Department of Mathematics and Statistics
Work by the faculty and students of the Department of Mathematics and Statistics
Recent Submissions
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Lower Semicontinuity in L¹ of a Class of Functionals Defined on BV with Caratheodory Integrands
(Hindawi Limited, 2021)We prove lower semicontinuity in 𝐿¹(Ω) for a class of functionals 𝒢 :𝐵𝑉(Ω) →ℝ of the form 𝒢(𝑢)=∫Ω𝑔(𝑥, 𝛻𝑢)𝑑𝑥 + ∫Ω𝜓(𝑥)𝑑|Dˢ𝑢| where 𝑔 :Ω⨉ℝᴺ→ℝ, Ω⊂ℝᴺ is open and bounded, 𝑔(.,𝑝) ∊ 𝐿¹(Ω) for each 𝑝 satisfies ... -
The Kumaraswamy Pareto IV Distribution
(Austrian Statistical Society, 2021)We introduce a new model named the Kumaraswamy Pareto IV distribution which extends the Pareto and Pareto IV distributions. The density function is very flexible and can be left-skewed, right-skewed and symmetrical shapes. ... -
Using Fractional Bernoulli Wavelets for Solving Fractional Diffusion Wave Equations with Initial and Boundary Conditions
(MDPI, 2021)In this paper, fractional-order Bernoulli wavelets based on the Bernoulli polynomials are constructed and applied to evaluate the numerical solution of the general form of Caputo fractional order diffusion wave equations. ... -
The role of vigilance on a discrete-time predator-prey model
(American Institute of Mathematical Sciences, 2022)The change of behaviors of prey in the form of vigilance significantly affects the dynamics of a predator-prey system. In this paper, we consider a discrete-time predator-prey model, where the vigilance of prey acts as a ... -
Embedding and global stability in periodic 2-dimensional maps of mixed monotonicity
(Elsevier, 2022-02)In this paper, we consider nonautonomous second order difference equations of the form xn+1 = F(n, xn, xn−1), where F is p-periodic in its first component, non-decreasing in its second component and non-increasing in its ... -
Joshi’s Split Tree for Option Pricing
(MDPI, 2020)In a thorough study of binomial trees, Joshi introduced the split tree as a two-phase binomial tree designed to minimize oscillations, and demonstrated empirically its outstanding performance when applied to pricing American ... -
Compound distributions for financial returns
(PLOS, 2020)In this paper, we propose six Student’s t based compound distributions where the scale parameter is randomized using functional forms of the half normal, Fréchet, Lomax, Burr III, inverse gamma and generalized gamma ... -
Ramsey numbers of partial order graphs (comparability graphs) and implications in ring theory
(De Gruyter, 2020)For a partially ordered set(A, ≤), letGA be the simple, undirected graph with vertex set A such that two vertices a ≠ ∈ b A are adjacent if either a ≤ b or b a ≤ . We call GA the partial order graph or comparability graph ... -
Weighted multimodal family of distributions with sine and cosine weight functions
(Cell Press, 2020)In this paper, the moment of various types of sine and cosine functions are derived for any random variable. For an arbitrary even probability density function, the sine and cosine moments are used to define new families ... -
Analytical study and parameter-sensitivity analysis of catalytic current at a rotating disk electrode
(IOP Publishing, 2020)A convective-diffusion equation with semi-infinite boundary conditions for rotating disk electrodes under the hydrodynamic conditions is discussed and analytically solved for electrochemical catalytic reactions. The ... -
On the dot product graph of a commutative ring II
(International Electronic Journal of Algebra, 2020)In 2015, the second-named author introduced the dot product graph associated to a commutative ring A. Let A be a commutative ring with nonzero identity, 1 ≤ n < ∞ be an integer, and R = A × A × · · · × A (n times). We ... -
Stability and bifurcation analysis of a discrete-time predator-prey model with strong Allee effect
(Taylor & Francis, 2020-03-16)In this paper, we investigate the impact of Allee effect on the stability of a discrete-time predator-prey model with a non-monotonic functional response. The proposed model supports the coexistence of two steady states, ... -
The effect of maps permutation on the global attractor of a periodic Beverton-Holt model
(Elsevier, 2020-04-01)Consider a p-periodic difference equation xn+1 = fn(xn) with a global attractor. How does a permutation [fσ(p−1), . . . , fσ(1), fσ(0)] of the maps affect the global attractor? In this paper, we limit this general question ... -
The impact of constant effort harvesting on the dynamics of a discrete-time contest competition model
(Wiley, 2017)In this paper, we study a general discrete–time model representing the dynamics of a contest competition species with constant effort exploitation. In particular, we consider the difference equation xn+1 = xnf(xn−k) − hxn ... -
Advances in periodic difference equations with open problems
(Springer, 2014)In this paper, we review some recent results on the dynamics of semi-dynamical systems generated by the iteration of a periodic sequence of continuous maps. In particular, we state several open problems focused on the ... -
Folding and unfolding in periodic difference equations
(Elseiver, 2014)Given a p-periodic difference equation xn+1 = fn mod p(xn), where each fj is a continuous interval map, j = 0, 1, . . . , p − 1, we discuss the notion of folding and unfolding related to this type of non-autonomous equations. ... -
Harvesting and stocking in discrete-time contest competition models with open problems and conjectures
(Palestine Polytechnic University, 2016)In this survey, we present a class of first and second-order difference equations representing general form of discrete models arising from single-species with contest competition. Then, we consider various harvesting/stocking ... -
The dynamics of some discrete models with delay under the effect of constant yield harvesting
(Elsevier, 2013)In this paper, we study the dynamics of population models of the form xn+1 = xnf(xn−1) under the effect of constant yield harvesting. Results concerning stability, boundedness, persistence and oscillations of solutions are ... -
The solution of a recursive sequence arising from a combinatorial problem in botanical epidemiology
(Taylor & Francis, 2013)One of the central problems in botanical epidemiology is whether disease spreads within crops in a regular pattern or follows a random process. In this paper, we consider a row of n plants in which m are infected. We then ... -
A new characterization of periodic oscillations in periodic difference equations
(Elsevier, 2011-11)In this paper, we characterize periodic solutions of p-periodic difference equations. We classify the periods into multiples of p and nonmultiples of p. We show that the elements of the set of multiples of p follow the ...
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