Browsing Department of Mathematics and Statistics by Issue Date
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On phiDedekind rings and phiKrull rings
(University of Houston, 2005)The purpose of this paper is to introduce two new classes of rings that are closely related to the classes of Dedekind domains and Krull domains. Let H = {R  R is a commutative ring with 1 and Nil(R) is a divided prime ... 
On phiMori rings
(University of Houston, 2006)A commutative ring R is said to be a phiring if its nilradical Nil(R) is both prime and comparable with each principal ideal. The name is derived from the natural map phi from the total quotient ring T(R) to R localized ... 
On the periodic logistic equation
(Elsevier, 2006)We show that the 𝒑periodic 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 ... 
Strong ring extensions andphipseudovaluation rings
(University of Houston, 2006)In this paper, we extend the concept of strong extensions of domains to the context of (commutative) rings with zerodivisors. We show that the theory of strong extensions of rings resembles that of strong extensions of domains. 
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 pperiodic difference equation having an rperiodic geometric ... 
Martingale problem for superprocesses with nonclassical branching functional
(Elsevier, 2006)The martingale problem for superprocesses with parameters (𝛏, Ф, 𝑘) is studied where 𝑘(𝒹𝑠) may not be absolutely continuous with respect to the Lebesgue measure. This requires a generalization of the concept of ... 
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 pperiodic difference equation with delays xₙ = f(n  1, xₙ₋ₖ). We show that the periodic orbits of this equation depend on the periodic ... 
Exercisability Randomization of the American Option
(Taylor & Frances Online, 2008)The valuation of American options is an optimal stopping time problem which typically leads to a free boundary problem. We introduce here the randomization of the exercisability of the option. This method considerably ... 
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 Ӷset to be the set of minimal periods that are not ... 
Some finiteness conditions on the set of overrings of a phiring
(University of Houston, 2008)Let H = {R  R is a commutative ring and Nil(R) is a divided prime ideal of R}. For a ring R in H with total quotient ring T(R), Let phi be the natural ring homomorphism from T(R) into R_Nil(R). An integral domain R is ... 
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 ... 
The Beverton–Holt model with periodic and conditional harvesting
(Taylor & Francis Online, 2009)In this theoretical study, we investigate the effect of different harvesting strategies on the discrete Beverton–Holt model in a deterministic environment. In particular, we make a comparison between the constant, periodic ... 
The Discrete BevertonHolt Model with Periodic Harvesting in a Periodically Fluctuating Environment
(Springer, 2010)We investigate the effect of constant and periodic harvesting on the BevertonHolt model in a periodically fluctuating environment. We show that in a periodically fluctuating environment, periodic harvesting gives a better ... 
Market Efficiency of Floating Exchange Rate Systems: Some Evidence from PacificAsian Countries
(Elsevier, 2011)This paper examines the random walk hypothesis (RWH) and the martingale difference hypothesis (MDH) for the Australian dollar and five Asian emerging currencies relative to three benchmark currencies. We use Wright’s (2000) ... 
A new characterization of periodic oscillations in periodic difference equations
(Elsevier, 201111)In this paper, we characterize periodic solutions of pperiodic 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 ... 
Convergence rate of the binomial tree scheme for continuously paying options
(Université du Québec à Montréal, 2012)Continuously Paying Options (CPOs) form a very natural class of derivatives for hedging risks coming from adverse movements of a continuously traded asset. We study the rate of convergence of CPOs evaluated under the ... 
A European option general firstorder error formula
(Cambridge, 2013)We study the value of European security derivatives in the BlackScholes model, when the underlying asset 𝛏 is approximated by random walks 𝛏(𝑛). We obtain an explicit error formula, up to a term of order 𝒪(𝑛⁻³/² ), ... 
A Global Attractor in Some Discrete Contest Competition Models with Delay under the Effect of Periodic Stocking
(Hindawi, 2013)We consider discrete models of the form 𝒳ₙ₊₁= 𝒳ₙ𝒇(𝒳ₙ₋₁) + 𝒉ₙ , where 𝒉ₙ is a nonnegative 𝒑periodic sequence representing stocking in the population, and investigate their dynamics. Under certain conditions on the ... 
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 ... 
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 ...