Digital Commons Network^™

A Root Finding Algorithm For Parallel Architecture Machines, Stuti Moitra

Computer Science Theses & Dissertations

In this thesis a parallel algorithm for determining the zeros of any given analytic function is described. Parallelism is achieved by modifying the traditional bisection algorithm for architecture machines.

Given any user supplied function f(X), continuous on the interval A_o ≤ x ≤ B₀, and the tolerance of accuracy an algorithm of determining up to ten roots, with error of approximation less than or equal to tolerance, on parallel systems like Distributed Array Processor (OAP) and N-cube is considered.

A variation of the bisection method has been adapted for this purpose. At each level of iteration a …

Bimodules Over Cartan Subalgebras, Richard Mercer

Mathematics and Statistics Faculty Publications

Given a Cartan subalgebra A of a non Neumann algebra M, the techniques of Feldman and Moore are used to analyze the partial isometries v in M such that v* Av is contained in A. Orthonormal bases for M consisting of such partial isometries are discussed, and convergence of the resulting generalized fourier series is shown to take place in the Bures A-topology. The Bures A-topology is shown to be equivalent to the strong topology on the unit ball of M. These ideas are applied to A-bimodules and to give a simplified and intuitive proof of the Spectral Theorem …

Stability Of A Viscoelastic Burgers Flow, D. Glenn Lasseigne, W. E. Olmstead

Mathematics & Statistics Faculty Publications

The system of equations proposed by Burgers to model turbulent flow in a channel is extended to include viscoelastic affects. The stability and bifurcation properties are examined in the neighborhood of the critical Reynolds number. For highly elastic fluids, the bifurcated state is periodic with a shift in frequency.

On The Equivalence Of The Operator Equations Xa + Bx = C And X - P(-B)Xp(A)(-1) = W In A Hilbert-Space, P A Polynomial, Tapas Mazumdar, David Miller

Mathematics and Statistics Faculty Publications

We consider the solution of (*) XA+BX = C for bounded operators A,B,C and X on a Hilbert space, A normal. We establish the existence of a polynomial p and a bounded operator W with the property that the unique solution X of (*) also solves X − p(−B)Xp(A)⁻¹ = W uniquely. A known iterative algorithm can be applied to the latter equation to solve (*).

A Scale Of Linear Spaces Related To The Lp Scale, S J. Dilworth

Faculty Publications

No abstract provided.

Boundary Value Problems In Elasticity And Thermoelasticity, Stuart Davidson

Mathematics & Statistics Theses & Dissertations

In this dissertation the author solves a series of mixed boundary value problems arising from crack problems in elasticity and thermoelasticity. Using integral transform techniques and separation of variables appropriately, it is shown that the solutions can be found by solving a corresponding set of triple or dual integral equations in some instances, while in others the solutions of triple or dual series relations are required. These in turn reduce to various singular integral equations which are solved in closed form, in two cases, or by numerical methods. The stress intensity factors at the crack tips, the physical parameters of …

Graphs, Maneuvers, And Turnpikes, Arthur T. Benjamin

All HMC Faculty Publications and Research

We address the problem of moving a collection of objects from one subset of Z^m to another at minimum cost. We show that underfairly natural rules for movement assumptions, if the origin and destination are far enough apart, then a near optimal solution with special structure exists: Our trajectory from the originto the destination accrues almost all of its cost repeatingat most m different patterns of movement. Directions for related research are identified.

Evaluation Of The Function Exp (X2) Erfc (X) To Higher Precisions For Higher-Order Derivative Polarography Of Ce-Type Electrode Process, Myung-Hoon Kim, Veriti P. Smith, Tae-Kee Hong

Chemistry & Biochemistry Faculty Publications

The function exp(x2)erfc(x), which is often encountered in studies of electrode kinetics, is evaluated to an extended precision with 32 significant decimal digits in order to find theoretical relationships used in derivative polarography/voltammetry for a chemically-coupled electrode process. Computations with a lower precision are not successful. Evaluation of the function is accomplished by using three types of expansions for the function. Best ranges of arguments are selected for each equation for particular precisions for efficiencies. The method is successfully applied to calculate higher-order derivatives of the current-potential curves in all potential ranges for a reversible electron transfer reaction coupled with …

A Note On Intersection Numbers Of Difference Sets, K. T. Arasu, James A. Davis, Dieter Jungnickel, Alexander Pott

Department of Math & Statistics Faculty Publications

We present a condition on the intersection numbers of difference sets which follows from a result of Jungnickel and Pott [3]. We apply this condition to rule out several putative (non-abelian) difference sets and to correct erroneous proofs of Lander [4] for the nonexistence of (352, 27, 2)- and (122, 37, 12)-difference sets.

A Generalization Of Levy's Concentration-Variance Inequality, R. D. Foley, Theodore P. Hill, M. C. Spruill

Research Scholars in Residence

Sharp lower bounds are found for the concentration of a probability distribution as a function of the expectation of any given convex symmetric function φ. In the case φ(x)=(x-c)², where c is the expected value of the distribution, these bounds yield the classical concentration-variance inequality of Lévy. An analogous sharp inequality is obtained in a similar linear search setting, where a sharp lower bound for the concentration is found as a function of the maximum probability swept out from a fixed starting point by a path of given length.

Curvatures Of Left Invariant Metrics On Lie Group And Parametric Homotopy Principles For A Class Of Partial Differential Relations On Closed Manifolds., Amitabh Tiwari Dr.

Doctoral Theses

The title of this thesis refers to two problems of different nature having no connection between them. These problems ere presented in two parts. In Pert I we have settled two conjectures of Milnor, on Lie groups with left-invariant metrics, in the affirmative and in Part II we have obtained a now Smale - Hirsch - Gromov - type theorem on the homotopy classification of a close of portial differential relations on closed manifolds. More detailed introduotions to these parts are given at the beginning of each part, It has bean our attempt to make the presentations as self-contained as …

Disparities In Development: A Case Study Of Karnataka State (India)., Jayalaxmi Jayaram Dr.

Doctoral Theses

The Five Year Plans have recognised the need to bridge the developmental disparities across the regions and have formulated strategies for accelerated development of backward are as. However, the widening disparities between a few highly developed centres and vast areas of under development only bring out the inadequacies of the plans which are yet to integrate the resources of a region to its people. This study is an attempt to understand the spatial processes and patterns of development which offer an explanation to the intra/inter-regional contrasts in development. The study while high-lighting the importance of the Spatial approach has, in …

Semi-Martiangales Associated With Crossing, B. Rajeev Dr.

Doctoral Theses

In thia theoia ve study the locel behaviour or semi mertingalea. Civen e cant!nuoue sent rartineale and an i-tetval (n,t), ve define a new pracees which airrara the bereufour of the originel procese in the interval (a, b). Thie neu procees tur ns cut to he a semi-nartingale uhose junpa during [J,t: ere closely reinted to the number of croosinge of (o,t) during [0,t ].Jur sterting point is indned P, Levy's rortingale cherocterizotion of around an motion : If (xt) and (x2t - t) ore cantinuOun lacol nar- tingales then (xt) must be a Srownion mation. Let now Hn(x,t) denote …

Studies On Level Of Living And Poverty In Rural India., Padmaja Pal Dr.

Doctoral Theses

The present dissertation consists of several studies on disparities in level of living and poverty in rural India. These studies are based on a special tabulation of disaggregated household budget data, from the Central Sample of the Indian National Sample Survey (NSS) 28th round (october 1973- June 1974). This was based on a copy of the updated Honey- well tape provided by the authorities of the NSS Organisation, Government of India. Two of the main aims of this dissertation are to study disparities in level of living and incidence of poverty across (1) Social groups, such as Scheduled Castes, Scheduled …

Supercomputer Simulation Of Liquid Drop Formation On A Solid Surface, Donald Greenspan

Mathematics Technical Papers - Archive

Using a molecular dynamics type approach, we show how to simulate the formation of a liquid drop on a solid surface. Application is made to the case in which the liquid is water and the solid is graphite. The dynamical equations are large systems of nonlinear, ordinary differential equations which must be solved numerically. CRAY X-MP/ 24 simulations and related contact angle calculations are described and discussed.

On Two Function-Spaces Which Are Similar To L0, S J. Dilworth, D A. Trautman

Faculty Publications

No abstract provided.

The Impact Of The Capital Construction Fund On The Rhode Island Commercial Fishing Industry, Paul R. Helland

Marine Affairs Theses and Major Papers

The impact of the Capital Construction Fund, a tax deferral program utilized for the construction of fishing vessels, is examined in the context of Rhode Island's fishing industry. It was believed that the Capital Construction Fund contributed to overcapitalization, was an incentive to purchase a vessel, and was mainly used by individuals targeting underutilized species. Indicators of capitalization such as number, size, and ages of vessels owned were gathered from the owners of vessels home-ported in Rhode Island during personal interviews. Response of those that have used the Program were separated from those who have not. A frequency analysis was …

Composing Math Education In The Information Age: A Song Of Change, Camille Baker

Graduate Student Independent Studies

This research describes what happened when a teacher implemented change directed toward a relevant math curriculum and effective pedagogy which address present day needs. The assessment of these needs includes an investigation of today's reform literature and the nature of mathematics, along with the history of education and cognitive theory of the 1900's.

Multicolored Simon Newcomb Problems, Don Rawlings

Mathematics

Recent progress made by Desarmenien and Foata in the area of permutation statistics indirectly points out a certain gap in the theory of sequence enumeration. The remedy of the situation lies in the consideration of some colorful extensions of the Simon Newcomb problem.

Remarks On Estimates For The Green Function, Jose Luis Menaldi

Mathematics Faculty Research Publications

No abstract provided.

Particle Modelling Of Combustion, Donald Greenspan

Mathematics Technical Papers - Archive

Combustion is simulated by a molecular type model using classical molecular type interaction formulas. Supercomputer examples which emphasize turbulent motion are described and discussed.

Construction Of The Best Monotone Approximation On Lp [0, 1], J. J. Swetits, S. E. Weinstein

Mathematics & Statistics Faculty Publications

(First paragraph) For 1 ≤ p < ∞, let L_p, denote the Banach space of pth power Lebesgue integrable functions on [0, l] ∥ƒ∥_p = (∫¹₀∣ƒ∣ ^p)^1/p Let M_p denote the set of nondecreasing functions in L_p. For l < p < ∞ , each ƒ∊L_p has a unique best approximation from M_p, while, for p = 1, existence of a best approximation from M₁ follows from Proposition 4 of [6].

Ordered Ultraconnected Rings, Melvin Henriksen, Frank A. Smith

All HMC Faculty Publications and Research

A ring R with identity element 1 is called ultraconnected if for each unital homomorphism ϕ of Z^ω into R, there is an i < ω such that ϕ(f) = f(i) • 1 for every f € Z^ω . Our main result is that if no sum of nonzero squares in R is 0 and R has only trivial idempotents, then R fails to be ultraconnected iff R contains a subring isomorphic to Z^ω/P for some free minimal prime ideal P of Z^ω.

Faster Circuits And Shorter Formulas For Multiple Addition, Multiplication And Symmetric Boolean Functions, Michael Paterson, Uri Zwick, Nicholas Pippenger

All HMC Faculty Publications and Research

A general theory is developed for constructing the shallowest possible circuits and the shortest possible formulas for the carry-save addition of n numbers using any given basic addition unit. More precisely, it is shown that if BA is a basic addition unit with occurrence matrix N, then the shortest multiple carry-save addition formulas that could be obtained by composing BA units are of size n1p+o(1)/, where p is the unique real number for which the Lp norm of the matrix N equals 1. An analogous result connects the delay matrix M of the basic addition unit BA and the minimal …

Arbitrary Order, Hamiltonian Conserving Numerical Solutions Of Calogero And Toda Systems, Donald Greenspan, Andrzej Marciniak

Mathematics Technical Papers - Archive

For Calogero and Toda dynamical equations two numerical methods of arbitrary high order, conserving the Hamiltonian are developed. The methods consist of modifications of conventional polynomial extrapolation with the Gragg method used as a basic method. The theoretical study is confirmed by a number of numerical examples.

Energy Conserving Numerical Solutions Of Simplified Turbulence Equations, Donald Greenspan, Andrzej Marciniak

Mathematics Technical Papers - Archive

The purpose of this paper is to develop some numerical methods for solving non-Hamiltonian nonintegrable simplified turbulence equations which conserve the energy. We present two kinds of conservative methods for solving these equations: a second order method which uses simple differences, and an arbitrary high order method based on a modification of conventional polynomial extrapolation.

On Some Queue Length Controlled Stochastic Processes, Lev M. Abolnikov, Alexander M. Dukhovny, Jewgeni H. Dshalalow

Mathematics and System Engineering Faculty Publications

The authors study the input, output and queueing processes in a general controlled single-server bulk queueing system. It is supposed that inter-arrival time, service time, batch size of arriving units and the capacity of the server depend on the queue length. The authors establish an ergodicity criterion for both the queueing process with continuous time parameter and the embedded process, study their transient and steady state behavior and prove ergodic theorems for some functionals of the input, output and queueing processes. The following results are obtained: Invariant probability measure of the embedded process, stationary distribution of the process with continuous …

A Theorem On Many Fixed Points For Nonlinear Operator, Yong Sun, Jingxian Sun

Mathematics and System Engineering Faculty Publications

Multiple fixed points of weakly inward mappings are investigated by means of ordinary differential equations in abstract spaces.

Error Bounds For Two Even Degree Tridiagonal Splines, Gary W. Howell

Mathematics and System Engineering Faculty Publications

We study a C(¹) parabolic and a C(²) quartic spline which are determined by solution of a tridiagonal matrix and which interpolate subinterval midpoints. In contrast to the cubic C(²) spline, both of these algorithms converge to any continuous function as the length of the largest subinterval goes to zero, regardless of “mesh ratios”. For parabolic splines, this convergence property was discovered by Marsden [1974]. The quartic spline introduced here achieves this convergence by choosing the second derivative zero at the breakpoints. Many of Marsden’s bounds are substantially tightened here. We show that for functions of two or fewer coninuous …

A Statistical Theory Of Digital Circuit Testability, Sharad C. Seth, Vishwani D. Agrawal, Hassan Farhat

Mathematics Faculty Publications

When test vectors are applied to a circuit, the fault coverage increases. The rate of increase, however, could be circuit dependent. A relation between the average fault coverage and circuit testability is developed in this paper. The statistical formulation allows computation of coverage for deterministic and random vectors. We discuss the following applications of this analysis: determination of circuit testability from fault simulation, coverage prediction from testability analysis, prediction of test length, and test generation by fault sampling.