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Partitioning Inequalities In Probability And Statistics, Theodore P. Hill

Research Scholars in Residence

This article surveys fair-division or cake-cutting inequalities in probability statistics, including bisection inequalities, basic fairness inequalities, convexity tools, superfairness inequalities, and partitioning inequalities hypotheses testing and optimal stopping theory. The emphasis is measure theoretic, as opposed to game theoretic or economic, and a number of open problems in the area are mentioned.

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.

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.

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 Applications Of Little's Formula, Jewgeni H. Dshalalow

Mathematics and System Engineering Faculty Publications

In classical Little's formula L=λW used in queueing, the parameter λ serves as the intensity of the input process. In various applications this parameter may not be known. The author discusses important classes of modulated input processes, where this parameter can be found.

Radial Symmetry Of Positive Solutions Of Nonlinear Elliptic Equations In Rn, Yi Li, Wei-Ming Ni

Mathematics and Statistics Faculty Publications

No abstract provided.

On The Positive Solutions Of The Matukuma Equation, Yi Li

Mathematics and Statistics Faculty Publications

No abstract provided.

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 …

Dynamics Of Population Growth, Jennifer Fess

Honors Theses, 1963-2015

The objective of this project was to examine the dynamics of population size based on age-specific life history parameters, as well as on genetic information. Two basic models were developed and exercised based upon the Leslie Matrix. the first model examined different life history patterns and their impact on the resulting dynamics of population growth. The second model expanded the first to include different genotypes. The life history parameters, fecundity and survivorship, were the same for both models. Four fecundity patterns represented age-specific fecundity that is monotonically increasing, monotonically decreasing, constant, and peaking at an intermediate age; three survivorship patterns …

The Force On A Sphere In A Tightly Focused Laser Beam, Marc Knudson

Honors Theses, 1963-2015

An investigation of the trapping force on a sphere in a tightly focused laser beam is carried out using a geometrical optics approximation. This calculation generalizes earlier work by allowing the spheres to be located off the beam axis. Additionally, a fifth-order, instead of zeroth-order, Gaussian approximation is used, and beam polarization is explicitly taken into account. The results suggest an interesting experiment, involving a driven damped harmonic oscilator system, which could be performed to test the validity of the theory. This experiment will be the focus of a future study.

Analysis Of Factors Contributing To Environmental Activism: A Case Study Of Beach Clean-Up Participants, Elizabeth Ann Fuller

Marine Affairs Theses and Major Papers

This study was initiated to investigate factors which contribute to environmental activism. Towards this end, three hypotheses were investigated. First, it was hypothesized that beach clean-up participants would harbor pro-environmental attitudes. Second, it was hypothesized that participants would be relatively young, politically liberal, well-educated, and wealthy. Finally, it was hypothesized that particular types of social structure would influence a person's decision to participate in a beach clean-up. Specifically, it was hypothesized that participants at each clean-up location would be clique members and/or would be structurally equivalent. Surprising, it was revealed that there was virtually no difference in attitude between the …

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 …

Bochner Integrals And Vector Measures, Ivaylo D. Dinov

Dissertations, Master's Theses and Master's Reports

This project extends known theorems for scalar valued functions to the context of Banach space valued functions. In particular, it contains generalizations of the classical theory of Lebesgue Integrals, complex measures, Radon-Nikodym theorem and Riesz Representation theorem. We explore some properties of functions whose domains are abstract Banach spaces, where the usual derivatives are replaced by Radon-Nikodym derivatives.

The first two Chapters are devoted to infinite dimensional measurable functions and the problem of integrating them. Most of the basic properties of Bochner integration are forced on it by the classical Lebesgue integration and the usual definition of measurability.

The Radon-Nikodym …

Only Problems, Not Solutions! (Fourth Edition), Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

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 …

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 …

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

Mathematics Sciences: Faculty Publications

No abstract provided.

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 …

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 …

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 …

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.