Physical Sciences and Mathematics Commons^™

Biometrics Of Bilateral Symmetry In Plants., T. Davis Dr.

Doctoral Theses

During the past ten deendes, observation rolating to ayune try, asymmatry, dis-oyame try, radlal symmetry, rotatiÉ”nal Bymne try, bilateral aymme try and ambidextry in the fields of bo tany, Boology, geology, chemiatry, eryatellography, physics, astronomy, engineering, mathematics, sunio, poetry and art vere recorded by various scientists. The prevent treatise is a sua- mary of an elaborato study on bilaterai syame try or microrinage symse try occurring in vari us plant organs. Unlike moet of the earlior reports, the problem here has been takled unified on a quantitative basis, thereby ereating situations where sophisti-cated techniques of statietios could be effectively employed. …

Stochastic Integro-Differential Equations Of Volterra Type, William J. Padgett, Chris P. Tsokos

Faculty Publications

No abstract provided.

Nonnegative Matrices Whose Inverses Are M-Matrices, Thomas L. Markham

Faculty Publications

A characterization of a class of totally nonnegative matrices whose inverses are M-matrices is given. It is then shown that if A is nonnegative of order n and A^-1 is an M-matrix, then the almost principal minors of A of all orders are nonnegative.

Flexible Algebras Of Degree Two, Joseph H. Mayne

Mathematics and Statistics: Faculty Publications and Other Works

All known examples of simple flexible power-associative algebras of degree two are either commutative or noncommutative Jordan. In this paper we construct an algebra which is partially stable but not commutative and not a noncommutative Jordan algebra. We then investigate the multiplicative structure of those algebras which are partially stable over an algebraically closed field of characteristic p A 2, 3, 5. The results obtained are then used to develop conditions under which such algebras must be commutative.

Linear Estimation: The Kalman-Bucy Filter, William Douglas Schindel

Graduate Theses - Mathematics

The problem of linear dynamic estimation, its solution as developed by Kalman and Bucy, and interpretations, properties and illustrations of that solution are discussed. The central problem considered is the estimation of the system state vector X, describing a linear dynamic system governed by

dx/dt = F(t)X(t) + G(t)U(t)

Y(t) = H(t)X(t) + V(t)

for observations of Y (system output), where V is a random observation-corrupting process, and U is a random system driving process.

An extension of the Kalman-Bucy filter to estimation in the absence of priori knowledge of the random process U and V is developed and illustrated.

Completions Of Lattices With Semicomplementation, Alan A. Bishop

Dissertations

No abstract provided.

On The Genus Of Hamiltonian Groups, Paul E. Himelwright

Masters Theses

No abstract provided.

Reducing Uncertainty, Richard C. Heyser

Unpublished Writings

Intended for audio engineers, Richard C. Heyser meant for this paper to bring attention to the misapplication of the theoretical concept, the Uncertainty Principle. Heyser argues that this concept has been "freely applied without regard to the errors which may result due to lack of understanding of its derivation."

Professor Leo Moser -- Reflections Of A Visit, Walter E. Mientka

Department of Mathematics: Faculty Publications

Professor Leo Moser' was known throughout the Mathematical Community as a significant researcher and excellent lecturer. I first met Leo during the Summer Research Institute in the Theory of Numbers held at the University of Colorado in 1959. After talking with him and hearing his lectures during the Institute, I felt that arrangements would have to be made in the near future for a visit to Nebraska. During the academic year 1962-63 while Professor Moser was on a lecture tour for the MAA, I invited him to present two research lectures to the Nebraska Section on May 3 and 4, …

Isopathic Graphs And Airport Graphs, Kim T. Rawlinson

Mathematics & Statistics ETDs

This paper explores two kinds of graphs, isopathic graphs and air­ port graphs. A distance property of graphs in general is also examined.

Isopathic graphs are graphs in which every maximal path has the same length. The major theorem of this section characterizes isopathic graphs as extended stars, bipartite or hamiltonian. There is then a discussion of the latter two classes of isopathic graphs.

At the end of Section I, there is an introduction to isopathic di­graphs, a natural concern after an exposure to isopathic graphs.

Airport graphs, more appropriately snob graphs, can be thought of in the following way. …

Convergence Of Bounds In Optimization, Pascal D. Mubenga

Dissertations

No abstract provided.

Discrete Approximations To Continuous Optimal Control Problems, Maurice L. Eggen

Dissertations

No abstract provided.

The Major Contribution Of Leibniz To Infinitesimal Calculus, Carolyn Rhodes

Honors Theses

A study of the work of Leibniz is of importance for at least two reasons. In the first place, Leibniz was not alone among great men in presenting in his early works almost all the important mathematical ideas contained in his mature work, In the second place, the main ideas of his philosophy are to be attributed to his mathematical work, not vice versa. He was perhaps, the earliest to realize fully and correctly the important influence of a calculus on discovery. The almost mechanical operations which one goes through when one is using a calculus enables one to discover …

The Regular Polyhedra: A Study In Visual Aids For Teaching Geometry, Sammye Halbert

Honors Theses

Traditionally, mathematics, past simple addition, subtraction, multiplication, and division, has been taught of as being so boring, irrelevant, and in short, one of the unavoidable evils of school. An advertisement in The Mathematics Teacher expressed the general attitude of many students when it said, "mathematics was invented by an old magician in the desert who, with the help of his talking monkey, bakes equations and cupcakes in the hot sun." It seems that many students think mathematics is just one problem after another that has some mystical answer floating around in the air somewhere. The object is to get that …

Contributions To Measure Theory., Merepalli Bhaskara Rao Dr.

Doctoral Theses

This thesis 1s devoted to a study of measures vith emplas sis on nonatonie nea sures. Me briefrly desoribe here the work carried out in various chapters. In Chapter 1, we study various aspects of nonatomic nea sures based on some characterisations obtained early in the Chapter. In Chapter 2, the problem - when a mixture of nonatoftic mea sures is nonatomic - is exanined. An example and rive sufficient conditions are given. In Chapter 3, we examine when a mixture of 1nvariant non-ergorlie mesures is non-ergodic. An example and three sufficient eonditions are given. In Chapter 4, we study …

Some Contribution To The Theory Applications And Computations Of Generalized Inverses Of Matrices., Pochiraju Bhimasankaram Dr.

Doctoral Theses

The origin of the concept of a generalized inverse dates back to as early as 1920 when Moore defined the generalized inverse of matrix which is equivalent toDefinition 1 (Moore) : Let A be a m >< n matrix over the field of complex numbers. Then a is the generalized Inverse of A if AG is the orthogonal projection operator projecting arbitrary vectors onto the column space of A and GA is the orthogonal projection operator projecting arbitrary sectors onto, the column space of G.Mod re (1935) discussed this concept and its properties in some detail. Tsong (1949a, 1949b, 1956) discussed about generalized 1nverses of operators in more general spaces and Bjerhammer (1951) discussed the generalized inverse of a matrix in connection with an application to geodetic calculations. Unaware of the work of Hoore and others, Penrose (1955) defined a generalized inverse of a matrix as follows :Definition 2 (Penrosel) : Let A be a m *n -matrix over the field of complex numbers. Then G is a generalized inverse of a if (i) AFA= A; (ii) GAG=G; (iii) (AG)*=AG and (iv) (GA)*-GA.Penrose (1955,1956) showed that for every matrix there exists a unique generalized inverse, discussed several of its important properties, gave applications to solution of matrix equations and suggested a practical method of computation of the generalised inverse.As was pointed out by Rado (1956) Moo res definition of generalized inverse is equivalent to that of Penrose, Such generalized inverse is called the Moore-Penrose inverse and A is used to denote the Moore-Penrose inverse of A.Rao (1955), unaware of the earlier or contemporary Work, constructed a pseudo-inverse of a matrix which he used in some least squares computations, In a paper in 1962, he defined a generalized inverse (g-inverse) as follows, proved some interesting properties and gave applications of g-inverses to Mathomatical Statistics.Definition 3 (Rao) : Lot A be am x n matrix, Then a n >< m matrix. Then a n >< m matrix G is a g-inverse of A if x = Gy is a solution of the linear system Ax = y whenever it is consistent.A g-inverse if u matrix (in the sense of Rao) is in general not unique, As 1s easily observed (from definitions 2 and 4) the class of all g-inverses of a matrix A contains A*. Rạo (1965, 1967) developed a calculus of g-inverses, classified the g-inverses according to their use and according to the proporties they possess similar to those of the inverse of a nonsingular matrix and suggested further applications to Mathematical Statistics. Mitra (1968a, 1968b) gave an equivalem definition of a g-inverse, developed further calculus of z-inverses, used g-invorses to solve some matrix equations of interest and explored the possibilities of some new classes of g-inverses with applications. In a series of papers, and a monograph Mitra and Rao (1968, 1970) pursued the research on generalized inverses of matrix's and their applications to various scientific disciplines.

Mathematical Foundations For Structured Programming, Harlan D. Mills

The Harlan D. Mills Collection

No abstract provided.

Some Quasi-Uniform Space Examples, Troy L. Hicks, J. W. Carlson

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.

The Jordan Canonical Form, Richard A. Freeman

Legacy ETDs

No abstract provided.

Radicals And Torsion Theories In Locally Compact Groups, Robert R. Bruner

Mathematics Faculty Research Publications

In this paper we will study the properties of locally compact Abelian Hausdorff topological groups (hereafter known as LCA groups) by means of their mapping properties. The results contained herein are an outgrowth of work done by Professor Armacost [Al] on "sufficiency classes" of LCA groups. The sufficiency class S\textunderscore(H) of an LCA group H is the class of all LCA groups G such that there are sufficiently many continuous homomorphisms from G to H to separate the points of G. This condition is easily seen to be equivalent to the requirement that ∩ker(f)=0, where f ranges over all elements …

Nonrandom Characteristics Of Common Stock Prices, Donald Leroy Gaitros

Doctoral Dissertations

"This study presents an application of operations research techniques to the development of stock price generation and simulation models to aid in the understanding of price movement. Relationships between stock price and volume and stock price and market averages which follow descernible trends and patterns are discovered. Technical trading rules are developed based on these relationships which empirically have shed doubt on the random walk hypothesis of price movement. This in turn gives evidences that technical analysis can be an aid to price forecasting"--Abstract, page ii.

Statistical Studies Of Various Time-To-Fail Distributions, James Addison Eastman

Doctoral Dissertations

"Three models are considered that have U-shaped hazard functions, and a fourth model is considered that has a linear hazard function. Several methods for estimating the parameters are given for each of these models. Also, various tests of hypotheses are considered in the case of the model with the linear hazard function. One of the models with a U-shaped hazard function has a location and a scale parameter, and it is proved in general that any other parameters in a distribution of this type are distributed independently of the location and scale parameters.

A new method used to estimate the …

Classifications Of Plane Continua, Steven Ray Matthews

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

In the course of studying continua in the plane it has been asked if a given continuum has uncountably many disjoint duplications in the plane, and if so, what are the consequences of the existence of such a collection. The object of this paper is to study these problems and to develop some machinery useful in their resolution. In Section I, we review the definition of convergence and homeomorphic convergence of point sets in a metric space S. We then consider the space, π of all continuous functions from a compact metric space P to a separable metric space Q …

Quasi-Pseudometrics Over Tikhonov Semifields And Fixed Point Theorems, Ronald Evans Satterwhite

Doctoral Dissertations

"It has been shown that topological spaces are characterized as quasi-pseudometric spaces over some Tikhonov semifield.

Sufficient conditions are given for a T₁ space to be metrizable over some Tikhonov semifield.

Completely regular (uniform) spaces are characterized as pseudornetric spaces over some Tikhonov semifield.

Certain metric, pseudornetric, quasi-metric, quasipseudometric spaces over a Tikhonov semifield are shown to be respectively metric, pseudometric, quasi-metric, quasipseudometric spaces in the usual sense.

Several results from fixed point theory in the metric space setting are generalized to the setting of completely regular (uniform) Hausdorff spaces."--Abstract, page ii.

Elementary Length Topologies Constructed Using Pseudo-Norms With Values In Tikhohov Semi-Fields, Jackie Ray Hamm

Doctoral Dissertations

"Elementary length topologies defined on normed and pseudo-normed linear spaces are studied. It is shown that elementary length topologies constructed with different pseudo-norms are never equivalent. Elementary length topologies are constructed on certain topological spaces and some of their properties are investigated. It is shown that certain "measuring devices" (i.e., norms, pseudo-norms, semi-norms, and pseudo-metrics) which take their values in Tikhonov semifields may be used to construct elementary length topologies on any topological linear space. Relationships between two elementary length topologies generated with different measuring devices are considered.

Let (X,t) be a topological linear space such that t is determined …

Mathematical Modeling Of River Water Temperatures, Leland Lovell Long

Doctoral Dissertations

"The applicability of power spectral density techniques, Fourier series analysis, and linear regression to the mathematical modeling of river water temperature is demonstrated. Consideration is also given to the problem of estimating thermal inputs to rivers from man-made sources such as electrical power plants. First, power spectral density techniques are used in the time-series analysis of water temperature records which were taken from the Missouri River. Two spectral ranges are then studied from the standpoint of their applicability to (1) mathematical model building and (2) detection and identification of cyclic thermal inputs. Next, a Fourier regression fit to the time-series …

D-Structures And Their Semantics, Rohit J. Parikh

Publications and Research

"Many logicians are familiar with the game theoretic approach to semantics, due to Jaakko Hintikka. This paper by me contains class notes of a logic course at Boston University in fall 1972. It has similar game theoretic ideas, developed quite independently, but influenced by the work of A. Ehrenfeucht. It applies to a larger class of logics, including classical logic, intuitionistic logic and the *-semantics of Ehrenfeucht. The treatment is via D-structures which are finite approximations of infinite structures. For various reasons I did not publish this paper then, but some abstracts, both by myself as well as joint abstracts …

Structure Of Zero Divisors, And Other Algebraic Structures, In Higher Dimensional Real Cayley-Dickson Algebras, Harmon Caril Brown

Doctoral Dissertations

"Real Cayley-Dickson algebras are a class of 2ⁿ-dimensional real algebras containing the real numbers, complex numbers, quaternions, and the octonions (Cayley numbers) as special cases. Each real Cayley-Dickson algebra of dimension greater than eight (a higher dimensional real Cayley-Dickson algebra) is a real normed algebra containing a multiplicative identity and an inverse for each nonzero element. In addition, each element a in the algebra has defined for it a conjugate element ā analogous to the conjugate in the complex numbers. These algebras are not alternative, but are flexible and satisfy the noncommutative Jordan identity. Each element in these algebras can …

An Acceleration Technique For A Conjugate Direction Algorithm For Nonlinear Regression, Larry Wilmer Cornwell

Doctoral Dissertations

"A linear acceleration technique, LAT, is developed which is applied to three conjugate direction algorithms: (1) Fletcher-Reeves algorithm, (2) Davidon-Fletcher-Powell algorithm and (3) Grey's Orthonormal Optimization Procedure (GOOP). Eight problems are solved by the three algorithms mentioned above and the Levenberg-Marquardt algorithm. The addition of the LAT algorithm improves the rate of convergence for the GOOP algorithm in all problems attempted and for some problems using the Fletcher-Reeves algorithm and the Davidon-Fletcher-Powell algorithm. Using the number of operations to perform function and derivative evaluations, the algorithms mentioned above are compared. Although the GOOP algorithm is relatively unknown outside of the …

Asymptotic Behavior Of Solutions Of Lu=G(T,U,Dots,U^(K-1)), William F. Trench

William F. Trench

No abstract provided.