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A novel (G'/G)-expansion method and its application to the Boussinesq equation

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Chinese Physics B 2014年第2期23卷 34-43页

作者： Md.Nur Alam Md.Ali Akbar Syed Tauseef Mohyud-Din department of mathematics Pabna University of Science and Technology department of applied mathematics University of Rajshahi department of mathematics HITEC UniversityTaxila Cantt

In this article, a novel （G＇/G）-expansion method is proposed to search for the traveling wave solutions of nonlinear evolution equations. We construct abundant traveling wave solutions involving parameters to the Boussinesq equation by means of the suggested method. The performance of the method is reliable and useful, and gives more general exact solutions than the existing methods. The new （G＇/G）-expansion method provides not only more general forms of solutions but also cuspon, peakon, soliton, and periodic waves.

关键词： (G'/G)-expansion method Boussinesq equation solitary wave solutions auxiliary nonlinear ordinary differential equation

A Note on the Essential Norm of Composition Operators from H^p(B_N ) to H^q(B_N )

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Chinese Annals of mathematics,Series B 2013年第5期34卷 683-690页

作者： Zhihua CHEN Liangying JIANG Qiming YAN department of mathematics Tongji University department of applied mathematics Shanghai Finance University

The authors give an upper bound of the essential norms of composition opera- tors between Hardy spaces of the unit ball in terms of the counting function in the higher dimensional value distribution theory defined by ... 详细信息

关键词： Essential norm Composition operator Hardy space

CHARACTERIZATIONS OF SOME MATRIX CLASSES OF QUASI-HOMOGENEOUS OPERATORS

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Acta Mathematica Scientia 2012年第6期32卷 2285-2294页

作者：陈爱红李容录 department of mathematics Harbin Institute of Technology department of applied mathematics Yanshan University

In this paper, we give a general characterization of a class of matrices of quasi-homogeneous operators between topological vector spaces.

关键词： matrix transformation quasi-homogeneous operator gliding hump property

Entropy generation analysis of natural convective radiative second grade nanofluid flow between parallel plates in a porous medium

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applied mathematics and Mechanics(English Edition) 2019年第4期40卷 481-498页

作者： K.RAMESH O.OJJELA department of applied mathematics Defence Institute of Advanced Technology

The present article explores the entropy generation of radiating viscoelastic second grade nanofluid in a porous channel confined between two parallel plates. The boundaries of the plates are maintained at distinct temperatures and concentrations while the fluid is being sucked and injected periodically through upper and lower plates. The buoyancy forces, thermophoresis and Brownian motion are also considered due to the temperature and concentration differences across the channel. The system of governing partial differential equations has been transferred into a system of ordinary differential equations(Odes) by appropriate similarity relations, and a shooting method with the fourth-order Runge-Kutta scheme is used for the solutions. The results are analyzed in detail for dimensionless velocity components. The temperature, concentration distributions, the entropy generation number, and the Bejan number corresponding to various fluid and geometric parameters are shown graphically. The skin friction, heat and mass transfer rates are presented in the form of tables. It is noticed that the temperature profile of the fluid is enhanced with the Brownian motion, whereas the concentration profile of the fluid is decreased with the thermophoresis parameter, and the entropy and Bejan numbers exhibit the opposite trend for the suction and injection ratio.

关键词： nanofluid thermophoresis Brownian motion shooting method thermal radiation

Rayleigh-type wave propagation through liquid layer over corrugated substrate

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applied mathematics and Mechanics(English Edition) 2017年第6期38卷 851-866页

作者： A.K.SINGH A.DAS A.RAY department of applied mathematics Indian Institute of Technology(ISM)

The propagation of the Rayleigh-type wave in a fluid layer overlying a corrugated substrate is studied. The corrugated substrate is considered as a fluid satu- rated poroelastic substrate and a quadratically heterogeneous isotropic elastic substrate in Case I and Case II, respectively. Closed form expressions of dispersion relation for Case I and Case II ave obtained. The influence of corrugation, porosity, and hetero- geneity on the phase velocity of Rayleigh-type wave, for both cases, is highlighted and demonstrated through numerical computation and graphical discussion. Neglecting cor- rugation at the common interface, expressions of phase velocity of the Rayleigh-type wave for both cases ave derived in a closed form as a special case of the problem. Comparison between the presence and the absence of both heterogeneity and poroelasticity in the substrate of the composite structure is a key in the present study.

关键词： Rayleigh-type wave porosity heterogeneity corrugation

Persistence and Extinction in Two Species Models with Impulse

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Acta Mathematica Sinica,English Series 2006年第2期22卷 447-454页

作者： Xian Zhang WEN Zhi Cheng WANG department of mathematics Hunan Normal University department of applied mathematics Hunan University

Both uniform persistence and global extinction are established for a two species predatorprey and competition system with impulse by appealing to theories of abstract persistence, asymptotically autonomous semiflows, ... 详细信息

关键词： Impulse Persistence Extinction

Rayleigh-type wave propagation in incompressible visco-elastic media under initial stress

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applied mathematics and Mechanics(English Edition) 2018年第3期39卷 317-334页

作者： P.SINGH A.CHATTOPADHYAY A.K.SINGH department of applied mathematics Indian Institute of Technology (ISM)

Propagation of Rayleigh-type surface waves in an incompressible visco-elastic material over incompressible visco-elastic semi-infinite media under the effect of initial stresses is discussed. The dispersion equation is determined to study the effect of differ- ent types of parameters such as inhomogeneity, initial stress, wave number, phase velocity, damping factor, visco-elasticity, and incompressibility on the Rayleigh-type wave prop- agation. It is found that the affecting parameters have a significant effect on the wave propagation. Cardano＇s and Ferrari＇s methods are deployed to estimate the roots of dif- ferential equations associated with layer and semi-infinite media. The MATHEMATICA software is applied to explicate the effect of these parameters graphically.

关键词： Rayleigh-type wave inhomogeneity initial stress visco-elasticity incom-pressible

Subharmonic response of single-degree-of-freedom linear vibroimpact system to narrow-band random excitation

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applied mathematics and Mechanics(English Edition) 2011年第9期32卷 1159-1168页

作者：戎海武王向东罗旗帜徐伟方同 department of mathematics Foshan University department of applied mathematics Northwestern Polytechnical University

The subharmonic response of a single-degree-of-freedom linear vibroimpact oscillator with a one-sided barrier to the narrow-band random excitation is *** analysis is based on a special Zhuravlev transformation,which reduces the system to the one without impacts or velocity jumps,and thereby permits the applications of asymptotic averaging over the period for slowly varying the inphase and quadrature *** averaged stochastic equations are exactly solved by the method of moments for the mean square response amplitude for the case of zero offset.A perturbation-based moment closure scheme is proposed for the case of nonzero *** effects of damping,detuning,and bandwidth and magnitudes of the random excitations are *** theoretical analyses are verified by the numerical *** theoretical analyses and numerical simulations show that the peak amplitudes can be strongly reduced at the large detunings.

关键词： single-degree-of-freedom linear vibroimpact system subharmonic response Zhuravlev transformation method random averaging method

Transference of Love-type waves in a bedded structure containing a functionally graded material and a porous piezoelectric medium

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applied mathematics and Mechanics(English Edition) 2019年第8期40卷 1083-1096页

作者： S.MONDAL S.A.SAHU K.K.PANKAJ department of applied mathematics Indian Institute of Technology (ISM)

The frequency of the Love-type surface waves in a bedded structure con- sisting of a porous piezoelectric (PP) medium and a functionally graded material (FGM) substrate is approximated. The FGM layer is assumed to have a constant initial stress. The Wentzel-Kramers-Brillouin (WKB) approximation technique is used for the wave solution in the FGM layer, and the method of separation of variables is applied for the solution in the porous piezoelectric medium. The dependence of the wave frequency on the wave number is obtained for both electrically open and short cases. The effects of the gradient coefficient of the FGM layer, the initial stresses (tensile stress and compressive stress), and the width of the FGM layer are marked distinctly and shown graphically. The findings may contribute towards the design and optimization of acoustic wave devices.

关键词： porous piezoelectric (PP) material functionally graded material (FGM) Love-type wave Wentzel-Kramers-Brillouin (WKB) approximation