Physical Sciences and Mathematics Commons^™

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

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 …

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.

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.

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 .

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.

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.

Counting Nilpotent Pairs In Finite Groups: Some Conjectures, H Dubose-Schmidt, Michael D. Galloy, D,L, Wilson

Mathematical Sciences Technical Reports (MSTR)

The number of nilpotent pairs is determined for a number of small groups.

Σary, Moorhead State University, Mathematics Department

Math Department Newsletters

No abstract provided.

Logical "Paradox": A Response To Fallacies, Flaws, And Flimflam #36, Calvin Jongsma

Faculty Work Comprehensive List

Response to "Fallacies, Flaws, and Flimflam" by Ed Barbeau in The College Mathematics Journal, Vol. 23, No. 3 (May, 1992), pp. 203-206. Fallacies, Flaws, and Flimflam is a column in The College Mathematics Journal edited by Ed Barbeau of the Department of Mathematics at the University of Toronto.

A Maple Package For The Variational Calculus, Cinnamon Hillyard

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The HELMHOLTZ package, written in Maple V, is a collection of commands to support research in the variational calculus. These commands include the standard operators on differential forms, Euler-Lagrange operators, homotopy operators, Lie bracket, Lie derivatives, and the prolongation of a vector field. We give a brief introduction to the variational calculus. We describe each of the commands in the HELMHOLTZ package completely along with numerous examples of each. Applications of the package include verification of symmetry groups for differential equations, solving the inverse problem of the calculus of variations, computing generalized symmetries, and finding variational integrating factors. A complete …

A Comparison Of Two Linear Nonparametric Regression Techniques, Sylvain Sardy

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

This thesis presented a useful tool in regression. Nonparametric linear regression techniques were described in the general context of regression. A comparison of two of these techniques, kernel regression and iterative regression, showed various aspects of nonparametric linear regressors.

Disconjugacy And Oscillation Theory Of Linear Differential And Difference Equations, Yuhua Xu

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

This dissertation is both a literature survey and a presentation of new and independent results.

The survey gives an overview of disconjugacy and oscillation theory for linear differential and difference equations with an emphasis on comparing the theory of difference equations to the theory of differential equations. Second order scalar equations, higher order scalar equations, matrix equations (systems) and Hamiltonian systems are discussed. A chapter on three-term recurrences of systems is also included. Both similarities and differences between differential and difference equations are described.

The new and independent results are for Hamiltonian systems of difference equations. Those results include the …

Inverse Problem In Porous Medium Using Homogenization, Helen Alkes

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The problem under consideration is that of obtaining a representation of the permeability of a porous medium which is heterogeneous and anisotropic from limited information. To solve this inverse problem we propose the use of two different pieces that work together. A simulated annealing algorithm is presented and coupled with an homogenization technique; together these solve the problem which was posed. Further, numerical simulation results are presented illustrating the use of the simulated annealing algorithm as well as a coupling with the homoginization technique. This study illustrates that the performance of the annealing algorithm is enhanced with usage of homogenization.

Hopf Bifurcation In A Parabolic Free Boundary Problem, Yoon-Mee Lee

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

We deal with a free boundary problem for a nonlinear parabolic equation, which includes a parameter in the free boundary condition. This type of system has been used in models of ecological systems, in chemical reactor theory and other kinds of propagation phenomena involving reactions and diffusion.

The main purpose of this dissertation is to show the global existence, uniqueness of solutions and that a Hopf bifurcation occurs at a critical value of the parameter r. The existence and uniqueness of the solution for this problem are shown by finding an equivalent regular free boundary problem to which existence …

Optimal Control Of A Heat Flux In A Parabolic Partial Differential Equation, Katherine Renee Deaton

Masters Theses

We consider the problem of controlling the solution of a parabolic partial differential equation with non-homogeneous Neumann boundary conditions, taking the flux as the control. We take as our cost functional the sum of the L² norms of the control and the difference between the temperature distribution attained and the desired temperature profile. We establish the existence of an optimal control that minimizes the cost functional. The optimal control is characterized in a constructive way through the solution to the optimality system, which is the original problem coupled with an adjoint problem. We establish existence and uniqueness of the …

Mielnik Probability Spaces And Functional Equations, J. J. Mitchell

Opportunities for Undergraduate Research Experience Program (OURE)

The invariance properties of the solutions of those functional equations naturally occurring in the construction of Mielnik probability spaces are studied, and in turn are related to one another. In particular, the possibilities for fixed points of these solutions are found, and the relationships between these results are discussed. The two functional equations studied include a representation of the generalized parallelogram law and an equation used in the modeling of polarization phenomena. The main result of the paper lies in the extention of previous research on Mielnik probability spaces to a higher dimension, as well as a discussion of their …

Shooting Method Solutions Of Eigenvalue Problems, Xi Chen

Opportunities for Undergraduate Research Experience Program (OURE)

A shooting method was developed to study eigenvalue problems derived from Schrodinger equation. The challenging problem, the two-dimensional hydrogen system with the logarithmic potential function, was successfully solved by the shooting method. But no complete proof was given for its rationale and correctness. This paper not only gives the complete proof for the shooting method, but also generalizes it to solve a large class of eigenvalue problems. In a certain sense, the shooting method proves more effective numerically and more powerful theoretically than the classical functional analysis approach.