Mathematics
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Item STUDIES IN THE THEORY OF MULTIPLIERS WITH APPLICATIONS TO SEMIGROUPS OF OPERATORS(1974-08) ADEWOYE, T. O.This thesis divides naturally into two parts. The first half is a study of the general theory of multipliers, while the second half deals with applications of the theory of multipliers to the theory of semigroups of operators defined on a Banach spice. We study the multiplier problem for an abstract Hilbert space li, and generalise to H certain important results established for La(G)-multipliers (Larsen [12], Hewitt and Ross [8]). A significant result of this study is the Identification of certain projection operators on L2(G) which are, in several respects. Like the translation operators on Ls (G). We also discuss the restricted multiplier problem for the Banach algebra L1(G) of all absolutely integrable complex-valued functions defined on a compact group G, and we obtain results which are analogous to those obtained by Brainerd and Edwards [1] for L1 (G), where G is a locally compact abelian group. In connection with, semigroups of operators, we discuss, in the context of various Banach spaces, the representation of the multipliers which arise semigroups of operators on these Banach spaces. In this respect, we extend the results of Hille and Phillips [10] proved for the circle group (and generalised to compact abelian groups by Olubummo A. and Babalola V.A. [13]) to certain Banach spaces which are not even function spaces. All these results put together provide a good link between the theory of multipliers for a Banach space and the theory of semigroups of operators on the Banach space.Item Units of burnside rings of cyclic groups(Faculty of Science, University of Ibadan, Nigeria, 1999) Alawode, M. A.Item Existence results for some interval differential equations(American Mathematical Society, 2000) Arawomo, P. O.This paper is concerned with the problem of existence of solutions to interval differential equations which result from attempts to provide a concide interval solution to some differential equations with inexact data or parameters contained in an interval. An extension of the interval iterative scheme of Moore is used to establish the main results which include those of Sveloslav Merkov’s.Item Units of burnside rings of elementary abelian 2-groups(Academic Press, 2001) Alawode, M. A.Item A connection between units of burnside rings and the exterior algebra of elementary abelian 2-groups(Academic Press, 2001) Alawode, M. A.Item An interval analytic method in constructive existence theorems for initial value problems(Dynamic Publishers, 2002) Arawomo, P. O.; Akinyele, O.The method of interval analysis is employed to show that the solution, if it exists, of a first order initial value problem is majorised by an interval function whose end- functions satisfy some prescribed conditions. An interval operator is constructed and shown to be a contraction on the majorising interval function. Using this operator, the existence and uniqueness of the solution is established.Item On the number of cyclic quotients of some abelian p-groups(2007-11) EniOluwafe, M.We determine in this paper, the precise number of cyclic quotients of Abelian p-groups of exponent p and rank r > 1; / = 1 and 2Item Vectorial Mechanics(Distance Learning Centre, University of Ibadan, 2008) EniOluwafe M.Vectors in space are the three-dimensional analog of vectors in the plane and are sub ject to the same rules of addition, subtraction, and scalar multiplication that govern vectors in the plane. We shall discuss length or magnitude and direction of vectors.Item Algebra 1(Distance Learning Centre, University of Ibadan, 2008) EniOluwafe M.We shall expose the meaning of a set and state the different ways of naming a set. We shall also reveal the different types of sets, subsets, equality of sets and the universe of discourse. We shall then interact various sets which belong to the same universe, using the definitions of union, intersection, power set, complements, relative complements and symmetric difference to form new sets. Geometry representation of sets shall be presented in the form of Venn diagrams which will then be used in solving problems on sets. We also study some similarities of algebra of numbers to algebra of set theory and give a theorem on the number of elements in setsItem Stability results for the solutions of a certain third order nonlinear differential equation(Global Publishing Company, 2008) Ademola, T. A.; Ogundiran, M. O.; Arawomo, P. O.; Adesina, O. A.The paper is concerned with the uniform asymptotic stability for all solutions of a third order nonlinear differential equation (1.1). Sufficient conditions under which all solutions x(t), its first and second derivatives tend to zero as t —∞ are givenItem On the stability and ultimate boundedness of solutions for certain third order differential equations(Science Publications, 2008) Ademola, T. A.; Arawomo, P. O.With respect to our observation in the relevant literature, work on stability and boundedness of solution for certain third order nonlinear differential equations where the nonlinear and the forcing terms depend on certain variables are scare. The objective of this study was to get criteria for stability and boundedness of solutions for these classes of differential equations. Approach: Using Lyapunov second or direct method, a complete Lyapunov function was constructed and used to obtain our results. Results: Conditions were obtained for: (i) Uniform asymptotic stability and, (ii) Uniform ultimate boundedness, of solutions for certain third order non-linear non-autonomous differential equations. Conclusion: Our results do not only bridge the gap but extend some well-known results in the literature.Item On the precise order of unit groups of burnside rings of some finite abelian group(2008-05) EniOluwafe, M.We determine the precise order of B * (G), for G = ©i Gi, a bounded abelian 2-group, where G, is a direct sum of r copies of a cyclic group of order 2". The cases r = 1 and r = k, for some natural number k, are respectively considered in this paper.Item Boundedness and stability of solutions of some nonlinear differential equations of the third-order(2009) Ademola, T. A.; Arawomo, P. O.Sufficient conditions are established for the uniform ultimate boundedness of solutions of a third-order nonlinear differential equation (1). When, p(t,x,x',x")=0, criteria under which all solutions x(t), its first and second derivatives tend to zero as t→∞, are given.Item G-Theory of Group Rings for Groups of ElementsAbelian p-Groups(Department of Mathematics, University of Ibadan, 2009) EniOluwafe M.The formula for the G— theory of the group ring of a finite group G given by H. co. Lenstra is shown to be valid for groups of elementary abelian P— groups. Keywords: Group rings , G— theoryItem A VECTOR MATRIX APPROACH OF COUNTING CYCLIC QUOTIENTS OF SOME ABELIAN P-GROUPS(2009) Enioluwafe, M.We determine in this paper, the precise number of cyclic quotients of Abelian p-groups of exponent p i and rank r > 1, i = 1, 2, . . . , n for all natural numbers nItem Interval valued extension of wendroff type integral inequalities(Elsevier, 2009) Arawomo, P. O.In this paper we extend the theory of integral inequalities to interval valued mappings in two independent variables. By this, set inclusions are used instead of partial order relation and this enables us to obtain simultaneous upper and lower bounds instead of a pair of inequalities.Item G-theory of group rings for groups of elementary abelian p-groups(2009) EniOluwafe, M.Item Stability and ultimate boundedness of solutions to Certain third-order differential equations(2010) Ademola, T. A.; Arawomo, P. O.We employ Lyapunov’s second method to investigate uniform asymptotic stability, ultimate boundedness and uniform ultimate boundedness of solutions to certain third-order non-linear differential equations. Our results improve some well-known results in the literature.Item Stability and uniform ultimate boundedness of solutions of a third-order differential equation(Academic Publications, 2010) Ademola, T. A.; Arawomo, P. O.This paper is concerned with uniform ultimate boundedness of solutions of a third-order nonlinear differential equation (1.1). Sufficient conditions under which all solutions x(t), its first and second derivatives tend to zero as t —∞, when p(t,x,x',x") = 0, are presented.Item Boundedness results for a certain third order nonlinear differential equation(Elsevier Inc., 2010) Ademola, T. A.; Ogundiran, M. O.; Arawomo, P. O.; Adesina, O. A.Sufficient conditions for the existence of solutions to boundedness and ultimate boundedness problems associated to a certain third order nonlinear differential equation are given by means of the Lyapunov’s second method. The appropriate Lyapunov function is given explicitly. Our results complement some well known results on the third order differential equations in the literature.