Paper's Title:

Dyadic Riesz Wavelets on Local Fields of Positive Characteristics

Author(s):

Kartik Garg, Raj Kumar, Satyapriya

Department of Mathematics,
University of Delhi,
Delhi,
India.
kartikgarg1421@gmail.com,
rajkmc@gmail.com
kmc.satyapriya@gmail.com

 

Abstract:

In this research paper, we introduce a novel theory for the construction of a Riesz wavelet basis in the space L²(K), where K is a local field with positive characteristics. Our approach is two fold: firstly, we derive some essential characterizations of the scaling function associated with the structure of a Riesz MRA on a local field, and secondly, we review existing methods for constructing wavelet frames in L²(K). We also present a well elaborated example for a better comprehension of our theory. Due to mathematical convenience, we limit ourselves to the case of dyadic dilations only.

Paper's Title:

Inequalities of Gamma Function Appearing in Generalizing Probability Sampling Design

Author(s):

Mohammadkheer M. Al-Jararha And Jehad M. Al-Jararha

Department of Mathematics,
Yarmouk University,
Irbid 21163,
Jordan.
E-mail: mohammad.ja@yu.edu.jo

Department of Statistics,
Yarmouk University,
Irbid 21163,
Jordan.
E-mail: jehad@yu.edu.jo

Abstract:

In this paper, we investigate the complete monotonicity of some functions involving gamma function. Using the monotonic properties of these functions, we derived some inequalities involving gamma and beta functions. Such inequalities can be used to generalize different probability distribution functions. Also, they can be used to generalize some statistical designs, e.g., the probability proportional to the size without replacement design.

Paper's Title:

Solving Non-Autonomous Nonlinear Systems of Ordinary Differential Equations Using Multi-Stage Differential Transform Method

Author(s):

K. A. Ahmad, Z. Zainuddin, F. A. Abdullah

School of Mathematical Sciences Universiti Sains Malaysia
11800 USM Penang
Malaysia.
E-mail: abumohmmadkh@hotmail.com
zarita@usm.my
farahaini@usm.my

Abstract:

Differential equations are basic tools to describe a wide variety of phenomena in nature such as, electrostatics, physics, chemistry, economics, etc. In this paper, a technique is developed to solve nonlinear and linear systems of ordinary differential equations based on the standard Differential Transform Method (DTM) and Multi-stage Differential Transform Method (MsDTM). Comparative numerical results that we are obtained by MsDTM and Runge-Kutta method are proposed. The numerical results showed that the MsDTM gives more accurate approximation as compared to the Runge-Kutta numerical method for the solutions of nonlinear and linear systems of ordinary differential equations

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