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)

Homotopy Perturbation Method (HPM) is applied to solve stochastic models and in the simialr context Fokker-Planck equation for non-equilibrium statistical systems and Black-Scholes model for pricing stock options are tackled The analytical solutions are calculated in the form of convergent power series. The results reveal that HPM is very effective and convenient for stochastic models.

/pdf/analytical-approximate-solutions-of-stochastic-models-1kj2ffesch.pdf

Analytical Approximate Solutions of Stochastic Models Arising in Statistical Systems and Financial Markets

MacMillan's equations are extended to Poincare's formalism, and MacMillan's equations for nonlinear nonholonomic systems are obtained in terms of Poincare parameters. The equivalence of the results obtained here with other forms of equations of motion is demonstrated. An illustrative example of the theory is provided as well.

Poincaré-MacMillan Equations of Motion for a Nonlinear Nonholonomic Dynamical System

This paper investigates the effect of elevated temperatures on the properties of high strength mortars (HSMs) containing ground calcined diatomite (GCD) produced with limestone sand (LS). In the HSM mixtures at a water-binder ratio of 0.35, GCD is employed in place of cement at replacement ratios of 0, 5, 10, 15 and 20% by weight. The mechanical and microstructural properties of HSMs containing GCD produced with LS are investigated separately at different curing days and elevated temperatures. The results of these properties have indicated that GCD can be employed instead of cement in the HSMs containing GCD produced with LS, and GCD content up to %15 improve the mechanical properties of HSMs. Especially, deteriorations and cracks in the HSMs are seen due to the calcification and expansion of LS used as sand in the mixtures at 1000 °C temperature, and consequently, high decreases in the mechanical properties are observed. 

Effect of elevated temperatures on properties of high strength mortars containing ground calcined diatomite with limestone sand

In this paper, we apply Homotopy Perturbation Transformation Method (HPM) using the Laplace transformation to tackle time-fractional systems of Partial Differential equations. The proposed technique is fully compatible with the complexity of these problems and obtained results are highly encouraging. Numerical results coupled with graphical representations explicitly reveal the complete reliability and efficiency of the suggested algorithm.

/pdf/on-system-of-time-fractional-partial-differential-equations-3ku8scmwmb.pdf

On System of Time-Fractional Partial Differential Equations

In this paper, the He’s parameter-expanding method (HPEM) and the 4q-Boubaker Polynomials Expansion Scheme (BPES) are used in order to obtain analytical solutions to the non-linear modified Van der Pol’s oscillating circuit equation. The resolution protocols are applied to the ordinary Van der Pol equation, which annexed to conjoint delayed feedback and delay-related damping terms. The results are plotted, and compared with exact solutions proposed elsewhere, in order to evaluate accuracy.

https://file.scirp.org/pdf/CS20110300011_17318172.pdf

Ahmet Yildirim

Papers

Analytical Approximate Solutions of Stochastic Models Arising in Statistical Systems and Financial Markets

Poincaré-MacMillan Equations of Motion for a Nonlinear Nonholonomic Dynamical System

Effect of elevated temperatures on properties of high strength mortars containing ground calcined diatomite with limestone sand

On System of Time-Fractional Partial Differential Equations

A Comparative Study of Analytical Solutions to the Coupled Van-der-Pol's Non-linear Circuits Using the He's Method (HPEM) and (BPES)