In this paper we further improve the modified extended tanh-function method to obtain new exact solutions for nonlinear partial differential equations. Numerical applications of the proposed method are verified by solving the improved Boussinesq equation and the system of variant Boussinesq equations. The new exact solutions for these equations include Jacobi elliptic doubly periodic type, Weie...

Aalto University, P.O. Box 11000, FI-00076 Aalto www.aalto.fi Author Harri Hakula, Tri Quach, Antti Rasila Name of the publication Conjugate function method for numerical conformal mappings Publisher School of Science Unit Department of Mathematics and Systems Analysis Series Aalto University publication series SCIENCE + TECHNOLOGY 21/2011 Field of research Abstract We present a method for nume...

We study the structure function gT = g1+g2, using the factorisation method. It turns out that gT has a much simpler operator structure as compared to g2, in spite of the fact that, like g2, gT has a twist-three component not suppressed by powers of Q . We demonstrate factorisation of the hadronic tensor into hard and soft parts for the case of gT , even though g2 does not admit of such a demons...

Infinite integrals involving Bessel functions are recast, by means of an Abel transform, in terms of Fourier integrals. As there are many efficient numerical methods for computing Fourier integrals, this leads to a convenient way of approximating Bessel function integrals.

Since Casimir's paper [1] on the attraction of two neutral parallel (perfectly) conducting plates due to the vacuum uctuations of the electromagnetic eld, a considerable amount of work has been done on this subject, varying from the application of alternative techniques to the exploration of new geometries and theories. Excellent reviews as well as a large list of relevant references on this su...

Abstract The transfer function of a piezoelectric transducer, buffer rod and sample assembly is used to measure the sound velocity of solid materials. From the recorded transfer function, pulse echo patterns at frequencies of the passband of the input signal are reproduced after convoluting with monochromatic RF input signals. The time delay is obtained by performing pulse echo overlap and phas...

Abstract: This is the first of two articles devoted to a exposition of the generatingfunction method for computing fusion rules in affine Lie algebras. The present paper is entirely devoted to the study of the tensor-product (infinite-level) limit of fusions rules. We start by reviewing Sharp’s character method. An alternative approach to the construction of tensor-product generating functions ...

In this study, we presented the high-order fundamental solutions and general solutions of convection-diffusion equation. To demonstrate their efficacy, we applied the highorder general solutions to the boundary particle method (BPM) for the solution of some inhomogeneous convection-diffusion problems, where the BPM is a new truly boundaryonly meshfree collocation method based on multiple recipr...

An application of the Exp-function method to search for exact solutions of nonlinear differential equations is analyzed. Typical mistakes of application of the Exp-function method are demonstrated. We show it is often required to simplify the exact solutions obtained. Possibilities of the Exp-function method and other approaches in mathematical physics are discussed. The application of the sing...