Research Groups

1- Mathematical Analysis

Scientific Research Priorities

• Maximum Principle (MP) .
• Existence and stability of weak solutions for non-linear systems.
• Ideal Structure of Operator Algebras (C*-algebras and von Neuman algebras ).
• The pure state spaces of C*-Algebras..
• The Fractional Calculus Theorem.
• Sampling Theorem and Fourier Analysis.

Objectives

• Studying MP for some nonlinear systems.
• Applying some methods (Theory of nonlinear operators method - Approximation method - Browder theorem method) to study the existence, non-existence and uniqueness of weak solution for some nonlinear systems.
• Studying Stability properties of  weak solution for some nonlinear systems..
• State spaces of operator algebra such as algebra.
• Studying the pure state spaces of algebra.
• Studying the existence and uniqueness of mild solutions to some fractional nonlinear differential equations with discussing when this mild solution will be strong one.
• Studying fractional Euler-Lagrange equations and Hamiltonian equations different senses and discussing their applications.
• Studying the Paly-Weiner theory and its applications.
• Using the Fourier series in Sampling Theorem.

Group Members

• Dr. Salah Khafagy
• Dr. Omar Hassan Khalil
• Dr. Wasim Ulhaq
• Dr. Huda Almorad

2- Applied Mathematics Group

Scientific Research Priorities

• .Non-Newtonian fluids , Micro polar Fluids
• .Heat and Mass transfer in Fluid Dynamics
• .Nano Fluid
• .Radiation ,Thermal dispersion ,magnetic field,heat generation ,thermal dispersion
• .Bifurcation in Fluid dynamics

Objectives

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Group Members

• Dr. Sayer Alharbi
• Dr. Mohamed Omar Mahgoub
• Dr. Jawdat Alebrahim
• Dr. Omaima Alnoor

3- Mathematics for Applied Sciences Group

Scientific Research Priorities

• Special functions and their applications.
• Statistics.

Objectives

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Group Members

• Dr. Ziyad A. Alhussain
• (Dr. Wathek chammam (Head of the Group
• Dr.Abdullah A. Ansari
• Dr.Humaira yassin

4-Algebra, Geometry and Discrete Mathematics Group

This  group is a research group of the Department of Mathematics at the College of Science of Majmaah University. The group performs a research activity in many areas of abstract algebra and its applications in various domains as coding theory (finite  fields), cryptography (finite fields) , abstract computer science (semirings),  genetics (biordered sets), tropical geometry , etc.

Scientific Research Priorities

• Particular groups and Semigroups.
• Semirings.
• Ternary algebraic structures.
• General tropical semirings.
• Coding theory on general rings.

Objectives

• Determine some particular properties of morphic groups.
• As an application of the semigroups in  computer science; we study the  semigroup actions since they are closely related to automata with as a set models;  the state of the automaton and the action models transformations of that state in response to inputs.
• Since the works of  Kleene and after those of Samuel Eilenberg, Semirings can  be applied in automata theory and formal language, where a comprehensive algebraic theory has been constructed  and published in four volumes on  Automata, Languages, and Machines. The basic algebraic structures used in these books, and the publications of many other researchers, were semirings. Our research is concerned with study some new properties and  to study which properties can be obtained in the ternary semirings.
• One of our recent axe of our interest is the study of tropical geometry  and our idea is to define general tropical semiring and extract the properties in view of those known in the case of the tropical semifield (R,max,+).

Group Members

• Dr. Naveed Yakoub
• Dr. Mahasen Ali

5-Dynamical Models, Rough, fuzzy , Gas and adaptive systems Group

There is currently no machine that can provide us with perfectly certain medical imaging data. Errors from multiple sources including noise, patient movement, and partial volume effect due to limited resolution are polluting the data. Since medical experts rely on these images to bring conclusions about the existence and severity of a potential disease, we aim to provide approaches to convey these errors.

The Rough Set theory is mathematically relatively simple. Despite of this, it has shown its fruitfulness in a variety of data mining areas. Among these are information retrieval, decision support, machine learning, and knowledge based systems. A wide range of applications utilize the ideas of the theory. Medical data analysis, aircraft pilot performance evaluation, image processing, and voice recognition are a few examples.

We extend the concept of topological spaces in the context of multisets (mset, for short). we begins with basic definitions and operations on msets.  Different types of submsets, collections of submsets and operations under such collections of msets will study . The notion of M-topological space and the concept of open multisets also will study. Furthermore the notions of basis, sub basis, closed sets, closure and interior in topological spaces are extended to M-topological spaces and many related theorems we will prove.

Scientific Research Priorities

• Rough and Fuzzy functions in classification .
• rough and Fuzzy set-based image compression.
• The notion of M-topological space and the concept of open multisets

Objectives

• The notion of a multiset  is well established  both in mathematics and computer science .  In mathematics, a multiset is considered to be the generalization of a set.
• In classical set theory, a set is a well-defined collection of distinct objects. If repeated occurrences of any object is allowed in a set, then a mathematical structure, that is known as multiset (mset, for short), is obtained .
• In various counting arguments it is convenient to distinguish between a set like {a, b, c} and a collection like {a, a, a, b, c, c}.
• The latter, if viewed as a set, will be identical to the former.  However, it has some of its elements purposely listed several times.  We formalize it by defining a multiset .

Group Members

• Dr. Ahmed Elmoasry
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