containing.recycled concrete ag.reg.te(RCA). Mixes with different RCA replacement ratios and different PPF content were desig.ed and tested. The test results showed that the addition of PPF did not chang. sig.ificantly the compressive streng.h and the density of the concrete, but slig.tly decreased its modulus of elasticity and Poisson’s ratio. The drop in the splitting.tensile streng.h and the flexural streng.h due to RCA inclusions was to a larg. extent compensated by the PPF addition. The water absorption decreased and the percent voids increased with increased PPF addition. Correlations between the RCA content, the PPF content and the properties of concrete were studied. Useful reg.ession models were proposed to predict the properties of concrete in relevant rang.s of RCA and PPF content.

关键词： concrete recycled ag.reg.te fiber reinforcement physical properties mechanical properties

Beneficial effect of whole-g.ain wheat on liver fat:a role for the g.t microbiota?

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Hepatobiliary Surg.ry and Nutrition 2021年第5期10卷 708-710页

作者： philippe g.rard Micalis Institute UniversitéParis-SaclayINRAEAgroParisTechJouy-en-JosasFrance

In meta-analyses of prospective studies,hig. whole g.ain(Wg.intake has been acknowledg.d for its potential role in lowering.risk of type 2 diabetes,cancer,cardiovascular disease and all cause mortality(1,2).Unlike Refined wheat(RW)flours from which the bran and g.rm of the wheat kernel have been removed,whole-g.ain wheat(Wg.)products retain these elements and are rich sources not only of dietary fiber,but also of betaine,choline,important minerals and vitamins,components with antioxidant properties,and other phytochemicals(3).They are thus considered nutritionally superior but previous Wg.interventions in human subjects have reported conflicting.results in improvements in health parameters.

关键词： g.ain wheat removed

Role of iron in hepatic fibrosis: One piece in the puzzle

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World Journal of g.stroenterolog. 2007年第35期13卷 4746-4754页

作者： Marie A philippe Richard g.Ruddell g.ant A Ramm Hepatic Fibrosis g.oup The Queensland Institute of Medical ResearchPO Royal Brisbane and Women's HospitalBrisbane 4029Australia

Iron is an essential element involved in various biolog.cal pathways. When present in excess within the cell, iron can be toxic due to its ability to catalyse the formation of damag.ng.radicals, which promote cellular injury and cell death. Within the liver, iron related oxidative stress can lead to fibrosis and ultimately to cirrhosis. Here we review the role of excessive iron in the patholog.es associated with various chronic diseases of the liver. We also describe the molecular mechanism by which iron contributes to the development of hepatic fibrosis.

关键词： Iron Fibrosis Oxidative stress Hepatic stellate cell Haemochromatosis Hepatitis C Non-alcoholic fatty liver disease Alcoholic liver disease