Physical Sciences and Mathematics Commons^™

Asymptotic Numbers: Algebraic Operations With Them, Christo Ya. Christov, Todor D. Todorov

Mathematics

The main subject of the present paper is to define the four algebraic operations - additions, subtraction, multiplication and division in the set of the asymptotic numbers A [7] and to deduce the corresponding formulas for the components of the asymptotic number, representing the result as functions of the components of the arguments. The definitions of the operations, in fact, are introduced as a special case of the more general notion of a quasiclassical function - one special class of functions defined on A. The discussion of the algebraic and some other properties of the asymptotic numbers is put …

A Class Of Functional Equations And Mielnik Probability Spaces, S. J. Guccione, Caslav V. Stanojevic

Mathematics and Statistics Faculty Research & Creative Works

Let S be the unit sphere of a normed real linear space N and let (S, p) be a Mielnik space of dimension two. For p(x, y) = f(‖x+y‖), x, yєS, where /is a continuous, strictly increasing function from [0, 2] onto [0, 1], it has been shown that (S, p) being two dimensional is equivalent to N being an inner product space. In some polarization problems modeled on the unit sphere of an inner product space, the transition probability p(x, y) may not be as well behaved as p(x, y) = f(‖x + y‖). In order to provide a …

Quasi-Unmixedness And Integral Closure Of Rees Rings, Peter G. Sawtelle

Mathematics and Statistics Faculty Research & Creative Works

For certain Rees rings ℛ of a local domain R, the quasiunmixedness of R is characterized in terms of a certain transform of ℛ being contained in the integral closure of ℛ. © 1976 American Mathematical Society.

On L¹ Convergence Of Certain Cosine Sums, John W. Garrett, Caslav V. Stanojevic

Mathematics and Statistics Faculty Research & Creative Works

It is shown that to a certain cosine series f, a Rees-Stanojević cosine sumn can be associated such that gn converges to f pointwise, and a necessary and sufficient condition for L1 convergence of gn to f is given. As a corollary to that result we have a generalization of the classical result of this kind. Other corollaries are given concerning the well-known integrability conditions. © 1975, American Mathematical Society.

On L¹ Convergence Of Certain Cosine Sums, John W. Garrett, Caslav V. Stanojevic

Mathematics and Statistics Faculty Research & Creative Works

Rees and Stanojevic introduced a new class of modified cosine sums (equation omitted) and found a necessary and sufficient condition for integrability of these modified cosine sums. Here we show that to every classical cosine series f with coefficients of bounded variation, a Rees-Stanqjevic cosine sum gn can be associated such that gn converges to f pointwise, and a necessary and sufficient condition for Lx convergence of gn to f is given. As a corollary to that result we have a generalization of the classical result of this kind. Examples are given using the well-known integrability conditions. © 1976 American …

Univalence Of Derivatives Of Functions Defined By Gap Power Series. Ii, S. M. Shah, S. Y. Trimble

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.

Asymptotic Integration Of Linear Differential Equations Subject To Integral Smallness Conditions Involving Ordinary Convergence, William Trench

William F. Trench

No abstract provided.

It's A Great Day Tomorrow, Richard C. Heyser

Unpublished Writings

This paper with its combined slides was presented by Richard C. Heyser to explain his theories for measuring sound.

The Extremal Structure Of Locally Compact Convex Sets, J. C. Hankins, Roy M. Rakestraw

Mathematics and Statistics Faculty Research & Creative Works

Let X be a locally compact closed convex subset of a locally convex Hausdorff topological linear space E. Then every exposed point of X is strongly exposed. The definitions of denting (strongly extreme) ray and strongly exposed ray are given for convex subsets of E. If X does not contain a line, then every extreme ray is strongly extreme and every exposed ray is strongly exposed. An example is given to show that the hypothesis that X be locally compact is necessary in both cases. © 1976 Pacific Journal of Mathematics. All rights reserved.

On Graphs Which Contain All Small Trees, Ii, F. R. K. Chang, R. L. Graham, Nicholas Pippenger

All HMC Faculty Publications and Research

No abstract provided.

Multiplicatively Periodic Rings, Ted Chinburg, Melvin Henriksen

All HMC Faculty Publications and Research

We prove a generalization of Luh's result without using Dirichlet's Theorem. We then use Theorem 1 to show that the J-subrings of a periodic ring form a lattice with respect to join and intersection (the join of two subrings is the smallest subring containing both of them). After noting that every J-ring has nonzero characteristic, we determine for which positive integers n and m there exist J-rings of period n and characteristic m. This generalizes a problem posed by G. Wene.

On The Juror Utilization Problem, Melvin Henriksen, George H. Orland

All HMC Faculty Publications and Research

One of the authors, after hearing complaints night after night from his wife who was on jury duty, and finding it too much to bear, agreed to do something about the situation in return for peace. And so this study for the more efficient use of jurors was born. The aspects and magnitude of this problem have been discussed in many places. Basically we are concerned with achieving a better match between the number of jurors in a courthouse on a given day and those used in the judicial process.

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.

Approximation Of Compact Homogeneous Maps, John R. Hubbard

Department of Math & Statistics Faculty Publications

Within the clasp of continuous homogeneous maps between Banach spaces, it is proved that every compact map can be uniformly approximated by finite-rank maps. This result is obtained by means of the classical metric projection on Banach spaces.

The Extendability And Uniqueness Of Solutions Of Ordinary Differential Equations, Stephen R. Bernfeld

Mathematics Technical Papers

In a recent paper [1] the author obtained results on the extendability of solutions of perturbed differential equations. The question of the extendability of solutions of differential equations is a fundamental and important property since questions of stability and boundedness require extendability. In this paper we continue our study of extendability of perturbed scalar differential equations. Our somewhat surprising results also extend to the question of uniqueness of the zero solution of perturbed equations satisfying an Osgood condition [4] (See also [2] for recent results on the uniqueness of perturbed systems.) Examples are provided to demonstrate the strength of our …

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.

Sufficient Conditions For An Operator-Valued Feynman-Kac Formula, Michael D. Grady

Mathematics, Statistics and Data Science Faculty Works

Let E be a locally compact, second countable Hausdorff space and let X(t) be a Markov process with state space E. Sufficient conditions are given for the existence of a solution to the initial value problem, ∂u/∂t,=Au + V(x) * u, u(0) = f, where A is the infinitesimal generator of the process X on a certain Banach space and for each x ∈ E, V(x) is the infinitesimal generator of a C₀ contraction semigroup on another Banach space.

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.

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

Lawrence N. Stout

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.

Orthogonal Polynomial Expansions With Nonnegative Coefficients, William F. Trench

William F. Trench

No abstract provided.

Irrational Numbers And Reality, Arnold H. Veldkamp

Pro Rege

No abstract provided.

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

Mathematics Technical Papers

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 …

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.

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

Mathematics Technical Papers

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

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 …

Self-Dual Embeddings Of Graphs, Saul Stahl

Dissertations

No abstract provided.

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

Dissertations

No abstract provided.

Indegrees, Outdegrees, And The Hamiltonian Theme, John Roberts

Dissertations

No abstract provided.