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)

Exp -function method is extended to construct new exact solution for the Schamel-Korteweg-de Vries (S-KdV) equation which plays a pivitol role in mathematical physics and engineering sciences. A concrete relation between the basic ideas of the proposed technique and the existing literature is also presented. Numerical work re-confirms the efficieincy and accuracy of the proposed algorithm.

/pdf/new-exact-solutions-for-schamel-korteweg-de-vries-equation-47agos4ce8.pdf

New Exact Solutions for Schamel-Korteweg-de -Vries Equation

The aim of this paper is to solve one-dimensional wave equations that combine classical and integral boundary conditions using the homotopy perturbation method (HPM). The studied equations are changed into direct problems easy to be handled by the homotopy perturbation method. Several examples are given and the results are compared with exact solutions, revealing effectiveness and simplicity of the method.

Numerical solutions of wave equations subject to an integral conservation condition by he's homotopy perturbation method

We combined the Homotopy perturbation method (HPM) and Pade techniques to solve the well-known Blaszak–Marciniak lattice. Blaszak–Marciniak lattice has rich mathematical structures and many important applications in physics, engineering and mathematics. Generally, the truncated series solution of HPM is adequate only in a small region when the exact solution is not reached. We overcame this limitation by using the Pade techniques, which have the advantage in turning the polynomials approximation into a rational function, are applied to the series solution to improve the accuracy and enlarge the convergence domain. Using this combined technique, the soliton solutions of the Blaszak–Marciniak lattice are constructed with better accuracy and better convergence than by using the HPM alone. An example of computed calculation is followed by comparative plots of the solutions obtained through the (HPM) and (HPM-Pade) methods. Graphics are gathered for discussion of convergence. The same protocol is applied to Blaszak–Marciniak four-field lattice.

An efficient technique for solving the blaszak–marciniak lattice by combining homotopy perturbation and padé techniques

In this work, we investigate the linear and the nonlinear Goursat problems. The solution of the Goursat problem is presented by means of the homotopy perturbation method (HPM). The application of HPM to this problem shows the rapid convergence of the sequence constructed by this method to the exact solution. The linear and the nonlinear structures are handled in a similar manner without any need to restrictive assumptions. The accuracy level of the obtained results reveals the power of this method over existing numerical methods. Copyright © 2009 John Wiley & Sons, Ltd.

The homotopy perturbation method for solving the linear and the nonlinear Goursat problems

In this article differential transformation method (DTMs) has been used to solve neutral functional-differential equations with proportional delays. The method can simply be applied to many linear and nonlinear problems and is capable of reducing the size of computational work while still providing the series solution with fast convergence rate. Exact solutions can also be obtained from the known forms of the series solutions. The results show that the method is effective, suitable, easy, practical and accurate.

http://cjms.journals.umz.ac.ir/article_5_560f72464b2ef8adfe141ec1ad36b55d.pdf

Ahmet Yildirim

Papers

New Exact Solutions for Schamel-Korteweg-de -Vries Equation

Numerical solutions of wave equations subject to an integral conservation condition by he's homotopy perturbation method

An efficient technique for solving the blaszak–marciniak lattice by combining homotopy perturbation and padé techniques

The homotopy perturbation method for solving the linear and the nonlinear Goursat problems

Differential transformation method for solving a neutral functional-differential equation with proportional delays