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 Faculty Research Interest

TopicDescriptionMath Dept Faculty Collaboration
Statistical Process Control
In manufacturing and service processes, monitoring is a needed to timely mark the special causes happening in process. SPC tools help to timley indicate any such issues and improve process quality. Apllication areas include health, business, engineering among others.
Dr. Nasir Abbas and Dr. Jimoh Ajadi 
Solid-Fluid Interaction, Heat TransferThe research is focused on flow through channels with different cross-sections, capillary rise, and steady streaming. The research extends to heat transfer (conduction and convection). In particular, heat from particles with different shapes in relation to a flowing fluid are investigated.Dr. Faisal Fairag
Stochastic Partial differential equations.
Stochastic Processes.
Asymptotic and Perturbation Theory.
The above areas are well used by non-Mathematician also, applications to the above areas includes: Finance, Physics, Engineering,..
Dr. Brahim Mezerdi and Dr. Dhaker Kroumi
Theory of Categories, Combinatorics on Words, General Topology and its ApplicationsCombinatorics on Words and Category theory may be of interest to researchers in Computer science. Digital Topology. as a subfield of general topology, could be applied to ``digital Image Processing."
Dr. Jawad Abuhlail, Dr. Adel Khalfallah, Dr. Dhaker Kroumi
and Prof.Monther Alfuraidan
Ordinary Differential Equations
Partial differential equations of parabolic type
Partial differential equations of hyperbolic type
Partial differential equations of mixed type
Integro-differential equations
Fractional differential equations
Inequalities (algebraic and differential)
Neural Network Theory
I am interested in investigating the questions of local existence, global existence, boundedness, regularity and asymptotic behavior (in particular: stability, rates of decay and blow up) of solutions for the above different problems (equations and systems). All these problems (viscoelastic, Timoshenko, thermoelastic, laminated  structures, population dynamic, etc) arise in applications.
Prof. Khaled Furati, Dr. Mohammed Kafini, Dr. Shahzad Sarwar,
Dr. Ahmed Bonfoh, Dr. M. Yousuf, Dr. Waled Al-Khulaifi and 
Dr. Ibrahim Sarumi
1.Computational Fluid Dynamics,
2.Two-Phase flows,
3.Numerical Linear Algebra.
Many important physical processes in nature are governed by partial differential equations (PDEs). So, it is important to understand the physical behavior of the models represented by PDEs. With the rapid development in computational techniques, there has been a continuously widening scope of scientific and engineering problems that can be solved numerically.  In principle, all mathematical equations can be solved numerically in comparison to the theoretical and experimental approaches. They are low cost, high efficiency, and are of no danger when compared with the experimental approach.
The numerical solution of the Navier-Stokes equations that describe incompressible viscous fluids has been a very active research field in computational fluid dynamics(CFD). Numerous computational methods have been developed and are in use today for steady and time-accurate computation of these equations. However, the desire of developing high-order and robust methods are still required.
The moving-free boundary problems or multi-phase flows are present in nature and in many areas of physical and biological sciences. In two-phase flow problems, discontinuities arise in the pressure and the gradient of the velocity field due to surface tension forces and differences in the fluids' viscosity. Examples include the impact of a droplet on a solid surface, surface waves, jet breakup, crystal, and tumor growth, oil and gas, image segmentation, and many others where the simulation of moving interfaces plays a key role.  Although research in interfacial phenomena has a long history. However, tremendous interest has been observed in recent years due to the availability of  CFD tools and algorithms.
Numerical discretization of the nonlinear partial differential equations results in a system of nonlinear system of algebraic equations that requires fast linear and nonlinear solvers. One of my focuses in recent years is on the implementation of fast solvers such as the conjugate gradient (CG) methods that are commonly recognized for their low memory requirement and strong global convergence properties.
Commutative AlgebraThis area of Mathematics is related to Multiplicative Ideal Theory, Rings Theory and Modules Theory. However, as a pure mathematics branch, any applications seem to be far from being understood. 
Prof. Salah Kabbaj and Dr. Abdelilah Kadiri
Shape OptimizationMy main field of interest is proving sharp spectral inequalities. For example, proving inequalities involving the eigenvalues of the Laplacian on a measurable set and geometrical functionals.  
Commutative Algebra and its Homological & Geometric Aspects.<<Commutative algebra is essentially the study of commutative rings. Roughly speaking, it has developed from two sources: (1) Algebraic Geometry and (2) Algebraic Number Theory. In (1) the prototype of the rings studied is the ring of polynomials in several variables over a field; in (2) it is the ring of rational integers. Of these two, the Algebro-Geometric case is the more far-reaching and, in its modern development by Grothendieck, it embraces much of algebraic number theory. Commutative algebra is now one of the foundation stones of this new algebraic geometry. It provides the complete local tools for the subject in much the same way as differential analysis provides the tools for differential geometry. [Atiyah-MacDonald]>>
Prof. Jawad Abuihlail, Prof. Othman Echi, Dr. Abdelilah Kadri and
Prof. Abdelslam Mimouni
Categorical Quantum MechanicsCategorical Quantum Mechanics explores Quantum Mechanical Phenomena using category theory. It has applications to natural language processing from foundational perspective unlike common empirical approaches.
Game Theory & Heuristic Optimization
My research interests are mainly focused on Algorithmic design for theoretical and real-life applications:
- Vehicle Routing Problems: input forecasting, solution design and heuristic optimization.
- Smart grids: input forecasting, solution design, exact and heuristic optimization.
- Equilibrium Enumeration and Refinement in Game Theory.
- Solution Design in other fields: management conflicts, operations management...
Dr. Mohamed Al-Shahrani, Prof. Izhar Ahmad and
Prof. Suleman Al-Homidan
Hyperbolic complex spaces & Nonstandard Analysis
1-In mathematics, hyperbolic geometry is a non-Euclidean geometry. A typical example is the unit disc or the upper half plane.
 2- Nonstandard analysis is a branch of mathematical logic which introduces hyperreal numbers to allow for the existence of "genuine infinitesimals."
Multiscale Simulation in Porous MediaIn many practical applications such as those arising from petroleum engineering and geosciences, one has to perform simulations of mathematical systems defined in heterogeneous porous media. Computations with traditional methods are inefficient and expensive due to the need of high resolution meshes. In order to obtain efficient computational models, some type of multiscale methods are needed.
Convex Analysis and Vector OptimizationDr. Izhar Ahmad's research interest includes the derivation of optimality conditions and duality results for a vector optimization problem under convexity/generalized convexity. Furthermore, he also establishes the relation between vector variational inequalities (VVI) and vector optimization (VOP) on Riemannian manifolds.
Prof. Suleman Al-Homidan and Dr. Mohammed Alshahrani
Semigroup theoryCombinatorial properties of transformation semigroups
Distribution Theory
Extreme value theory and its applications, and
General statistical modeling.
Basically, my research is centered on development of new distributional 
based models to solve a range of real-life problems, especially those that are motivated by various financial issues.
Dr. Mohammed Omar
Image Analysis and Processing
Numerical Method for Differential Equations
Machine Learning for PDE
My current research deals with the design of structure-preserving numerical methods for partial differential equations and their comparison with physical informed neural networks based solutions 
Prof. Khaled Furati and Dr. Ibrahim Sarumi
General Relativity, Differential Geometry, Lie Symmetry Methods for PDEs, Non standard Einstein theoriesMy main area of research is General Relativity and Differential Geometry. The focus of my earlier research was on spacetime symmetries, which followed on famous work on Lie groups by Chevelley in the 1950's and by Petrov and others in 1960's. Since then, I have extended my research investigations to Lie symmetries of the Ricci and then the Riemann tensors in General Relativity. Most recently, I have been involved using the idea of Lie point symmetries in finding analytic solutions of nonlinear partial differential equations. Presently, my focus of research has shifted towards studies encompassing particle dynamics in the vicinity of massive objects in non-standard Einstein theories.
Dr. Muhammad Yousuf, Dr. Khairul Saleh and Dr Jae-Chean Joo
Differential Geometry, Complex AnalysisComplex analysis and geometry is a brach of pure mathematics about spaces of complex structures and analytic functions on the spaces. It is not only a main subject of mathematics but also related with some mordern physical models. Dr. Adel Khalfallah
Graph Theory
Graph theory is used in dealing with problems which have a fairly natural graph/network structure, for example: road networks - nodes = towns/road junctions, arcs = roads. communication networks - telephone systems. computer systems.
Prof. Monther Alfuraidan and Dr. Ibrahim Sarumi