Paper's Title:

Wavelet Frames in Higher Dimensional Sobolev Spaces

Author(s):

Raj Kumar, Manish Chauhan, and Reena

Department of Mathematics,
Kirori Mal College, University of Delhi,
New Delhi-110007,
India.
E-mail: rajkmc@gmail.com

Department of Mathematics,
University of Delhi,
New Delhi-110007,
India
E-mail: manish17102021@gmail.com

Department of Mathematics,
Hans Raj College, University of Delhi,
New Delhi-110007,
India
E-mail: reena.bhagwat29@gmail.com

Abstract:

In this paper, we present sufficient condition for the sequence of vectors to be a frame for H^s(R^d) are derived. Necessary and sufficient conditions for the sequence of vectors to be tight wavelet frames in H^s(R^d) are obtained. Further, as an application an example of tight wavelet frames for H^s(R²) as bivariate box spline over 3-direction are given.

Paper's Title:

Solving Two Point Boundary Value Problems by Modified Sumudu Transform Homotopy Perturbation Method

Author(s):

Asem AL Nemrat and Zarita Zainuddin

School of Mathematical Sciences,
Universiti Sains Malaysia,
11800 Penang,
Malaysia.
E-mail: alnemrata@yahoo.com
zarita@usm.my

Abstract:

This paper considers a combined form of the Sumudu transform with the modified homotopy perturbation method (MHPM) to find approximate and analytical solutions for nonlinear two point boundary value problems. This method is called the modified Sumudu transform homotopy perturbation method (MSTHPM). The suggested technique avoids the round-off errors and finds the solution without any restrictive assumptions or discretization. We will introduce an appropriate initial approximation and furthermore, the residual error will be canceled in some points of the interval (RECP). Only a first order approximation of MSTHPM will be required, as compared to STHPM, which needs more iterations for the same cases of study. After comparing figures between approximate, MSTHPM, STHPM and numerical solutions, it is found through the solutions we have obtained that they are highly accurate, indicating that the MSTHPM is very effective, simple and can be used to solve other types of nonlinear boundary value problems (BVPs).

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