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 obtains the soliton solutions of the Ito integro-differential equation. The / GGmethod will be used to carry out the solutions of this equation and then the solitary wave ansatz method will be used to obtain a 1-soliton solution of this equation. Finally, the invariance and multiplier approach will be applied to recover a few of the conserved quantities of this equation. GGmethod.

https://www.academiaromana.ro/sectii2002/proceedings/doc2012-3/05-Ebadi.pdf

Solitons and conserved quantities of the ito equation

This paper is devoted to the study of a free-convective boundary-layer flow modeled by a system of nonlinear ordinary differential equations. We apply a modified variational iteration method (MVIM) coupled with He's polynomials and Pade approximation to solve free-convective boundary-layer equation. It is observed that the combination of MVIM and the Pade approximation improves the accuracy and enlarges the convergence domain.

/pdf/modified-variational-iteration-method-for-free-convective-4cu4p1xjbw.pdf

Modified Variational Iteration Method for Free-Convective Boundary-Layer Equation Using Padé Approximation

A residual power series scheme is developed for mixed-type p-system of conservation laws. The residual power series method (RPSM) does not require discretization, reduces the system to an explicit system of algebraic equations and consequently of massive computations. Convergence hypotheses are discussed and error bounds of exponential rates are derived. The scheme is numerically tested to several cases of the van der Waals equations which arise in fluid dynamics. Stability is obtained graphically while transition through regions. The reported results reveal the reliability, efficiency and economical implementation of the proposed algorithm for handling nonlinear partial differential equations in applied mathematics.

The residual power series method for the one-dimensional unsteady flow of a van der Waals gas

In this study, we investigate the magnetohydrodynamic (MHD) viscous flow due to a shrinking sheet by employing the homotopy perturbation method (HPM) and Pade approximation. The series solution of the governing nonlinear problem is developed. Generally, the truncated series solution 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 polynomial approximation into a rational function, are applied to the series solution to improve the accuracy and enlarge the convergence domain. Comparison of the present solutions is made with the results obtained by other applied methods and excellent agreement is noted.

http://iauksh.ac.ir/content/users/user_iauksh/www.iauksh.ac.ir/admins/rezome%20asatid/raftari/4.pdf

Series solution of a nonlinear ODE arising in magnetohydrodynamic by HPM-Padé technique

In this paper, we consider a Sturm---Liouville problem which contains an eigenparameter appearing linearly in two boundary conditions, in addition to an internal point of discontinuity. Eigenvalue problems with eigenparameter appearing in the boundary conditions usually have complicated characteristic determinant where zeros cannot be explicitly computed. We apply the sinc method, which is based on the sampling theory to compute approximations of the eigenvalues. An error analysis is exhibited involving rigorous error bounds. Using computable error bounds we obtain eigenvalue enclosures in a simple way. Illustrative examples are included to demonstrate the validity and applicability of the presented technique.

Ahmet Yildirim

Papers

Solitons and conserved quantities of the ito equation

Modified Variational Iteration Method for Free-Convective Boundary-Layer Equation Using Padé Approximation

The residual power series method for the one-dimensional unsteady flow of a van der Waals gas

Series solution of a nonlinear ODE arising in magnetohydrodynamic by HPM-Padé technique

Numerical computation of eigenvalues of discontinuous Sturm---Liouville problems with parameter dependent boundary conditions using sinc method