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

### Recent Submissions

• #### 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 ...
• #### Periodic Orbits in Periodic Discrete Dynamics ﻿

(Elsevier, 2008)
We study the combinatorial structure of periodic orbits of nonautonomous difference equations 𝒳ₙ₊₁ = 𝒇ₙ(𝒳ₙ) in a periodically fluctuating environment. We define the Ӷ-set to be the set of minimal periods that are not ...
• #### An Extension of Sharkovsy’s Theorem to Periodic Difference Equations ﻿

(Elsevier, 2006)
We present an extension of Sharkovsky’s Theorem and its converse to periodic difference equations. In addition, we provide a simple method for constructing a p-periodic difference equation having an r-periodic geometric ...
• #### Existence and stability of periodic orbits of periodic difference equations with delays ﻿

(World Scientific Publishing, 2008)
In this paper, we investigate the existence and stability of periodic orbits of the p-periodic difference equation with delays xₙ = f(n - 1, xₙ₋ₖ). We show that the periodic orbits of this equation depend on the periodic ...
• #### Coexistence and extinction in a competitive exclusion Leslie/Gower model with harvesting and stocking ﻿

(Taylor & Francis Online, 2009)
The principle of competitive exclusion states that when the competition between species is sufficiently strong, only the dominant species survives. In this paper, we examine the strategies of using stocking and harvesting ...
• #### On the periodic logistic equation ﻿

(Elsevier, 2006)
We show that the 𝒑-periodic logistic equation 𝒳ₙ₊₁ = μₙ mod 𝒑𝒳ₙ(1 - 𝒳ₙ) has cycles (periodic solutions) of minimal periods 1; 𝒑; 2𝒑; 3𝒑; …. Then we extend Singer’s theorem to periodic difference equations, and use ...