Physical Sciences and Mathematics Commons^™

Series Solutions Of Multi-Layer Boundary Value Problems, Amr Saad Hassan Bolbol

Theses

It is well known that differential equations (DEs) play an important role in many sciences. They are mathematical representations of many physical systems. By studying such DEs, one gains many important insights about the physical system. Solutions of DEs provide information on the physical system behavior. As many physical systems are nonlinear in nature, this naturally gives rise to nonlinear differential equations (NLDEs). Such NLDEs are, in most cases, hard or sometimes impossible to solve analytically. In such situations, we resort to numerical techniques to approximate the solutions. The purpose of this thesis is to consider nonlinear multi-layer boundary value …

Some Algebraic Aspect And Applications Of A Family Of Functions Over Finite Fields, Shaima Ahmed Thabet

Theses

We study two families of functions over finite fields; the Multivalued Threshold

Functions and the Multivariate Polynomials. Recent advances made in our Conception and our understanding of Boolean Threshold Functions and Multivariate Threshold Functions have considerably increased the importance of the role that they Play in our days in areas like cryptography, circuit complexity, learning theory, social choice, quantum complexity, and in many other areas. Theoretical aspects of Bovid and Gauche who gave an algebraic first studied threshold functions Approach of Boolean Threshold Functions using group ring theory. We will present some algebraic properties of Boolean threshold functions. For the …

Finite Semifields And Their Applications, Shamsa Ali Rashed Al Saedi

Theses

This thesis is concerned with finite semi fields. The objective of this thesis is to give a full description of Knuth orbits of known commutative semi fields. We also describe planar functions corresponding to commutative semi fields. Results are presented by tables. Nuclei of semi fields are studied. Finally we consider applications of semi fields, planar functions and spreads to construction of mutually unbiased bases.