Physical Sciences and Mathematics Commons^™

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.

Comparative Studies Of The Computational Analysis Of One Dimensional Gas Flow, Johnny Ziebarth

Masters Theses

No abstract provided.

Imbedding Cayley Graphs, Brian L. Garman

Masters Theses

No abstract provided.

Models For Molecular Vibration, Allan Bruce Capps

Masters Theses

“The purpose of the investigation is to determine if a classical model can be used to characterize molecular vibrational and librational (restricted rotation) frequencies. In general, the model treats a molecule as asymmetrical and rigid and simulates the intermolecular forces by springs along the bonds. Molecules constrained to a plane and molecules free to move in three dimensions are analyzed. The frequencies of water molecules are investigated, in particular. The model and analytic components are found to function well. Within the limits set for the model, the water molecule simulation is not successful as the motion becomes anharmonic for energy …

A Characterization Of Metric Spheres In Hyperbolic Space By Morse Theory, Thomas E. Cecil

Mathematics and Computer Science Department Faculty Scholarship

Let Mⁿ be a differentiable manifold of class C^¥. By a Morse function f on Mⁿ, we mean a differentiable function f on Mⁿ having only non-degenerate critical points. A well-known topological result of Reeb states that if Mⁿ is compact and there is a Morse function f on Mⁿ having exactly 2 critical points, then Mⁿ is homeomorphic to an n-sphere, Sⁿ (see, for example, [3], p. 25).

In a recent paper, [4], Nomizu and Rodriguez found a geometric characterization of a Euclidean n-sphere S^{n Ì …}

The Theoretical Distribution Of Forces In The Rigid Component Of The Buccal Arch Positioner, Dennis H. Teruya

Loma Linda University Electronic Theses, Dissertations & Projects

The distribution of an applied force to the rigid component of the Buccal Arch Positioner was determined with a theoretically formulated model. The rigid component was assumed to be a free body without the semi-rigid attachments and was evaluated at four points for the force distribution. The summation of the forces and the moments were equated to zero and were utilized to derive equations to solve for the unknown forces. The unknown forces at each point of the rigid component were solved for in terms of the given force applications.

A laterally directed force application at one of the posterior …

A General Lr(K) Parser Building Algorithm, Thomas Joshua Sager

Mathematics & Statistics ETDs

The problem is to find an efficient algorithm that, given the productions of a context-free grammar G, will discover whether G is LR(k) for given k and if it is build an efficient parser for G . The algorithm is given in Section 8. It is essentially a synthesis of the best parts of Knuth's and DeRemer's algorithms. On simple LR(k) grarranars it yields a result equivalent to DeRemer's algorithm, and like Knuth's algorithm it will work on all LR(k) grammars.

Objective Measurement And The Stud Breeder, B R. Beetson

Journal of the Department of Agriculture, Western Australia, Series 4

The movement towards sale of wool by certificate and sample highlights the significance of objective measurement in the Merino stud breeders' selection of his top rams.

This article suggests how stud breeders should use the Department of Agriculture's Flock Testing Service to gain genetic progress in wool producing ability without loss of visual buyer appeal.

Studs' use of the service will be evaluated in 1974.

Numerical Study Of Slow Motion Of A Smoke Filament, Tapan Sen

Masters Theses

No abstract provided.

Strong Discrete Minimum Variance Estimation Of A Polynomial Plus Random Noise, William F. Trench

William F. Trench

No abstract provided.

A Mathmatical Model Of Primary Productivity And Limnological Patterns In Lake Mead, Lorne G. Everett

Publications (WR)

The temporal and spatial changes in chemical and biological properties of Lake Mead have been investigated, thereby indicating the sources of water pollution and the time of highest pollution potential. Planktonic organisms have been shown to indicate the presence of water problems. Macro- and micro-nutrient analyses have shown that primary productivity is not inhibited by limiting concentrations. A mathematical model has been developed, tested with one set of independent data, and shown worthy of management utility. Although the model works very well for the Lake Mead area, the physical reality of the Multiple Linear Regression equation should be tested on …

Metric Conversion For Agriculture, Department Of Agriculture, Western Australia

Journal of the Department of Agriculture, Western Australia, Series 4

Farmers are already becoming involved with metric units and by 1974 conversion of the farming industry will be well advanced. Wool sales converted to metric measurements in August, 1971, and sales by the various grain marketing boards will be largely in metric terms in the 1972 harvest. Weather information to the public has been given in metric terms since September 1.

Stability Of A Class Of Discrete Minimum Variance Smoothing Formulas, William F. Trench

William F. Trench

No abstract provided.

A New Test For Normality, Richard Leroy Roller

All Master's Theses

This paper presents a new test for normality which is based on a complete characterization of the normal distribution. Motivation for the test is given in terms of a proof of this characterization. The test is derived and evaluated by computer-simulated sampling from alternative distributions. The empirical powers of the test generated from such samplings are tabled and compared to nine commonly used tests. Evaluation of the proposed test is discussed and further avenues of investigation are suggested.

Orthogonality In Normed Spaces, Martin R. Mccarthy

All Master's Theses

This paper presents three definitions of orthogonality in normed spaces. Each definition is shown equivalent to the inner product being zero when restricted to an inner product space. The definitions arise from such properties in two space as the diagonals of a rectangle being equal and the Pythagorean Theorem. The third definition shows that the idea of an inner product can be generalized under certain conditions.

A New Confidence Interval For The Mean Of A Normal Distribution, David Lee Wallace

All Master's Theses

A typical problem in statistical inference is the following: An experimenter is confronted with a density function f(x; ϴ) which describes the underlying population of measurements. The form of f may or may not be known, and ϴ is a parameter (possibly vector-valued) which describes the population. The statistician's job is to estimate or to test hypotheses about the unknown parameter ϴ. In this paper, we shall consider interval estimation of the mean of the normal density function.

Convergence Rates For The Central Limit Theorem For Random Sums, Christopher E. Olson

Mathematics & Statistics ETDs

Let (X_i} be a sequence of independent, identically-distributed random variables with EX²_i < ꝏ and E(X_i - EX_i)² = 1.

Random Evolutions On Diffusion Processes, Donald Quiring

Mathematics & Statistics ETDs

Let {V(t,ω), t ≥ O, ω ε Ω} be a diffusion process on the real line with infinitesimal operator 1/2σ²(⋅)D² + m(⋅)D. Markov processes {V_n, n = 1,2,....} on the real line are constructed in such a way that the paths of V_n are step functions with jump size n^-1/2 and

P_O [lim sup |V_n(s)-V(s)| = 0] =1

n∞ 0≤s≤t,

where P_O assigns probability one to paths starting at the origin at t = 0.

Let {T_V(t), t≥0, vε R} be a family of linear contraction operators …

Toeplitz Operators On Locally Compact Abelian Groups, Henry A. Krieger, C.A. Schaffner

All HMC Faculty Publications and Research

The problem of global optimization of M incoherent phase signals in N complex dimensions is formulated. Then, by using the geometric approach of Landau and Slepian, conditions for optimality are established for $N = 2$, and the optimal signal sets are determined for $M = 2,3,4,6$ and 12.

The method is the following: The signals are assumed to be equally probable and to have equal energy, and thus are represented by points ${\bf s}_j $, $j = 1,2, \cdots ,M$, on the unit sphere $S_1 $ in $C^N $. If $W_{jk} $ is the half space determined by ${\bf s}_j …

Bayesian Statistics: The Fundamental Theorem, Carolyn Rhodes

Honors Theses

The problem of the foundation of statistics is to state a set of principles which entail the validity of all correct statistical inference, and which do not imply that any fallacious inferences is valid. This sentence describes the purpose of much writing on statistical inferences, in general, and Bayesian statistics, in particular. Bayesian statistics was first introduced in a publication by Thomas Bayes in The London Philosophical Transactions, volumes 53 and 54 for the years 1763 and 1764, after Bayes' death in 1761. However, since the entire statistical research of Bayes' involves enormous study, this paper will limit itself to …

Bounded Energy-Finite Solutions Of Delta U=Pu On A Riemannian Manifold, Young Koan Kwon, J. Schiff, L. Sario

Research Collection School Of Accountancy

The classification of Riemann surfaces with respect to the equation Δu = Pu (P^O, PΞ£ 0) was initiated by Ozawa [13] and further developed by L. Myrberg [8,9], Royden [14], Nakai [10,11], Sario-Nakai [15], Nakai-Sario [12], Glasner-Katz [3], and Kwon-Sario [7].

Mathematics Of Investment, Claudia Morgan Griffin

Honors Theses

By using the text Mathematics of Investment by William L. Hart, Griffin examines the mathematics of investments.

Prime Ideals In A Large Class Of Nonassociatiye Rings, Paul J. Zwier

University Faculty Publications and Creative Works

In this paper a definition is given for a prime ideal in an arbitrary nonassociative ring N under the single restriction that for a given positive integer 5^2, if A is an ideal in N, then A* is also an ideal. (N is called an snaring.) This definition is used in two ways. First it is used to define the prime radical of N and the usual theorems ensue. Second, under the assumption that the.s-naring N has a certain property (a), the Levitzki radical L(N) of N is defined and it is proved that L(N) is the intersection of those …

Discrete Minimum Variance Smoothing Of A Polynomial Plus Random Noise, William F. Trench

William F. Trench

No abstract provided.

I. Existence Of Eigenvalues For Integral Equations; Ii. A Collocation Method For Boundary Value Problems, Robert Dodd Russell

Mathematics & Statistics ETDs

I. The existence of eigenvalues is shown for certain classes of integral equations with continuous kernels. A number of interesting and useful results are thereby treated in a unified and relatively elementary way. The simplicity of these new proofs make the results accessible to introductory courses on the theory of integral equations.

II. Collocation with piecewise polynomial functions is developed as a method for solving two-point bour:rlary value problems. Convergence is shown for a general class of linear problems and a rather broad class of nonlinear problems. Some computational examples are presented to illustrate the wide applicability and efficiency of …

Goursat Problems For The Abstract Equation Urs = Lu, Walter J. Roth

Mathematics & Statistics ETDs

Player Win Averages: A Complete Guide To Winning Baseball Players, Eldon G. Mills, Harlan D. Mills

The Harlan D. Mills Collection

No abstract provided.

A Special Studies Paper On The General Mathematics Requirements At Ouachita Baptist University, Linda Gamble

Honors Theses

The object of this paper has been to study the opinions of graduates and present students about the required math hours (presently three hours) at Ouachita Baptist University. It has formerly been my opinion that this may be insufficient math background for many of our students going out seeking jobs. Many times the student, while still in college does not realize he may need more math but it may show up on graduate tests, in his occupational work, or personal matters such as income tax calculations, bookkeeping, or budgeting.

To compile the opinions of students on this subject a form …

A Special Studies Paper On Mathematics In Computer Programing, Linda Gamble

Honors Theses

The profession of programing has existed for two decades or longer. Computer programing and the organization of computer analysis have gone beyond the reach of careful clerks with high school education. There is a growing demand for persons who are competent researchers, experienced in the use of multivariate methods, and skilled as computer users and programers. Mathematics and engineering predominate. The programer should have a knowledge of mathematics and a familiarity with computer hardware and must understand the content of the problem to be solved.

Continuous Smoothing With Polynomial Weighting, William F. Trench

William F. Trench

No abstract provided.