Digital Commons Network^™

A Coordinate Oriented Algorithm For The Traveling Salesman Problem, Joseph Sidney Greene

Doctoral Dissertations

"The traveling salesman problem may be stated as follows: "A salesman is required to visit each of n given cities once and only once, starting from any city and returning to the original place of departure. What route should be chosen in order to minimize the total distance traveled?" A new algorithm is developed which gives a good approximation to the solution for a large number of cities using reasonable computer time and which will converge to the exact solution if allowed to continue. This algorithm is a branch and bound technique which utilizes the distance between cities in its …

Extension Of Some Theorems Of Complex Functional Analysis To Linear Spaces Over The Quaternions And Cayley Numbers, James E. Jamison

Doctoral Dissertations

"In this work certain aspects of Functional Analysis are considered in the setting of linear spaces over the division rings of the real Quaternions and the real Cayley algebra. The basic structure of Banach spaces over these division rings and the rings of bounded operators on these spaces is developed. Examples of finite and infinite dimensional spaces over these division rings are given. Questions concerning linear functionals, the Hahn-Banach Theorem and Reflexivity are considered. The Stone-Weierstrass Theorem is proven for functions with values in a real Cayley Dickson algebra of dimension n. The concepts of inner product spaces and Hilbert …

A New Characterization Of Besicovitch Almost Periodic Functions., Abdallah N. Dabboucy

Mathematics & Statistics ETDs

Besicovitch and Bohr have given an internal description or Besicovitch almost periodic functions which involves the notion of “satisfactory uniformity” and is somewhat complicated. Raouf Doss has given an alternative simpler internal description, which, however, involves an infinity of independent conditions. Theorem. Let f E Lp(a,b) for all real numbers a,b. Then ff (BP-AP}

if end only if (1) the functions fn obtained by truncating f atn=l,2, … !·ll-converge to f; (2) lim)C+{) x llf-fl! BP =O; (3a) for every f: > 0 the set (x: l!f x -fl' P < eJ is relatively dense; and (3b) for every E: > 0

for all sufficiently large T, where E = {x: l\fx-fllB < e). Here fx(y) = f(x+y), XE denotes the characteristic function of E and 1 :Sp< oo. The theorem extends to LC connected groups, compactly generated Abelian groups and a somewhat stronger version of it extends to discrete countable Abelian groups.

Right Baer Semigroups., William Christopher Hardy

Mathematics & Statistics ETDs

In his paper, "A Semigroup Approach to Lattices, 11 (Canad . Jour. Math., Vol. 18 (1966)), M. F. Janowitz showed that every lattice with 0 and 1 is isomorphic to the lattice formed by the left annihilators of a suitably chosen Baer semigroup when they are ordered under set inclusion. A Baer semigroup, s~ was then said to coordinatize a lattice, L, if Lis isomorphic to the lattice of left annihilators of S. This dissertation presents a similar semigroup approach to lattices by showing that a poset, P, with O and 1 forms a meet semilattice if and only if …

Characterizations Of Some Functors Of Categories Of Banach Spaces, Kenneth L. Pothoven

Dissertations

No abstract provided.

Analysis Of Heat Transfer In A Two-Layer Circular Cylinder:Constant Flux On Outer Surface And Zero Flux On Inner Surface, Mary Elena Franklin

Mathematics & Statistics ETDs

The one-dimensional time-dependent equation of heat conduction is solved analytically for an infinite two-layer circular cylinder whose core may be either hollow or solid. On the outer surface of the cylinder, which has no heat loss due to convection, a constant heat flux from an external source of heating is applied uniformly. The layers are in perfect thermal contact, and there is no heat loss at their interface. At the smaller radius of the inner layer is a perfect insulator so that the heat flux on the inner surface of the two-layer cylinder is zero. The temperature is uniform initially …

Adaptive Nonlinear Prediction And Convergence Rates., Dirk Andrew Dahlgren

Mathematics & Statistics ETDs

Let x1,…,xm be radom variables with an arbitrary (initial) distribution functions F. For i>=m, define

Xi+1=f(theta,x1,…,x1-m+1)+oZi

Where theta is an unknown parameter in Euclidean r space and {Zi}inf m is a sequence of independent, identically distributed random variables with E[Zi]=0 and E[Z 2 i]=1. This type of process will be termed a generalized autoregressive process in the sequel.

On The Derivative Of Bounded Functions, Wimberly C. Royster

Mathematics Faculty Publications

No abstract provided.

A Combinational Analysis Of Finite Minimal Uniform Covers, Gustavus J. Simmons

Mathematics & Statistics ETDs

No abstract provided.

The Fresnel Integrals, Jean Therese Powers

Master's Essays (1922 - )

In the study of complex analysis, and in particular in the area of complex integration, there arise a series of integrals whose evaluation require more than an thing else, a great deal of mathematical ingenuity. Among these classical integrals are two known as the Fresnel Integrals and it is the purpose of this paper to discuss one method of evaluation of this pair of functions.

On The Theory Of Quaternions, Earle David Smith

All Master's Theses

Ordered triplets serve to describe space geometrically just as ordered pairs serve to describe the plane. A multiplication can be defined on pairs consistent with the complex numbers. However, as this paper will show, one cannot define a multiplication on triplets which is consistent with the complex numbers.

Pseudo-Lattices With Application To Topology And Analysis., Ih-Ching Hsu

Mathematics & Statistics ETDs

In recent times, lattice theory has pervaded many branches of mathematics. Usually, however, the structures of primary interest are not lattices themselves. The lattice structure is arrived at by passing to a quotient set.

Most Stable Tolerance Limits For Log-Convex Distributions, John Richard Ellefson

Mathematics & Statistics ETDs

Necessary and sufficient conditions are given for reversing Jensen's inequality for continuous convex functions, and the result is then stated for the discrete case. The main theorem of Hanson and Koopmans' (1964) pioneering tolerance limit paper is extended to the case of any finite number of order statistics from a probability distribution F for which either -log(1 - F) or - log F is convex. In the first case upper tolerance limits and in the second case lower tolerance limits are exhibited for any content p and any confidence ɣ, 0 < p, ɣ < 1 whenever the sample size is not less than two. When F is such that both functions are convex, two-sided, p-content tolerance intervals at confidence level rare constructed for any sample size greater than one. The distributions for which both functions are convex include the Pólya distribution functions of order two, which includes the normal and exponential families. The distribution of the coverage of the tolerance limits is calculated using an extension of Renyi’s (1953) work on exponential random variables. Goodman and Madansky's (1962) most stable criterion for tolerance intervals is characterized in terms of its second moment about a point, and some of its other properties are established. The results are applied to develop a method for finding the most stable one-sided tolerance limits. The general method is applicable to the problem of finding the most stable two-sided tolerance intervals, but the required explicit calculation of the probability distribution function is lacking. Instead the two-sided tolerance interval is found in terms of two one-sided tolerance limits.

Semi-Groups And A Class Of Singular Perturbation Problems, Andrew Y. Schoene

Mathematics & Statistics ETDs

No abstract provided.

Enumeration Of Certain Binary Arrays, Douglas Jackson

Mathematics & Statistics ETDs

T.V. Narayana [9] and later L. Carlitz [3] have solved the following problem. Given positive integers n, r, L₁,…,L_n-1, a₁,…,a_n such that a_i ≥ r, i = 1,...,n and a_i + L_i ≥ a_i+l, i = 1,…,n-1, how many n x r matrices [a_ij] of positive integers are there which satisfy

1.) a_i1 = a_i i=1,...,n

2.) a_ij > a_i,j+1 i = 1,...,n j = 1,..., r-1

3.) a_ij + L_i ≥ a_i+1,j i=1,...,n-1 j=1,...,r.

Narayana gave a formula for …

The Convergence Of Numerical Solutions Of Hydrodynamic Shock Problems., Darrell Lee Hicks

Mathematics & Statistics ETDs

In 1944 von Neumann Conjectures that only averages of numerical solutions, produced by a discrete scheme he had proposed to solve hydrodynamic shock problems, would converge as the meshes were refined. The hydrodynamic shock problem is defined here as: Find a solution, allowing discontinuous solutions, to the three conservation laws, the increasing-entropy law, and the ideal-gas law when giben physically acceptable initial and boundary values. For discrete schemes similar to von Neumann’s, it is verified that the averages do converge and it appears that von Neumann was also correct in surmising that only the averages converge. A smoothing device named …

Stochastic Processes Model And Its Application In Operations Research, Chun Yuan Hsu

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

Just as the probability theory is regarded as the study of mathematical models of random phenomena, the theory of stochastic processes plays an important role in the investigation of random phenomena depending on time. A random phenomenon that arises through a process which is developing in time and controlled by some probability law is called a stochastic process. Thus, stochastic processes can be referred to as the dynamic part of the probability theory. We will now give a formal definition of a stochastic process.

Let T be a set which is called the index set (thought of as time), then, …

Bayesian Inference For Decision Making, Ming-Yih Kao

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

In recent years, Bayesian inference has become very popular in applied statistics. This study will present the fundamental concept of Bayesian inference and the basic techniques of application to statistical quality control, marketing research, and other related fields.

Computer Programs For Incomplete Block Designs, Fred Miller

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

In most disciplines where research is involved, there exists an occasional problem of having minimal facilities and/or funds for conducting experiments. This often necessitates the use of designs known as incomplete block designs.

Since the calculations needed to provide an appropriate statistical analysis are somewhat tedious, particularJ..y in the larger designs, it is advantageous to have computer programs to do the necessary calculations.

There are several computer programs at Utah State University written in Fortran II language with Forcom subroutines that perform the analyses for incomplete block designs. These programs, for the most part, were authored by Justus Seely and …

A Study Of The Exponential Distirbutions And Their Applications, Michael Chang-Yu Wang

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

The exponential distribution is a widely known distribution i n statistical theory. It can be regarded as the continuous analogue of the Poisson distribution, discussed by S. D. Poisson in 1837. The Poisson is a limiting form of the Binomial distribution which can be t race d back as early as 1700, discussed by James Bernoulli. A paper by Marsden and Barratt (1911) on the radioactive disintegration of thorium gives a typical frequency distribution which follows the exponential law (8, p. 89). The exponential distribution has achieved importance recently in connection with the theory of stochastic process and has found …

A Concept Of Buoyancy In Topological Spaces, With Applications To The Foundations Of Real Variables, Elwyn David Cutler

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The Buoyancy Theorem states that a compact set is buoyant if every point of the compact set has a neighborhood whose intersection with the compact set is buoyant. In this paper, the Buoyancy Theorem is used to prove several standard results involving compact sets. The proof of such a result may be a direct application of the Buoyancy Theorem or the proof may rely on a certain compactness argument which follows from the Buoyancy Theorem. The last application in this paper is such an example.

The method used is to, first of all, define a buoyancy on the compact set; …

Analysis Of Contingency Tables, James Joseph Biundo

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Two methods of analyzing multi-dimensional frequency data are detailed.

The Second Order Exponential (SOE) model is applicable for dichotomous classifications. The distribution has two sets of parameters, ϴ_i's and ϴ_j's. The ϴ_i's are interpreted as the log of the odds of the marginal probabilities if no two factor relationships exist. Or if all ϴ_ij are not zero, then the ϴ_i's are analogous to a main effect in a 2^m factorial analysis, (m = number of factors or classifications). The ϴ_if's may be interpreted as a measure and direction …

Generation Of Random Numbers, Keith H. Eberhard

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Subroutines are written to generate random numbers on the computer. Depending on the subroutine used, the generated random numbers follow the uniform, binomial, normal, chi-square, t, F, or gamma distribution. Each subroutine is tested using the chi-square goodness of fit test to verify that the random numbers generated by each subroutine follow the statistical distribution for which it is written. The interpretation of the test results indicates that each subroutine generates random numbers which closely approximates the theoretical distribution for which it is designed.

The approach used in the subroutine which generates gamma distributed random numbers involves the use of …

Contribution To The Ergodic Theory., S. Natarajan Dr.

Doctoral Theses

Ergodic theory is chiefly concerned with the study of transformations on a measure space which preserve the measure. Interesting classes of such transformations are the classes of ergodic, weakly mixing and mixing transformations. The bulk of this thesis is devoted to the study of a closely related family of transformations called the we akly stable transformations; these are more general than the weakly mäxing transformations.This thesis is divided into three parts. Part I contains preliminary ideas, notations and some results on the invertibility and continuity properties of transition functions (Chapters 1 and 2). In Chapter 3 we collect known results …

Some Stochastic Models In Reliability., R. Natarajan Dr.

Doctoral Theses

The work presented in this thesis was carried out under the supervision of Dr. J. Sethuraman, Research & Training School, Indian Statistical Institute, Calcutta, and is devoted to the study of some stochastic models of standby and parallel redundant systems. Some of the reliability characteristics studied are the expected time to system failure, the long-run availability, expected number of system failures in a given interval of time, interval reliability etc. These reliability characteristics will be useful in the better design of systems and making management decisions in improving system reliability.The investigations carried out in this thesis are presented in four …

Contribution To Linear Quaternionic Analysis., K. Viswanath Dr.

Doctoral Theses

Several articles have appeared in recent years which discuss linear transformations on finite-dimensional vector spaces over the quaternions in terms of matrices, but the general infinite -dimensional situation does not seen to have received much attention. In particular, very little is known about linear transformations on quaternionic Hilbert spaces apart from the obvious theory of Hermitian operators. There are hardly any discussion of this subject, apart from the brief treatment of Finkelstein, Jauch, Schiminovitch and Speiser in their fundamental paper on the foundations of quaternion quantum mechanics (1962), which gives spectral theorems for unitary operators and skew hermitian operators and …

On Semigroups Of Functions On Topological Spaces, Troy L. Hicks, A. G. (Glen) Haddock

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.

The Eigenvalue Set Of A Class Of Equimodular Matrices, Gerald L. Bradley

CMC Faculty Publications and Research

The paper is divided into four sections, the first of which is basically introductory and contains definitions, notational conventions, and well-known results. The second section contains a fundamental theorem on multilinear polynomials which forms the crux of all our mail results, and the final two sections are devoted to discussions of the combinatorial and boundary properties of Y(A), respectively.

Manifold Phenomena In The Theory Of Polyhedra, Ethan Akin

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.

Exact Test For Simple Correlation In Analysis Of Dispersion, James E. Dunn

Journal of the Arkansas Academy of Science

No abstract provided.