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STABILITY OF subharmonic SOLUTIONS OF FIRST-ORDER HAMILTONIAN SYSTEMS WITH ANISOTROPIC GROWTH

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Acta Mathematica Scientia 2019年第1期39卷 111-118页

作者： Chungen LIU Xiaofei ZHANG School of Mathematics and Information Science Guangzhou University School of Mathematics Nankai University

Using the dual Morse index theory, we study the stability of subharmonic solutions of first-order autonomous Hamiltonian systems with anisotropic growth, that is, we obtain a sequence of elliptic subharmonic solutions... 详细信息

关键词： Hamiltonian system the dual Morse index subharmonic solution stability

Existence of periodic and subharmonic solutions for second-order superlinear difference equations

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Science China Mathematics 2003年第4期46卷 506-515页

作者：郭志明庾建设 Department of Applied Mathematics Hunan University Changsha 410082China Department of MathematicsTaiyuan Normal CollegeTaiyuan 030012China Department of Applied Mathematics Hunan University Changsha 410082China

By critical point theory, a new approach is provided to study the existence and multiplicity results of periodic and subharmonic solutions for difference equations. For secord-order difference equations $$\Delta ^2 x_{n - 1} + f(n, x_n ) = 0,$$ some new results are obtained for the above problems when f(t, z) has superlinear growth at zero and at infinity in z.

关键词： superlinear difference equation, periodic solution, subharmonic solution, critical point, linking.

Brake subharmonic solutions of first order Hamiltonian systems

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Science China Mathematics 2010年第10期53卷 2719-2732页

作者： LI Chong & LIU ChunGen School of Mathematical Sciences and LPMC,Nankai University,Tianjin 300071,China School of Mathematical Sciences and LPMC Nankai University Tianjin China

In this paper,we mainly use the Galerkin approximation method and the iteration inequalities of the L-Maslov type index theory to study the properties of brake subharmonic solutions for the first order non-autonomous Hamiltonian *** prove that when the positive integers j and k satisfy the certain conditions,there exists a jT-periodic nonconstant brake solution zj such that zj and zkj are distinct.

关键词： brake subharmonic solution L-Maslov type index Hamiltonian systems

Bifurcations of Invariant Tori and subharmonic Solutions for Periodic Perturbed Systems

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Science China Mathematics 1994年第11期37卷 1325-1336页

作者：韩茂安 Department of Mathematics Shandong Mine InstituteTaian 271019PRC

The time-periodic perturbations of planar Hamiltonian systems are investigated.A necessary condition for the existence of an invariant torus,a sufficient condition for the bifurcation of a unique invariant torus and a... 详细信息

关键词： periodic perturbed system invariant torus subharmonic solution.

FIRST subharmonic OF SOUND IN DISTURBED WATER

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Chinese Physics Letters 1987年第3期4卷 133-135页

作者： SHAO Daoyuan QIAN Zuwen Institute of Acoustics Academia SinicaBeijing

It is shown by this experiment that an appreciable first subharmonic component(one-half of driving frequency)can be observed when a traoelling wave of low-intensity sound goes through the disturbed water in a tank.

关键词： disturbed frequency subharmonic

The viscoelasticity of lipid shell and the hysteresis of subharmonic in liquid containing microbubbles

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Chinese Physics B 2006年第7期15卷 1526-1531页

作者：龚燕君章东龚秀芬谭开彬刘政 Institute of Acoustics Nanjing University Nanjing 210093 China Xinqiao Hospital Third Military Medical University Chongqing 400037 China

The viscoelasticity and subharmonic generation of a kind of lipid ultrasound contrast agent are investigated. Based on the measurement of the sound attenuation spectrum, the viscoelasticity of the lipid shell is estimated by use of an optimization method. Shear modulus Gs=10MPa and shear viscosity μs=1.49N.S/m^2 are obtained. The nonlinear oscillation of the encapsulated microbubble is studied with Church＇s model theoretically and experimentally. Especially, the dependence of subharmonic on the incident acoustic pressure is studied. The results reveal that the development of the subharmonic undergoes three stages, i.e. occurrence, growth and saturation, and that hysteresis appears in descending ramp insonation.

关键词： lipid shell viscoelasticity subharmonic hysteresis

subharmonic and ultraharmonic emissions based on the nonlinear oscillation of encapsulated microbubbles in ultrasound contrast agents

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Science Bulletin 2005年第18期 9-12页

作者： GONG Yanjun, ZHANG Dong & GONG Xiufen State Key Lab of Modern Acoustics, Institute of Acoustics, Nanjing University, Nanjing 210093, China

subharmonics or ultraharmonics provides better contrast-to-tissue ratio (CTR) than the fundamental or the second harmonics, having prospective application in medical diagnosis. In this paper, subharmonic and ultra-harmonic emissions are theoretically studied through nonlinear oscillation of encapsulated bubbles. The optimized frequencies for emissions of the subharmonics and ultra-harmonics are discussed. In addition, sound pressure de-pendences of the subharmonics and ultraharmonics are studied in theory as well as in measurement. Results reveal that the developments of both subharmonics and ultrahar-monics have the same trend, i.e. occurrence, growth and saturation, but the generation of ultraharmonic is a little earlier than that of subharmonic.

关键词： ultrasound contrast agent subharmonic ultraharmonic.

Infinite subharmonic Solutions of the Forced Relativistic Oscillators

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Journal of Applied Mathematics and Physics 2019年第7期7卷 1498-1512页

作者： Zaihong Wang Tiantian Ma School of Mathematical Sciences Capital Normal University Beijing China Editorial Department of Journal Capital Normal University Beijing China

In this paper, we study the multiplicity of subharmonic solutions of the nonlinear differential equation of the forced relativistic oscillators. By using the generalized Poincaré-Birkhoff fixed point theorem, we prov... 详细信息

关键词： Relativistic Oscillator subharmonic Solution Poincaré-Birkhoff Fixed Point Theorem

On the Existence of subharmonic Screech in Choked Circular Jets from a Sharp-Edged Orifice

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Open Journal of Acoustics 2014年第1期4卷 20-25页

作者： Max Kandula ESC-Team QNA NASA Kennedy Space Center USA

Experiments are performed in choked circular hot and cold nitrogen jets issuing from a 2.44 cm diameter sharp-edged orifice at a fully expanded jet Mach number of 1.85 in an effort to investigate the character of screech phenomenon. The stagnation temperature of the cold and the hot jets are 299 K and 319 K respectively. The axial distribution of the centerline Mach number was obtained with a pitot tube, while the screech data (frequency and amplitude) at different axial and radial stations were measured with the aid of microphones. The fundamental screech frequency of the hot jet is slightly increased relative to that of the cold jet. It is concluded that temperature effects on the screech amplitude are manifested with regard to the fundamental and the subharmonic even at relatively small temperature range considered.

关键词： subharmonic Screech Sharp-Edged Orifice Circular Jets Thermal Effects