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Phragmén-Lindelf and continuous dependence type results in a Stokes flow

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applied mathematics and Mechanics(English Edition) 2010年第7期31卷 875-882页

作者： J.C.SONG department of applied mathematics Hanyang University

This paper investigates the asymptotic behavior of end effects for a Stokes flow defined on a three-dimensional semi-infinite cylinder. With homogeneous Dirichlet conditions of the velocity on the lateral surface of the cylinder, solutions either grow or decay exponentially in the distance from the finite end of the cylinder. In the case of decay, the effect of perturbing the equation parameters is also investigated.

关键词： Phragmen-Lindelof continuous dependence decay bounds Stokes flow

Effects of three-phase-lag on two-temperature generalized thermoelasticity for infinite medium with spherical cavity

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applied mathematics and Mechanics(English Edition) 2012年第4期33卷 483-498页

作者： S. BANIK M. KANORIA department of applied mathematics University of Calcutta

The thermoelastic interaction for the three-phase-lag （TPL） heat equation in an isotropic infinite elastic body with a spherical cavity is studied by two-temperature generalized thermoelasticity theory （2TT）. The heat conduction equation in the theory of TPL is a hyperbolic partial differential equation with a fourth-order derivative with respect to time. The medium is assumed to be initially quiescent. By the Laplace trans- formation, the fundamental equations are expressed in the form of a vector-matrix differ- ential equation, which is solved by a state-space approach. The general solution obtained is applied to a specific problem, when the boundary of the cavity is subjected to the ther- mal loading （the thermal shock and the ramp-type heating） and the mechanical loading. The inversion of the Laplace transform is carried out by the Fourier series expansion tech- niques. The numerical values of the physical quantity are computed for the copper like ma- terial. Significant dissimilarities between two models （the two-temperature Green-Naghdi theory with energy dissipation （2TGN-III） and two-temperature TPL model （2T3phase）） are shown graphically. The effects of two-temperature and ramping parameters are also studied.

关键词： two-temperature generalized thermoelasticity Green-Naghdi model three-phase-lag model spherical cavity state-space approach

Hall effects on hydromagnetic flow on an oscillating porous plate

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applied mathematics and Mechanics(English Edition) 2009年第4期30卷 503-512页

作者： S.L.Maji A.K.Kanch M.Guria R.N.Jana department of applied mathematics Vidyasagar University

In this paper, an analysis is made on the unsteady flow of an incompressible electrically conducting viscous fluid bounded by an infinite porous flat plate. The plate executes harmonic oscillations at a frequency n in its own plane. A uniform magnetic field Ho is imposed perpendicular to the direction of the flow. It is found that the solution also exists for blowing at the plate. The temperature distribution is also obtained by taking viscous and Joule dissipation into account. The mean wall temperature θo（O） decreases with the increase in the Hall parameter m. It is found that no temperature distribution exists for the blowing at the plate.

关键词： Hall effects oscillation resonance heat transfer and mean temperature

NEW METHOD TO OPTION PRICING FOR THE GENERAL BLACK-SCHOLES MODEL-AN ACTUARIAL APPROACH

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applied mathematics and Mechanics(English Edition) 2003年第7期24卷 826-835页

作者：闫海峰刘三阳 department of applied mathematics Xidian University

Using physical probability measure of price process and the principle of fair premium, the results of Mogens Bladt and Hina Hviid Rydberg are generalized. In two cases of paying intermediate divisends and no intermediate dividends, the Black_Scholes model is generalized to the case where the risk_less asset (bond or bank account) earns a time_dependent interest rate and risk asset (stock) has time_dependent the continuously compounding expected rate of return, volatility. In these cases the accurate pricing formula and put_call parity of European option are obtained. The general approach of option pricing is given for the general Black_Scholes of the risk asset (stock) has the continuously compounding expected rate of return, volatility. The accurate pricing formula and put_call parity of European option on a stock whose price process is driven by general Ornstein_Uhlenback (O_U) process are given by actuarial approach.

关键词： option pricing Black_Scholes model fair premium O_U process

Adaptive Iterative Learning Control of Non-uniform Trajectory Tracking for Strict Feedback Nonlinear Time-varying Systems

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International Journal of Automation and computing 2014年第6期11卷 621-626页

作者： Chun-Li Zhang Jun-Min Li department of applied mathematics Xidian University

In this paper, an iterative learning control strategy is presented for a class of nonlinear time-varying systems, the timevarying parameters are expanded into Fourier series with bounded remainder term. The backstepping design technique is used to deal with system dynamics with non-global Lipschitz nonlinearities and the approach proposed in this paper solves the non-uniform trajectory tracking problem. Based on the Lyapunov-like synthesis, the proposed method shows that all signals in the closed-loop system remain bounded over a pre-specified time interval [0, T ]. And perfect non-uniform trajectory tracking of the system output is completed. A typical series is introduced in order to deal with the unknown bound of remainder term. Finally, a simulation example shows the feasibility and effectiveness of the approach.

关键词： Iterative learning control time-varying systems Lyapunov-like non-uniform trajectory tracking Fourier series expansion backstepping

CONSTRUCTION OF PLURIHARMONIC MAPS INTO COMPLEX GRASSMANN MANIFOLDS

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Acta Mathematica Scientia 2003年第2期23卷 185-191页

作者：潮小李 department of applied mathematics Southeast University

In this paper, some construction theorems of pluriharmonic maps into complex Grassmann manifolds axe obtained. By these, there exists a characterization of strongly isotropic pluriharmonic maps.

关键词： pluriharmonic map complex Grassmann manifold construction diagram

Modelling,Analysis and Computation in Plasticity

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Acta Mathematica Sinica,English Series 2019年第1期35卷 64-82页

作者： B.Daya REDDY department of mathematics and applied mathematics University of Cape Town

The typical problem in the mechanics of deformable solids comprises a mathematical model in the form of systems of partial differential equations or inequalities. Subsequent investigations are then concerned with analysis of the model to determine its well-posedness, followed by the development and implementation of algorithms to obtain approximate solutions to problems that are generally intractable in closed form. These processes of modelling, analysis, and computation are discussed with a focus on the behaviour of elastic-plastic bodies;these are materials which exhibit path-dependence and irreversibility in their behaviour. The resulting variational problem is an inequality that is not of standard elliptic or parabolic type. Properties of this formulation are reviewed, as are the conditions under which fully discrete approximations converge. A solution algorithm, motivated by the predictor-corrector algorithms that are common in elastoplastic problems, is presented and its convergence properties summarized. An important extension of the conventional theory is that of straingradient plasticity, in which gradients of the plastic strain appear in the formulation, and which includes a length scale not present in the conventional theory. Some recent results for strain-gradient plasticity are presented, and the work concludes with a brief description of current investigations.

关键词： Elastoplasticity variational inequalities finite elements algorithms convergence pre-dictor-corrector schemes strain-gradient plasticity

A RIEMANN-HILBERT PROBLEM IN A RIEMANN SURFACE

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Acta Mathematica Scientia 2011年第6期31卷 2233-2246页

作者： Spyridon Kamvissis department of applied mathematics University of Crete

One of the inspirations behind Peter Lax＇s interest in dispersive integrable systems, as the small dispersion parameter goes to zero, comes from systems of ODEs discretizing 1-dimensional compressible gas dynamics [17]. For example, an understanding of the asymptotic behavior of the Toda lattice in different regimes has been able to shed light on some of von Neumann＇s conjectures concerning the validity of the approximation of PDEs by dispersive systems of ODEs. Back in the 1990s several authors have worked on the long time asymptotics of the Toda lattice [2, 7, 8, 19]. Initially the method used was the method of Lax and Levermore [16], reducing the asymptotic problem to the solution of a minimization problem with constraints （an ＂equilibrium measure＂ problem）. Later, it was found that the asyraptotic method of Deift and Zhou （analysis of the associated Riemann-Hilbert factorization problem in the complex plane） could apply to previously intractable problems and also produce more detailed information. Recently, together with Gerald Teschl, we have revisited the Toda lattice; instead of solu- tions in a constant or steplike constant background that were considered in the 1990s we have been able to study solutions in a periodic background. Two features are worth noting here. First, the associated Riemann-Hilbert factorization problem naturally lies in a hyperelliptic Riemann surface. We thus generalize the Deift- Zhou ＂nonlinear stationary phase method＂ to surfaces of nonzero genus. Second, we illustrate the important fact that very often even when applying the powerful Riemann-Hilbert method, a Lax-Levermore problem is still underlying and understanding it is crucial in the analysis and the proofs of the Deift-Zhou method!

关键词： Riemann-Hilbert problem Toda lattice

On the Stability of the Generalized Sine Functional Equations

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Acta Mathematica Sinica,English Series 2009年第1期25卷 29-38页

作者： Gwang Hui KIM department of applied mathematics Kangnam University

The aim of this paper is to study the stability problem of the generalized sine functional equations as follows：g（x）f（y）=f（x＋y/2）^2-f（x-y/2）^2 f（x）g（y）=f（x＋y/2）^2-f（x-y/2）^2,g（x）g（y）=f（x＋y/2）... 详细信息

关键词： stability superstability sine functional equation cosine functional equation.