Digital Commons Network^™

A Summary Of Menon Difference Sets, James A. Davis, Jonathan Jedwab

Department of Math & Statistics Faculty Publications

A (v, k, λ) difference set is a k-element subset D of a group G of order v for which the multiset {d₁d₂^-1 : d_1,d₂ ∈ D, d₁ ≠ d₂} contains each nonidentity element of G exactly λ times. A difference set is called abelian, nonabelian or cyclic if the underlying group is. Difference sets a.re important in design theory because they a.re equivalent to symmetric (v, k, λ) designs with a regular automorphism group. Abelian difference sets arise naturally in …

Orbifolds Of Maximal Diameter, Joseph Borzellino

Mathematics

In this paper the Maximal Diameter Theorem of Riemannian geometry is proven for Riemannian orbifolds. In particular, it is shown that a complete Riemannian orbifold with Ricci curvature bounded below by (n−1) and diameter = π, must have constant sectional curvature 1, and must be a quotient of the sphere (Sn, can) of constant sectional curvature 1 by a subgroup of the orthogonal group O(n+1) acting discontinuously and isometrically on Sn. It is also shown that the singular locus of the orbifold forms a geometric barrier to the length minimization property of geodesics. We also extend the Bishop relative volume …

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

College of Graduate Studies: Theses & Dissertations (1964–2006)

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 & Statistical Sciences Faculty Publications

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.

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

Identifiability Of Semiconductor Defects From Lbic Images, Weifu Fang, Kazufumi Ito

Mathematics and Statistics Faculty Publications

The identifiability of defects in a semiconductor from its laser-beam-induced current (LBIC) image is studied. It is shown that the LBIC technique is reliable for detecting any spatial defects in the semiconductor material. Continuous dependence of the current measurements on the spatial defects is proved, and sensitivity is also discussed in certain cases.

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.

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

Mathematics Technical Papers - Archive

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.

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 …

The Management Of Replicated Data, Hsueh-Chi Shih, C. Y. Ho, S. Alptekin

Computer Science Technical Reports

Data replication, which has the benefits of improving system availability and read performance, proved to be indispensable to many database applications. In a replicated database, the one-copy serializability of transaction executions can be ensured by employing a replica control mechanism on top of the traditional concurrency control mechanism. This work contains two replica control algorithms and a read-only transaction processing algorithm. Both replica control algorithms handle multiple site, communication and partitioning failures. The replica control algorithms achieve read operation efficiency by always translating a logical read operation into one local physical read operation and by taking advantage of the locality …

An Animation System For Shift Reduce Parsers, M. S. Mandl, T. J. Sager, D. C. St. Clair

Computer Science Technical Reports

This paper presents the design and implementation of the Parse Display Utility (POU) system. This system introduces a mechanism to augment traditional methods of exploring parsing theory by providing a PRESENTATION scheme which allows a user to view the operation of a shift-reduce parser.

The overall operation of the tool revolves around an LALR (LookAhead LR) parser/parser generator and is managed by a Graphical User-Interface (GUI) developed using Borland's Turbo Vision product. The GUI allows access to a facility which draws derivation trees in Turbo Pascal graphics. This parse tree facility utilizes an algorithm which can easily be ported to …

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 - Archive

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.

Some Upper Bounds For Commutativity And Cyclicity Measures In Finite Groups, David Patrick, Catherine Sugar, Eric Wepsic

Mathematical Sciences Technical Reports (MSTR)

The number of commuting and cyclic n-tuples in a group are enumerated for certain classes of groups.

Another Way Of Counting Nᴺ, Arthur T. Benjamin, Fritz Juhnke

All HMC Faculty Publications and Research

An original combinatorial proof of a combinatorial identity is presented.

Inverse Problems For Metal Oxide Semiconductor Field-Effect Transistor Contact Resistivity, Weifu Fang, Ellis Cumberbatch

Mathematics and Statistics Faculty Publications

Inverse problems arising from the identification of transistor contact resistivity and contact window location are studied. A one-point boundary measurement of the potential is shown to be sufficient to identify each from a one-parameter monotone family, and such identification is both stable and continuously dependent on the parameter. For a nonmonotone family of locations with resistivity given, similar results are obtained for measurement made on almost all boundary points.

On The Game Of Googol, Theodore P. Hill, Ulrich Krengel

Research Scholars in Residence

In the classical secretary problem the decision maker can only observe the relative ranks of the items presented. Recently, Ferguson — building on ideas of Stewart — showed that, in a game theoretic sense, there is no advantage if the actual values of the random variables underlying the relative ranks can be observed (game of googol). We extend this to the case where the number of items is unknown with a known upper bound. Corollary 3 extends one of the main results in [HK] to all randomized stopping times. We also include a modified, somewhat more formal argument for Ferguson's …

Planning For Basic Needs In India: A Supplement., Monoj Kumar Panda Dr.

Doctoral Theses

Problems of economic development have received a great deal of attention in the last four decades. This has led to the evolution of several development goals like growth, redistribution, poverty alleviation and basic needs satiafac- tion. Initially, development atrategies e eared to were achieve maximum feasible growth rates. It was generally felt that the benefits of growth would spread widely to different sections of the population and in particular would percolate to the lower income groups. Judged by growth in national income, the development efforts have been successful, though to varying ext ent in different countries. But the percola- tion …

Construction Of Relative Difference Sets In P-Groups, James A. Davis

Department of Math & Statistics Faculty Publications

Jungnickel (1982) and Elliot and Butson (1966) have shown that (p^j+1,p,p^j+1,p^j) relative difference sets exist in the elementary abelian p-group case (p an odd prime) and many 2-groups for the case p = 2. This paper provides two new constructions of relative difference sets with these parameters; the first handles any p-group (including non-abelian) with a special subgroup if j is odd, and any 2-group with that subgroup if j is even. The second construction shows that if j is odd, every abelian group …

On The Construction Of Prime Desert N-Tuplets, Derek M. Marusarz '92

Honors Projects

If we were able to show that there is an infinite number of prime desert n-tuplets of length k, for any appropriate odd k, then we would have solved the twin prime conjecture because then we would know that there would be an infinite number of prime desert 1-tuplets of length k =1, i.e., an infinite number of twin primes.