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ANALYTICAL SMOOTHING EFFECT OF SOLUTION FOR THE BOUSSINESQ EQUATIONS

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Acta Mathematica Scientia 2019年第1期39卷 165-179页

作者： Feng CHENG Chao jiang XU Hubei Key Laboratory of Applied mathematics School of mathematics and Statistics Hubei University School of mathematics and Statistics Wuhan University Universite de Rouen CNRS UMR 6085 Laboratoire de Mathématiques

In this article, we study the analytical smoothing effect of Cauchy problem for the incompressible Boussinesq equations. Precisely, we use the Fourier method to prove that the Sobolev H^1 -solution to the incompressible Boussinesq equations in periodic domain is analytic for any positive time. So the incompressible Boussinesq equations admit exactly same smoothing effect properties of incompressible Navier-Stokes equations.

关键词： analyticity smoothing effect of solutions Boussinesq equation

Weighted variation inequalities for differential operators and singular integrals in higher dimensions

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Science China mathematics 2017年第8期60卷 1419-1442页

作者： MA Tao TORREA Jose L. XU QuanHua School of mathematics and Statistics Wuhan University departamento de Matemticas Universidad Autónoma de Madrid Institute for Advanced Study in mathematics Harbin Institute of Technology laboratoire de Mathematiques Universite de Franche-Comte Institut Universitaire de France

We prove weighted q-variation inequalities with 2 详细信息

We prove weighted q-variation inequalities with 2

关键词： variation inequalities A_(p) weights differential operators singular integrals vector-valued variationin equalities

PHONONS IN POLYACENIC CHAINS

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Chinese Journal of Polymer Science 2006年第3期24卷 229-236页

作者： O.Rafil M.Tamine B.Bourahla R.Tigrine S.Amoudache A.Khater laboratoire de Physique et Chimie Quantique laboratoire de Physique de l'Etat Condensé

We have theoretically resolved phonon excitations in quasi-two-dimensional organic crystals of polyacenic semiconductor material which may be obtained by the pyrolytic treatment of phenol-formaldehyde resin. A model for studying the dynamical properties using three polyacene chains is proposed with the aim to present the vibrational properties of this structure. It employs the formalism of solid states in two dimensions which admit phonons. A simulation process of the two-dimensional lattice structure shows that elastic waves may explain the existence of vibrational modes in the frequency range 100-400 cm^-1. The presence of acoustic and optical like phonons is discussed in terms of the elastic force constants. A hyperfine resonance structure is obtained. It allows the analysis of the dynamical evolution in thin films of polyacene. It is found that the behavior of the phonon density of states exhibits resonance between modes in the structure.

关键词： Polymers Elastic waves Surface phonons Localized modes

Blasius flow and heat transfer of fourth-grade fluid with slip

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Applied mathematics and Mechanics(English Edition) 2013年第12期34卷 1465-1480页

作者： B.SAHOO S.PONCET department of mathematics National Institute of Technology laboratoire de Mecanique Modelisation and Procedes PropresAix-Marseille Universite

This investigation deals with the effects of slip, magnetic field, and non- Newtonian flow parameters on the flow and heat transfer of an incompressible, electrically conducting fourth-grade fluid past an infinite porous plate. The heat transfer analysis is carried out for two heating processes. The system of highly non-linear differential equations is solved by the shooting method with the fourth-order Runge-Kutta method for moderate values of the parameters. The effective Broyden technique is adopted in order to improve the initial guesses and to satisfy the boundary conditions at infinity. An exceptional cross-over is obtained in the velocity profile in the presence of slip. The fourth-grade fluid parameter is found to increase the momentum boundary layer thickness, whereas the slip parameter substantially decreases it. Similarly, the non-Newtonian fluid parameters and the slip have opposite effects on the thermal boundary layer thickness.

关键词： Blasius flow partial slip fourth-grade fluid shooting method Broyden'smethod

Local solvability of the k-Hessian equations

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Science China mathematics 2016年第9期59卷 1753-1768页

作者： TIAN GuJi WANG Qi XU Chao-Jiang Wuhan Institute of Physics and mathematics Chinese Academy of Sciences The School of Statistics and mathematics Zhongnan University of Economics and Law School of mathematics and Statistics Wuhan University laboratoire de Math'ematiques CNRS UMR 6085 Universite de Rouen

We give a classification of second-order polynomial solutions for the homogeneous k-Hessian equation σ_k[u] = 0. There are only two classes of polynomial solutions: One is convex polynomial; another one must not be(k + 1)-convex, and in the second case, the k-Hessian equations are uniformly elliptic with respect to that solution. Based on this classification, we obtain the existence of C∞local solution for nonhomogeneous term f without sign assumptions.

关键词： k-Hessian equations local solution uniform ellipticity implicit function theorem

Rotating instability in the vaneless diffuser of a radial flow pump

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Journal of Thermal Science 2008年第4期17卷 368-374页

作者： A.Dazin O.Coutier-delgosha P.Dupont S.Coudert G.Caignaert G.Bois laboratoire de Mécanique de Lille(UMR CNRS 8107) Arts et Métiers ParisTech laboratoire de Mécanique de Lille Ecole Centrale de Lille laboratoire de Mécanique de Lille CNRS

The paper refers to the behavior of a vaneless diffuser of a radial flow pump in partial flow operating conditions. Some experimental data have been obtained using 2D/2C PIV and unsteady pressure measurements within the diffuser, in various operating conditions. The experimental results at the lower flow rate are compared with two-dimensional numerical calculations.

关键词： Vaneless diffuser Radial flow pump Instability Particle Image Velocimetry Pressure measurements 2D calculations.

Existence of a Hartmann layer in the peristalsis of Sisko fluid

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Chinese Physics B 2014年第5期23卷 368-372页

作者： Saleem Asghar Tayyaba Minhas Aamir Ali department of mathematics COMSATS Institute of Information Technology department of mathematics King Abdul Aziz University CNRS UMR 7351 Laboratoire Jean Alexandre DieudonneUniversite de Nice Sophia Antipolis

Analytical solutions for the peristaltic flow of a magneto hydrodynamic （MHD） Sisko fluid in a channel, under the effects of strong and weak magnetic fields, are presented. The governing nonlinear problem, for the strong magnetic field, is solved using the matched asymptotic expansion. The solution for the weak magnetic field is obtained using a regular perturbation method. The main observation is the existence of a Hartman boundary layer for the strong magnetic field at the location of the two plates of the channel. The thickness of the Hartmann boundary layer is determined analytically. The effects of a strong magnetic field and the shear thinning parameter of the Sisko fluid on the velocity profile are presented graphically.

关键词： magneto hydrodynamic Sisko fluid asymmetric channel Peristaltic flow non-Newtonian fluid

X Y Z particles at BABAR

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Chinese Physics C 2010年第6期34卷 644-649页

作者： E.Prencipe LAPP-laboratoire de Annecy de Physique de Particules

This paper intends to shortly summarize the recent results on Spectroscopy, published from the BABAR Collaboration. The BABAR experiment is a B-factory, at SLAC, where asymmetric energy beams of electron-positron are accelerated and collide at the energy in the center of mass of T（4S）. In 9 years of data taking, BABAR had collected 433 fb^-1 equivalent luminosity on-peak-data at the T（4S） energy, 30 fb^-1 data at the T（3S） energy, 15 fb^-1 data at the T（2S） energy, and a scan around T（4S） was done, collecting 25 pb^-1 every 5 MeV. Thanks to the high luminosity achieved, it is possible to perform high precision measurements, and spectroscopy studies. An update on the measurement of the state X（3872） will be given, as final result published by using the whole dataset available. Then, a new preliminary Y（4260） measurement is reported, and the study of the invariant mass J/ψπ^＋π^- in ISR events is shown, where no evidence of the state Y（4050） is highlighted. As conclusion, the results on the angular distribution analysis performed on the state Z（4430） are reported.

关键词： spectroscopy charmonium BABAR

Limit theorems for a supercritical branching process with immigration in a random environment

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Science China mathematics 2017年第12期60卷 2481-2502页

作者： WANG YanQing LIU QuanSheng School of Statistics and mathematics Zhongnan University of Economics and Law Wuhan 430073 China laboratoire de Mathematiques de Bretagne-Atlantique Universitd de Bretagne-Sud Vannes F-56017 France

Let(Z_n) be a supercritical branching process with immigration in a random environment. Firstly, we prove that under a simple log moment condition on the offspring and immigration distributions, the naturally normalized population size W_n converges almost surely to a finite random variable W. Secondly, we show criterions for the non-degeneracy and for the existence of moments of the limit random variable W. Finally, we establish a central limit theorem, a large deviation principle and a moderate deviation principle about log Z_n.

关键词： branching process with immigration random environment almost sure convergence nondegeneration Lpconvergence and moments large and moderate deviations central limit theorem