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Fractional Fourier transform of Cantor sets: further numerical study

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Chinese Physics B 2008年第6期17卷 2018-2022页

作者：高穹廖天河崔远峰 department of mathematics and Physics Information Engineering University

This paper is a further work of the authors＇ paper published previously （Liao T H and Gao Q 2005 Chin. Phys. Lett. 22 2316）. The amplitudes of fractional Fourier transform of Cantor sets are analysed from the viewpoint of multifractal by wavelet transform maxima method （WTMM）. An integral operation is carried out before the application of WTMM, such that the function obtained can be considered as the perturbed devil staircase. Also, wavelets with large number of vanishing moments are used, which makes the complete singularity spectrum more accessible. The validity of multifractal formalism is guaranteed by restricting parameter q to a proper range, so that the phenomenon of multifractal phase transition can be explained reasonably. Particularly, the method of determining the range of parameter q in the above paper is developed to be more operational and rigorous.

关键词： multifractal fractional Fourier transform wavelet transform perturbed devil staircase

Parameter Extension and the Quasi-Rational Solution of a Lattice Boussinesq Equation

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Chinese Physics Letters 2013年第4期30卷 1-4页

作者： NONG Li-Juan ZHANG Da-Jun SHI Ying ZHANG Wen-Ying department of mathematics Shanghai UniversityShanghai 200444

For a lattice Boussinesq equation,we introduce a simple-parameter invertible transformation by which the equation is transformed into an extended *** new equation admits solitons and nonzero quasi-rational solutions,b... 详细信息

关键词： equation. Boussinesq equation

Variable Separation and Exact Solutions to Generalized Nonlinear Diffusion Equations

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Chinese Physics Letters 2002年第12期19卷 1741-1744页

作者： Zhang Shun-Li Lou Sen-Yue Qu Chang-Zheng department of mathematics Northwest University Xi'an 710069

We study in detail a method to find the generalized nonlinear diffusion equations, which can be solved by means of the variableseparation approach. A complete list of canonical forms for such equations, which admit th... 详细信息

关键词： Nonlinear equations

Almost Automorphic Solutions for Quaternion-Valued Hopfield Neural Networks with Mixed Time-Varying Delays and Leakage Delays

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Journal of Systems Science & Complexity 2020年第1期33卷 100-121页

作者： LI Yongkun MENG Xiaofang department of mathematics Yunnan UniversityKunming 650091China

This paper considers a class of quaternion-valued Hopfield neural networks with mixed time-varying delays and leakage *** utilizing the exponential dichotomy of linear differential equations,Banach’s fixed point theorem and differential inequality techniques,the authors obtain some sufficient conditions to ensure the existence and global exponential stability of almost automorphic solutions for this class of quaternion-valued neural *** results are completely ***,the authors give an example to illustrate the feasibility of the results.

关键词： Almost automorphic solutions exponential stability Hopfield neural networks leakage delays quaternion-valued functions

A MULTISTEP FINITE VOLUME METHOD WITH PENALTY FOR THERMAL CONVECTION PROBLEMS IN TWO OR THREE DIMENSIONS

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Journal of Systems Science & Complexity 2008年第1期21卷 129-143页

作者： Min YANG department of mathematics Yantai University Yantai 264005 China

The author considers a thermal convection problem with infinite Prandtl number in two or three dimensions. The mathematical model of such problem is described as an initial boundary value problem made up of three partial differential equations. One equation of the convection-dominated diffusion type for the temperature, and another two of the Stokes type for the normalized velocity and pressure. The approximate solution is obtained by a penalty finite volume method for the Stokes equation and a multistep upwind finite volume method for the convection-diffusion equation. Under suitable smoothness of the exact solution, error estimates in some discrete norms are derived.

关键词： Error estimate finite volume thermal convection problem unstructured meshes.

Stability of buoyancy-driven convection in an Oldroyd-B fluid-saturated anisotropic porous layer

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Applied mathematics and Mechanics(English Edition) 2018年第5期39卷 653-666页

作者： K.R.RACHUNATHA I.S.SHIVAKUMARA SOWBHAGYA department of mathematics Bangalore UniversityBangalore 560056India

The nonlinear stability of thermal convection in a layer of an Oldroyd-B fluid-saturated Darcy porous medium with anisotropic permeability and thermal diffu- sivity is investigated with the perturbation method. A modified Darcy-Oldroyd model is used to describe the flow in a layer of an anisotropic porous medium. The results of the linear instability theory are delineated. The thresholds for the stationary and oscillatory convection boundaries are established, and the crossover boundary between them is de- marcated by identifying a codimension-two point in the viscoelastic parameter plane. The stability of the stationary and oscillatory bifurcating solutions is analyzed by deriving the cubic Landau equations. It shows that these solutions always bifurcate supercritically. The heat transfer is estimated in terms of the Nusselt number for the stationary and oscillatory modes. The result shows that, when the ratio of the thermal to mechanical anisotropy parameters increases, the heat transfer decreases.

关键词： convection porous medium Oldroyd-B fluid cubic Landau equation

Energy and spatial momentum of charged rotating frames in tetrad gravity

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Chinese Physics B 2011年第11期20卷 90-101页

作者： Gamal G.L.Nashed mathematics department Faculty of ScienceAin Shams University

We compute the total energy and the spatial momentum of four charged rotating （Kerr-Newman） frames by using the gravitational energy-momentum 3-form within the framework of the tetrad formulation of the general relativity theory. We show how the effect of the inertial always makes the total energy divergent. We use a natural regularization method, which yields the physical value for the total energy of the system. We show how the regularization method works on a number of different rotating frames that are related to each other by the local Lorentz transformation. We also show that the inertial has no effect on the spatial momentum components.

关键词： teleparallel gravity energy-momentum Weitzenbock connection regularization teleparallelism

THE FULL DISCRETE DISCONTINUOUS FINITE ELEMENT ANALYSIS FOR FIRST-ORDER LINEAR HYPERBOLICEQUATION

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Journal of Computational mathematics 1999年第1期17卷 97-112页

作者： Che Sun Shu-jie Qin(department of mathematics, Nankai University, Tianjin 300071, China) department of mathematics Nankai University Tianjin 300071 China

In this paper, the full discrete discontinuous Galerkin finite element method to solove 2-dimensional first-order linear hyperbolic problem is considered. Two practical schemes, Euler scheme and Crank-Nicolson scheme, are constructed. For each of them, the stability and error estimation with optimal order approximation is established in the norm stronger than L-2-norm.

关键词： hyperbolic equation discontinuous FEM Euler scheme

AN ASYMPTOTIC-NUMERICAL ANALYSIS FOR THE LOWER BOUND DYNAMIC BUCKLING ESTIMATES

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Acta Mechanica Sinica 1997年第2期13卷 165-170页

作者：吴柏生 department of mathematics Jilin UniversityChangchun 130023China

A finite element asymptotic analysis for determining the lower bound dynamic buckling estimates of imperfection-sensitive structures under step load of infinite duration is presented. The lower bound dynamic buckling loads and the corresponding displacements are sought in the form of asymptotic expansions based on the static stability criterion and they can be determined by solving numerically (FEM) several linear problems with a single nonsingular sub-stiffness matrix.

关键词： dynamic buckling lower bound estimate FEM implementation