Browsing Department of Mathematics by Issue Date
Now showing items 21-40 of 570
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A New Approach to the Method of Nonlinear Variation of Parameters
(University of Texas at ArlingtonDepartment of Mathematics, 1975-01)**Please note that the full text is embargoed** ABSTRACT: As is well-known [3] the method of variation of parameters is a very useful tool in studying the properties of solutions of perturbed differential equations. Extending ... -
On the Existence of Zeros of Lyapunov-Monotone Operators
(University of Texas at ArlingtonDepartment of Mathematics, 1975-02)**Please note that the full text is embargoed** ABSTRACT: Consider a nonlinear operator T from a Banach space into itself. The study of the existence of zeros of T plays an important role in yielding fixed points of ... -
Block Diagonalization and Eigenvalues
(University of Texas at ArlingtonDepartment of Mathematics, 1975-03)**Please note that the full text is embargoed** ABSTRACT: Let A denote an Algebra with an identity element. Consider an [see pdf for notation] matrix [see pdf for notation] with a partitioning [see pdf for notation] where ... -
Unitary Perfect Polynomials Over GF(q)
(University of Texas at ArlingtonDepartment of Mathematics, 1975-03)**Please note that the full text is embargoed** ABSTRACT: For monic polynomials A(x), B(x) e GF[q,x], call B(x) a unitary divisor of A(x) provided (B(x),A(x)/B(x)) = 1 . The polynomial A(x) is called unitary perfect over ... -
Vector Lyapunov Functions and Perturbations of Nonlinear Systems
(University of Texas at ArlingtonDepartment of Mathematics, 1975-03)**Please note that the full text is embargoed** ABSTRACT: Two recent papers [2,3] have combined the techniques of the Lyapunov method and the nonlinear variation of parameters to study the effects of perturbations of ... -
Perfect Polynomials Over GF(q)
(University of Texas at ArlingtonDepartment of Mathematics, 1975-03)**Please note that the full text is embargoed** ABSTRACT: A monic polynomial [see pdf for notation] is called perfect over GF(q) if and only if the sum [see pdf for notation] of the distinct monic divisors in GF[q,x] of ... -
Statistical Analysis of Fourier Coefficients in a Restricted Harmonic Dial
(University of Texas at ArlingtonDepartment of Mathematics, 1975-04)**Please note that the full text is embargoed** ABSTRACT: Due to the physical nature of certain periodic data, the harmonic dial points (the Fourier coefficients obtained from harmonic analysis of the data) are sometimes ... -
On the Existence of Solutions of Differential Equations of Retarded Type in a Banach Space
(University of Texas at ArlingtonDepartment of Mathematics, 1975-06)**Please note that the full text is embargoed** ABSTRACT: The existence and uniqueness of solutions of differential equations of retarded type in a Banach space are considered under a monotonicity type condition. The tools ... -
Remarks on Nonlinear Contraction and Comparison Principle in Abstract Cones
(University of Texas at ArlingtonDepartment of Mathematics, 1975-06)**Please note that the full text is embargoed** ABSTRACT: The contraction mapping principle and the Schauder principle can both be viewed as a comparison of maps. For the former one has a condition of the type [see pdf for ... -
Maximal and Minimal Solutions and Comparison Principle for Differential Equations in Abstract Cones
(University of Texas at ArlingtonDepartment of Mathematics, 1975-06)**Please note that the full text is embargoed** ABSTRACT: Existence of maximal and minimal solutions for differential equations in abstract cones is established without requiring uniform continuity. Utilizing such a result ... -
On a Measure of Nonconvexity and Applications
(University of Texas at ArlingtonDepartment of Mathematics, 1975-06)**Please note that the full text is embargoed** ABSTRACT: The measure of noncompactness which was introduced by Kuratowski [8] (in 1930) has now become an important tool in nonlinear analysis (although its value in that ... -
On the Convergence of Successive Approximations for Quasi-Nonexpansive Mappings Through Abstract Cones
(University of Texas at ArlingtonDepartment of Mathematics, 1975-07)**Please note that the full text is embargoed** ABSTRACT: In a recent paper, Petryshyn and Williamson [4] investigated the convergence of successive approximations of quasi- nonexpansive mappings in a Banach space. This ... -
On the Zeros of Monotone Operators of Retarded Type in a Banach Space
(University of Texas at ArlingtonDepartment of Mathematics, 1975-09)**Please note that the full text is embargoed** ABSTRACT: Recent interest in the Cauchy problem for differential equations in a Banach space [9] has stimulated a similar interest for differential equations of a retarded ... -
A Survey of Techniques for Determining Lower Confidence Bounds on Series System Reliability Based on Subsystem Test Data
(University of Texas at ArlingtonDepartment of Mathematics, 1975-09)**Please note that the full text is embargoed** ABSTRACT: A problem of considerable interest and for which a great deal of research has been expended is that of determining lower confidence bounds on series system ... -
Structural Inference on Reliability in a Lognormal Model
(University of Texas at ArlingtonDepartment of Mathematics, 1975-12)**Please note that the full text is embargoed** ABSTRACT: The theory of structural inference, as developed by Fraser (1968), is based on a group-theoretic approach using invariant Haar measures to Fisher's fiducial theory. ... -
The Extendability and Uniqueness of Solutions of Ordinary Differential Equations
(University of Texas at ArlingtonDepartment of Mathematics, 1976)**Please note that the full text is embargoed** ABSTRACT: In a recent paper [1] the author obtained results on the extendability of solutions of perturbed differential equations. The question of the extendability of solutions ... -
On the Construction of a Norm Associated with the Measure of Noncompactness
(University of Texas at ArlingtonDepartment of Mathematics, 1976-02)**Please note that the full text is embargoed** ABSTRACT: It is shown that the bounded, nonempty subsets of a reflexive Banach space g can be imbedded in another Banach space B(E) in such a manner so that the measure of ... -
A Nonlinear Variation of Constants Method for Integro-Differential and Integral Equations
(University of Texas at ArlingtonDepartment of Mathematics, 1976-02)**Please note that the full text is embargoed** ABSTRACT: It is well known that a very important technique in obtaining the asymptotic behavior of solutions of linear and nonlinear ordinary differential equations ... -
The Method of Quasilinearization and Positivity of Solutions in Abstract Cones
(University of Texas at ArlingtonDepartment of Mathematics, 1976-03)**Please note that the full text is embargoed** ABSTRACT: The method of quasilinearization was first introduced by Bellman (Ref. 1) and was developed further by Kalaba (Ref. 2). More detailed information concerning the ... -
Fixed Point Theorems on Closed Sets Through Abstract Cones
(University of Texas at ArlingtonDepartment of Mathematics, 1976-03)**Please note that the full text is embargoed** ABSTRACT: Let D be a closed subset of a complete metric space (X,p). We seek (i) conditions upon which a map T : D -> X has a fixed point in D and (ii) the construction of ...