Digital Commons Network^™

Multiple Solutions For A Semilinear Dirichlet Problem, Alfonso Castro, Jorge Cossio

All HMC Faculty Publications and Research

The authors prove that a semilinear elliptic boundary value problem has five solutions when the range of the derivative of the nonlinearity includes at least the first two eigenvalues. Extensive use is made of Lyapunov–Schmidt reduction arguments, the mountain pass lemma, and characterizations of the local degree of critical points.

Multiple Solutions For A Nonlinear Dirichlet Problem, Alfonso Castro, Jorge Cossio

All HMC Faculty Publications and Research

The authors prove that a semilinear elliptic boundary value problem has five solutions when the range of the derivative of the nonlinearity includes at least the first two eigenvalues. Extensive use is made of Lyapunov-Schmidt reduction arguments, the mountain pass lemma, and characterizations of the local degree of critical points.

Lajos Takács And His Work, Jewgeni H. Dshalalow, Ryszard Syski

Mathematics and System Engineering Faculty Publications

This paper, written in honor of the 70th birthday of Lajos Takács, addresses his life and work, and includes some personal observations and appreciation of his contributions. In particular, it includes a short biography, an informal discussion of some of his major research areas (queueing, fluctuations, waiting time processes, and random rooted trees), and an account of the relationship of his work to that of Félix Pollaczek.

Studies On Design, Routing And Fault Tolerance Of Interconnection Network., Krishnendu Mukhopadhyay Dr.

Doctoral Theses

A recent trend in computing is to distribute the computations among a set of processing elements. There are two basic appronches to this - one is to build a loosely-coupled system and the other is to form a tightly-coupled system [PS85].In a loosely-coupled system, the processors do not share common memory or a common clock; but sharing of important resources like data files, softwares, special hardware components etc., is possible without duplicating the resources themselves. The processing nodes may even be geographicully separated from each other and are connected through databuses, telephone/radio links, satellite, etc. Such loosely- coupled systems are …

Commutators As Powers In Free Products Of Groups, Leo Comerford, Charles Edmunds, Gerhard Rosenberger

Faculty Research and Creative Activity

The ways in which a nontrivial commutator can be a proper power in a free product of groups are identified

Lattice-Ordered Algebras That Are Subdirect Products Of Valuation Domains, Melvin Henriksen, Suzanne Larson, Jorge Martinez, R. G. Woods

All HMC Faculty Publications and Research

An f-ring (i.e., a lattice-ordered ring that is a subdirect product of totally ordered rings) A is called an SV-ring if A/P is a valuation domain for every prime ideal P of A. If M is a maximal ℓ-ideal of A , then the rank of A at M is the number of minimal prime ideals of A contained in M, rank of A is the sup of the ranks of A at each of its maximal ℓ-ideals. If the latter is a positive integer, then A is said to have finite rank, and if A …

Commutators As Powers In Free Products Of Groups, Leo Comerford, Charles C. Edmunds, Gerhard Rosenberger

Faculty Research and Creative Activity

The ways in which a nontrivial commutator can be a proper power in a free product of groups are identified

Perturbations Of Certain Reflexive Algebras, David R. Pitts

Department of Mathematics: Faculty Publications

In this note we use cohomological techniques to prove that if there is a linear map between two CSL algebras which is close to the identity, then the two CSL algebras are similar. We use our result to show that if 2' is a purely atomic, hyperreflexive CSL with uniform infinite multiplicity which satisfies the 4-cycle interpolation condition, then there are constants d, C > 0 such that whenever L is another CSL such that d(Alg2' , AlgL) < d, then there is an invertible operator S such that S Alg2'S-1 = AlgL and IISII liS-III < 1 + Cd(AIg2' , AIgL).

Lattice-Ordered Algebras That Are Subdirect Products Of Valuation Domains, Melvin Henriksen, Suzanne Larson, Jorge Martinez, R. G. Woods

Mathematics, Statistics and Data Science Faculty Works

An f-ring (i.e., a lattice-ordered ring that is a subdirect product pf totally ordered rings) A is called an SV-ring if AIP is a valuation domain for every prime ideal P of A. If M is a maximal e-ideal of A,then the rank of A at M is the number of minimal prime ideals of A contained in M, rank of A is the sup of the ranks of A at each of its maximal e-ideals. If the latter is a positive integer, then A is said to have finite rank, and if A = C(X) is the ring of …

On Lexical And Syntactic Processing Of Bangla Language By Computer., Probal Sengupta Dr.

Doctoral Theses

A distinctive intelligent trait of human beings is the ability to carry out meaningful communication through language. The communication may be direct as in spoken conversation or indirect as in written form, through the audio-visual media, etc. Linguistic ability in humans have fascinated scholars ever since man first learnt to use language. Linguistics, the branch of study involved in studying the nature of human linguistic communication, is perhaps as old as language itself. The invention of the computer added a new dimension to linguistics. Making the computer emu- late human linguistic behaviour was taken up as a challenge by computer …

An Algebraic Approach To Derivatives, Julia Lee Roman

Theses & Dissertations

The purpose of this thesis is to relate a unique method of dealing with the concept of the derivative of a function. The traditional approach to teaching calculus introduces the idea of the limit of a function early in the course as evidenced in the Essential Elements of the State Board of Education of Texas which places the limit concept as the second essential element of calculus in Texas high schools (Texas Education Agency (TEA) Essential Elements 1991). The "concepts and skills associated with the derivative" (TEA Essential Elements 1991) follow immediately after the introduction of the limit of a …

Letter From The Editor, Issue 10, 1994, Alvin White

Humanistic Mathematics Network Journal

No abstract provided.

Female Voices In Mathematics: A New Course, Shobha Gulati

Humanistic Mathematics Network Journal

No abstract provided.

Epsilon And Delta: A Little Love Story, Bonnie Shulman

Humanistic Mathematics Network Journal

No abstract provided.

What Changes Should Be Made For The Second Edition Of The Nctm Standards?, Zalman Usiskin

Humanistic Mathematics Network Journal

No abstract provided.

Math: It's Not Just A Four Letter Word, Susan Byerly

Humanistic Mathematics Network Journal

No abstract provided.

Poetry, Helen Lewy

Humanistic Mathematics Network Journal

No abstract provided.

Mathematics In Literature And Poetry, Joanne S. Growney

Humanistic Mathematics Network Journal

No abstract provided.

Nctm Standards, Second Edition: A Review And Commentary On Zalman Usiskin's Address, Harald M. Ness

Humanistic Mathematics Network Journal

No abstract provided.

Humacrostic, Stephen I. Brown

Humanistic Mathematics Network Journal

No abstract provided.

Reconstruction Of Semiconductor Doping Profile From Lbic Image, Weifu Fang, Kazufumi Ito

Mathematics and Statistics Faculty Publications

In this paper, the authors study the reconstruction of a semiconductor doping profile or, equivalently, the equilibrium potential, from its LBIC (laser-beam-induced current) image. For the one-dimensional case, the authors first characterize the attainable class of current measurements, and from this they show the nonuniqueness of the inverse problem. Then the reconstruction of the equilibrium potential is reduced to finding two constants subject to some constraints. A reconstruction algorithm is established based on a least squares formulation of the problem. The case of noise-collapsed data is also discussed. For a special case of two-dimensional domain, the authors apply the one-dimensional …

Partial Difference Sets In P-Groups, James A. Davis

Department of Math & Statistics Faculty Publications

Most of the examples of PDS have come in p-groups, and most of these examples are in elementary abelian p-groups. In this paper, we will show an exponent bound for PDS with the same parameters as the elementary abelian case.

Acoustic-Wave Nonlinearity In Stimulated Brillouin Scattering, Evangelos A. Coutsias, Bruce S. Masson

Branch Mathematics and Statistics Faculty and Staff Publications

Stimulated Brillouin scattering is investigated here under conditions characterized by high optical pump intensity. Calculations are carried out at 1.3 and 3.8 /jm with pump intensities equal to approximately three times the threshold. Such strong optical forcing leads to significant self-distortion of the density profile in the material wave serving as the optical grating. The method of multiple scales is used to find a uniform asymptotic expansion in the coupling. At the first perturbation level the resonant portion of the problem yields abridged equations for the incident and the scattered waves with frequencies CWaLn d ws = L - 0 …

Bergman Spaces On An Annulus And The Backward Bergman Shift, William T. Ross

Department of Math & Statistics Technical Report Series

In this paper, we will give a complete characterization of the invariant subspaces M (under ƒ → zƒ) of the Bergman space L^p_a(G), 1 < p < 2, G an annulus, which contain the constant function 1. As an application of this result, we will characterize the invariant subspaces of the adjoint of multiplication by z on the Dirichlet spaces D_q, q > 2, as well as the invariant subspaces of the backward Bergman shift ƒ → (ƒ – ƒ(0))/z on L^p_a(𝔻), 1 < p < 2.

Evolving Plane Curves By Curvature In Relative Geometries Ii, Michael E. Gage, Yi Li

Mathematics and Statistics Faculty Publications

In this paper we prove the existence of self-similar solutions to the anisotropic curve shortening equation.

Minimax-Optimal Strategies For The Best-Choice Problem When A Bound Is Known For The Expected Number Of Objects, Theodore P. Hill, D. P. Kennedy

Research Scholars in Residence

For the best-choice (or secretary) problem with an unknown number N of objects, minimax-optimal strategies for the observer and minimax distributions for N are derived under the assumption that N is a random variable with expected value at most M, where M is known. The solution is derived as a special case of the situation where N is constrained by Ef(N) ≤ M, where f is increasing with f(i)-f(i-1) convex.

Rational Cubic B-Spline Interpolation And Its Applications In Computer Aided Geometric Design, Kotien Wu

Mathematics & Statistics Theses & Dissertations

Because of the flexibility that the weights and the control points provide, NURBS have recently become very popular tools for the design of curves and surfaces. If the weights are positive then the NURB will lie in the convex hull of its control points and will not possess singularities. Thus it is desirable to have positive weights.

In utilizing a NURB a designer may desire that it pass through a set of data points {x_i} This interpolation problem is solved by the assigning of weights to each data point. Up to now little has been known regarding the …

Some Sampling Designs And Estimation Problems, Hassan Lakkis

Mathematics & Statistics Theses & Dissertations

In the first chapter we review some standard estimators in sampling from a finite population, and some design-based estimators in sampling from a continuous universe.

In concert with the theory initiated by professor Douglas Robson (personal communication) and later presented by Cordy (1993), we consider design-based variance estimation for probability sampling from a continuous and spatially distributed universe. Using this theory in chapter two, the sampling design of one random point from each cell of a translated grid is investigated and the problem of edge effects on estimation is illustrated with examples. Also in chapter four, standard systematic sampling methods …

Optimum Continuous Sampling Plans And A Few Other Sqc Problems., D Ghosh Dr.

Doctoral Theses

The wide acceptance of Statistics as a basic tool in technölogical growth, later recog- nised as a Key technology, gained ground with the pioneering work of Shewhart in 20s, introducing Statistical Quality Control (SQC) in manufacturing industry. Around the same time a solid statistical basis was being worked out for the ageold concepts of sampling inspection for industrial products. By 1930, acceptance sam- pling for lot by lot inspection was being applied in Western Electric Company and elsewhere. Since then statistical tools have been the major technical inputs of To- tal Quality Management which has spread far and wide as …

Pinching Theorems For Teardrops And Footballs Of Revolution, Joseph E. Borzellino

Mathematics

We give explicit optimal curvature pinching constants for the Riemannian (p, q)- football orbifolds under the assumption that they are realised as surfaces of revolution in ³. We show that sufficiently pinched sectional curvature assumptions imply that a (p, q)-football must be good.