Department of Mathematics and Statistics
Work by the faculty and students of the Department of Mathematics and Statistics
Recent Submissions

The Boyle–Romberg trinomial tree, a highly efficient method for double barrier option pricing
(MDPI, 20240324)Oscillations in option price convergence have long been a problematic aspect of tree methods, inhibiting the use of repeated Richardson extrapolation that could otherwise greatly accelerate convergence, a feature integral ... 
Effects of mechanoelectrical feedback on the onset of alternans: A computational study
(AIP, 201906)Cardiac alternans is a heart rhythm instability that is associated with cardiac arrhythmias and may lead to sudden cardiac death. The onset of this instability, which is linked to perioddoubling bifurcation and may be a ... 
A Simulation Study of the Role of Mechanical Stretch in Arrhythmogenesis during Cardiac Alternans
(Biophysical Society, 202101)The deformation of the heart tissue due to the contraction can modulate the excitation, a phenomenon referred to as mechanoelectrical feedback (MEF), via stretchactivated channels. The effects of MEF on the electrophysiology ... 
Efficiency of semiimplicit alternating direction implicit methods for solving cardiac monodomain model
(Elsevier, 202101)It is well known that numerical simulations of the cardiac monodomain model require fine mesh resolution, which increases the computational resources required. In this paper, we construct three operatorsplitting alternating ... 
A projection scheme for phase change problems with convection
(Elseiver, 202201)Numerical modeling of phase change problems with convection is known to be computationally expensive. The main challenge comes from the coupling between Navier–Stokes and heat energy equations. In this paper, we develop a ... 
Efficiency of parallel anisotropic mesh adaptation for the solution of the bidomain model in cardiac tissue
(Elsevier, 202204)Electrocardiology models are nonlinear reaction–diffusion type systems, where the numerical simulation requires extremely fine meshes to accurately compute the heart’s electrical activity. Anisotropic mesh adaptation methods ... 
Numerical modelling of hyperbolic phase change problems: Application to continuous casting
(Elsevier, 202303)Heat diffusion processes are generally modeled based on Fourier’s law to estimate how the temperature propagates inside a body. This type of modeling leads to a parabolic partial differential equation, which predicts an ... 
A mixed finite element method for nonlinear radiation–conduction equations in optically thick anisotropic media
(Elsevier, 202309)We propose a new mixed finite element formulation for solving radiation–conduction heat transfer in optically thick anisotropic media. At this optical regime, the integrodifferential equations for radiative transfer can ... 
Liposomal Encapsulation of Chemotherapeutics Agents Combined with the Use of Ultrasound in Cancer Treatment
(American Scientific Publishers, 202307)Ultrasound (US) has numerous uses in the medical field, including imaging, tumor ablation, and lithotripsy; another interesting application of US in cancer therapy is as an external trigger in targeted drug delivery. ... 
Modeling of the In Vitro Release Kinetics of Sonosensitive Targeted Liposomes
(MDPI, 20221205)Targeted liposomes triggered by ultrasound are a promising drug delivery system as they potentially improve the clinical outcomes of chemotherapy while reducing associated side effects. In this work, a comprehensive model ... 
Graph of Linear Transformations Over R
(Springer, 20221201)In this paper, we study a connection between graph theory and linear transformations of finite dimensional vector spaces over R (the set of all real numbers). Let Rm, Rn be finite vector spaces over R, and let L be the set ... 
Maximum principles and overdetermined problems for Hessian equations
(ISTE Group, 2021)In this article we investigate some Hessian type equations. Our main aim is to derive new maximum principles for some suitable Pfunctions, in the sense of L.E. Payne, that is for some appropriate functional combinations ... 
Fractional Integrodifferentiation and Toeplitz Operators with Vertical Symbols
(Birkhäuser, 2020)We consider the socalled vertical Toeplitz operators on the weighted Bergman space over the half plane. The terminology “vertical” is motivated by the fact that if a is a symbol of such Toeplitz operator, then a(z) depends ... 
On the powers of quasihomogeneous Toeplitz operators
(Springer, 2021)In this article, a fixed point iterative scheme involving Green's function is applied to reach a solution for the buckling of nanoactuators under nonlinear forces. Our solution is convergent. The nanoactuators problem ... 
A Numerical Investigation of the Buckling of Doubly Clamped NanoActuators Governed by an IntegroDifferential Equation
(Springer, 2022)In this article, a fixed point iterative scheme involving Green's function is applied to reach a solution for the buckling of nanoactuators under nonlinear forces. Our solution is convergent. The nanoactuators problem ... 
On 1absorbing primary ideals of commutative rings
(World Scientific, 20190430)Let R be a commutative ring with nonzero identity. In this paper, we introduce the concept of 1absorbing primary ideals in commutative rings. A proper ideal I of R is called a 1absorbing primary ideal of R if whenever ... 
On Weakly 1Absorbing Primary Ideals of Commutative Rings
(World Scientific, 2022)Let R be a commutative ring with 1 ≠ 0. In this paper, we introduce the concept of weakly 1absorbing primary ideal which is a generalization of 1absorbing primary ideal. A proper ideal I of R is called a weakly 1absorbing ... 
On nsemiprimary ideals and npseudo valuation domains
(Taylor and Francis, 20200814) 
The nzerodivisor graph of a commutative semigroup
(Taylor and Francis, 20220416)Let S be a (multiplicative) commutative semigroup with 0, Z(S) the set of zerodivisors of S, and n a positive integer. The zerodivisor graph of S is the (simple) graph Γ(S) with vertices Z(S) ∗ = Z(S) \ {0}, and distinct ...