ABSTRACT In this work a deterministic and stochastic model is developed to investigate the deterministic and stochastic model of dynamics of Ebola virus. The model includes susceptible, exposed, infected, quarantined and removed or recovered individuals. The model used in this work is based on a deterministic model. The Chowell (2015) work on early detection of Ebola is modified by introducing an assumption that the quarantined class is totally successful and cannot infect the susc...
This Project primarily falls into the field of Linear Functional Analysis and its Applications to Eigenvalue problems. It concerns the study of Compact Linear Operators (i.e., bounded linear operators which map the closed unit ball onto a relatively compact set) and their spectral analysis applicable to Fourier Analysis and to the solvability of Fredholm Integral Equations, linear elliptic Partial Differential Equations (PDEs) with the Dirichlet boundary condition, Sturm-Liouville problems, a...
ABSTRACT We consider classical Finite Difference Scheme for a system of singularly perturbed convection-diffusion equations coupled in their reactive terms, we prove that the classical SFD scheme is not a robust technique for solving such problem with singularities. First we prove that the discrete operator satisfies a stability property in the l2-norm which is not uniform with respect to the perturbation parameters, as the solution blows up when the perturbation parameters goes to zero. An e...
ABSTRACT In this thesis, we treated a Standard Finite Difference Scheme for a singularly perturbed parabolic reaction-diffusion equation. We proved that the Standard Finite Difference Scheme is not a robust technique for solving such problems with singularities. First we discretized the continuous problem in time using the forward Euler method. We proved that the discrete problem satisfied a stability property in the l∞ − norm and l2 − norm which is not uniform with respect to the pertu...
This project concerns Evolution Equations in Banach spaces and lies at the interface between Functional Analysis, Dynamical Systems, Modeling Theory and Natural Sciences. Evolution Equations include Partial Dierential Equations (PDEs) with time t as one of the independent variables and arise from many elds of Mathematics as well as Physics, Mechanics and Material Sciences (e.g., Systems of Conservation Law from Dynamics, Navier-Stokes and Euler equations from Fluid Mechanics, Diusion equation...
ABSTRACT This thesis is a contribution to Control Theory of some Partial Functional Integrodifferential Equations in Banach spaces. It is made up of two parts: controllability and existence of optimal controls.
ABSTRACT Let E be a uniformly convex and uniformly smooth real Banach space and E ∗ be its dual. Let A : E → 2 E∗ be a bounded maximal monotone map. Assume that A−1 (0) 6= ∅. A new iterative sequence is constructed which converges strongly to an element of A−1 (0). The theorem proved, complements results obtained on strong convergence of the proximal point algorithm for approximating an element of A−1 (0) (assuming existence) and also resolves an important open question. Further...
INTRODUCTION Questions about controllability and stability arise in almost every dynamical system problem. As a result, controllability and stability are one of the most extensively studied subjects in system theory. A departure point of control theory is the dierential equation
The cardinal goal to the study of theory of Partial Differential Equations (PDEs) is to insure or find out properties of solutions of PDE that are not directly attainable by direct analytical means. Certain function spaces have certain known properties for which solutions of PDEs can be classified. As a result, this work critically looked into some function spaces and their properties. We consider extensively, L p − spaces, distribution theory and sobolev spaces. The emphasis is made on sob...
ABSTRACT Let E be a real normed space with dual space E ∗ and let A : E → 2 E∗ be any map. Let J : E → 2 E∗ be the normalized duality map on E. A new class of mappings, J-pseudocontractive maps, is introduced and the notion of J-fixed points is used to prove that T := (J − A) is J-pseudocontractive if and only if A is monotone. In the case that E is a uniformly convex and uniformly smooth real Banach space with dual E ∗ , T : E → 2 E∗ is a bounded J-pseudocontractive map wi...
The exploitation of nature's propensity offers us ample opportunities to achieve or deal with an optimal objective concerning constrained shape, volume, time, velocity, energy or gain. This vivifies the need to study Optimization Theory and related topics. In order to make the concepts clear, let us recall some keywords. Given a nonempty set X and a function f : X → R which is bounded below, computing the number
Abstract The goal of this thesis is to extend the notion of integration with respect to a measure to Lattice spaces. To do so the paper is first summarizing the notion of integration with respect to a measure on R. Then, a construction of an integral on Banach spaces called the Bochner integral is introduced and the main focus which is integration on lattice spaces is lastly addressed.
Abstract This paper investigates the task of scheduling jobs across several servers in a software system similar to the Enterprise Desktop Grid. One of the features of this system is that it has a specific area of action – collects outbound hyperlinks for a given set of websites. The target set is scanned continuously (and regularly) at certain time intervals. Data obtained from previous scans are used to construct the next scanning task for the purpose of enhancing efficiency (shortening ...
ABSTRACT The work of Osilike and Isiogugu, Nonlinear Analysis, 74 (2011), 1814-1822 on weak and strong convergence theorems for a new class of k-strictly pseudononspreading mappings in real Hilbert spaces is reviewed. We studied in detail this new class of mappings which is more general than the class of nonspreading mappings studied by Kurokawa and Takahashi, Nonlinear Analysis 73 (2010) 1562-1568. Many incisive examples establishing the relationship of the class of k-strictly pseudononspre...
Abstract Stochastic calculus has been applied to the problems of pricing financial derivatives since 1973 when Black and Scholes published their famous paper ”The pricing of options and corporate liabilities” in the journal of political economy. In this work, we introduce basic concepts of probability theory which gives a better understanding in the study of stochastic processes, such as Markov process, Martingale and Brownian motion. We then construct the Itˆo’s integral under stocha...