Digital Commons Network^™

Automorphisms Of Normal Transformation Semigroups, Inessa Levi

Faculty Bibliography

No abstract provided.

On The Steepest Descent For Nonpotential Locally Lipschitzian Vector Fields, Alfonso Castro

All HMC Faculty Publications and Research

In [4] J. Neuberger gave various sufficient conditions for the solvability of nonvariational operator equations via a variant of the steepest descent method. In this note we give versions of these conditions under weaker assumptions on the smoothness of the operators.

Asymptotic Functions As Kernels Of The Schwartz Distributions, Todor D. Todorov

Mathematics

Using a version of the sequential method we introduce a class of generalized functions called here "asymptotic functions''. This class contains kernels of all Schwartz distributions and is equipped with a correctly defined multiplication operation. So, in a sense, one solves the problem of "multiplication of Schwartz distributions" although the solution refers to the class of the asymptotic functions and not to the Schwartz distributions themselves. The paper is a continuation of a series of works [1-10] but here only part of the results of [5], [6] and [8] will be needed.

On The Notion Of Precohomology, Goro Kato

Mathematics

ABSTRACT. For a cochain complex one can have the cohomology functor. In this paper we introduce the notion of precohomology for a cochain that is not a complex, i. e., d^q+1 o d^q may not be zero. Such a cochain, with objects and morphisms of an abelian category A, is called a cochain precomplex whose category is denoted by Pco (A). If a cochain precomplex is actually a cochain complex, then the notion of precohomology coincides with that of cohomology, i. e., precohomology is a gene¬ralization of cohomology. For a left exact functor F from an abelian category …

The Products Δn2(X), Δ(X). X-N, ϴ(X). X-N, Etc. In The Class Of The Asymptotic Functions, Todor D. Todorov

Mathematics

Several products like δⁿ(x), δ(x)ϴ(x), δ^(m)(x). X^-n, ϴ(x). X^-n, etc., where δ(x), ϴ(x), X^-n, etc., are kernels of the corresponding Schwartz distributions, are studied in the framework of the class of the asymptotic functions F₀ introduced in a previous paper [11]. In some particular cases many formulae are derived and several examples are presented. The work is of mathematical type but its motivations lie in some problems in quantum theory. It is closely …

Necessary And Sufficient Conditions For Certain Homology 3-Spheres To Have Smooth Zp-Actions, Erica Flapan

Pomona Faculty Publications and Research

We derive necessary and sufficient conditions for a broad class of homology 3-spheres, obtained as the gluing of two knot complements, to have Zp-actions.

We explore when a homology sphere, obtained as the gluing of two knot complements has any smooth periodic diffeomorphisms.

Infinitely Periodic Knots, Erica Flapan

Pomona Faculty Publications and Research

One aspect of the study of 3-manifolds is to determine what infinite group actions a given manifold has. Some important questions that one can ask about these actions on a given manifold are: What periods could they have? and, what sets of points may be fixed by the action?

The Problem Of Managing A Strategic Reserve, David Cole, Loren Haarsma, Jack Snoeyink, Gene A. Klaasen

University Faculty Publications and Creative Works

We develop a method of managing strategic reserves, in this case, the U.S. Strategic Cobalt Reserve. A rationale for the stockpiling of cobalt is presented, followed by a method for bringing the stockpiled amount from any level to a desired goal, in this case an amount determined by the Federal Emergency Management Agency to last through three years of conventional warfare. The method involves solving a stochastic programming problem in order to balance the expected values of the social benefit and the social cost of building the stockpile-Social benefit is accrued by decreasing the impact and the probability of a …

Embeddings Of Locally Connected Compacta, Gerard A. Venema

University Faculty Publications and Creative Works

vLet A(formula presented) -dimensional compactum and (formula presented)Mn a map into a piecewise linear (formula presented). The main result of this paper asserts that if X is locally (formula presented)-connected and/is (formula presented)-connected, then/is homotopic to a CE equivalence. In particular, every f-dimensional, f-connected, locally f-connected compactum is CE equivalent to a compact subset of (formula presented)as long as (formula presented).

Hydrogenic Formulas For Excited States Of The Atoms Through Carbon, Donald Greenspan

Mathematics Technical Papers - Archive

One of the beautiful consequences of Bohr's simplistic theory for hydrogen was a single formula for the excited states of the atom. Since this formula can be stated in terms of the constants of the hydrogen atom, it is called a hydrogenic formula. In this paper, analogous formulas are developed for the atoms through carbon.

Comparison Of Bootstrap And Jacknife Statistical Procedures, Amanuel Gobena

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

This report compares the bootstrapping to jacknifing statistical procedures in terms in bias, confidence interval and estimation of median. Related literature have been reviewed. A bootstrap allows a researcher to get an approximation to the distribution of possibly complicated statistical summaries. It is based on random sampling with replacement from experimental units. Jacknife has also been in operation prior to bootstrapping statistical procedure. The jacknife divides the data into subgroups and obtains partial estimates of these subgroups by omitting one subgroup at a time. When both of these statistical resampling procedures are compared the bootstrap has less bias, more accurate …

Some Graph-Colouring Theorems With Applications To Generalized Connection Networks, David G. Kirkpatrick, Maria M. Klawe, Nicholas Pippenger

All HMC Faculty Publications and Research

With the aid of a new graph-colouring theorem, we give a simple explicit construction for generalized n-connectors with 2k - 1 stages and O( n^{1 + 1 / k} (log n )^{( k - 1)/ 2} ) edges. This is asymptotically the best explicit construction known for generalized connectors.

Rapid Computation Of The Energy States Of Two-Electron Systems, Donald Greenspan

Mathematics Technical Papers - Archive

A new deterministic approach to modelling atoms and molecules is developed which uses static and dynamic numerical methods. The estimate for the ground state energy of [see pdf for notation] is closer to the experimental estimate than is the quantum mechanical result. for the hydrogen molecule ion, the result obtained is entirely comparable to that from quantum mechanics. For various atomic calculations, the results deviate from experimental results by less than one half of one percent. The theory incorporates a classical interpretation of electron pairing from a superstring point of view. The approach leads to a new, explicit formula for …

Cramer Type Large Deviations For Generalized Rank Statistics, Munsup Seoh, Stegan S. Ralescu, Madan L. Puri

Mathematics and Statistics Faculty Publications

A Cramer type large deviation theorem is proved under alternatives as well as under hypothesis for the generalized linear rank statistic which includes as special cases (unsigned) linear rank statistics, signed linear rank statistics, linear combination of functions of order statistics, and a rank combinatorial statistic.

Analytical And Numerical Studies On The States Of Ions And Atoms, Donald Greenspan

Mathematics Technical Papers - Archive

A speculative model is described which refines and extends the method of Bohr to various atoms and ions which have four or fewer electrons. The results for ground, single, and multiple excited states are of unexpectedly high accuracy for so simplistic an approach.

Elliptic Regularization For A Class Of Strongly Nonlinear Degenerate Eigenvalue Problems On Orlicz-Sobolev Spaces. I: The Ode Case, Pierre A. Vuillermot

Mathematics Technical Papers - Archive

This paper is devoted to proving sharp Holder-Lipschitz regularity estimates for the eigensolutione to a class of degenerate Sturm-Liouville eigenvalue problems with polynomial and exponential nonlinearities. The general method of proof represents as blending of a suitable regularization procedure along with a new method of auxiliary solutions, which we develop in detail. it allows one to exhibit a phenomenon of screening to regularity due to degeneracy and a new phenomenon of breakdown of regularity at short distances: while all of the eigensolutions are Lipschitz-continuous functions of their argument, their first derivatives exhibit a transition from Lipschitz-continuity to Hoder-continuity when the …

Particle Simulation Of Spiral Galaxy Evolution, Donald Greenspan

Mathematics Technical Papers - Archive

Spiral galaxies are modelled as n-body systems by means of long range and molecular-type short range forces. A relatively massive, elliptic, type core is sit into rotational motion in a less dense, tidal prone medium. Pressure waves result along whose leading edges there is increased luminosity, which develops in a spiral pattern.

Nonexistence Of Spatially Localized Free Vibrations For A Class Of Nonlinear Wave Equations, Pierre A. Vuillermot

Mathematics Technical Papers - Archive

We prove the nonexistence of free vibrations of arbitrary period with polynomially decreasing profiles for a large class of nonlinear wave equations in one space dimension. Our class of admissible models includes examples of non integrable wave equations with certain polynomial nonlinearities, as well as examples of completely integrable ones with exponential nonlinearities related to Mikhailov's equations. Our result thus proves a particular case of a conjecture first formulated by Eleonskii, Kulagin, Novozhilova and Silin, and dispels some confusion regarding the relationship between the existence of so-called breather-solutions and the complete integrability of the wave equation. Our class of admissible …

Monte Carlo Simulation Of The Game Of Twenty-One, Douglas E. Loer

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

The purpose of this paper is to demonstrate the application of computer simulation to the game of Twenty-One to predict a player's expected return from the game. Twenty-One has traditionally been one of the most popular casino games and has attracted much effort to accurately estimate the house's true advantage. Probability theory has been tried, but the thousands of different combinations of cards possible in all hands throughout the entire pack make it practically impossible to apply probability theory without overlooking some possibilities. For this reason, Twenty-One is a perfect candidate for simulation. By blocking several simulations, normal theory can …

Semiclassical Modeling Of The H2 Covalent Bond, Donald Greenspan

Mathematics Technical Papers - Archive

A semiclassical model is developed for the covalent bond of the H2 molecule. The model utilizes a classical analogue of electron pairing and requires an electron excitation mechanism. The computational technique used to solve the associated mathematical equations is fast and economical. The molecular ion H2 is then analyzed directly by applying a minimum-escape-velocity algorithm to one electron of a ground state H2 molecule.

Commutator Identities Obtained By The Magnus Algebra, Anthony M. Gaglione, Dennis Spellman

Mathematics Faculty Publications

In this paper, two related commutator identities are established through the use of the Magnus Algebra (the algebra of noncommutative formal power series with integral coefficients).

The Algorithmic Way Of Life Is Best, Stephen B. Maurer , '67

Mathematics & Statistics Faculty Works

No abstract provided.

Interpolating Sequences On Curves, Samih Obaid, D. Rung

Faculty Publications

We established a condition on boundary curves (ending at points) lying either in the unit disc or the upper half plane which implies that any consecutively separated sequence, in the hyperbolic distance, lying on one of these curves is an interpolating sequence for bounded holomorphic functions.

On Endomorphism Algebras Of Mixed Modules, Brendan Goldsmith, B. Franzen

Articles

No abstract available

Multiple Shooting, Monique St-Maurice

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

The purpose of this report was to study the Multiple Shooting method, a numerical method to solve boundary value ordinary differential equation. A FORTRAN program was written to solve the specific problem.

y'' = -y, y(0) = 0, y(π/2) = 1

on a microcomputer, using the microsoft FORTRAN compiler and the 8087 coprocessor.

Economic Genuine Link: Impacts On Liberian Flag Shipping, Victor E. Dougba

Marine Affairs Theses and Major Papers

Phasing out of open registries, supported by most developing nations at the United Nations Conference on Trade and Development (UNCTAD), would have triggered a chain reaction among open registries, ship owners, seafarers, and the revenues earned by those supplying shipboard labor. Adherence to the criteria proposed by developing states concerning economic "genuine link" is unsatisfactory to ship owners of developed nations, since it would increase their operating costs. Additionally, if the concept was enforced, it is likely that open registries would have experienced a massive dis-enrollment. The application of three techniques, the Chi-Square Statistic, and Index of Seafarer Displacement, and …

The Energy States Of Helium Via Bohr-Einstein Determinism, Donald Greenspan

Mathematics Technical Papers - Archive

Correct ground, ionization, singly excited and doubly (excited energy states are deduced deterministically by a direct extension of Bohr's method for hydrogen. The theory incorporates a classical interpretation of electron pairing and requires computer methodology to solve the resulting mathematical equations.

On Finite Element Methods For The Euler-Poisson-Darboux Equation, Anatoly M. Genis

Mathematics and System Engineering Faculty Publications

We deal primarily with the derivation of various convergence estimates for some semidiscrete and fully discrete procedures which might be used in the approximation of exact solutions of initial-boundary value problems with homogeneous Dirichlet boundary conditions for the Euler-Poisson-Darboux equation. Although the equation is of hyperbolic type, the results are somewhat analogous to those known for parabolic equations, due to the presence of a limited 'smoothing' property. This paper contain L//2 estimates, maximum norm estimates, negative norm estimates, interior estimates of difference quotients and superconvergence estimates of the error.

Life Table Construction From Population Age Distributions Suffering From Response Biases In Age-Reporting:A New Technique(Not Requiring Age Smoothing)With Application To Indian Census Age-Returns., Subrata Lahiri Dr.

Doctoral Theses

Preliminary concepts of life tables, its role in demographic analysis, a brief chronological review of various literature on the construction of life table starting from John Grants investigation on mortality, along with an introduction to the basic problem and objectives of the present study.Chapter II describes the concept and utility of cumulative census survival ratios, first introduced by Professors Ansley J. Coale and Paul Demeny (1967) as the ratio of the number of persons aged x+10 end above enumerated at time t+10 to the number of persons aged x and above enumerated at time t. These are compared to the …

U.S. Input-Output Data: A 1984 Update, Ronald E. Miller

Accounts and Data

This paper calls attention to the U.S. national input-output data for 1977 and the U.S. multiregional input-output data for the same year; both of these data sets became available during 1984. In particular, the commodity-by- industry accounting scheme which underpins both the 1972 and 1977 U.S. national models (as well as the U.S. 1977 multiregional model), is contrasted with the industry-by-industry approach of the original Leontief framework, which was the basis of the pre-1972 U.S. national tables.