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

The properties of graphs can be studied via the algebraic characteristics of its adjacency or Laplacian matrix. The second eigenvector of the graph Laplacian is one very useful tool which provides information as to how to partition a graph. In this thesis, we study spectral clustering and how to apply it in solving the image segmentation problem in computer vision.

Abstract In this thesis, an iterative algorithm for approximating the solutions of a variational inequality problem for a strongly accretive, L-Lipschitz map and solutions of a multiple sets split feasibility problem is studied in a uniformly convex and 2-uniformly smooth real Banach space under the assumption that the duality map is weakly sequentially continuous. A strong convergence theorem is proved.

Abstract This paper looks at the study of a derivation of a known inequality for spectral functions of products of exponentials using the Baker - Campbell - Hausdor for- mula. This known inequality is called the Golden-Thompson inequality. The Kalman and the Gramian matrices, Lyapunov equation and matrix exponen- tial, Hadamard's lemma and Duhamel formula as well as the trace inequality due to Araki-Lieb-Thirring are all considered in this work.

ABSTRACT In this work, necessary and sufficient conditions are investigated and proved for the controllability of nonlinear functional neutral differential equations. The existence, form, and uniqueness of the optimal control of the linear systems are also derived. Global uniform asymptotic stability for nonlinear infinite neutral differential systems are investigated and proved and ultimately, the Shaefers’ fixed point theorem is used to forge a new and farreaching result for the exi...

Abstract Chaos poses technical challenges to constrained Hamiltonian systems. This is an important topic for discussion, because general relativity in its Hamiltonian formulation is a constrained system, and there is strong evidence that it exhibits chaotic features. We review concepts in gauge systems and their association with Hamiltonian constraints, relational Dirac observables as gauge-invariant encodings of physical information, and chaos in unconstrained Hamiltonian systems. We then ...

Abstract We show that the normal Appell subgroup of the Riordan group is a pseudo ring under a multiplication given by the componentwise composition. We develop formulae for calculating the degree of the root in generating trees and we establish isomorphisms between the four groups : the hitting time, Bell, associated and the derivative which are all subgroups of the Riordan group. We have found the average number of trees with left branch length in the class of ordered trees and the Motzkin ...

Abstract Linear Quadratic Control Problems are control problems with a quadratic cost function and linear dynamic sytem and a linear terminal constraint. This work looks at linear quadratic control problems without terminal conditions. We will first look at the controllability and observability of linear dynamical systems and then establish the necessary conditons for the variation in the cost criterion to be nonnegative for strong perturbations in the control. These conditions are the first ...

ABSTRACT It is well know that many physically significant problems in different areas of research can be transformed into an equation of the form Au = 0, (0.0.1) where A is a nonlinear monotone operator from a real Banach space E into its dual E∗ . For instance, in optimization, if f : E −→ R ∪ {+∞} is a convex, Gˆateaux differentiable function and x ∗ is a minimizer of f, then f 0 (x ∗ ) = 0. This gives a criterion for obtaining a minimizer of f explicitly. However, most of th...

ABSTRACT This study was carried out to investigate the effects of teaching methods (Discovery and lecture method), gender and school location on the performance of secondary school students in mathematics. A proportionate random sample of 356 senior secondary students was drawn from 20 secondary schools from Kano central senatorial zone using Morgan and Krejcie (1970) table for determining sample size. The sample was drawn from urban/rural dichotomy and gender wise. The sampled students were...

ABSTRACT This dissertation presents a systematic and critical study of the fundamenta.lli of soft set theory which includes soft set operations, soft set relations and functions, soft matrices and their properties. In course of studying operations on soft sets, the complementation operation is strengthened, some new results on distributive and absorption properties with respect to various soft set operations are obtained,and soft set operations and their corresponding soft matrix operations a...

Abstract ln this work, the researchers consider the concept of Information Security by the application of firewall and encryption techniques. Also, the problem of explicitly exposing infonnation in transit is discussed. We developed several algorithms. Among the algorithms are those of random sequence and non-arithmetic sequence using modified ' generators for the problem to secure information that may pass through intermediate computers l inked in the Internet. Some of these algorithms emplo...

ABSTRACT A Krasnoselskii-type algorithm for approximating a common element of the set of solutions of a variational inequality problem for a monotone, k-Lipschitz map and solutions of a convex feasibility problem involving a countable family of relatively nonexpansive maps is studied in a uniformly smooth and 2-uniformly convex real Banach space. A strong convergence theorem is proved. Some applications of the theorem are presented.

The contribution of this project falls within the general area of nonlinear functional analysis and applications. We focus on an important topic within this area: Inequalities in Banach spaces and applications. As is well known, among all infinite dimensional Banach spaces, Hilbert spaces generally have simple geometric structures. This makes problems posed in them easier to handle, this is as a result of the existence of inner product, the proximity map, and the two characteristic identitie...

ABSTRACT The Pentagram map is a well notable integrable system that is dened on the moduli space of polygons. In 2005, Richard Evan Schwartz introduced certain polynomials called pentagram integrals (Monodromy invariants) of the pentagram map and dened certain associated integrals, the analogous rst integrals. Schwartz further studied in 2011 with S. Tabachnikov on how these integrals behave on inscribed polygons. They discovered that the integrals are equal for every given weight of polygon...