Let us first introduce some keywords that will enable us to specify our principal objective. Given a nonempty set X and a function f : X → R which is bounded below, computing the number
Abstract Key to Escherichia coli (E-coli) bacteria survival is its ability to direct its movement to greener pasture and flee harmful environment - also known as chemotaxis. This thesis focuses on the modelling of E-coli chemotaxis in twodimensions with emphasis on trying to understand the basic physics of how such a tiny microswimmer swim up a concentration gradient despite the enormous thermal fluctuations in its environment. E-coli strategically employs near straight swimming (also known ...
Abstract Timetabling presents an NP-hard combinatorial optimization problem which requires an efficient search algorithm. This research aims at designing a genetic algorithm for timetabling real-world school resources to fulfil a given set of constraints and preferences. It further aims at proposing a parallel algorithm that is envisaged to speed up convergence to an optimal solution, given its existence. The timetable problem is modeled as a constraint satisfaction problem (CSP) and a theor...
Abstract Let X be a uniformly convex and uniformly smooth real Banach space with dual space X∗ . Let F : X → X∗ and K : X∗ → X be bounded monotone mappings such that the Hammerstein equation u + KF u = 0 has a solution in X. An explicit iteration sequence is constructed and proved to converge strongly to a solution of the equation. This is achieved by combining geometric properties of uniformly convex and uniformly smooth real Banach spaces recently introduced by Alber with our met...
This project is mainly focused on the theory of Monotone (increasing) Operators and its applications. Monotone operators play an important role in many branches of Mathematics such as Convex Analysis, Optimization Theory, Evolution Equations Theory, Variational Methods and Variational Inequalities.
Abstract The power conversion efficiency of perovskite solar cells has risen from as low as 3.8% to as high as 19.3% in just five years with yet a projected value of over 20% in the next few years by experimentalists. Such a tremendous breakthrough is one of its kind in photo-voltaic research with thin film solar cells as the only major competitor. The light harvesting layer in these new devices has a crystalline structure called the perovskite structure which is capable of absorbing photons...
Abstract We propose DEVS-Driven Modeling Language (DDML), a graphical notation for DEVS [1] modeling and an Eclipse-based graphical editor, Eclipse-DDML. DDML attempts to bridge the gap between expert modelers and domain experts making it easy to model systems, and capture the static, dynamic, and functional aspects of a system. At the same time, it unifies CDEVS and P-DEVS models. DDML integrates excellent modeling concepts from powerful formalisms and glues them in one unique consistent fr...
ABSTRACT The study of variational inequalities frequently deals with a mapping F from a vector space X or a convex subset of X into its dual X 0 . Let H be a real Hilbert space and a(u, v) be a real bilinear form on H. Assume that the linear and continuous mapping A : H −→ H 0 determines a bilinear form via the pairing a(u, v) = hAu, vi. Given K ⊂ H and f ∈ H 0 . Then, Variational inequality(VI) is the problem of finding u ∈ K such that a(u, v − u) ≥ hf, v − ui, for all v ∈ ...
ABSTRACT Breast cancer is a prevalent disease that affects mostly women, an early diagnosis will expedite the treatment of this ailment. In recent times, Machine Learning (ML) techniques have been employed in biomedical and informatics to help fight breast cancer. This research work proposed an ML model for the classification of breast cancer. To achieve this we employed logistic regression (LR) and also compared our model’s performance with other extant ML models namely, Support Vector Ma...
This body of work introduces exterior calculus in Euclidean spaces and subsequently implements classical results from standard Riemannian geometry to analyze certain differential forms on a manifold of reference, which here is a symmetric ellipsoid in R n . We focus on the foundations of the theory of differential forms in a progressive approach to present the relevant classical theorems of Green and Stokes and establish volume (length, area or volume) formulas. Furthermore, we introduce the ...
ABSTRACT We propose a framework for formal analysis of DEVS Driven Modeling Language (DDML) models in order to assess and evaluate the properties of DDML models. This framework semantically maps the hierarchical levels of DDML: Input Output system (IOS), Input Output Relation Observation (IORO) and Coupled Network (CN) levels to corresponding formal methods: Labeled Transition System (LTS), Linear Temporal Logic (LTL) and Computation Tree Logic (CTL), and Communicating Sequential Processes (C...
ABSTRACT Malicious user requests pose a vicious threat to backend devices which execute them; more so, could result in the compromise of other user accounts, exposing them to theft and blackmail. It becomes imperative to sanitize such requests before they are treated by the servers as access to a single malicious request is enough to cause a disaster. A number of authors suggest that sanitizing models built on support vector machines guarantee optimum classification of malicious from non-mal...
ABSTRACT Let H be a real Hilbert space. Let K, F : H → H be bounded, continuous and monotone mappings. Let {un}∞ n=1 and {vn}∞ n=1 be sequences in E defined iteratively from arbitrary u1, v1 ∈ H by
Abstract The thesis presents the modeling and simulation of three types of lasers namely; Semicondoctor laser, Solid state laser and CO2 laser. The rate equations were derived and simulated to examine the dynamic behaviour of the three types of lasers under investigation. The result shows that the Semicondoctor laser has the longest latency period, highest intensity spikes and takes a longer time to come to relaxation oscillation (RO) while the CO2 laser has the shortest latency time, the lo...
Abstract This thesis presents an overview on the theory of stopping times, martingales and Brownian motion which are the foundations of stochastic modeling. We started with a detailed study of discrete stopping times and their properties. Next, we reviewed the theory of martingales and saw an application to solving the problem of "extinction of populations". After that, we studied stopping times in the continuous case and finally, we treated extensively the concepts of Brownian motion and th...