Physical Sciences and Mathematics Commons^™

Search Designs And Other Topic In Fractional Replication., Kashinath Chatterjee Dr.

Doctoral Theses

This thesis primarily deals with search designs (see Srivastava (1975)) of various types for general symmetric and asymmetric factorials. The thesis also considers some other types on fractional factorials. We have made use of Kronecker products and various other results from matrix theory.In the first four chapters, different types of search designs have been studied. Chapter 5A considers the construction of orthogonal main-effect plans for general factorial experiments under the presence of a linear time trend. Chapter 5B extends the calculus for factorial arrangements to a fractional factorial set-up and examines critically the proportional frequency plans from the point of …

Notes On Sufficient Conditions For A Graph To Be Hamiltonian, Michael Joseph Paul, Carmen Baytan Shershin, Anthony Connors Shershin

School of Computing and Information Sciences

The first part of this paper deals with an extension of Dirac's Theorem to directed graphs. It is related to a result often referred to as the Ghouila-Houri Theorem. Here we show that the requirement of being strongly connected in the hypothesis of the Ghouila-Houri Theorem is redundant.

The Second part of the paper shows that a condition on the number of edges for a graph to be hamiltonian implies Ore's condition on the degrees of the vertices.

A Nonstandard Delta Function, Todor D. Todorov

Mathematics

We prove that the Dirac delta distribution has a kernel in the class of the pointwise nonstandard functions.

Dihedral Rewriteability, Cheryl P. Grood

Mathematical Sciences Technical Reports (MSTR)

In this paper we compute the probability that an n-tuple for a group G is S-rewritable for a given set S of permutations for several classes of groups.

Some Facts About Cwat-Sets, Martin Wattenburg

Mathematical Sciences Technical Reports (MSTR)

In [1] and [2], Sherman and Atkins, in connection with a problem in statistics, introduced a generalization of the concept of a subgroup of Z₂. These generalized subgroups, which we call CWAT-sets (where "CWAT" is an acronym for "Closed With A Twist" ), have a rich algebraic structure. In this paper we establish some simple combinatorial facts about CWAT-sets, as well as provide two construction methods, prove a divisibility theorem, and make a classification conjecture.

Degree Of Adaptive Approximation, Ronald A. Devore, Ming Yu Xiang

Faculty Publications

We obtain various estimates for the error in adaptive approximation and also establish a relationship between adaptive approximation and free-knot spline approximation.

Mathematical Visions: The Pursuit Of Geometry In Victorian England (Book Review), Calvin Jongsma

Faculty Work Comprehensive List

Reviewed Title: Joan L. Richards. Mathematical Visions: The Pursuit of Geometry in Victorian England. xiii + 266 pp., illus., figs., bibl., index. Boston/New York: Academic Press, Harcourt Brace Jovanovich, 1988.

A Numerical Approach To Rewriteability In Finite Groups, J.L. Leavitt, G.J. Sherman, M.E. Walker

Mathematical Sciences Technical Reports (MSTR)

In this paper we compute the probability that an n-tuple for a group G is S-rewritable for a given set S of permutations for several classes of groups.

Maximal Order Three-Rewriteable Subgroups Of Symmetric Groups, John T. O'Bryan

Mathematical Sciences Technical Reports (MSTR)

Recently, Burns and Goldsmith [2] characterized the maximal order Abelian subgroups of the symmetric groups using elementary techniques and the results of Hoffman [5]. This classification could also be directly inferred from the results of Kovacs and Praeger [7]. A natural extension would be to consider the weaker, more general form of commutativity, three-rewriteability. The purpose of this paper is to completely characterize the maximal order three-rewriteable subgroups of the symmetric groups.

How Hamiltonian Can A Finite Group Be?, G.J. Sherman, T.J. Tucker, M.E. Walker

Mathematical Sciences Technical Reports (MSTR)

No abstract provided.

Fibonacci Sequences In Finite Groups, Steven W. Knox

Mathematical Sciences Technical Reports (MSTR)

This paper extend the notion of Fibonacci sequence mod m to Fibonacci sequences in finite groups.

Sets Of Typical Subsamples, Joel Atkins, G.J Sherman

Mathematical Sciences Technical Reports (MSTR)

A group theoretic condition on a set of subsamples of a random sample from a continuous random variable symmetric about 0 is shown to be sufficient to provide typical values for 0.

Berry-Esseen-Type Bounds For Signed Linear Rank Statistics With A Broad Range Of Scores, Munsup Seoh

Mathematics and Statistics Faculty Publications

The Berry-Esseen-type bounds of order N^−1/2 for the rate of convergence to normality are derived for the signed linear rank statistics under the hypothesis of symmetry. The results are obtained with a broad range of regression constants and scores (allowed to be generated by discontinuous score generating functions, but not necessarily) restricted by only mild conditions, while almost all previous results are obtained with continuously differentiable score generating functions. Furthermore, the proof is very short and elementary, based on the conditioning argument.

Notions Of Relative Ubiquity For Invariant Sets Of Relational Structures, Paul Bankston, Wim Ruitenburg

Mathematics, Statistics and Computer Science Faculty Research and Publications

Given a finite lexicon L of relational symbols and equality, one may view the collection of all L-structures on the set of natural numbers w as a space in several different ways. We consider it as: (i) the space of outcomes of certain infinite two-person games; (ii) a compact metric space; and (iii) a probability measure space. For each of these viewpoints, we can give a notion of relative ubiquity, or largeness, for invariant sets of structures on w. For example, in every sense of relative ubiquity considered here, the set of dense linear orderings on w is …

Rewriteable Sequencings Of Groups, Jeanne Nielsen

Mathematical Sciences Technical Reports (MSTR)

A finite group is called P_n-sequenceable if its nonidentity elements can be listed x₁ , x₂ , ..., x_k so that the product x _i x _i+i · · · x _i+n-1 can be rewritten in at least one nontrivial way for all i. It is shown that S_n , A_n , D_n are P₃-sequenceable, that every finite simple group is P₄ -sequenceable, and that every finite group is P_s-sequenceable. It is conjectured that every finite group is P₃-sequenceable.

Sums Of Semiprime, Z, And D L-Ideals In A Class Of F-Rings, Suzanne Larson

Mathematics Faculty Works

In this paper it is shown that there is a large class of f-rings in which the sum of any two semiprime i-ideals is semiprime. This result is used to give a class of commutative f-rings with identity element in which the sum of any two z-ideals which are i-ideals is a z-ideal and the sum of any two d-ideals is a d-ideal.

Some Np-Complete Problems In Linear Algebra, Santhosh Sastry '90

Honors Projects

This research project is aimed at studying the theory of NP-Completeness and determining the complexity of certain problems in linear algebra. The first chapter introduces the reader to Complexity theory and defines NP-Completeness. It is supported by Appendices 1 and 2. Appendix 3 lists some known NP-Complete problems.

Remarks On Tensor Operators, Daniel Flath

Daniel Flath

No abstract provided.

A Mathematical Model Of The Dynamics Of An Optically Pumped Codoped Solid State Laser System, Thomas G. Wangler

Mathematics & Statistics Theses & Dissertations

This is a study of a mathematical model for the dynamics of an optically pumped codoped solid state laser system. The model comprises five first order, nonlinear, coupled, ordinary differential equations which describe the temporal evolution of the dopant electron populations in the laser crystal as well as the photon density in the laser cavity. The analysis of the model is conducted in three parts.

First, a detailed explanation of the modeling process is given and the full set of rate equations is obtained. The model is then simplified and certain qualitative properties of the solution are obtained.

In the …

The Fokker-Planck And Related Equations In Theoretical Population Dynamics, George Derise

Mathematics & Statistics Theses & Dissertations

The population growth of a single species is modeled by a differential equation with initial condition(s) so that the number of organisms in the population is derived using some mechanism of growth, i.e. a growth rate function. However, such deterministic models are often highly unrealistic in population dynamics because population growth is basically a random event. There are a large number of chance factors influencing growth that might not be taken into account by deterministic models. The effect of other species (for example, in the chance meeting of a predator), population fluctuations due to weather changes that would alter food …

Oscillations In Lotka-Volterra Systems Of Chemical Reactions, Roger H. Hering

Mathematics and Statistics Faculty Research & Creative Works

For a chemical reaction system modeled by x =k₁Ax -k₂x² -k₃xy +k₄y², y =k₃xy -k₄y² -k₅y +k₆B, it is shown that for each positive choice of parameters k₁A, B there exists a unique stationary state which is globally asymptotically stable in the positive quadrant. A criterion for the non-existence of periodic solutions is given for the generalized Lotka-Volterra system:x = f(x)h(x, y), y. © 1990 J.C. Baltzer AG, Scientific Publishing Company.

Lifted P-Adic Homology With Compact Supports Of The Weierstrass Family And Its Zeta Endomorphism, Goro Kato

Mathematics

The relations among the generators for the lifted p-adic homology with compact supports of the various subfamilies of the Weierstrass family in characteristic p > 0 (p ≠ 2, 3) are explicitly given in Section 2. Then, the universal coefficient spectral sequence and the zeta endomorphism in Section 3 enable one to compute explicitly the lifted p-adic homology with compact supports of all fibres, including all the elliptic curves and all their singular degenerations in the family.

Eigenvalue Problems Of Ginzburg–Landau Operator In Bounded Domains, Kening Lu, Xing-Bin Pan

Faculty Publications

In this paper we study the eigenvalue problems for the Ginzburg–Landau operator with a large parameter in bounded domains in [openface R]2 under gauge invariant boundary conditions. The estimates for the eigenvalues are obtained and the asymptotic behavior of the associated eigenfunctions is discussed. These results play a key role in estimating the critical magnetic field in the mathematical theory of superconductivity.

Taxonomies Of Model-Theoretically Defined Topological Properties, Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

A topological classification scheme consists of two ingredients: (1) an abstract class K of topological spaces; and (2) a "taxonomy", i.e. a list of first order sentences, together with a way of assigning an abstract class of spaces to each sentence of the list so that logically equivalent sentences are assigned the same class.K, is then endowed with an equivalence relation, two spaces belonging to the same equivalence class if and only if they lie in the same classes prescribed by the taxonomy. A space X in K is characterized within the classification scheme if whenever Y _{E …}

Some Contributions To Generalized Inverse And The Linear Complementarity Problem., N. Eagambaram Dr.

Doctoral Theses

A generalized inverse (g-inverse) of a matrix A is a solution x to the matrix equationA XA = A(1.1.1)A g-inverse of A can be defined alternatively as a matrix x such that x = Xb is a solution to the linear equation Ax -b for any b that makes - b consistent. There is a vast literature on g-inverse. For a number of results on g-inverses and their applications one may refer to the well known books in the literature by Rao and Mitra (1971); and by Ben Israel and Greville (1974).Another inverse that lies hidden in the definition of …

Σary, Moorhead State University, Mathematics Department

Math Department Newsletters

No abstract provided.

Editorial, Issue 5, 1990, Alvin White

Humanistic Mathematics Network Journal

No abstract provided.

The Humanistic Aspects Of Mathematics And Their Importance, Philip J. Davis

Humanistic Mathematics Network Journal

No abstract provided.

Mathematics — A Significant Force In Our Culture, Harald M. Ness

Humanistic Mathematics Network Journal

No abstract provided.

Heuristic Thinking And Mathematics, J. F. Lucas

Humanistic Mathematics Network Journal

No abstract provided.