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Σary N=0, Moorhead State University, Mathematics Department

Math Department Newsletters

No abstract provided.

On The Atomic Decomposition Of H^1 And Interpolation, Robert Sharpley

Faculty Publications

© 1986 by American Mathematical Society

Improving The Skill Of Analysis In Fifth And Sixth Grade Academic Excellence Students, Sandra Stein

Abraham S. Fischler College of Education ETD Archive

The writer initiated and implemented a program designed to increase the higher cognitive skill of analysis in fifth and sixth grade Academic Excellence students. This was to be achieved by an eclectic approach involving language arts, mathematics, and social studies. The program employed daily and weekly lessons, as well as a three week research project.

The primary objective was improvement of scores on the “Ross Test of Higher Cognitive Skills” as evidence by percentile upgrades on spring testing as compared to fall testing. Assessment was done on a weekly basis through oral and written evaluation in the form of anecdotal …

Nonexistence Of Stable Harmonic Maps To And From Certain Homogeneous Spaces And Submanifolds Of Euclidean-Space, Ralph Howard, S Walter Wei

Faculty Publications

Call a compact Riemannian manifold M a strongly unstable manifold if it is not the range or domain of a nonconstant stable harmonic map and also the homotopy class of any map to or from M contains elements of arbitrarily small energy. If M is isometrically immersed in Euclidean space, then a condition on the second fundamental form of M is given which implies M is strongly unstable. As compact isotropy irreducible homogeneous spaces have "standard" immersions into Euclidean space this allows a complete list of the strongly unstable compact irreducible symmetric spaces to be made.

Optimum Sampling Strategies., T. V. Hanurav Dr.

Doctoral Theses

The advantages sample surveys over complete censuses are well known and seem to be fully appreaciated as is evidenced by the increasing use of sample surveys now a days as a means of collecting information.The use of probability theory to make rigorous inductive inferences has been well recognised for a long time. Such inferences can be made only when observations which form the basis of the infe- rence are generated by some chance mechanism, In traditional applica- tions, the statistician usually assume s or takes for granted some kind of chan ce mechanism behind the o bservations, where as in …

Numerical Techniques For Free Surface Problems In Viscous Incompressible And Porous Flows, Ching Yuen Loh

Digitized Theses

Three free surface problems have been investigated. The first two involve incompressible flows and the last one involves porous flow. These problems are solved numerically by finite difference technique. In each problem the original physical domain with a free surface is transformed into a rectangular domain and then the appropriate finite difference schemes are used in the new transformed domain to carry out the computation.;In the first problem the attenuation of a large amplitude standing capillary-gravity wave is considered. A finite difference scheme similar to the Crank-Nicolson scheme is developed to handle the equation of the free surface. Convergent numerical …

Sphericals And Primitives Classes In The Bordism Of Compact Lie Groups, Rodrigo-Guillermo Moreno-Rodriguez

Digitized Theses

The main purpose of this thesis is to study the following question: Do primitives and sphericals agree in MU(,*)(X)/tor when X is a 1-connected compact Lie group. Our answers appear in Part IV for the classical groups (stable cases) and in Part V for two exceptional cases namely G(,2) and F(,4) (ignoring the prime 2).;The main tool for our study is the rational MU operation P : MU(,*)(X)(CRTIMES) (--->) MU(,*)(X)(CRTIMES) ; P = (SIGMA)(,E) m(,E)S(,E) which detects primitives rationally. Our method is to find the least positive integer k(,(alpha)) (ELEM) such that k(,(alpha))P((alpha)) (ELEM) MU(,*)(X)/tor (L-HOOK) MU(,*)(X)(CRTIMES) for (alpha) …

Localized Algebraic K-Theory, Felipe De Zaldivar-Cruz

Digitized Theses

Let K(,*)(A; /L('n)) denote the mod-L('n) algebraic K-theory of a 1/L -algebra A. V. Snaith has studied Bott-periodic algebraic K-theory K(,i)(A; /L('n)) 1/(beta)(,n) , the direct limit of iterated multiplications by (beta)(,n), the 'Bott element', using the K-theory product. For L an odd prime, Snaith has given a description of K(,*)(A; /L('n))(1/(beta)(,n)) using Adams maps between Moore spectra. These constructions are interesting, in particular, for their connections with the Lichtenbaum-Quillen conjecture.;In this thesis we obtain an analogous description of K(,*)(A; /2('n)) 1/(beta)(,n) , n (GREATERTHEQ) 2, for an algebra A with 1/2 (ELEM) A and such that A contains a …

A Tauberian Theorem Concerning Borel-Type And Cesaro Methods Of Summability, Tom Nik Markovich

Digitized Theses

Let r > 0, (alpha) > 0, (alpha)N(,o) + (beta) > 0 where N(,o) is a non-negative integer, and let;(DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI);The Borel-type summability method (B,(alpha),(beta)) is defined as follows: s(,n) (--->) L(B,(alpha),(beta)) or;(DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI);The special case (B,1,1) is the ordinary Borel exponential method B.;The main result of this thesis is the following Tauberian theorem for summability (B,(alpha),(beta)):;If s(,n) is a real sequence that satisfies the slowly decreasing condition;(DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI);and s(,n) (--->) L(B,(alpha),(beta)), then s(,n) (--->) L(C(,2r)). Here C(,2r) denotes the Cesaro method of order 2r.;In …

Wooster Magazine: Winter 1986, Peter Havholm

Wooster Magazine: 1981-1990

This edition of the Wooster Magazine was published in the winter of 1986. The first article of the magazine, "Inside Taylor Hall," explores the physics and mathematics departments at the College of Wooster. Taylor Hall and the departments housed within it are the main focus of this edition. The next section debates the usefulness and necessity of personal computers. Later articles discuss computer games, alumni careers in physics and math, the renovations done to Taylor Hall, and the role of machines in teaching. The Class Notes begin on page 46 and detail notes from classes all the way back …

Expanding Horizons In Intermediate Mathematics, Sheri Pindel

Honors Capstones

This project is aimed at providing teachers with activities that could be used to increase students’ understanding of mathematics. The activities listed are aimed for students in fifth through eighth grade. Many of the concepts presented have strong upper level mathematical background, but a complete understanding of the background of the material is not necessary to effectively present the material to students. A teacher who understands the material that is presented to the students in the everyday textbooks should find these supplement activities interesting and enjoyable to teach their students.

The Contraction Mapping Principle, Elaine Rosenbloom

Honors Capstones

In the world of mathematics, it is often necessary to approximate the solution to a problem by using an iterative method. One such method, not totally dependent on the initial guess, is the contraction mapping method. This paper will explore the contraction mapping principle for the real line, some extensions of it, and the principle in other contexts.

Qualitative Theory Of Differential Equations, Sheri Homeyer

Honors Capstones

The problem of stability is of primary concern in the qualitative theory of differential equations and has occupied mathematicians for the past century. The problem appears when considering solutions to the differential equation x-f(t,x) where x=( x1(t),…,xn(t) )T and f(t,x) is a nonlinear function of x1,…,xn. While no known method of solving this equation explicitly exists even for the case n=2, it is possible to discuss the qualitative properties of x1(t) and x2(t) where x1(t) and x2(t) denote, for example, the populations, at time t, of two competing species. The qualitative attributes under consideration include points of equilibrium and the …

Extreme Elements In Semigroups (Quasiorders, Green's)., Carol Esther Collins

LSU Historical Dissertations and Theses

We study the elements of a semigroup which are minimal or maximal with respect to Green's quasiorders. Part 1 begins with a preliminary review. The sets of minimal elements are characterized in terms of minimal ideals. We discuss the relationship between the min set of a semigroup and the min set of a subsemigroup. The sets of maximal elements are characterized, and it is shown that these sets do not necessarily satisfy any inclusion relationships to each other. We discuss the max sets of subsemigroups and product semigroups. Conditions are given under which the max sets and min sets can …

Operator Ranges Of Shifts And C*-Algebras (Strange Range, Quasi-Similarity, Lattice), Charles Lucien Roy

Doctoral Dissertations

It is shown that Lat(, 1/2)(H('(INFIN))(S)), the invariant operator ranges of the commutant of the unilateral shift, is a proper sub-lattice of the lattice of invariant operator ranges of the unilateral shift, S. The notion of a strange operator range for S of order n where n (ELEM) is introduced and it is demonstrated that there exist strange ranges for S of every order. This is done by deriving an operator range condition which is sufficient to insure that a pair of quasi-similar compressions of shifts really be similar. A set of operator ranges which forms a sub-lattice of Lat(, …

The Role Of Error Analysis, Diagnostic Grading Procedures, And Student Reflection In First Semester Calculus Learning (Epistemology, Metacognition, Inquiry), Karen Jean Geuther

Doctoral Dissertations

The present study is an integrative study designed to explore the nature of student difficulties within the context of a first semester college calculus course. The techniques of error analysis were used to identify and categorize the student difficulties. Insights gained from this categorization served as the basis for the design and development of calculus grader preparation materials implemented with a subgroup of undergraduate calculus graders. These grader preparation materials emphasized grader diagnosis of student difficulties and student reflection on errors and process. Current preparation procedures served as the control on the basis of which comparisons and evaluations were made. …

Multivariate Rational Approximation, Ronald A. Devore, Xiang Ming Yu

Faculty Publications

No abstract provided.

Dyadic Ramification In Quartic Algebraic Number Fields., Stella Roberson Ashford

LSU Historical Dissertations and Theses

This dissertation is concerned with dyadic ramification in quartic number fields E. If f(x) is a defining polynomial for E, then E (TURNEQ) IQ x /(f(x)). The problem is to decide whether or not 2 ramifies in E, in terms of the coefficients of f(x). In this dissertation, this problem is. studied when f(x) is an irreducible quartic trinomial. That is, f has one of the forms (UNFORMATTED TABLE FOLLOWS). (1) f(x) = x('4) + cx + d. (2) f(x) = x('4) + cx('2) + d c,d in ZZ. (TABLE ENDS). (any irreducible trinomial can be reduced to one of …

Linear Measurement: A Prevocational Skills Curriculum Based On The Brigance Inventory Of Essential Skills, Linda Jane Kittle

All Graduate Projects

Student progress toward an educational goal can be enhanced by the use of a curriculum containing both assessment and instruction. This project is such a curriculum based on the linear measurement items of the Brigance Inventory of Essential Skills. The careful sequencing and prevocational nature of this curriculum, along with its record-keeping forms, make it especially useful for special education. It is also available as a data disk for use with Apple microcomputers.

Selection In Genetics : A Mathematical Model, Sarah J. Blean

Honors Capstones

There are many areas of study in the field of genetics which continually affect our highly technological society. In particular, the idea of being able to predict the time when, given the current distribution of a population, a specific inherited trait might disappear from the population is one important question that is being raised. In order to accurately make such a prediction, a mathematical model will be built. Since there are several variables that enter into such a model, certain assumptions will initially be made. After studying the original model, a selected group of the variables and their corresponding assumptions …

Some Insights Into Partitioning And Repartioning Behaviors, Gina Marie Conner

Honors Capstones

Recently, in mathematical educational research, there has been quite a bit of work focusing on the acquisition of rational numbers concepts by school age children. It is believed that partitioning, the act of dividing a quantity into a given number of parts which are quantitatively equal, is one of the necessary behaviors for students to obtain in order to fully understand the rational numbers. The first part of this paper will discuss the research that has examined the partitioning behaviors of school age children. The latter part of this paper will contain an analysis of data collected from videotapes of …

On The Martingale Problem For Infinite Dimensional Stochastic Differential Equations., Robert W. Riordan

LSU Historical Dissertations and Theses

The purpose of this dissertation is to establish, in a certain infinite dimensional setting, some existence and uniqueness results pertaining to the type of exponential martingale problem previously considered by Strook and Varadhan in the finite dimensional setting. The setting is among those considered by K. Ito in his work on stochastic differential equations in infinite dimensional spaces. Briefly, the martingale problem takes the following form: to show the existence and uniqueness of a measure m on the space S of continuous functions defined on the nonnegative real lien with values in some state space, having the property that exp(f(t,w)) …

Sequences In Power Residue Classes, Duncan A. Buell, Richard H. Hudson

Faculty Publications

Using A. Weil’s estimates the authors have given bounds for the largest prime P₀ such that all primes P > P₀ have sequences of quadratic residues of length m. For m ≤ 8 the smallest prime having m consecutive quadratic residues is ≡ 3(mod 4) and P₀ ≡ 1 (mod 4). The reason for this phenomenon is investigated in this paper and the theory developed is used to successfully uncover analogous phenomena for r^th power residues, r ≥ 2, r even.

Certain Generalisations Of Acceptance Sampling Plans By Attributes., R. J. Pandey Dr.

Doctoral Theses

The use of inspection gained importance when people started getting conscious of maintaining the quality of manufactured product. According to Anscombe (1958) inspection for quality in the form of acceptance sampling plans originated around 1920. The classical work of Dodge and Romig (1929) put acceptance sampling on a firm footing. In general, sampling inspection can be broadly classified into (i) lot- by-lot inspection (11) bulk sampling inspection and (iii) "continuous; sampling inspection.The lot-by-lot sampling inspection is applied where a series of lots or batches of discrete items are available for inspection. On the other hand, a batch of cotton, a …

Inequalities Relating Sectional Curvatures Of A Submanifold To The Size Of Its 2nd Fndamental Form And Applications To Pinching Theorems For Submanifolds, Ralph Howard, S Walter Wei

Faculty Publications

No abstract provided.

Σary N=0, Moorhead State University, Mathematics Department

Math Department Newsletters

No abstract provided.

Some Spectral Properties Of Three And Four Body Scrodinger Operators By The Methods Of Time Dependent Scattering Theory., M. Krishna Dr.

Doctoral Theses

In the present work we shall deal with the asymptotic completeness problem in three and four (Quantum Mechanical) particle scattering. This thesis is divided into three chapters. In the first chapter we give an introduction to Scattering Phencmenon and give a description of the N-particle completeness problem.Then we collect some results preliminary to the later chapters and some results that would complete a discussion of the problem.The second chapter consists of some technical results and a reduction of the asymptotic completeness problem in N-particlerscattering via time dependent methods. The last chapter has two sections. The first section deals with verifying …

The Monte Carlo Method : An Alternative Method Of Numerical Integration, Karen A. Haas

Honors Capstones

In the world of mathematics, one of the more fundamental ideas that exists is the idea of a function, mathematically described as a correspondence that associates with each element x, of a set S, a unique element y, of a set Y. This concept is basic to many of the applications of higher mathematics, as are the concepts of integrating a function and differentiating a function. It is the former concept which shall be dealt with here.

Homology And K-Theory Of Loop Spaces, Jesus-Manuel Mayorquin-Garcia

Digitized Theses

Part 1 of this work is an application of the Dyer-Lashof Algebra modulo p, an odd prime, to the determination of the Steenrod annihilated indecomposables in the /p homology of the infinite loop space associated to a CW-complex.;Part 2 is concerned with the determination of the algebra struc- ture of K(,*)((OMEGA)('2)S('2n+1); /2) where K(,*)((,-); /2) stands for mod 2, periodic, reduced, complex K-homology theory. Moreover the Atiyah-Hirzebruch spectral sequence for K(,*)((OMEGA)('m)S('n)X; /2) is studied. The main tool in Part 2 are the mod 2 Dyer-Lashof operations acting on finite loop spaces, as well as the Atiyah-Hirzebruch spectral sequence for K-homology.

Some Results About Value Sets Of Quadratic Forms Over Fields., David Litton Foreman

LSU Historical Dissertations and Theses

In 1979, Solow defined the square class invariant of a quadratic form q over a field F to be a function from the square classes of F into the integers. For each square class of F, this function indicates the maximum number of coefficients in all diagonalized quadratic forms equivalent to q that lie in that square class. The intent of Chapter I is to determine the fields over which the square class invariant classifies quadratic forms. It will be proved that if the level of the field is at most two and if the square class invariant classifies the …