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Group Of Point Transformations Of Time Dependent Harmonic Oscillators, Jose Ricardo Bernal

University of the Pacific Theses and Dissertations

In general, a physical system has invariant quantities which are very often related to its symmetry and to the invariance of the equation that describe it. A detailed study of the invariance property of the differential equation will be helpful in understanding this relation.

The work is concerned with a preliminary investigation of the Lie-group which leaves invariant the Newtonian and Lagrangian equation of motion for a one-dimensional harmonic oscillator. A brief review of Ehrenfest's adiabatic principle and the later treatments on exact and adiabatic invariants will be presented.

Some Applications Of Lie Transformation Groups To Classical Hamiltonian Dynamics, Donald Robert Peterson

University of the Pacific Theses and Dissertations

Recent work has established that a group theoretical viewpoint of completely integrable dynamical systems with N degrees of freedom yields an algorithm that provides new information concerning the symmetry transformation group structure of this class of dynamical systems. The work presented here rests heavily on the results presented in reference and it is recommended that the reader consult this reference for a more rigorous discussion of the results given in this thesis.

A Characterization Of The Einstein Tensor In Terms Of Spinors, Ian M. Anderson, D. Lovelock

Mathematics and Statistics Faculty Publications

All tensors of contravariant rank two which are divergence‐free on one index, concomitants of a spinor field σ_iAX′ together with its first two partial derivatives, and scalars under spin transformations are constructed. The Einstein and metric tensors are the only candidates.

Extremal Structure Of Convex Sets, J. C. Hankins

Doctoral Dissertations

"Let X be a locally compact closed convex subset of a locally convex Haus Dorff topological linear space E. It is shown that every exposed point, respectively, ray of Xis a strongly exposed point, respectively, ray of X. Also, every extreme point, respectively, ray of Xis a denting point, respectively, ray of X. When the above results are combined one can restate two well-known Krein Milman type theorems due to Klee. There exists a closed convex set that has an extreme point that is neither a denting point nor an exposed point.

In Banach spaces, necessary and sufficient conditions are …

Topological Properties Of The Real Numbers Object In A Topos, Lawrence Stout

Scholarship

In his presentation at the categories Session at Oberwolfach in 1973, Tierney defined the continuous reals for a topos with a natural numbers object (he called them Dedekind reals). Mulvey studied the algebraic properties of the object of continuous reals and proved that the construction gave the sheaf of germs of continuous functions from X to R in the spatial topos Sh( X). This paper presents the results of the study of the topological properties of the continuous reals with an emphasis on similarities with classical mathematics and applications to familiar concepts rephrased in topos terms.

Structural Inference On Reliability In A Lognormal Model, Danny D. Dyer

Mathematics Technical Papers - Archive

The theory of structural inference, as developed by Fraser (1968), is based on a group-theoretic approach using invariant Haar measures to Fisher's fiducial theory. Structural inference theory constructs a unique distribution, conditional on the given sample information only, for the parameters of a measurement model. Based on the structural density for the two-parameter lognormal distribution, the structural density and distribution function for the reliability function are derived. Consequently, expressions for structural point and interval estimates of the reliability function are developed. Approximations for large sample sizes and/or moderately reliable components are also discussed. An example based on lognormal data is …

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. …

On The Zeros Of Monotone Operators Of Retarded Type In A Banach Space, Patrick Sutherland, V. Lakshmikantham

Mathematics Technical Papers - Archive

Recent interest in the Cauchy problem for differential equations in a Banach space [9] has stimulated a similar interest for differential equations of a retarded type in a Banach space. The difficulty in imposing assumptions due to a different range and domain space has been overcome in [4] where existence of solutions is established using a monotoni- city type condition in terms of norm and weaker forms of differential inequalities. The theory of existence of solutions of differential equations has been used in [1,2,5,6,7] to obtain existence of zeros and fixed points for nonlinear operators from E into E. In …

A Survey Of Techniques For Determining Lower Confidence Bounds On Series System Reliability Based On Subsystem Test Data, Danny D. Dyer

Mathematics Technical Papers - Archive

A problem of considerable interest and for which a great deal of research has been expended is that of determining lower confidence bounds on series system reliability based on subsystem failure data. With regard to the types of failure data taken on the subsystems, primary consideration is given to binomial (pass-fail) data, exponentially distributed time-to-fail data for both Type I censoring (fixed test times) and Type II censoring (fixed number of failures), or any mixture thereof. In this survey we shall examine optimum solutions whenever they exist, approximate optimum solutions, and nonoptimum solutions. Numerical examples are given to illustrate the …

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.

The Geometry Of Commutative Symmetric Loops, Hussein M. Karanda

Tanzania Journal of Science

The aim of this paper is to show the connection existing between a commutative symmetric loop and an euclidean space.

On The Convergence Of Successive Approximations For Quasi-Nonexpansive Mappings Through Abstract Cones, B. B. Williams, J. C. Bolen

Mathematics Technical Papers - Archive

In a recent paper, Petryshyn and Williamson [4] investigated the convergence of successive approximations of quasi- nonexpansive mappings in a Banach space. This paper contains an outline, in chronological order, of the main results concerning the convergence of iteration method and consequently includes a number of references. Perov and Kibenko [3] employed generalized Banach spaces to extend contraction mapping principal and to show the flexibility of such an approach in applications. See also Bernfeld and Lakshmikantham [1]. More recently, Eisenfeld and Lakshmikantham [5,6] proved some fixed point theorems in abstract cones which extend and generalize many known results. In this …

Remarks On Nonlinear Contraction And Comparison Principle In Abstract Cones, V. Lakshmikantham, Jerome Eisenfeld

Mathematics Technical Papers - Archive

The contraction mapping principle and the Schauder principle can both be viewed as a comparison of maps. For the former one has a condition of the type [see pdf for notation] and for the latter one has a condition of the type [see pdf for notation] where p is the metric and y is the Kuratowski measure of noncompactness. If p is a linear map [see pdf for notation] from the nonnegative reals [see pdf for notation] into itself then the map T satisfying (1.1) is said to be k-contractive and the map satisfying (1.2) is said to be k-set …

On The Existence Of Solutions Of Differential Equations Of Retarded Type In A Banach Space, V. Lakshmikantham, Roger W. Mitchell, A. Richard Mitchell

Mathematics Technical Papers - Archive

The existence and uniqueness of solutions of differential equations of retarded type in a Banach space are considered under a monotonicity type condition. The tools that are available for the study of equations without delay pose problems in this case since the domain and the range come from different Banach spaces. To overcome this difficulty, subsets of the domain have to be chosen carefully and weaker forms of differential inequalities have to be employed.

Maximal And Minimal Solutions And Comparison Principle For Differential Equations In Abstract Cones, Roger W. Mitchell, A. Richard Mitchell, V. Lakshmikantham

Mathematics Technical Papers - Archive

Existence of maximal and minimal solutions for differential equations in abstract cones is established without requiring uniform continuity. Utilizing such a result an abstract comparison principle is developed. The results of the paper significantly improve earlier results of the authors and also simplify the proofs of other known results.

On A Measure Of Nonconvexity And Applications, V. Lakshmikantham, Jerome Eisenfeld

Mathematics Technical Papers - Archive

The measure of noncompactness which was introduced by Kuratowski [8] (in 1930) has now become an important tool in nonlinear analysis (although its value in that regard was not appreciated until much later). Following Kuratowski we introduce a measure of nonconvexity which has many properties in common with the measure of noncompactness and therefore we may now have "convex" where previously we had "compact" in the statements of some theorems.

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 …

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.

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 …

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.

Statistical Analysis Of Fourier Coefficients In A Restricted Harmonic Dial, Danny D. Dyer

Mathematics Technical Papers - Archive

Due to the physical nature of certain periodic data, the harmonic dial points (the Fourier coefficients obtained from harmonic analysis of the data) are sometimes restricted to circular regions in the dialplane. It is proposed that a circular normal distribution (CND) truncated outside a circular region be used to describe the probabilistic behavior of the random phenomena. Recurrence relations for the population moments of a CND truncated outside a circular region are derived. These recurrence relations are used to obtain consistent asymptotically (jointly) normal estimators of the unknown parameters of the distribution. A numerical example based on the harmonic dial …

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.

Perfect Polynomials Over Gf(Q), James R. O'Connell Jr., Jacob T. B. Beard Jr., Karen I. West

Mathematics Technical Papers - Archive

A monic polynomial [see pdf for notation] is called perfect over GF(q) if and only if the sum [see pdf for notation] of the distinct monic divisors in GF[q,x] of A(x) equals A(x). Principal results characterize all perfect polynomials over GF(p) which split in GF[p,x]. Related results lead to conjectured analogs of the classical problem on the existence of odd perfect numbers.

Vector Lyapunov Functions And Perturbations Of Nonlinear Systems, Marion E. Moore, Roger W. Mitchell

Mathematics Technical Papers - Archive

Two recent papers [2,3] have combined the techniques of the Lyapunov method and the nonlinear variation of parameters to study the effects of perturbations of nonlinear differential systems. In this paper, we generalize the results obtained in [2,3] by the use of several Lyapunov functions and the concept of a generalized norm. To convince ourselves that we do have more flexibility in working with the generalized norm and vector Lyapunov functions see [1,4].

Block Diagonalization And Eigenvalues, Jerome Eisenfeld

Mathematics Technical Papers - Archive

Let A denote an Algebra with an identity element. Consider an [see pdf for notation] matrix [see pdf for notation] with a partitioning [see pdf for notation] where E and H have respective orders [see pdf for notation] and [see pdf for notation]. We seek to obtain conditions under which A is similar to a matrix D of the form [see pdf for notation] where [see pdf for notation] denotes the zero [see pdf for notation] matrix over A. Some advantage is gained in working in a general algebra. The algebra A may be taken as a Banach algebra of …

Unitary Perfect Polynomials Over Gf(Q), Jacob T. B. Beard

Mathematics Technical Papers - Archive

For monic polynomials A(x), B(x) e GF[q,x], call B(x) a unitary divisor of A(x) provided (B(x),A(x)/B(x)) = 1 . The polynomial A(x) is called unitary perfect over GF(q) if and only if the sum [see pdf for notation] of the distinct unitary divisors of A(x) equals A(x). Principal results characterize all unitary perfect polynomials over GF(p) which split in GF[p,x].