Physical Sciences and Mathematics Commons^™

The Walker Endomorphism Algebra Of A Mixed Module, Brendan Goldsmith, P. Zanardo

Articles

Archimedian valuation domains R are characterised in terms of the endomorphism algebras of non-splitting mixed modules of rank 1, in the Walker category.

The Kaplansky Test Problems - An Approach Via Radicals, R. Gobel, Brendan Goldsmith

Articles

The existence of non-free, K-free Abelian groups and modules (over some non-left perfect rings R) having prescribed endomorphism algebra is established within ZFC + 0 set theory. The principal technique used exploits free resolutions of non-free R-modules X and is similar to that used previously by Griffith and Eklof; much stronger results than have been obtained heretofore are obtained by coding additional information into the module X. As a consequence we can show, inter alia, that the Kaplansky Test Problems have negative answers for strongly K,-free Abelian groups of cardinality K1 in ZFC and assuming the weak Continuum Hypothesis.

On Matching Ann Structure To Problem Domain Structure, George G. Lendaris, Martin Zwick, Karl Mathia

Systems Science Faculty Publications and Presentations

To achieve reduced training time and improved generalization with artificial neural networks (ANN, or NN), it is important to use a reduced complexity NN structure. A "problem" is defined by constraints among the variables describing it. If knowledge about these constraints could be obtained a priori, this could be used to reduce the complexity of the ANN before training it. Systems theory literature contains methods for determining and representing structural aspects of constrained data (these methods are herein called GSM, general systems method). The suggestion here is to use the GSM model of the given data as a pattern for …

The Sharp Lipschitz-Constants For Feasible And Optimal-Solutions Of A Perturbed Linear Program, Wu Li

Mathematics & Statistics Faculty Publications

The purpose of this paper is to derive the sharp Lipschitz constants for the feasible solutions and optimal solutions of a linear program with respect to right-hand-side perturbations. The Lipschitz constants are given in terms of pseudoinverses of submatrices of the matrices involved and are proven to be sharp.

A Semiclassical, Dynamical Model Of Methane, Donald Greenspan

Mathematics Technical Papers

In this paper we present a semiclassical, dynamical model of the ground state methane molecule. The resulting 13-body problem is solved numerically using energy conserving methodology. The bond length and bond angle results are in complete agreement with experimental results.

Particle Simulation Of Large Carbon Dioxide Bubbles In Water, Donald Greenspan

Mathematics Technical Papers

A method which can be applied to simulate the motion of fluid drops within fluids is described through a detailed study of a prototype problem, that is, the motion of carbon dioxide bubbles in water. The mathematical formulation uses classical molecular type formulas and results in an n-body problem which is solved numerically. The rise of the bubbles is described, as is the motion of the water near the bubbles. For variety, both H2O water and D20 heavy water are considered. Only workstation computer capabilities are required.

Cotorsion-Free Algebras As Endomorphism Algebras In L - The Discrete An Topological Cases., R. Gobel, Brendan Goldsmith

Articles

The discrete algebras A over a commutative ring R which can be realised as the full endomorphism algebra of a torsion-free R-module have been investigated by Dugas and Gobel under the additional set-theoretic axiom of constructibility, V = L. Many interesting results have been obtained for cotorsion-free algebras but the proofs involve rather elaborate calculations in linear algebra. Here these results are rederived in a more natural topological setting and substantial generalizations to topological algebras (which could not be handled in the previous linear algebra approach) are obtained. The results obtained are independent of the usual Zermelo-Fraenkel set theory ZFC.

Quality Control In Induction Hardness And Computer Numerical Control Grinding, Sandra Wynne Bevill

Legacy ETDs

The purpose of this research was to conduct an investigation into the improvement of quality of the products produced by the Cooper Hand Tools Division of Cooper Industries and make recommendations where applicable. Two processes were chosen: induction hardness and computer numerical control (CNC) grinding. The Jaw 0010C and the Jaw 311C were two products involved in the induction hardness process that were under experimentation. In the CNC grinding area, the following products' quality were studied: 166L shear (top blade only), 766 shear ( bottom blade only), and the IDS-SB shear (top blade only). Using statistical procedures and designs, some …

A New Completely Integrable Liouville's System Produced By The Kaup-Newell Elgenvalue Problem, Zhijun Qiao

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Under the constraint between the potentials and eigenfunctions, the Kaup–Newell eigenvalue problem is nonlinearized as a new completely integrable Hamiltonian system (R2N,dpΛdq,H): H=i〈Λ2p,q〉+1/2〈Λq,q〉〈Λp,p〉. Furthermore, the involutive solution of the high‐order Kaup–Newell equation is obtained. Specifically, the involutive solution of the well‐known derivative Schrödinger equation ut=1/2iuxx+1/2(u‖u‖2)x is developed.

Prime Decomposition Of Knots In Lorenz-Like Templates, Michael C. Sullivan

Articles and Preprints

In [8] R.F. Williams showed that all knots in the Lorenz template are prime. His proof included the cases where any number of positive twists were added to one of the template’s branches. However [8] does give an example of a composite knot in a template with a single negative twist. Below we will show that in all the negative cases composite knots do exist, and give a mechanism for producing many examples. This problem was cited in a list of problems in dynamics in [1, problem 4.2].

A Note On Computing Eigenvalues Of Banded Hermitian Toeplitz Matrices, William F. Trench

William F. Trench

No abstract provided.

Interlacement Of The Even And Odd Spectra Of Real Symmetric Toeplitz Matrices, William F. Trench

William F. Trench

No abstract provided.

Asymptotic Behavior Of Solutions Of Poincar'e Difference Equations, William F. Trench

William F. Trench

No abstract provided.

Sliding Mode Control Of The Systems With Uncertain Direction Of Control Vector, Sergey V. Drakunov

Sergey V. Drakunov

No abstract provided.

Vertex Coloring For Weighted Graphs With Application To Timetabling, Lynn Kiaer, Jay Yellen

Mathematical Sciences Technical Reports (MSTR)

This paper applies the methods of vertex coloring to timetabling problems

What They Didn’T Tell Me About Calculus And The Computer, Melvin Henriksen

All HMC Faculty Publications and Research

My first attempt at using computers as an aid to teaching calculus began in 1966 and culminated with the publication in 1971 of Single Variahle Calculus, written jointly with Milton Lees. Everyone used a mainframe and punched cards and few knew how to program. Computer use was limited to supplementary exercises that could be done today with a hand-held programmable calculator. A constructive sequential approach to limits and elementary numerical analysis were emphasized. The absence of programming displeased computer scientists, but it was too avant garde for all but a tiny minority of teachers of calculus. Attempts by others …

A New Proof Of The Aubry-Mather's Theorem, Christophe Golé

Mathematics Sciences: Faculty Publications

No abstract provided.

Almost Difference Sets And Reversible Divisible Difference Sets, James A. Davis

Department of Math & Statistics Faculty Publications

Let G be a group of order mn and N a subgroup of G of order n. If D is a k-subset of G, then D is called a (m, n, k, λ₁, λ₂) divisible difference set (DDS) provided that the differences dd^'-1 for d, d' ∈ D, d ≠ d' contain every nonidentity element of N exactly λ₁ times and every element of G - N exactly λ₂ times. Difference sets are used to generate designs, as described by [4] and [9]. D will be …

Rural Labour Markets And Seasonality: A Theoretical And Empirical Analysis., Anindita Mukherjee Dr.

Doctoral Theses

A large proportion of the labour force in India (that is, 66.56% of the main workers according to the Census of India, 1981) is engaged in agriculture. Just this simple fact would make a study of the functioning of agricultural labour markets highly important. But quite apart from this observation, there are several reasons for a detailed study of rural labour markets, particularly in the context of the problem of economic development.A major issue facing developing economies is industrial growth. The agricultural sector can foster growth by creating demand for industrial products, by providing a supply of certain primary inputs, …

Nonstandard And Standard Compactifications Of Ordered Topological Spaces, Sergio Salbany, Todor D. Todorov

Mathematics

We construct the Nachbin ordered compactification and the ordered realcompactification, a notion defined in the paper, of a given ordered topological space as nonstandard ordered hulls. The maximal ideals in the algebras of the differences of monotone continuous functions are completely described. We give also a characterization of the class of completely regular ordered spaces which are closed subspaces of products of copies of the ordered real line, answering a question of T.H. Choe and Y.H. Hong. The methods used are topological (standard) and nonstandard.

Labeling Graphs With A Condition At Distance 2, Jerrold R. Griggs, Roger K. Yeh

Faculty Publications

No abstract provided.

Imsa Math Journal: A Resource Notebook For High School Mathematics, Illinois Mathematics And Science Academy

IMSA Math Journal

Dear Friends of Mathematics:

It is with great pleasure that the Illinois Mathematics and Science Academy distributes to you our first IMSA Math Journal, designed to serve as a resource and an invitation to mathematical inquiry and engagement.

Excerpt by Stephanie Pace Marshall, Ph.D.

Design And Implementation Of Fuzzy Logic Controllers, Osama A. Abihana

Electrical & Computer Engineering Theses & Dissertations

The main objectives of our research are to present a self-contained overview of fuzzy sets and fuzzy logic, develop a methodology for control system design using fuzzy logic controllers, and to design and implement a fuzzy logic controller for a real system. In this thesis we first present the fundamental concepts of fuzzy sets and fuzzy logic. Fuzzy sets and basic fuzzy operations are defined. In addition, for control systems, it is important to understand the concepts of linguistic variables, linguistic values, term sets, fuzzy rule base, inference methods, and defuzzification methods. Second, we introduce a four-step fuzzy logic control …

Melting Points Of Atomic And Homogeneous, Diatomic Molecular Solids Via The Four-Body Problem, Donald Greenspan

Mathematics Technical Papers

For a regular tetrahedral arrangement of four identical atoms, the minimum velocity of one atom, required for that atom to pass through the plane of the other three, is used to define the melting point of any solid composed of such atoms. The formula which results is [see pdf for notation], in which h is Planck's constant. Computations and results are described for helium, neon, argon, krypton, xenon and copper. The methodology is then extended to homogeneous, diatomic molecular solids and results are described for H2, D2, N2, 02, and C12.

Divisibility By |G| For Powers Of Ordered K-Sets, Jeffery Vanderkam

Mathematical Sciences Technical Reports (MSTR)

It is shown that the number of ordered k-sets of a group G whose nth power contains exactly i elements is always a multiple of IGI. An elementary proof of the fact that the number of ordered pairs ( x , y ) such that x² = y² is equal to k_r lGI is also given.

Cubing Ordered 2-Sets, Jeffery Vanderkam

Mathematical Sciences Technical Reports (MSTR)

Given a group G, we define p_i as the probability that, given an ordered pair X = (x,y), there are exactly i elements in X³ = {x₁x₂x₃ l x_i in X}. We show that P₂( G) = 0 if, and only if, IGI is odd, and that p₃(G) = 0 if, and only if, IGI is not divisible by three. The groups for which p₄ ( G) = 0 and p₅ ( G) = 0 are also determined.

Counting Nilpotent Pairs, Jason Fulman, Michael Galloy, Jeffery Vanderkam

Mathematical Sciences Technical Reports (MSTR)

In this paper , we consider the probability that two elements chosen at random from a finite group G generate a subgroup of a given nilpotency class. It is shown that in solvable non­-nilpotent groups, the probability that two elements generate a nilpotent subgroup is <= l/p,, where p, is the smallest prime dividing the order of the group, and it is also shown that there exist groups such that the probability of two elements generating a subgroup of class i approaches one (and other groups for which it approaches zero) for all i =>2. It is also shown …

Simultaneous Rational Approximations And Related Diophantine Equations, John Rickert

Mathematical Sciences Technical Reports (MSTR)

In this paper we consider simultaneous approximations to algebraic numbers a₁,...,a_m .

An Average Per Capita Formula For The Shapely Value, Irinel C. Dragan

Mathematics Technical Papers

A new formula for the Shapley value is given which does not require the storage of the [see pdf for notation] values of the characteristic function in the computer, and avoids the search in the memory for such data.

The 2/3 Bound For Rewritable N-Tuples, Lawren Smithline, Catherine Sugar

Mathematical Sciences Technical Reports (MSTR)

We study the number of rewritings of an n-tuple in a finite a group, for certain classes of groups.