to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).

日本物理学会誌及びJournal of the Physical Society of Japanの月刊について

EDDINGTON'S “Internal Constitution of the Stars” was published in 1926 and gives what now ranks as a classical account of his own researches and of the general state of the theory at that time. Since then, a tremendous amount of work has appeared. Much of it has to do with the construction of stellar models with different equations of state applying in different zones. Other parts deal with the effects of varying chemical composition, with pulsation and tidal and rotational distortion of stars, and with the precise relations between the interior and the atmosphere of a star. The striking feature of all this work is that so much can be done without assuming any particular mechanism of stellar energy-generation. Only such very comprehensive assumptions are made about the distribution and behaviour of the energy sources that we may expect future knowledge of their mechanism to lead mainly to more detailed results within the framework of the existing general theory. An Introduction to the Study of Stellar Structure By S. Chandrasekhar. (Astrophysical Monographs sponsored by The Astrophysical Journal.) Pp. ix+509. (Chicago: University of Chicago Press; London: Cambridge University Press, 1939.) 50s. net.

An Introduction to the Study of Stellar Structure

Finite element methods for Maxwell's equations.

The main purpos e of this chapter is to present a direct and systematic way of finding exact solutions and Backlund transformations of a certain class of nonlinear evolution equations. The nonlinear evolution equations are transformed, by changing the dependent variable(s), into bilinear differential equations of the following special form 
 
$$ F\left( {\frac{\partial }{{\partial t}} - \frac{\partial }{{\partial {t^1}}},\frac{\partial }{{\partial x}} - \frac{\partial }{{\partial {x^1}}}} \right)f(t,x)f({t^1},{x^1}){|_{t = {t^1},x = {x^1}}} = 0 $$ 
 
, which we solve exactly using a kind of perturbational approach.

Direct Methods in Soliton Theory (非線形現象の取扱いとその物理的課題に関する研究会報告)

Purpose – The purpose of this paper is to consider analytical solution of wave system in Rn with coupling controllers by using the homotopy perturbation method (HPM).Design/methodology/approach – HPM is applied to the system of linear partial differential equations, i.e. the system of waves in the two‐dimensional version of system equations (1) and (2). This problem is motivated by an analogous problem in ordinary differential equations for coupled oscillators and has potential application in isolating a vibrating object from the outside disturbances. For example, rubber or rubber‐like materials can be used to either absorb or shield a structure from vibration. As an approximation, these materials can be modeled as distributed springs.Findings – In this paper, HPM was used to obtain analytical solution of wave system in with coupling controllers. The method provides the solutions in the form of a series with easily computable terms. Unlike other common methods for solving any physical problem, linear or n...

Analytical solution of wave system in Rn with coupling controllers

This paper studies the optical solitons in birefringent fibers and DWDM systems in presence of log-law nonlinearity with inter-modal dispersion. The Gaussian ansatz is used to carry out the integration of the governing equation. The exact solutions are obtained and the constraint conditions, for the existence of these Gaussons, fall out during the course of derivation of the solution. A brief discussion on Thirring solitons is also included.

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Optical gaussons in birefringent fibers and dwdm systems with inter-modal dispersion

A modified homotopy perturbation method coupled with the Fourier transform for nonlinear and singular Lane–Emden equations

In this paper, He's variational iteration method (VIM) is employed successfully for solving modified Camassa–Holm and Degasperis–Procesi equations. In this method, the solution is calculated in the form of a convergent series with an easily computable component. This approach does not need linearization, weak nonlinearity assumptions or the perturbation theory. The results show applicability, accuracy and efficiency of VIM in solving nonlinear differential equations with fully nonlinear dispersion term. It is predicted that VIM can be widely applied in science and engineering problems. Copyright © 2008 John Wiley & Sons, Ltd.

Variational iteration method for modified Camassa-Holm and Degasperis-Procesi equations

This article presents a numerical method for solving nonlinear mixed Volterra–Fredholm integral equations. The method combined with the noise terms phenomena may provide the exact solution by using two iterations only. Two numerical illustrations are given to show the pertinent features of the technique. The results reveal that the proposed method is very effective and simple.

Ahmet Yildirim

Papers

Analytical solution of wave system in Rn with coupling controllers

Optical gaussons in birefringent fibers and dwdm systems with inter-modal dispersion

A modified homotopy perturbation method coupled with the Fourier transform for nonlinear and singular Lane–Emden equations

Variational iteration method for modified Camassa-Holm and Degasperis-Procesi equations

Homotopy perturbation method for the mixed Volterra–Fredholm integral equations