Digital Commons Network^™

What Is Number?, Willis J. Alberda

Pro Rege

No abstract provided.

Some Aspects Of Topological Semigroup Acts And Machines., Kripasindhu Sikdar Dr.

Doctoral Theses

No abstract provided.

On A General Class Of Unbiased Ratio, Product, Ratio-Cum-Product And Regression Type Estimators., N. S. Sastry Dr.

Doctoral Theses

Probability enmpling methods ha ve extenaive a pplication in la rge- eca le agricultural and socio economic surve ys, Sampling is ale used in one or more stages of a census and sometimes as a mubstitute for a complete Census. Over the pa st four deca de s, confidence in the use of san pling and a ppreciation for the technique have stee dily grown thanks to the pi onee ring efforts of Neyman, Hansen, Hurwit z, Maha lanobis, Sukha tme, Cochran, Yate s and others.2. It is well known that the principa i problem of the theory of sampling …

Generalized Inverses Of Special Types Of Matrices., Rao Vara Prasada Pullepu Sree Satya Narayana Dr.

Doctoral Theses

Inverses, in the regular sense of the term, do not exist for singular square matrices and rectangular matrices. however for such matrices there exist matrices which satisfy many important properties similar to those of inverses of nonsingular matrices and for many purposes, can be used in the same way as regular inverses. These matrices are named generalised inverses (g-inverses) to distinguish then from the inverses of nonsingular matricos. Only since 1955 this field of study af generalized inverse was: invostigated systenatically and was expiorcd for nany beautiful and interesting results and applications though the concept of generalizod inverse was first …

Some Combinatorial Arrangements And Incomplete Block Designs Through Them., Anis Chandra Mukherjee Dr.

Doctoral Theses

The use and importance, in Statistical Experimental, of Incomplete Block Designs, particularly, Balanced Incomplete Block (BIB) Designs, Doubly Balanced Incomplete Block (DBIB) Designs and Partially Balanced Inçomplete Block (PBIB) Designs are well known. Several combinational arrangements, including the incidence matrices of these Incomplete Block Designs and association matrices associated with PBIB Designs are known to be of use in Design of Experiments. In this thesis, we consider the construction problems pertaining to some of these combinational arrangements and take up the problem of construction of BIB, DBIB and FBIB Designs through them. The combinational arrangements studied in the thesis have, …

On Some Problems Of Sequenting And Grouping., T. S. Arthanari Dr.

Doctoral Theses

The problems of sequencing arise in almost all walks of life. Theory of scheduling deals with such problems. Usually, these probl ems are stated in the literature in terms of jobs, machines, operations, penalties, due dates et cetera, that is, in the language of machine shops. The real life problems of In machine - shop job sequencing are of a complex nature. general, we consider processing n items on a certain group of machines, so as to optimize certain objective, subject to various cons traints on precedence, machine availability, due date and so on. The job sequencing problems are includ …

On The Existence Of Zeros Of Lyapunov-Monotone Operators, S. Leela, V. Lakshmikantham

Mathematics Technical Papers - Archive

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 nonlinear operators. The operator T has a zero if and only if the initial value problem [see pdf for notation],has a constant solution. If T is a monotone operator then (1.1) has a unique solution [see pdf for notation] defined on [see pdf for notation] and the solution operator [see pdf for notation] is nonexpansive for all [see pdf for notation]. Imposing further assumptions one can show that U(t) must have …

The Geometry Of Symmetric Loops, Hussein M. Karanda

Tanzania Journal of Science

This paper is intended to deal with the geometry of locally analytic loops. In it we will show which loops generate symmetric spaces, the connection between the constructions of Sabinin and Loos, and examples of symmetric loops. The main results of these articles were published in 1972 (Karanda 1972).

An Iteration Formula For Finding Roots Of Equations, R. W. P. Masenge

Tanzania Journal of Science

We seek the roots of the equation f(x) = 0.

Univalence Of Derivatives Of Functions Defined By Gap Power Series, S. M. Shah, S. Y. Trimble

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.

A Coefficient Inequality For Convex Univalent Functions, S. Y. Trimble

Mathematics and Statistics Faculty Research & Creative Works

A short proof of formula presented is given for normalized convex univalent functions. © 1975, American Mathematical Society.

On Functional Equations Related To Mielnik's Probability Spaces, C. F. Blakemore, Caslav V. Stanojevic

Mathematics and Statistics Faculty Research & Creative Works

It is shown that the method used by C. V. Stanojevic to obtain a characterization of inner product spaces in terms of a Mielnik probability space of dimension 2 does not admit a generalization to dimension n > 2. © 1975 American Mathematical Society.

Untitled (Subject: Measuring Sound), Richard C. Heyser

Unpublished Writings

In this essay, Richard C. Heyser explains his opinions and experiences on the measurement of sound. Heyser addresses the need to standardize language when addressing sound observations and discusses subjective perceptions of sound.

A Note On Elongations Of Abelian Groups, Brendan Goldsmith

Articles

No abstract available.

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.

The Absolute Continuity Of Phase Operators, Joanne Dombrowski, G. H. Fricke

Mathematics and Statistics Faculty Publications

This paper studies the spectral properties of a class of operators known as phase operators which originated in the study of harmonic oscillator phase. Ifantis conjectured that such operators had no point spectrum. It was later shown that certain phase operators were, in fact, absolutely continuous and that all phase operators at least had an absolutely continuous part. The present work completes the discussion by showing that all phase operators are absolutely continuous.

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 - Archive

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 - Archive

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

Mathematics Technical Papers - Archive

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 - Archive

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 …

Stiefel-Whitney Homology Classes And Bordism, Ethan Akin

Mathematics and Statistics Faculty Research & Creative Works

We develop the theory of mod 2 Stiefel-Whitney homology classes for Euler polyhedral. We then describe a simple method of obtaining pJ. bordism theories. Finally, we define the ungraded bordism theory of Euler spaces and show that it is isomorphic to ordinary total homology. © 1975 American Mathematical Society.

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

Dissertations, Theses, and Capstone Projects

No abstract provided.

A Study Of Several Substitution Ciphers Using Mathematical Models., Wanda Louise Garner

Masters Theses

"This paper will consider vector and matrix representations for several polyalphabetical substitution ciphers. Classical ciphers such as the Vigenère, the True Beaufort, the Variant Beaufort, and the autokey will be included. We shall also discuss ways to mathematically vary a substitution cipher. In addition, we shall employ our mathematical representations to decipher a fixed matrix substitution cipher"--Abstract, p. ii

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

Faculty Publications

No abstract provided.

A Blocked Orthogonalization Method For Nonlinear Regression, Daniel C. St. Clair

Doctoral Dissertations

"The blocked orthogonalization algorithm for nonlinear regression developed in this work results from a study of matching problems having certain identifiable characteristics with algorithms which exploit those characteristics. The new algorithm represents an extension of an earlier algorithm by D. S. Grey using a blocked orthogonalization technique proposed by R. E. von Holdt. The result is a generalization of the Grey and the Gauss-Hartley algorithms which maintains the desirable properties of these algorithms while avoiding their more serious limitations. The new algorithm was found to be quite effective for solving problems in which the parameters in the model under consideration …

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 …

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. …

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 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 Diagnostic-Prescriptive Procedure For Teaching Adolescent Dyscalculics, Constance Ellingson Byrnes

Dissertations and Theses @ UNI

A procedure of individual diagnosis and educational prescription was developed for classroom teachers in the regular school program. A means of gathering and managing data including the use of task analysis was recommended. The procedure was demonstrated in selected case studies. A five-part model was developed to systematically diagnose the learning problem manage the information gathered in the diagnosis, and present a prescription or teaching strategy to remediate the errors. Step I was the diagnosis of mathematical errors. Samples of mathematical computation were collected. Errors were selected for prescription if the student made systematic errors and if a series of …