Physical Sciences and Mathematics Commons^™

Irrational Numbers And Reality, Arnold H. Veldkamp

Pro Rege

No abstract provided.

The Mathematician, The Historian, And The History Of Mathematics, Judith V. Grabiner

Pitzer Faculty Publications and Research

The historian's basic questions, whether he is a historian of mathematics or of political institutions, are: what was the past like? and how did the present come to be? The second question --how did the present come to be?-- is the central one in the history of mathematics, whether done by historian or mathematician. But the historian's view of both past and present is quite different from that of the mathematician. The historian is interested in the past in its full richness, and sees any present fact as conditioned by a complex chain of causes in an almost unlimited past. …

Interview Of Albert Tucker, Terry Speed, Evar Nering

About Harlan D. Mills

No abstract provided.

Symmetric Maps Of S^3 Onto A Homotopy 3-Sphere, Kenneth P. Johnson

Dissertations

No abstract provided.

Self-Dual Embeddings Of Graphs, Saul Stahl

Dissertations

No abstract provided.

Indegrees, Outdegrees, And The Hamiltonian Theme, John Roberts

Dissertations

No abstract provided.

Estimation Of Growth Curves By Least Square Splines, Dorothy Rybaczyk Pathak

Mathematics & Statistics ETDs

The primary object of this dissertation is to present some con­tributions to the theory of estimation of growth curves by least square splines in the presence of unknown unequal variances. The theoretical developments rest heavily on the standard least square theory and the theory of polynomial spline functions. A modifica­tion of the Aitken procedure of weighted least squares is used to estimate regression parameters. It is shown that this modification of the Aitken procedure does not unduly influence the nice least square properties of estimators so obtained; the estimators re­ main unbiased, consistent and asymptotically efficient.

The techniques developed in …

The Differentiability Of AX, J. A. Eidswick

Department of Mathematics: Faculty Publications

A "from scratch" proof of the differentiability of a^x, a > 0, is avoided by essentially all modern-day authors. A slick and popular way of handling the problem is to define a^x as e^x log a its differentiability and other properties following from that of the functions e^x and log x. Unfortunately, the usual definitions of e^x and log x involve relatively sophisticated ideas (e.g., integration or power series). Furthermore, the student, having heard of e, the natural logarithm base, at an early stage of his development, is hardly enlightened when he is …

A Simple Characterization Of Commutative Rings Without Maximal Ideals, Melvin Henriksen

All HMC Faculty Publications and Research

In a course in abstract algebra in which the instructor presents a proof that each ideal in a ring with identity is contained in a maximal ideal, it is customary to give an example of a ring without maximal ideals.

An Evaluation Of Truncated Sequential Test, Ryh-Thinn Chang

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The development of sequential analysis has led to the proposal of tests that are more economical in that the Average Sample Number (A. S. N.) of the sequential test is smaller than the sample size of the fixed sample test. Although these tests usually have a smaller A. S. N. than the equivelent fixed sample procedure, there still remains the possibility that an extremely large sample size will be necessary to make a decision. To remedy this, truncated sequential tests have been developed.

A method of truncation for testing a composite hypotheses is studied. This method is formed by mixing …

Generalizing Binary Operations, Dennis C. Smolarski

Mathematics and Computer Science

Most day to day calculations take place within the field of real numbers with the two binary operations of addition and multiplication. In this field, these two operations are definitionally independent of one another. However, if we approach binary operations from a different point of view, e.g. that of recursive formulae, we can develop multipli cation from addition by use of the concept of repeated addition. Along similar lines, we can develop exponentiation from multiplication by re peated multiplication. The next logical step would be to try to develop another binary operation based on repeated exponentiation.

Steenrod Homology And Operator Algebras, Jerome Kaminker, Claude Schochet

Mathematics Faculty Research Publications

The recent work of Larry Brown, R. G. Douglas, and Peter Fillmore on operator algebras has created a new bridge between functional analysis and algebraic topology. This note constitutes an effort to make that bridge more concrete.

What Is Number?, Willis J. Alberda

Pro Rege

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 …

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

Doctoral Theses

No abstract provided.

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, …

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 …

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 …

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.

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.

Multivalue Methods, Clayton V. Henrie

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Methods of solving ordinary differential equations with initial conditions are of a great importance to engineers and scientists. Many of these equations can be solved by well-known analytical techniques, but a greater number of physically significant differential equations cannot be so solved. Thus, the solutions of these equations must be approximated numerically. It is the purpose of this paper to investigate the techniques used in solving differential equations with initial conditions by "multivalue methods."

An Evaluation Of Bartlett's Chi-Square Approximation For The Determinant Of A Matrix Of Sample Zero-Order Correlation Coefficients, Stephen M. Hattori

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

The single equation least-squares regression model has been extensively studied by economists and statisticians alike in order to determine the problems which arise when particular assumptions are violated. Much literature is available in terms of the properties and limitations of the model. However, on the multicollinearity problem, there has been little research, and consequently, limited literature is available when the problem is encountered. Farrar & Glauber (1967) present a collection of techniques to use in order to detect or diagnose the occurrence of multicollinearity within a regression analysis. They attempt to define multicollinearity in terms of departures from a hypothesized …

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.

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

Faculty Publications

No abstract provided.

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 …

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

Dissertations, Theses, and Capstone Projects

No abstract provided.