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On the composition operators on the Bloch space of several complex variables

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Science China mathematics 2005年第Z1期48卷 392-399页

作者： ZHOU Zehua & CHE Renyu Department of mathematics, Tianjin University, Tianjin 300072, China liuhui center for applied mathematics, Nankai University & Tianjin University,Tianjin 300072, China Department of mathematics Tianjin University Tianjin China liuhui center for applied mathematics Nankai University & Tianjin University Tianjin China

In this paper we first look upon some known results on the composition operator as bounded or compact on the Bloch-type space in polydisk and ball, and then give a sufficient and necessary condition for the compositio... 详细信息

关键词： Bloch space, bounded symmetric domains, composition operator, bergman metric.

NON-EQUILIBRIUM,NONLINEAR CRITICAL LAYERS IN LAMINAR-TURBULENT TRANSITION

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Acta Mechanica Sinica 2004年第4期20卷 327-339页

作者：吴雪松 Department of Mechanics Tianjin UniversityTianjin 300072China LiuHui Center for Applied MathematicsNankai University & Tianjin UniversityTianjin 300072China

We describe some recent developments of high-Reynolds-number asymptotic theory for the nonlinear stage of laminar-turbulent transition in nearly parallel *** classic weakly nonlinear theory of Landau and Stuart is briefly revisited with the dual purposes of highlighting its fundamental ideas,which continue to underlie much of current theoretical thinking,as well as its difficulty in dealing with unbounded *** show that resolving such a difficulty requires an asymptotic approach based on the high-Reynolds-number assumption,which leads to a nonlinear critical-layer *** recent results are reviewed with emphasis on the non-equilibrium *** directions of investigation are indicated.

关键词： Instability transition turb(?)ence non-equilibrium critical layer

BIFURCATION AND UNIVERSAL UNFOLDING FOR A ROTATING SHAFT WITH UNSYMMETRICAL STIFFNESS

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Acta Mechanica Sinica 2002年第2期18卷 181-187页

作者：陈芳启吴志强陈予恕 Department of mathematics Tianjin UniversityTianjin 300072China Liuhui Center for Applied MathematicsNankai University & Tianjin University Department of Mechanics Tianjin UniversityTianjin 300072China

The 1/2 subharmonic resonance bifurcation and universal unfoldingare studied for a rotating shaft with unsymmetrical *** bifurcation behav-ior of the response amplitude with respect to the detuning parameter was studied forthis class of problems by Xiao et ***,it is highly hnportant to research thebifurcation behavior of the response amplitude with respect to the unsymmetry ofstiffness for this ***,by means of the singularity theory,the bifurcationand universal unfolding of amplitude with respect to the unsymmetrical stiffness pa-rameter are *** results indicate that it is a high codimensional bifurcationproblem with codimension 5,and the universal unfolding is *** the mechan-ical background,we study four forms of two parameter unfoldings contained in theuniversal *** transition sets in the parameter plane and the bifurcationdiagrams are *** results obtained in this paper show rich bifurcation phe-nomena and provide some guidance for the analysis and design of dynamic bucklingexperiments of this class of system,especially,for the choice of system parameters.

关键词： shaft with unsymmetrical stiffness 1/2 subharmonic resonance bifurcation universal unfolding

The secondary periodic element ■ and its applications

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Science China mathematics 2025年第1期 207-222页

作者： Jianguo Hong Xiangjun Wang Yu Zhang Science College Shijiazhuang University School of Mathematical Sciences Nankai University center for applied mathematics Tianjin University

Let p≥7 be a *** prove that ■ survives to E∞in the Adams-Novikov spectral ***,using the Thom map Φ:■,we can see that h0h3also survives to E∞in the classical Adams spectral *** an application of these results,we ...

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Quantum Group Symmetry in Hofstadter Problem

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Communications in Theoretical Physics 2008年第8期50卷 517-520页

作者： LI Min-Si LIU Yan-Na Theoretical Physics Division Chern Institute of Mathematics Nanlaui University Tianjin 300071 China liuhui center for applied mathematics Nankai University Tianjin 300071 China Military Traffic Institute Tianjin 300161 China

We show that there is a quantum Sl_q(2) group symmetry in Hofstadter problem on square *** cyclic representation of the quantum group is discussed and its application for computing the degeneracy density of the model ... 详细信息

关键词： Hofstadter problem quantum Slq2 group cyclic representation

NUMERICAL STUDY OF LOCAL BOUNDARY LAYERRECEPTIVITY TO FREESTREAM VORTICALDISTURBANCES

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applied mathematics and Mechanics(English Edition) 2005年第5期26卷 547-554页

作者：张永明周恒 Department of Mechanics Tianjin University Tianjin 300072 P.R.China liuhui center of applied mathematics of Nankai University and Tianjin University Tianjin 300072 P.R.China

Method of direct numerical simulation was used for the investigation of the local receptivity of a 2-D boundary layer of a flat plate to harmonic vortical disturbances in the freestream. Under the interaction of the vortical disturbances in the freestream and the roughness element on the wall, Tollmein-Schlichting (T-S) waves were generated and detected in the boundary layer, thus confirming that the wavelength conversion mechanism and the local receptivity exist. Numerical simulations were performed to obtain the relations between the amplitude of the generated T-S wave and the amplitude of freestream disturbance, the roughness height, and the width of rectangular roughness elements, which agree with those obtained from experiments. Then the range of validity of the linear receptivity formula, which was determined by these relations,also agrees with that determined by experimental results.

关键词： boundary layer receptivity T-S wave wavelength conversion mechanism

Verification of parabolized stability equations for its application to compressible boundary layers

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applied mathematics and Mechanics(English Edition) 2007年第8期28卷 987-998页

作者：张永明周恒 Department of Mechanics Tianjin University Tianjin 300072P.R.China liuhui center of applied mathematics Nankai University and Tianjin University Tianjin 300072P.R.China

Parabolized stability equations （PSE） were used to study the evolution of disturbances in compressible boundary layers. The results were compared with those obtained by direct numerical simulations （DNS）, to check if the results from PSE method were reliable or not. The results of comparison showed that no matter for subsonic or supersonic boundary layers, results from both the PSE and DNS method agreed with each other reasonably well, and the agreement between temperatures was better than those between velocities. In addition, linear PSE was used to calculate the neutral curve for small amplitude disturbances in a supersonic boundary layer. Compared with those obtained by linear stability theory （LST）, the situation was similar to those for incom- pressible boundary layer.

关键词： direct numerical simulations linear stability theory parabolized stability equations

Sun's Log-concavity Conjecture on the Catalan–Larcombe–French Sequence

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Acta Mathematica Sinica,English Series 2016年第5期32卷 553-558页

作者： James J.Y.ZHAO center for applied mathematics Tianjin University

Let {Pn},n≥0 denote the Catalan-Larcombe-French sequence, which naturally came from the series expansion of the complete elliptic integral of the first kind. In this paper, we prove the strict log-concavity of the sequence { n√Pn}n≥1, which was originally conjectured by Z. W. Sun. We also obtain the strict log-concavity of the sequence {n√Vn}n≥1, where {Vn}n≥0 is the Fennessey-Larcombe- French sequence arising from the series expansion of the complete elliptic integral of the second kind.

关键词： The Catalan-Larcombe-French sequence the Fennessey-Larcombe-French sequence logconcavity three-term recurrence relation

NUMERICAL STUDY FOR RESONANT TRIAD INTERACTION AND SECONDARY INSTABILITY IN TWO-DIMENSIONAL SUPERSONIC BOUNDARY LAYER

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applied mathematics and Mechanics(English Edition) 2006年第2期27卷 141-148页

作者：董亚妮周恒 Department of MechanicsTianjin University Tianjin 300072P.R.China liuhui center of applied mathematics Nankai University and Tianjin UniversityTianjin 300072P.R.China (Contributed by ZHOU Heng)

By direct numerical simulation, a supersonic boundary layer was studied to see whether the mechanism for the generation of sub-harmonic waves, similar to those for the incompressible flows, existed in the process of laminar-turbulent transition. The results showed that mechanisms of both resonant triad and secondary instability did exist. Discussions were made on whether these two mechanisms are really important in laminarturbulent transition.

关键词： resonant triad secondary instability supersonic boundary layer T-S wave