Physical Sciences and Mathematics Commons^™

Sums Of Kth Powers In The Ring Of Polynomials With Integer Coefficients, Ted Chinburg, Melvin Henriksen

All HMC Faculty Publications and Research

A working through of two theorems.

Suppose R is a ring with identity element and k is a positive integer. Let J(k, R) denote the subring of R generated by its kth powers. If Z denotes the ring of integers, then G(k, R) = {a ∈ Z: aR ⊂ J(k, R)} is an ideal of Z.

Mixed Nonderivative Algorithms For Unconstrained Optimization, Roger Ellis Lessman

Doctoral Dissertations

"A general technique is developed to restart nonderivative algorithms in unconstrained optimization. Application of the technique is shown to result in mixed algorithms which are considerably more robust than their component procedures. A general mixed algorithm is developed and its convergence is demonstrated. A uniform computational comparison is given for the new mixed algorithms and for a collection of procedures from the literature"--Abstract, page ii.

A New Approach To The Method Of Nonlinear Variation Of Parameters, A. Richard Mitchell, M. E. Lord

Mathematics Technical Papers

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 the classical variation of constants formula for linear systems, Alekseev [1] obtained a variation of constants formula for nonlinear systems. In [2], Lakshmikantham developed a nonlinear variation of constants formula for a scalar differential equation whose unperturbed term is of variable separable type, under rather mild assumptions. In this paper, we wish to study the general problem under weaker assumptions. Our approach is parallel to the classical one and yields two different formulas, one …

On Massera Type Converse Theorem In Terms Of Two Different Measures (0), V. Lakshmikantham

Mathematics Technical Papers

The importance of uniform asymptotic stability in studying the stability properties of perturbed motions needs no emphasis. The converse theorem of Massera which results from uniform asymptotic stability has been widely used in perturbation theory (See [1,2,0]).Very recently [31 this powerful theorem has been fruitfully employed to investigate bifurcation problems and seems to have much future in that direction. The advantage of studying stability properties by means of two different measures, as given by Movehan [41 , is well-known (See also [2,51 ). However, there does not exist a converse theorem of Massera type when uniform asymptotic stability holds in …

On The Existence Of Solutions Of Differential Equations And Zeros Of Operators In K-Banach Spaces, Evin Bronson, R. L. Tennison, A. Richard Mitchell

Mathematics Technical Papers

The theory of existence of solutions of differential equations in a Banach space employing norm as a measure is sufficiently well known [5, 6, 8, 9]. Also utilizing this theory one can prove the existence of zeros of operators [2, 7, 8, 9, 11]. The advantage of using a generalized norm as a candidate in discussing the qualitative theory of differential equations is also known [1]. These thoughts naturally lead to the use of cone-valued norms as a measure since this approach unifies the existing theories as well as offers a more flexible mechanism for applications. In this paper, we …

Fixed Point Theorms Of Operators With Ppf Dependence In Banach Spaces, Stephen R. Bernfeld

Mathematics Technical Papers

In this paper we develop a theory of fixed points of a nonlinear operator, T, whose domain is the Banach space of continuous functions defined on an interval [a,b] with range in a Banach space E denoted by [see pdf for notation] and the range of the nonlinear operator T is in E. As we shall see delay differential equations form an important example of such a nonlinear operator. We shall obtain analogues of the contraction mapping principle, Krasnoselskii's fixed point theorem as well as a result on the convergence of iterations of quasi-nonexpansive mappings.

A Study Of Some Life Testing Distributions, Robert Marvin Smith

Doctoral Dissertations

"This dissertation is presented in publication form and consists of three articles. The first article considers a new life-testing distribution which has the property of possessing a failure rate function which can be U-shaped or exponentially increasing depending on the value of the shape parameter. In addition, this article considers generalized least squares type estimators for location-scale distributions, then uses these estimators in the analysis of the exponential-power distribution. Tables are provided for which inferences on the location and scale parameters and on the reliability can be obtained. The second article gives relationships between a goodness-of-fit statistic based on a …

A Heuristic Algorithm For The Multi-Terminal Vehicle Dispatch Problem Using The Modified Sweep Algorithm, Jerry George Johnson

Doctoral Dissertations

"A heuristic algorithm is developed for solving the multi-terminal vehicle dispatch problem. The demand points are first assigned to terminals using a scheme that minimizes the cost of each assignment. Single-terminal vehicle dispatch problems are then solved at each terminal using a heuristic procedure, called the Sweep Algorithm. A sequence of trial reassignments are then attempted in order to obtain further improvements in the overall solution. Eleven multi-terminal vehicle dispatch problems are presented and their solutions, derived by this procedure, are given.

Several changes are also proposed for the Sweep Algorithm in order to improve the solutions obtained and to …

A Note On Elongations Of Abelian Groups, Brendan Goldsmith

Articles

No abstract available.

Applications Of Metrics Over Tikonov Semifields And Fixed Points In Hilbert Spaces, John David Kubicek

Doctoral Dissertations

"For Non expansive mappings on locally convex spaces, sufficient conditions are given for the set of fixed points to be a Non expansive retract. Also, sufficient conditions are given for certain semigroups of asymptotically Non expansive mappings to have a common fixed point.

Several results concerning convergence of the sequence of iterates in metric spaces are generalized to Hausdorff uniform spaces.

In Hilbert spaces, sufficient conditions are given for convergence of a Mann iteration process of strictly quasi pseudo contractive mappings. An example is given to show the process does not, in general, converge for pseudo contractive mappings"-- Abstract, p. …

Application Of Separation Theorem For Hermitian Matrices, Thomas L. Markham

Faculty Publications

No abstract provided.

Class Groups Of Real Quadratic Number Fields, Paul B. Massell

Dissertations, Theses, and Capstone Projects

No abstract provided.

Proof Of A Conjecture Of Askey On Orthogonal Expansions With Positive Coefficients, William F. Trench

William F. Trench

No abstract provided.

Oscillation Properties Of Perturbed Disconjugate Equations, William F. Trench

William F. Trench

No abstract provided.

A Sufficient Condition For Eventual Disconjugacy, William F. Trench

William F. Trench

No abstract provided.

Models For Estimating Psychiatric Bed Needs, Patricia A. Brenneman

Loma Linda University Electronic Theses, Dissertations & Projects

Inland Counties Comprehensive Health Planning Council wished to estimate the psychiatric bed needs by type (such as state hospitals, board and care homes, etc.) in San Bernardino County from the distributions of patient arrivals and of lengths of stay. A statistical description of the system during 1973 was considered the first step toward estimating future bed needs. A computer simulation model using IBM's programming language General Purpose Simulation System (GPSS) was developed and was found to be unsatisfactory.

Theorems were then developed for a statistical model, seeking to predict future bed needs. The most convenient of these theorems states that …

Distribution-Free Interval Estimation Of The Largest Α-Quantile, William E. Plouff

Masters Theses

No abstract provided.

Matrix Fields Over The Integers Modulo M, Robert M. Mcconnel, Jacob T. B. Beard Jr.

Mathematics Technical Papers

Let Zm denote the ring of integers modulo m and let [see pdf for notation] denote the complete ring of all [see pdf for notation] matrices over Zm under the usual matrix addition and multiplication. The primary purposes of this paper are to characterize and count all subfields of the ring [see pdf for notation] . Related results are given on field extensions in [see pdf for notation] of subfields of [see pdf for notation] . Partial results on subfields of [see pdf for notation] when R is an arbitrary finite commutative ring with identity are also given. Having basic …

Measurable Choice And The Invariant Subspace Problem, Edward Azoff, Frank Gilfeather

Department of Mathematics: Faculty Publications

In [1], J. Dyer, A. Pedersen and P. Porcelli announced that an affirmative answer to the invariant subspace problem would imply that every reductive operator is normal. Their argument, outlined in [1], provides a striking application of direct integral theory. Moreover, this method leads to a general decomposition theory for reductive algebras which in turn illuminates the close relationship between the transitive and reductive algebra problems.
The main purpose of the present note is to provide a short proof of the technical portion of [1] : that invariant subspaces for the direct integrands of a decomposable operator can be assembled …

A Polynomial Dual Of Partitions, Jacob T. B. Beard, Ann D. Dorris

Mathematics Technical Papers

Let [see pdf for notation] be a non-negative integral polynomial. The polynomial P(x) is m-graphical, and a multi-graph G a realization of P(x), provided there exists a multi-graph G containing exactly P(1) points where [see pdf for notation] of these points have degree i for [see pdf for notation]. For multi-graphs G,H having polynomials P(x), Q(x) and number-theoretic partitions (degree sequences) [see pdf for notation], the usual product P(x)Q(x) is shown to be the polynomial of the Cartesian product [see pdf for notation], thus inducing a natural product [see pdf for notation] which extends that of juxtaposing integral multiple copies …

On The Method Of Vector Lyapunov Functions, V. Lakshmikantham

Mathematics Technical Papers

The method of vector Lyapunov functions consists of employing several Lyapunov-like functions and the theory of vectorial differential inequalities. This general comparison technic leads to a more flexible mechanism to study the qualitative properties of nonlinear differential systems. This method is also effective in discussing interconnected dynamical systems where a construction of a single Lyapunov function is difficult. However, an unpleasant fact in this approach is the requirement of quasimonotone property of the comparison system. An idea to get around this will be indicated which might be useful in applications. Also, an extension of this technic to abstract cones will …

On The Theory Of Hamiltonian Graphs, Linda M. Lesniak

Dissertations

No abstract provided.

The Automorphism Group Of The Wreath Product Of Finite Groups, Kenneth G. Hummel

Dissertations

No abstract provided.

Finite Topologies And Boolean Matrices, Jon Michael Kelley

Morehead State Theses and Dissertations

A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in the Department of Mathematics at Morehead State University by Jon Michael Kelley in July of 1974.

On The Redundancy Of Monotony Assumption, V. Lakshmikantham

Mathematics Technical Papers

It is well known that all the results in integral inequalities of Bellman-Gronwall-Reid type demand an assumption of monotony on the functions involved. Since the corresponding theory of differential inequalities does not require the monotonic assumption, it is believed that this extra condition is due to the technics employed rather than the necessity. It is also well known that in proving the convergence of successive approximations, it becomes crucial to suppose an additional restriction of monotony on the functions satisfying uniqueness criteria. The question whether this additional assumption is really needed has been open for many years. This problem was …

Existence And Comparison Results For Differential Equations In A Banach Space, V. Lakshmikantham

Mathematics Technical Papers

The study of the Cauchy problem for differential equations in a Banach space has taken two different directions. One direction is to find compactness type conditions that guarantee only existence of solutions and the corresponding results are extensions of the classical Peano's theorem. The other approach is to employ monotonicity (accretive or dissipative) type conditions that assure existence as well as uniqueness of solutions. In fact, this latter method shows that uniqueness conditions imply existence of solutions also [37] and therefore may be regarded as extensions of the classical Picard's theorem.

Differential Equations On Closed Subsets Of A Banach Space, V. Lakshmikantham

Mathematics Technical Papers

The problem of existence of solutions to the initial value problem [see pdf for notations], where [see pdf for notations], F is a locally closed subset of a Banach space E. Nonlinear comparison functions and dissipative type conditions in terms of Lyapunovlike functions are employed. A new comparison theorem is established which helps in surmounting the difficulties that arise in this general set-up.

A Technic In Perturbation Theory, G. S. Ladde, S. Leela, V. Lakshmikantham

Mathematics Technical Papers

A study of the effect of perturbations of differential equations depends on the method employed and on the nature of perturbations. One of the most used technics is that of Lyapunov method and the other is the nonlinear variation of parameters formula [3]. These methods dictate that we measure the perturbations by means of a norm and thus destroy the ideal nature, if any, of the perturbing terms. Recently an effort was made to correct this unpleasant situation [1,2]. In this paper, we wish to develop a new comparison theorem that connects the solutions of perturbed and unperturbed differential systems …

Is Mathematical Truth Time-Dependent?, Judith V. Grabiner

Pitzer Faculty Publications and Research

Another such mathematical revolution occurred between the eighteenth and nineteenth centuries, and was focused primarily on the calculus. This change was a rejection of the mathematics of powerful techniques and novel results in favor of the mathematics of clear definitions and rigorous proofs. Because this change, however important it may have been for mathematicians themselves, is not often discussed by historians and philosophers, its revolutionary character is not widely understood. In this paper, I shall first try to show that this major change did occur. Then, I shall investigate what brought it about. Once we have done this, we can …

Lyapunov-Like Vector Functions Using Pointwise Degenerate Systems As Comparison Functions, Bernard A. Asner, V. Lakshmikantham

Mathematics Technical Papers

The use of Lyapunov-like vector functions is recognized as an important tool for estimating the behavior of a dynamical system. In applications, one needs to determine a suitable comparison function which contains information or properties that can be used to obtain some information about the behavior of the dynamical system. In recent years, the remarkable property of pointwise degeneracy has been discovered for linear, autonomous, delay-differential equations. For this class of equations one knows that all solutions will reach a subspace in finite time and remain on the subspace thereafter. As this class of equations is particularly simple, it becomes …