Digital Commons Network^™

Conjugating Polynomials On Finite Rings, M. Insall, L. Mullin, R. Wilkerson

Computer Science Technical Reports

No abstract provided.

Square Roots Of Finite Groups, Kashi Abhyankar, Daniel Grossman

Mathematical Sciences Technical Reports (MSTR)

Let G be a finite group of order n². A perfect square root of G is a subset X of G such that |X| = n and X² = G. Neither generalized dihedral groups nor groups of nilpotency class two have perfect square roots.

Letter From The Editor, Issue 9, 1994, Alvin White

Humanistic Mathematics Network Journal

No abstract provided.

Mathematics And The Arts: Taking Their Resemblances Seriously, Frederick Reiner

Humanistic Mathematics Network Journal

No abstract provided.

Students' Understanding Of Functions In Calculus Courses, G. S. Monk

Humanistic Mathematics Network Journal

No abstract provided.

Poems, Lee Goldstein

Humanistic Mathematics Network Journal

No abstract provided.

Complete Issue 9, 1994

Humanistic Mathematics Network Journal

No abstract provided.

Letter To The Editor, Ken Ross

Humanistic Mathematics Network Journal

No abstract provided.

The Language Of Mathematics: A Quantitative Course For A General Audience, Stephanie F. Singer

Humanistic Mathematics Network Journal

No abstract provided.

Writing Mathematics, E. G. Bernard

Humanistic Mathematics Network Journal

No abstract provided.

Mathematics For Math Majors: Loss Of Self-Esteem, Chun-Ip Fung, Man-Keung Siu

Humanistic Mathematics Network Journal

No abstract provided.

Philosophy Of Mathematics, Mathematics Education, And Philosophy Of Mathematics Education, Yuxin Zheng

Humanistic Mathematics Network Journal

No abstract provided.

Space Venture, Edward E. Chipman

Humanistic Mathematics Network Journal

No abstract provided.

Back Matter, Issue 9, 1994

Humanistic Mathematics Network Journal

No abstract provided.

Composite Knots In The Figure-8 Knot Complement Can Have Any Number Of Prime Factors, Michael C. Sullivan

Articles and Preprints

We study an Anosov flow Ф_t in S³ – {figure-8 knots}. Birman and Williams conjectured that the knot types of the periodic orbits of this flow could have at most two prime factors. Below, we give a geometric method for constructing knots in this flow with any number of prime factors.

Uniqueness Of Stable And Unstable Positive Solutions For Semipositone Problems, Alfonso Castro, Sudhasree Gadam

All HMC Faculty Publications and Research

Abstract not included in this article.

An Involutive System And Integrable C. Neumann System Associated With The Modified Korteweg-De Vries Hierarchy, Zhijun Qiao

School of Mathematical & Statistical Sciences Faculty Publications

In this article, a system of finite-dimensional involutive functions is presented and proven to be integrable in the Liouville sense. By using the nonlinearization method, the C. Neumann system associated with the modified Korteweg-de Vries (mKdV) hierarchy is obtained. Thus, the C. Neumann system is shown to be completely integrable via a gauge transformation between it and an integrable Hamiltonian system. Finally, the solution of a stationary mKdV equation and the involutive solutions of the mKdV hierarchy are secured. As two examples, the involutive solutions are given for the mKdV equation: u,+ ;uXXX- $u2u,=0 and the 5th mKdV equation v,- …

Optical Hamiltonians And Symplectic Twist Maps, Christophe Golé

Mathematics Sciences: Faculty Publications

This paper concentrates on optical Hamiltonian systems of T*Tn, i.e., those for which Hpp is a positive definite matrix, and their relationship with symplectic twist maps. We present theorems of decomposition by symplectic twist maps and existence of periodic orbits for these systems. The novelty of these results resides in the fact that no explicit asymptotic condition is imposed on the system.

Gravity And Electromagnetism In Noncommutative Geometry, Giovanni Landi, Nguyen Ai Viet, Kameshwar C. Wali

Physics - All Scholarship

We present a unified description of gravity and electromagnetism in the framework of a Z 2 non-commutative differential calculus. It can be considered as a “discrete version” of Kaluza-Klein theory, where the fifth continuous dimension is replaced by two discrete points. We derive an action which coincides with the dimensionally reduced one of the ordinary Kaluza-Klein theory.

Injective Endomorphisms Of 풢X-Normal Semigroups: Finite Defects., Inessa Levi

Faculty Bibliography

A semigroup of transfonnations of an infinite set X is called ^'x-normal if S is invariant under conjugations by permutations of X. In this paper we describe injective endomorphisms of & x -normal semigroups of total one-to-one transformations / such that the range of / has a finite non-empty complement in X.

Projective Plane Embeddings Of Polyhedral Pinched Maps, Adrian Riskin

Mathematics

We give various conditions on pinched-torus polyhedral maps which are necessary for their graphs to be embeddable in the projective plane. Our other main result is that even if the graph of a polyhedral map in the pinched torus is embeddable in a projective plane, the map induced by the embedding cannot be polyhedral, but must have all faces bounded by cycles. Finally, we give a class of examples of graphs which have polyhedral embeddings on the pinched torus and also on orientable surfaces of arbitrary high genus.

Finite Groups Can Be Arbitrarily Hamiltonian, Stephen Ahearn, Mark Huber

Mathematical Sciences Technical Reports (MSTR)

Let r be a rational in (0,1]. There exists a finite group G which is the direct product of at most four metacyclic groups and whose proportion of normal subgroups is r. An analogous result holds for three other measures of "Hamiltonianess".

Elimination Of Supply Harmonics: An Evolution Of Current Compensation And Active Filtering Methods, Stephen L. Clark, P. Famouri, W. L. Cooley

Mathematics and Statistics Faculty Research & Creative Works

The price of the extensive use of power electronic devices is becoming clear: increasing harmonic "pollution." This survey takes a brief look at background information related to harmonics, including their sources, effects, and characteristics. Then, the evolution of the harmonics elimination approaches of current compensation and active filtering, which are becoming more feasible due to research and technological improvements, are discussed in order to give some insight into the directions that research is taking.

The Complexity Of Local Stratification, Peter Cholak, Howard A. Blair

College of Engineering and Computer Science - Former Departments, Centers, Institutes and Projects

The class of locally stratified logic programs is shown to be Π 1 1-complete by the construction of a reducibility of the class of infinitely branching nondeterministic finite register machines.

Counting Order Classes Of Triple Products In Finite Groups, Scott Annin, Jennifer Ziebarth

Mathematical Sciences Technical Reports (MSTR)

Let G be a finite group and let W_G denote the proportion of triples, (.x:, y , z) , i n G3 for which x yz , x zy, y x z, zx y , yzx , and z y x have the same order. The following results are established.

i) G is abelian if, and only if, W_G = 1.

ii) W_G can be arbitrarily close to 1.

iii) Additional estimates on W_G

On The Noninterpolation Of Polyhedral Maps, Adrian Riskin, D.W. Barnette

Mathematics

In this paper we show that if attention is restricted to polyhedral embeddings of graphs, no theorem analogous to the Duke interpolation theorem for 2-cell embeddings is true. We also give two interesting classes of graphs: (i) a class in which the members have polyhedral embeddings in the torus and also in orientable manifolds of arbitrarily high genus, (ii) and another in which the members have polyhedral embeddings in the projective plane and also in orientable and nonorientable manifolds of arbitrarily low Euler characteristic.

Review: J.M. Aarts And T. Nishiura, Dimension And Extensions (Amsterdam, London, New York, And Tokyo, 1993), Melvin Henriksen

All HMC Faculty Publications and Research

Reviewed work: J. M. Aarts and T. Nishiura. Dimension and extensions. North-Holland Math. Library, Amsterdam, London, New York, and Tokyo, 1993, xii + 331 pp., $106.50. ISBN 0444897402.

Hankel Transforms In Generalized Fock Spaces, John Schmeelk

Mathematics and Applied Mathematics Publications

A classical Fock space consists of functions of the form,ϕ↔(ϕ0,ϕ1,…,ϕq),where ϕ0∈ℂ and ϕq∈Lp(ℝq), q≥1. We will replace the ϕq, q≥1 with test functions having Hankel transforms. This space is a natural generalization of a classical Fock space as seen by expanding functionals having abstract Taylor Series. The particular coefficients of such series are multilinear functionals having distributions as their domain. Convergence requirements set forth are somewhat in the spirit of ultra differentiable functions and ultra distribution theory. The Hankel transform oftentimes implemented in Cauchy problems will be introduced into this setting. A theorem will be proven relating the convergence of …

Fixed Point Theorems For Non-Self Maps I, Troy L. Hicks, Unda Marie Sauga

Mathematics and Statistics Faculty Research & Creative Works

Suppose f:C→X where C is a closed subset of X. Necessary and sufficient conditions are given for f to have a fixed point. All results hold when X is complete metric space. Several results hold in a much more general setting. © 1994, Hindawi Publishing Corporation. All rights reserved.

A Qualitative Study Of Planar Elastic Deformations, Stephen Thomas Wentworth

Theses Digitization Project

No abstract provided.