Browsing Department of Mathematics and Statistics by Title
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Advances in periodic difference equations with open problems
(Springer, 2014)In this paper, we review some recent results on the dynamics of semidynamical systems generated by the iteration of a periodic sequence of continuous maps. In particular, we state several open problems focused on the ... 
Analytical study and parametersensitivity analysis of catalytic current at a rotating disk electrode
(IOP Publishing, 2020)A convectivediffusion equation with semiinfinite boundary conditions for rotating disk electrodes under the hydrodynamic conditions is discussed and analytically solved for electrochemical catalytic reactions. The ... 
Assessing test suites of extended finite state machines against model and code based faults
(John Wiley & Sons, 2021)Tests can be derived from extended finite state machine (EFSM) specifications considering the coverage of singletransfer faults, all transitions using a transition tour, alluses, edgepair, and prime path with side trip. ... 
Basin of Attraction through Invariant Curves and Dominant Functions
(Hindawi, 2015)We study a secondorder difference equation of the form 𝑧ₙ₊₁= 𝑧ₙ𝐹(𝑧ₙ₋₁) + ℎ, where both 𝐹(𝑧) and 𝑧𝐹(𝑧) are decreasing. We consider a set of invariant curves at ℎ = 1 and use it to characterize the behaviour of ... 
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 ... 
Can HighOrder Convergence of European Option Prices be Achieved with Common CRRType Binomial Trees?
(Springer, 2015)Considering European call options, we prove that CRRtype binomial trees systematically underprice the value of these options, when the spot price is not near the money. However, we show that, with a volatility premium to ... 
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 ... 
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 ... 
Control of cardiac alternans by mechanical and electrical feedback
(American Physical Society, 2014)A persistent alternation in the cardiac action potential duration has been linked to the onset of ventricular arrhythmia, which may lead to sudden cardiac death. A coupling between these cardiac alternans and the intracellular ... 
Convergence rate of regimeswitching trees
(Elseveir, 2016)Considering a general class of regimeswitching geometric random walks and a broad class of piecewise twice differentiable payoff functions, we show that convergence of option prices occurs at a speed of order 𝒪 (𝑛ᵝ), ... 
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 ... 
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 ... 
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 ... 
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 ... 
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 ... 
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 ... 
Embedding and global stability in periodic 2dimensional maps of mixed monotonicity
(Elsevier, 202202)In this paper, we consider nonautonomous second order difference equations of the form xn+1 = F(n, xn, xn−1), where F is pperiodic in its first component, nondecreasing in its second component and nonincreasing in its ... 
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 ), ... 
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 ... 
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 ...