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Weyl and Lidskiǐ Inequalities for General Hyperbolic Polynomials

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Chinese Annals of Mathematics,Series B 2009年第6期30卷 785-802页

作者： Denis SERRE cole Normale Suprieure de lyon UMPA (UMR 5669 CNRS)ENS de Lyon46alle d'ItalieF-69364 Lyoncedex 07France

The roots of hyperbolic polynomials satisfy the linear inequalities that were previously established for the eigenvalues of Hermitian matrices,after a conjecture by *** them are the so-called Weyl and Lidskiǐ *** elementary proof of the latter for hyperbolic polynomials is *** proof follows an idea from *** and is free from representation theory and Schubert calculus arguments,as well as from hyperbolic partial differential equations theory.

关键词： Hyperbolic polynomials Real roots Eigenvalues of Hermitian matrices

ASYMPTOTIC LIMITS OF ONE-DIMENSIONAL HYDRODYNAMIC MODELS FOR PLASMAS AND SEMICONDUCTORS

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Chinese Annals of Mathematics,Series B 2002年第1期23卷 25-36页

作者： PENG YUEJUN Laboratoire de Mathematiques Appliquees, cnrs umr 6620, Universite Blaise Pascal (Clermont-Ferrand 2), F-63177 Aubiere cedex, france. E-mail: peng@math.univ-bpclermont.fr Laboratoire de Mathématiques Appliquées CNRS UMR 6620 Université Blaise Pascal (Clermont-Ferrand 2) F-63177 Aubière cedex France

This paper studies the zero-electron-mass limit, the quasi-neutral limit and the zero-relaxation-time limit in one-dimensional hydrodynamic models of Euler-Poisson system for plasmas and semiconductors. For each limit in the steady-state models, the author proves the strong convergence of the sequence of solutions and gives the corresponding convergence rate. In the time-dependent models, the author shows some useful estimates for the quasi-neutral limit and the zero-electron-mass limit. This study completes the analysis made in [11,12,13,14,19].

关键词： Zero-electron-mass limit Quasi-neutral limit Zero-relaxation-time limit Hydrodynamic models Plasmas Semiconductors

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Cochlear Implant

系统仿真学报 2002年第1期14卷 55-59,83页

作者： Christian Berger-Vachon and Lionel Collet Neuroscience & Sensory Systems Laboratory (umr-cnrs 5020) Claude-Bernard University of lyon & Edouard-Herriot Hospital (ORL building) 69437 lyon-cedex 03-france Neuroscience & Sensory Systems Laboratory (umr-cnrs 5020) Claude-Bernard University of lyon & Edouard-Herriot Hospital (ORL-building) 69437 lyon-cedex 03-france

In this text, the authors recall the main principles and data ruling cochlear implants. Then, a first circle of technical equipment for assistance is presented. This circle includes: device setting (DS), Electrically evoked Auditory Brainstem Responses (EABR), Neural Response Telemetry (NRT), Stapedial Reflex (SR) and Electrodogram Acquisition (EA). This first cycle becomes more and more important as children are implanted younger and younger; the amount of data available with this assistance makes necessary the use of models (implicit or explicit) to handle this information. Consequently, this field is more open than ever.1 Introduction1 1.1 About Hearing Mechanisms The hearing function in human beings is something very specific and difficult to understand because it uses the brain highest functions. Basically, we can say (figure 1) that several stages are involved [1]: It is not easy to give a unique interpretation to each one of these stages, as most of the involved processes overlap at all levels. Nevertheless, as a brief summary, let us assume that [2]: l The ear transmits the air vibrations and transforms them into electric stimuli compatible with nerve excitation, l Auditory pathways carry the electric pulses; exchanges take place, through decussation and information goes up using left and right channels. Also, specific features in the signal are detected and encoded before reaching the brain (phonetic features), l Brain interpretation matches input cues with the previously stored data into the memory and make association at different levels of language. In this text, we will come back on some ear features, mostly on the transformation of acoustical vibrations into electrical information transmitted to the brain. We will focus on the technical circle, but people fitted with a cochlear implant (CI) must be seen at all levels of language [3] and a typical team is composed of: l a E.N.T. (Ear Nose Throat) practitioner, l the surgeon performing the implantation,

关键词：耳蜗植入片神经科学感觉系统神经响应镫骨反射电力探测

L2F Anemometry Measurements of the Inter-Row FlowField Within a Transonic Axial Compressor Providedwith Curved Windows

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Journal of Thermal Science 1999年第3期8卷 166-175页

作者： Xavier Ottavy Isabelle Trebinjac Andre Vouillarmet(Laboratoire de Mecanique des Fluides et d’Acoustique umr cnrs 5509/ECL/UCB lyon IEcole Centrale de lyon, 69131 Ecully cedex, france) Laboratoire de Mécanique des Fluides et d’Acoustique umr cnrs 5509/ECL/UCB lyon I Ecole Centrale de lyon Ecully Cedex France

When measurements are performed in high speed, small-scale compressors, the use of curved glasswindows is required in order to avoid any mismatch between the measurement window and the casing. However, the glass curvature leads to optical distortions, which hinder acceptable measurementsand can even prevent the acquisition of any data. Thus, an original optical assembly, which consistsin inserting a simple and inexpensive corrective window between the frontal lens of the anemometerand the shroud window, is proposed. The way of determining the geometric characteristics and theposition of this corrective window, which restores very acceptable fool, is presented in the paper. Thereliability of this corrective optical assembly is highlighted by comparative measurements in a test *** such an optical setting, L2F measurements were realized along a section, downstream of the inletguide vane (IGV) of a transonic compressor stage. The spatial resolution leads to a good descriptionof the interaction of the wake with the oblique shock emanating from the leading edge of the rotor.A phenomenological study of the wake/shock interaction with a change of frame is realized using thestreamwise equation of the transport of vorticity.

关键词： L2F anemometry curved windows distortions high-speed compressor wake/shock interaction.

DISCONTINUOUS FINITE ELEMENT METHOD FOR CONVECTION-DIFFUSION EQUATIONS

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Journal of Computational Mathematics 2000年第6期18卷 639-644页

作者： Abdellatif Agouzal (Laboratoire de Mathematiques Appliquees, Universite lyonl, 43 Boulevard du 11 Novembre 1918 69622 villeurbanne cedex, france.) Universite Lgonl 法国 Villeurban 1918 69622

A discontinuous finite element method for convection-diffusion equations is proposed and analyzed. This scheme is designed to produce an approximate solution which is completely discontinuous. Optimal order of convergence is obtained for model problem. This is the same convergence rate known for the classical methods. [ABSTRACT FROM AUTHOR]

关键词： Discontinuous finite element method Convection-diffusion equations.

SENSITIVITY ANALYSIS WITH RESPECT TO THE ELECTRICAL CONDUCTIVITY

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Journal of Computational Mathematics 2007年第3期25卷 244-251页

作者： Habib Ammari cedex france Hyeonbae Kang Centre de Mathématiques Appliquées CNRS UMR 7641 and Ecole Polytechnique91128 Palaiseau School of Mathematical Sciences Seoul National UniversitySeoul 151-747Korea Habib Zribi Centre de Mathématiques AppliquéesCNRS UMR 7641 and Ecole Polytechnique91128 Palaiseau CedexFrance

In this paper, we consider conductivity inclusions inside a homogeneous background conductor. We provide a complete asymptotic expansion of the solution of such problems in terms of small variations in the electrical conductivity of the inclusion. Our method is based on a boundary integral perturbation theory. Our results are valid for both high and low contrast inclusions.

关键词： High contrast material Full-asymptotic expansions Boundary integral equa-tion.

Absolute continuity of the distribution of some Markov geometric series

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Science China Mathematics 2007年第11期50卷 1521-1528页

作者： Ai-hua FAN~(1,2+) Ji-hong ZHANG~1 1 Department of Mathematics,Wuhan University,Wuhan 430072,China 2 LAMFA,umr 6140 cnrs,Universitéde Picardie Jules Verne,33,Rue Saint Leu,80039 Amiens cedex 1,france Department of Mathematics Wuhan University Wuhan 430072 China LAMFA UMR 6140 CNRS Université de Picardie Jules Verne 33 Rue Saint Leu 80039 Amiens Cedex 1 France

Let (■_n)≥0 be the Markov chain of two states with respect to the probability measure of the maximal entropy on the subshift spaceΣ_A defined by Fibonacci incident matrix *** consider the measureμ_λof the probability distribution of the random seriesΣ_(n=0)~∞■_nλ~n(02)-1)/2) and thatμ_λis absolutely continuous for almost allλ∈((5^(1/2)-1)/2,0.739).

关键词： Markov series absolute continuity measure of maximal entropy dimension of a measure transversality

Results and Analysis of a L2F Flow Field Investigation within a High-Speed High-Pressure Centrifugal Compressor

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Journal of Thermal Science 1997年第3期6卷 155-163页

作者： I.Thebinjac I.Claudin (Laboratoire de Mecanique des Fluides et d’Acoustique umr cnrs 5509 / ECL / UCB lyon I Ecole Celltrale de lyon, BP 163, 69131 Ecully cedex, france) Laboratoire de Mecanique des Fluides et d’Acoustique umr cnrs 5509 / ECL / UCB lyon I Ecole Centrale de lyon Ecully Cedex France

The paper describes experimental results obtained using a laser two-focus anemometry technique in a high-speed, high-pressure ratio unshrouded centrifugal compressor. Measurements in such a small impeller are extremely difficult as the flow is restricted to narrow passages and as the temperature rise is very high. Even if the working principle of laser anemometry is well documented in literature, some specialities of our LA system are discussed.A description and an analysis of the inlet now field, based on integral methods, are proposed. Some passage velocity contours are presented. Whereas a potential flow structure exists up to the high meridional curvature region, the throughfiow pattern is largely distorted in the radial part of the *** differences in ftow pattern between both channels are found, particularly through the low momentum fluid zone. A qualitative study of the vortical mechanisms ascribes them to the tip clearance effects.

关键词： High-speed high-pressure compressor laser anemometry flowfield

Lipschitz Properties in Variable Exponent Problems via Relative Rearrangement

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Chinese Annals of Mathematics,Series B 2010年第6期31卷 991-1006页

作者： Jean-Michel RAKOTOSON umr 6086 cnrs.Laboratoire de Mathématiques Université de Poitiers SP2MI Boulevard Marie et Pierre Curie Téléport 2 BP30179 86962 Futuroscope Chasseneuil Cedex France

The author first studies the Lipschitz properties of the monotone and relative rearrangement mappings in variable exponent Lebesgue spaces completing the result given in [9]. This paper is ended by establishing the Lipschitz properties for quasilinear problems with variable exponent when the right-hand side is in some dual spaces of a suitable Sobolev space associated to variable exponent.

关键词： Monotone rearrangement Relative rearrangement Variable exponents Quasi-linear equations