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).

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 investigates the drag exerted by randomly distributed, rigid, emergent circular cylinders of uniform diameter d . Laboratory measurements are presented for solid volume fraction ϕ=0.091 , 0.15, 0.20, 0.27, and 0.35 and cylinder Reynolds number Rep ≡ Up d∕ν=25 to 685, where Up =temporally and cross-sectionally averaged pore velocity and ν =kinematic viscosity. These ranges coincide with conditions in aquatic plant canopies. The temporally and cross-sectionally averaged drag coefficient, CD , decreased with increasing Rep and increased with increasing ϕ under the flow conditions investigated. The dimensionless ratio of the mean drag per unit cylinder length ⟨ fD ¯ ⟩H to the product of the viscosity, μ , and Up exhibits a linear Rep dependence of the form ⟨ fD ¯ ⟩H ∕(μ Up )= α0 + α1 Rep , consistent with Ergun’s formulation for packed columns. In the range of experimental conditions, α1 increases monotonically with ϕ . In contrast, α0 is constant within uncertainty for 0.15⩽ϕ⩽0.35 , which suggests...

Laboratory Investigation of Mean Drag in a Random Array of Rigid, Emergent Cylinders

Solutions of the system of differential equations by differential transform method

MHD flow and radiation heat transfer of nanofluids in porous media with variable surface heat flux and chemical reaction

On the two-dimensional differential transform method

Applications of differential transform method to differential-algebraic equations

In this paper, we aim to present a reliable algorithm in order to obtain exact and approximate solutions for the nonlinear dispersive KdV and mKdV equations with initial profile. The approach rest mainly on two-dimensional differential transform method which is one of the approximate methods. The method can easily be applied to many linear and nonlinear problems and is capable of reducing the size of computational work. Exact solutions can also be achieved by the known forms of the series solutions. We first present the definition and operation of the two-dimensional differential transform and investigate the soliton solutions of Kdv and mKdV equations are obtained by the present method. Therefore, in the present work, numerical examples are tested to illustrate the pertinent feature of the proposed algorithm.

Solitary wave solutions for the KdV and mKdV equations by differential transform method

The heat equation and its fractional generalization are used in various applications in science and engineering. In this paper firstly we introduce the double Laplace transform of the partial fractional integrals and derivatives which can be used to solve partial differential equations with Caputo fractional derivatives. Secondly, the fractional heat equation was investigated in details with the help of this new generalized transform

Fatma Ayaz

Papers

Solutions of the system of differential equations by differential transform method

On the two-dimensional differential transform method

Applications of differential transform method to differential-algebraic equations

Solitary wave solutions for the KdV and mKdV equations by differential transform method

Fractional caputo heat equation within the double laplace transform