Physical Sciences and Mathematics Commons^™

A Run-Time Decision Procedure For Responsive Computing Systems, Grace Tsai, Matt Insall, Bruce M. Mcmillin

Computer Science Technical Reports

A responsive computing system is a hybrid of real-time, distributed and fault-tolerant systems. In such a system, severe consequences will occur if the logical and physical specifications of the system are not met. In this paper, we present a logic, Interval Temporal Logic (ITL), to specify responsive systems and give decision procedures to verify properties of the system at run-time as follows. First, we collect, during execution, events occurring in the system to represent a distributed computation. Next, we specify properties of the system using ITL formulas. Finally, we apply the decision procedures to determine satisfaction of the formulas. Thus, …

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

IMSA Math Journal

Welcome to the second issue of the IMSA Math Journal, an official publication of the Illinois Mathematics and Science Academy. The purpose of the IMSAMJ i s to communicate through mathematics with both students and teachers. Some of our goals include:

• Presenting teaching insights, lessons, problems.
• Sharing mathematical ideas, mathematical teaching ideas, observations, approaches, connections, extensions, generalizations of interest to students and teachers of mathematics.
• Featuring mathematics problems for both in the classroom and outside the classroom, i.e. math contests, math competitions, etc.
• Discussing and sharing the role of technology including calculators and computers in the instruction and learning of …

On Revelation Transforms That Characterize Probability Distributions, Stefanka Chukova, Boyan N. Dimitrov, Jean Pierre Dion

Mathematics Publications

A characterization of exponential, geometric and of distributions with almost-lack-of-memory property, based on the revelation transform of probability distributions and relevation of random variables is discussed. Known characterizations of the exponential distribution on the base of relevation transforms given by Grosswald et al. [4], and Lau and Rao [7] are obtained under weakened conditions and the proofs are simplified. A characterization the class of almost-lack-of-memory distributions through the relevation is specified.

Σary, Moorhead State University, Mathematics Department

Math Department Newsletters

No abstract provided.

Harmonic-Analysis Of Fractal Measures Induced By Representations Of A Certain C*-Algebra, Palle Jorgensen, Steen Pedersen

Mathematics and Statistics Faculty Publications

We describe a class of measurable subsets Ω in R^d such that L²(Ω) has an orthogonal basis of frequencies e_λ(x) = e^i2πλ.x(x ε Ω) indexed by λ ∈ Λ ⊂ R^d. We show that such spectral pairs (Ω, Λ) have a self-similarity which may be used to generate associated fractal measures μ with Cantor set support. The Hilbert space L²(μ) does not have a total set of orthogonal frequencies, but a harmonic analysis of mu may be built instead from a natural representation of the Cuntz …

The Lazer Mckenna Conjecture For Radial Solutions In The Rn Ball, Alfonso Castro, Sudhasree Gadam

All HMC Faculty Publications and Research

When the range of the derivative of the nonlinearity contains the first k eigenvalues of the linear part and a certain parameter is large, we establish the existence of 2k radial solutions to a semilinear boundary value problem. This proves the Lazer McKenna conjecture for radial solutions. Our results supplement those in [5], where the existence of k + 1 solutions was proven.

A Note On New Semi-Regular Divisible Difference Sets, James A. Davis, Jonathan Jedwab

Department of Math & Statistics Faculty Publications

We give a construction for new families of semi-regular divisible difference sets. The construction is a variation of McFarland's scheme [5] tor noncyclic difference sets.

Joint Venture And Bargaining., Prabal Ray Chaudhuri Dr.

Doctoral Theses

My dissertation deals with some problems in theoretical economics. The five essays in this thesis can be classified under the broad categories of industrial organization and game theory.Part I of the thesis comprises three chapters. These deal with some issues in the area of joint ventures and technology transfer. Chapter 2 investigates the relationship between technological dissimilarity and joint venture success. The third chapter explores some policy issues related to joint product development. Chapter 4 examines the relative efficacy of centralized and decentralized bargaining schemes in technology transfer.In part II I examine some issues in bargaining theory. The fifth chapter …

Constructing An Interval Temporal Logic For Real-Time Systems, Grace Tsai, Matt Insall, Bruce M. Mcmillin

Computer Science Technical Reports

A real-time system is one that involves control of one or more physical devices with essential timing requirements. Examples of these systems are command and control systems, process control systems, flight control systems, and the space shuttle avionics systems. The characteristics of these systems are that severe consequences will occur if the logical and physical timing specifications of the systems are not met.

Formal specification and verification are among the techniques to achieve reliable software for real-time systems, in which testing may be impossible or too dangerous to perform. This paper presents a modal logic, Interval Temporal , built upon …

Approximation Methods For Singular Diffusions Arising In Genetics, Nacer E. Abrouk

Mathematical Sciences Technical Reports (MSTR)

Stochastic models in population genetics leading to diffusion equations are considered. When the drift and the square of the diffusion coefficients are polynomials, an infinite system of ordinary differential equations for the moments of the diffusion process can be derived using the Martingale property. An example is provided to show how the classical Fokker-Planck Equation approach may not be appropriate for this derivation. A Gauss-Galerkin method for approximating the laws of the diffusion, originally proposed by Dawson (1980), is examined. In the few special cases for which exact solutions are known, comparison shows that the method is accurate and the …

Classification Of The Tor-Algebras Of Codimension Four Almost Complete Intersections, Andrew R. Kustin

Faculty Publications

Let (R, m, k) be a local ring in which 2 is a unit. Assume that every element of k has a square root in k . We classify the algebras Tor'(R/J, k) as J varies over all grade four almost complete intersection ideals in R. The analogous classification has already been found when J varies over all grade four Gorenstein ideals [21], and when J varies over all ideals of grade at most three [5, 30]. The present paper makes use of the classification, in [21], of the Tor-algebraso f codimension four Gorenstein rings, as well as the (usually …

Coxeter Groups And Positive Matrices., Arbind Kumar Lal Dr.

Doctoral Theses

In this thesis, we study positive matrices (matrices whose entries are nonnegative as well as matrices which are positive semidefinite) with Coxeter groups as the underlying theme. For an exposition on Coxeter groups see Humphreys (1990).A Cozeter system consists of a pair (W, s); where W is a group and S is a set which consists of the generators of the group W. The elements of the set S have only the relations of the form (ss')m(s.) 1; where m(s, s) 1, m(s, s') = m(s,s) 2 2 for s s in S. In case no relation occurs for a …

Optimizing Communication Routing In Parallel Computer Architectures, Nikolaos T. Liolios

Masters Theses

This thesis is a research effort to improve on existing algorithms for processor placement and routing on hypercube and 2d-transputer parallel architectures that perform communications through message propagation. Given a set of processors N, randomly distributed on the parallel computer network, the problem is to find an optimal communication routing that minimizes the number of required links and intermediate processors. It was concluded that the spanning tree is the best starting heuristic for the routing problem. For hypercubes an algorithm was developed that outperforms all algorithms in the literature. For 2d-transputers the method of overlap maximization used in VLSI routing, …

Calculus Workshop Groups As A Humanistic Experience, Martin Vern Bonsangue

Humanistic Mathematics Network Journal

No abstract provided.

Like Poetry, Mathematics Is Beautiful, Joanne Growney

Humanistic Mathematics Network Journal

No abstract provided.

Writing Style - An Editorial Comment, Harald M. Ness

Humanistic Mathematics Network Journal

No abstract provided.

Toward A Philosophy Of Humanistic Mathematics, Bill Rosenthal

Humanistic Mathematics Network Journal

No abstract provided.

Letter About Philosophia Mathematica, Robert Thomas

Humanistic Mathematics Network Journal

No abstract provided.

Canadian Society For History And Philosophy Mathematics Speaker List

Humanistic Mathematics Network Journal

No abstract provided.

The Role Of Faith In Mathematics, Dick Wood

Humanistic Mathematics Network Journal

No abstract provided.

Math Nonsence Verse, Helen Lewy

Humanistic Mathematics Network Journal

No abstract provided.

A Reading List For Undergraduate Mathematics Majors: A Personal View, Paul Froeschl

Humanistic Mathematics Network Journal

No abstract provided.

Developing A Mathematical Mode Of Thinking In An Undergraduate Program, Ida Doraiswamy

Humanistic Mathematics Network Journal

No abstract provided.

On Attracting Mathematics Majors, Kazem Mahdavi

Humanistic Mathematics Network Journal

No abstract provided.

The Basis For The Success Of The Potsdam Program, Rick Luttmann

Humanistic Mathematics Network Journal

No abstract provided.

Mathematics And The Arts — A Bibliography, Joanne S. Growney

Humanistic Mathematics Network Journal

No abstract provided.

A Humanistic Academic Environment For Learning Undergraduate Mathematics, Clarence F. Stephens

Humanistic Mathematics Network Journal

No abstract provided.

Liberal Education In The Liberal Sense, Annalisa Crannell

Humanistic Mathematics Network Journal

No abstract provided.

The Popular Image Of Mathematics, Paul Ernest

Humanistic Mathematics Network Journal

No abstract provided.

Poems, Lee Goldstein

Humanistic Mathematics Network Journal

No abstract provided.