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)

This paper studies the 5 th order KdV equation with dual-power law nonlinearity. The non-topological as well as the singular soliton solution is obtained. Additionally the cnoidal wave solution is obtained for two values of the power law parameter. Finally, the Painleve analysis of the equation is also discussed.

/pdf/cnoidal-waves-solitary-waves-and-painleve-analysis-of-the-23xy4wh5cg.pdf

Cnoidal waves, solitary waves and painleve analysis of the 5th order kdv equation with dual-power law nonlinearity

In this paper we study the existence and exact solution of fuzzy Abel integral equation of first kind for the fuzzy continuous function. Otherwise solving this equation always isn't simple, we use fuzzy approximation for finding the approximation of the solution.

/pdf/numerical-method-for-solving-fuzzy-abel-integral-equations-30fz6nk1ug.pdf

Numerical method for solving fuzzy abel integral equations

Purpose – The purpose of this paper is to implement the variational iteration method and the homotopy perturbation method to give a rational approximation solution of the foam drainage equation with time‐ and space‐fractional derivatives.Design/methodology/approach – The fractional derivatives are described in the Caputo sense. In these schemes, the solution takes the form of a convergent series with easily computable components.Findings – Numerical examples are given to demonstrate the effectiveness of the present methods.Originality/value – Results show that the proposed schemes are very effective and convenient for solving linear and nonlinear fractional differential equations with high accuracy.

Rational approximation solution of the foam drainage equation with time‐ and space‐fractional derivatives

This article analyzes a strongly nonlinear oscillator with cubic and harmonic restoring force and proposes an efficient analytical technique based on the modified energy balance method (MEBM). The proposed method incorporates higher-order approximations. After applying the proposed MEBM, a set of complicated higher-order nonlinear algebraic equations are obtained. Higher-order nonlinear algebraic equations are cumbersome to investigate especially in the case of a large initial oscillation amplitude. This limitation is overcome in the proposed method by using the iterative procedure based on the homotopy perturbation method. The approximated results agree well with the numerically obtained exact solutions. These third-order approximate solutions are found to be almost the same as exact solutions, which cannot be found using the existing energy balance method. Highly accurate result and simple solution procedure are advantages of this proposed method, which could be applied to other nonlinear oscillatory problems arising in nonlinear science and engineering.

https://jacm.scu.ac.ir/article_14667_4cbfbc6281d4e4a80d1dfce81a4baf65.pdf

A Modified Energy Balance Method to Obtain Higher-order Approximations to the Oscillators with Cubic and Harmonic Restoring Force

In this study, we introduce an efficient method for solving the kinetic modeling of lactic acid fermentation and epidemic model. First model accounts for the transient response for the cell growth, substrate utilization and lactic acid production during the fermentation process and second model is the problem of spread of a non-fatal disease in a population that is assumed to have constant size over the period of the epidemic model. We use homotopy perturbation method (HPM) to solve kinetic model for the batch production of lactic acid under submerged fermentation of cheese whey using Lactobacillus helveticus and epidemic model in a population. Copyright © 2009 John Wiley & Sons, Ltd.

Numerical solution of the system of nonlinear ordinary differential equations arising in kinetic modeling of lactic acid fermentation and epidemic model

Ahmet Yildirim

Papers

Cnoidal waves, solitary waves and painleve analysis of the 5th order kdv equation with dual-power law nonlinearity

Numerical method for solving fuzzy abel integral equations

Rational approximation solution of the foam drainage equation with time‐ and space‐fractional derivatives

A Modified Energy Balance Method to Obtain Higher-order Approximations to the Oscillators with Cubic and Harmonic Restoring Force

Numerical solution of the system of nonlinear ordinary differential equations arising in kinetic modeling of lactic acid fermentation and epidemic model