Digital Commons Network^™

Square Roots Of Finite Groups - Ii, Matthew Devos, David Mcadams, Rebecca Rapoport

Mathematical Sciences Technical Reports (MSTR)

A subset R of a finite group G is a square root of G if R² = G. If R is a square root of G for which |R|² = G, then R is referred to as a perfect square root of G. It can be shown using character theory that perfect square roots do not exist. The purpose of this paper is to work toward an elementary proof of this result.

Computer Simplification Of Engineering Systems Formulas, J. W. Helton, Mark Stankus, John Wavrik

Mathematics

Currently, the three most popular commercial computer algebra systems are Mathematica, Maple, and MACSYMA (the 3 M’s). These systems provide a wide variety of symbolic computation facilities for commutative algebra and contain implementations of powerful algorithms in that domain. The Gröbner Basis Algorithm, for example, is an important tool used in computation with commutative algebras and in solving systems of polynomial equations.

On the other hand, most of the computation involved in linear control theory is performed on matrices and these do not commute. A typical issue of IEEE TAC is full of A B C D type linear systems …

Topologies Invariant Under A Group Action, Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

We study links between faithful group actions on a set and topologies on that set. In one direction, a group action has its invariant topologies (so we may regard members of the action to be homeomorphisms relative to those topologies); in the other direction, a topology has its preserving group actions (i.e., the subgroups of the homeomorphism group of the topology). This two-way passage allows us to discuss topological features of group actions as well as symmetry features of topologies.

Review Of “Linear Programming And Related Problems” By E. Nering And A. W. Tucker, Stephen B. Maurer

Mathematics & Statistics Faculty Works

No abstract provided.

A New Approach To Automatic Target Recognition Using Wavelet Transforms, Anitha Panapakkam, S. N. Balakrishnan, Daniel St. Clair

Computer Science Technical Reports

Automatic Target Recognition (ATR) systems have significant impact in defense applications. There is a continuing need to develop new and robust techniques to handle the increasingly complex ATR problem. The objectives of this thesis are two-fold. First a new technique to be used for ATR is developed and secondly an integrated ATR system to investigate and combine all subsystems is developed. In this thesis, we have developed a new technique for the feature extraction stage of ATR problem using wavelet transforms. Wavelet transforms have been one of the widely investigated areas of research in the past few years. The promising …

Quasireversibility Methods For Non-Well-Posed Problems, Gordon W. Clark, Seth F. Oppenheimer

Faculty Articles

The nal value problem,

ae u t + Au = 0 ; 0 ! t ! T u(T ) = f

with positive self-adjoint unbounded A is known to be ill-posed. One approach to dealing with this has been the method of quasireversibility, where the operator is perturbed to obtain a well-posed problem which approximates the original problem. In this work, we will use a quasi-boundary-value method, where we perturb the nal condition to form an approximate non-local problem depending on a small parameter. We show that the approximate problems are well posed and that their solutions u converge on …

First Passage Processes In Queuing System Mx/Gr/1 With Service Delay Discipline, Lev M. Abolnikov, Jewgeni H. Dshalalow, Alexander M. Dukhovny

Mathematics and System Engineering Faculty Publications

This article deals with a general single-server bulk queueing system with a server waiting until the queue will reach level r before it starts processing customers. If at least r customers are available the server takes a batch of the fixed size r of units for service. The input stream is assumed to be a compound Poisson process modulated by a semi-Markov process and with a multilevel control of service time. The authors evaluate the steady state probabilities of the queueing processes with discrete and continuous time parameter preliminarily establishing necessary and sufficient conditions for the ergodicity of the processes. …

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

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 …

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).

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 …