Digital Commons Network^™

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.

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 …

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.

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

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).

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.

Sample Solutions Of Stochastic Ordinary Differential Equations, K. Waling

Mathematics Technical Papers - Archive

Motivated by the stochastic differential equation[see pdf for notation] in [see pdf for notation] we prove a measurable dependence on parameters theorem for ODEs in case f is only continuous in [see pdf for notation] is done by means of a known result about measurable selections of multivalued maps. Afterwards we discuss consequences for stochastic ODEs.

An Elementary Algebraic Method For Approximating Average Radii Of First And Secong Ring Electrons, Donald Greenspan

Mathematics Technical Papers - Archive

In this paper, experimental ionization energies are used to determine algebraic equations whose solutions approximate relativistic quantum mechanical estimates of average atomic radii. These algebraic equations are nonlinear and are solved on a digital computer by Newton's method. Pairing is an essential element in the formulation.

Sample Solutions Of Stochastic Boundary Value Problems, V. Lakshmikantham, G. S. Ladde, K. Deimling

Mathematics Technical Papers - Archive

We prove existence theorems for nonlinear stochastic Sturmiouville problems which improve results from [4]. In the simplest case this is done by means of a known result about measurable selections of multivalued maps and a new fixed point theorem for stochastic nonlinear operators which is more realistic than existing ones.

Review Of "The Future Of College Mathematics" Edited By A. Ralston And G. S. Young, Stephen B. Maurer , '67

Mathematics & Statistics Faculty Works

No abstract provided.

Existence And Regularity Theory For Isoperimetric Variational Problems On Orlicz-Sobolev Spaces: A Review, Pierre A. Vuillermot

Mathematics Technical Papers - Archive

In this review article, we outline and discuss our most recent results regarding the existence and the regularity theory for a class of strongly nonlinear eigenvalue problems on Orlicz-Sobolev spaces, with a glance at other contemporary attempts to understand the structure of some strongly nonlinear variational boundary-value problems defined on certain nonreflexive Banach spaces. The class of eigenvalue problems recently investigated can best be defined as follows. With [see pdf for notation] be an open bounded domain with closure -6 and smooth [see pdf for notation] boundary asp; let [see pdf for notation] be a family of [see pdf for …

Interval Estimation Of The Noncentrality Parameter Of A Gamma Distribution, Chien-Pai Han, Paul Chiou

Mathematics Technical Papers - Archive

Asymptotic confidence interval for the noncentrality parameter of a Gamma distribution (or Chi-squared distribution) is derived. An algorithm for computing the maximum likelihood estimator of the non-centrality parameter is developed. A formula for the asymptotic variance of the maximum likelihood estimator is given. From the properties of the maximum likelihood estimator an asymptotic confidence interval is obtained.

On The Choice Of Shadow Prices For Project Evaluation., Jean Dreze Dr.

Doctoral Theses

Manohar athanna is one of the remotest parts of Jhalawar District (Rajasthan, India). In the month of June it offers a striking contrast of scenic beauty and economic destitution. Agricultural activity is at a virtual standstill. The soil is very arid, irrigation practically non-existent, and by then the villagers (many of them tribals) have resolved to wait upon the good will of the rain gods.. Hence they have very little to do, or at least so they believe. Some gather wood to sell it in Manohar, walking miles under the scorching sun for a meagre reward, and adding slowly but …

[See Pdf For Notation]-Reularity For The Solution Of Strongly Nonlinear Eigenvalue Problems On Orlicz-Sobolev Spaces, Pierre A. Vuillermot

Mathematics Technical Papers - Archive

We present a new method to prove the [see pdf for notation]-regularity of the eigenfunctions for Dirichlet problems with strictly convex Young functionnonlinearities in their principal part. The basic idea is threefold: we first invoke the topological methods of [12] to infer the existence of a countable infinity of [see pdf for notation]-eigensolutions; we then use Schauder's inversion technique to associate with each one of these eigensolutions a unique [see pdf for notation]-solution of an auxiliary Dirichlet problem; we finally prove the [see pdf for notation]-regularity of the original elgensolutions from the [see pdf for notation]-regularity of the auxiliary solutions, …

Deformation And Linkage Of Gorenstein Algebras, Andrew R. Kustin, Matthew Miller

Faculty Publications

General double linkage of Gorenstein algebras is defined. Rigidity, genericity, and regularity up to codimension six all pass across general double linkage. Rigid strongly unobstructed codimension four Gorenstein algebras which lie in different Herzog classes are produced.

On The Genus Of A Block Design, Joan Marie Rahn

Dissertations

The genus of a design (BIBD or PBIBD) is defined to be the genus of its corresponding hypergraph (objects as vertices, blocks as edges); that is, the genus of the bipartite graph associated with the hypergraph in a natural way. The Euler formula is used to establish a lower bound (gamma) for the genus of a block design. An imbedding of the design of the surface of genus (gamma) is then described by a voltage hypergraph or voltage graph. Use of the lower bound formula leads to a characterization of planar BIBDs. A connection between a block design derived from …

Difference Equations, Isoperimetric Inequality And Transience Of Certain Random Walks, Jozef Dodziuk

Publications and Research

No abstract provided.

Scs 94: Algebraic Theories For Proper Filter Monads, Oswald Wyler

Seminar on Continuity in Semilattices

No abstract provided.

On Maximizing The Average Time At A Goal, S. Demko, Theodore P. Hill

Research Scholars in Residence

In a decision process (gambling or dynamic programming problem) with finite state space and arbitrary decision sets (gambles or actions), there is always available a Markov strategy which uniformly (nearly) maximizes the average time spent at a goal. If the decision sets are closed, there is even a stationary strategy with the same property.Examples are given to show that approximations by discounted or finite horizon payoffs are not useful for the general average reward problem.

The Expectation Of Success Using A Monte Carlo Factoring Method – Some Statistics On Quadratic Class Numbers, Duncan A. Buell

Faculty Publications

A method has been proposed for factoring an integer N by using the structure of the class groups of quadratic fields of radicand – kN for various small multipliers k. We discuss the method and an implementation of the method, and various theoretical questions which have an impact on the practical use of the method in factoring. Some of the theoretical questions relate to the nature of class numbers and class groups; we present extensive statistical results on the class numbers and class groups of imaginary quadratic fields.