Digital Commons Network^™

Computer Banking And Cross-Referencing Of Mathematical Materials For The Elementary Grades, Daniel Jordan Martin

All Graduate Projects

The specific area and focus of this project will be that of arranging District and program math learning objectives for eventual computer banking along with materials cross-referenced to those objectives. In addition, the cross-referenced materials will be labeled as to grade level, interest level, mode of learning, and time needed for their use. The computer banking will facilitate use and prescriptive accessibility to given objectives.

The justification for such a project can be broken down into several areas: (1) the need of the elementary math teachers to have a bank of supplementary materials cross-referenced to facilitate their instruction of math …

Boundary Layer Flow In Streamwise Concave Corners, Steven Ray Wilkinson

Digitized Theses

Laminar boundary-layer theory has been correctly developed for streamwise corners using singular perturbation techniques. Theoretical predictions, however, do not compare well with experimental measurements due to the observed breakdown of flow stability and similarity. Both of these properties appear as basic assumptions of the boundary-layer theory, thereby providing needed simplification as well as imposing limitations upon the mathematical model.;Any theoretical investigation of similarity breakdown would require knowledge of the similar solution not only as an initial condition, but also for insight into how to proceed. Examination of the cross-flow behavior, which affects the onset of similarity breakdown, may suggest ways …

Numerical Solution Of Three Instability Problems, Jacob Greydanus

Digitized Theses

This thesis obtains numerical solutions for three instability problems.;The first is a Rayleigh-Taylor interfacial instability problem. Numerical solutions are obtained using a co-ordinate transformation technique and two approaches are tested for use in solving the field equation: (a) transformation and extremization of the variational integral, and (b) transformation of the differential equation itself. The latter is also tested with the use of higher order finite difference formulae. Solutions are generated with the most suitable method and compared with the predictions of Nayfeh's non-linear perturbation theory. While there is good qualitative agreement it is found that the quantitative agreement degrades with …

Pattern And Mathematics: Math Enrichment Activities For Gifted Fourth, Fifth And Sixth Grade Children, Janet K. Zuber

All Graduate Projects

The purpose of this project is to provide assistance to the elementary math teacher in meeting the needs of the student gifted in the area of math. A collection of activities is provided to use with gifted intermediate students and should serve as an example of the type of activities appropriate for the gifted student. These activities would be most appropriately used with gifted students in grades four through six. The activities would be of greatest benefit if students were grouped in a homogeneous manner with one teacher taking responsibility for their math needs, Homogeneous grouping would allow for faster-paced …

Problemes Avec Et, Sans Problemes!, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Mathematics: The Loss Of Certainty (Book Review), Calvin Jongsma

Faculty Work Comprehensive List

Morris Kline was a contentious mathematician and author, documenting (as he saw it) both the deficiencies of mid-twentieth-century reformist trends in mathematics education and formalist views of the foundations (and practice) of mathematics. This brief introduction to a discussion of Kline's 1980 book and its mixed reception by the mathematics community provides a context for assessing his ideas as part of his overall views on the nature of mathematics.

Newsletter, Moorhead State University, Mathematics Department, Moorhead State University, Mathematics Department

Math Department Newsletters

No abstract provided.

Pathwise Stochastic Calculus Of Continuous Semimartingales., Rajeeva L. Karandikar Dr.

Doctoral Theses

Stochastic integration with respect to Brownian motion was introduced by Ito. Stochastic integration with respect to martingales (and seminartingales) was developed by Kunita-Watanable [24 Fisk [9), Courrege D] and Meyer [33]. In this thesis, we study the path wise stochastic calculus restricting ourselves to continuous semimartingales. Here is a brief summary of our results.In Chapter I, we obtain a pathwise formula for the quadratic variation process < M > of a continuous local martingale M. Recall theat < M > is the natural increasing process in the Doob-Meyer decomposition of M. By a part wice formula for M> we mean a formula describing cxplicitly a w-path …

The Alfsen-Errors Structure Topology In The Theory Of Complex L1-Preduals., T. S.S.R.K. Rao Dr.

Doctoral Theses

A complex Banach space X is said to be an L1-predual if X* is isometric to L1() for some non-negative measure Well known examples of L1-preduals include the space C(X) of complex-valued continuous functions on a compact Hausdorff space and the abstract M-spaces of Kakutani. In [19], Grothendieck introduced a class of L'-preduals, now known as G-spaces, and conjectured that those are all the L'-preduals. In his 1964 memoir [35], Lândenstrauss settled this conjecture by exhibiting a wide class of Banach spaces, other than G-spaces, which are L1-preduals. He also gave several characterizations and interest- ing properties of L1-preduals in …

Spectral And Scattering Theory For Schrodinger Operator With A Class Of Momentum Dependent Long Range Potentials., P. L. Muthuramalingam Dr.

Doctoral Theses

No abstract provided.

Measurable Sets In Product Spaces And Their Parametrizations., V. V. Srivatsa Dr.

Doctoral Theses

No abstract provided.

On Multiple Solutions Of Nonlinear Elliptic Equations With Odd Nonlinearities, Alfonso Castro, J. V. A. Gonçalves

All HMC Faculty Publications and Research

In this paper we stablish results on multiplicity of solutions for the boundary value problem where a e IR and f: R - IR is an odd continuous function.

Ab?Ba : An Investigation Into The Historical Roots Of Noncommutative Algebra, Keith Chavey

Honors Capstones

Abstract Algebra is a branch of mathematics in which a large amount of research is currently taking place. This research includes the investigation into different types of algebraic structures such as fields, rings, groups, and their properties. The history of algebra is as rich as the science itself. It is my intention to investigate a crucial step in the development of algebra: the beginning of noncommutative algebra.

Generalized Hausdorff Matrices With Applications To Strong And Absolute Summability, John Edward Sayre

Digitized Theses

Hausdorff summability methods include such well known methods as those of Cesaro, Holder, and Euler. Consequently, the properties of Hausdorff matrices have been extensively investigated since 1921 when the German mathematician Flex von Hausdorff first published his paper entitled "Summationsmethoden und Momentfolgen I" {lcub}11{rcub}.;In 1922, Hausdorff published "Summationsmethoden und Momentfolgen II" {lcub}12{rcub} in which he defined what are now known as generalized Hausdorff matrices. The question then arose of finding appropriate conditions so that results about ordinary Hausdorff matrices would be true more generally. In this thesis, questions concerning strong and absolute summability are addressed.;In order to deal with the …

A Natural L(,P)-Metric For Spaces Composed Of Probability Measures With P-Th Moment., Mark William Scott

LSU Historical Dissertations and Theses

In the dissertation, it is seen that every probability measure with p-th moment on a complete, separable metric space can be viewed as a distribution of a metric space valued random variable. Between such random variables there exists an L(,p)-distance, and by finding the infimum of the L(,p)-distances between two types of random variables, it is possible to define a distance between distributions. It is seen that this distance can serve as a complete metric on the space of probability measures with p-th moment. The topology produced is shown to be equivalent to the topology of weak convergence of measures …

Eigenvalues Of Nuclear Operators Of Diagonal Type., Raymond J. Kaiser

LSU Historical Dissertations and Theses

A nuclear operator T on a Banach space is an operator admitting a representation T = (SIGMA) T(,n) where each operator T(,n) has rank one and (SIGMA) (VERT.BAR)(VERT.BAR)(TAU)(,n)(VBAR)(VBAR) < (INFIN). A. Grothendieck proved that the sequence of eigenvalues, repeated according to their multiplicities, of such a nuclear operator must be square summable and that, in fact, two is the best possible exponent of summability. This work uses operators of diagonal type, i.e., operators which admit a diagonal representation with respect to a biorthogonal system, to construct examples of eigenvalue behavior. In particular we show that all of the known results concerning eigenvalue summability of nuclear operators can be obtained using operators of diagonal type. In Chapter 1, we present the terminology and notation to be used in this work. Chapter 2 gives a summary of results concerning nuclear (trace class) operators on Hilbert space. In Chapter 3, some of the important known results concerning eigenvalue behavior of nuclear operators on general Banach spaces are presented. The convolution operators on L(,p)(0,1), 1 < p < (INFIN), p (NOT=) 2, are diagonal operators since the trigonometric system (e('2(pi)inx)) is a conditional basis of these spaces. In Chapter 4 we use these important operators to exhibit extremal behavior of eigenvalue summability of nuclear operators on the L(,p)-spaces. In Chapter 5, we study nuclear cyclic diagonal operators. If X(,1),... ,X(,n) are sequence spaces, an operator D on (CRPLUS)X(,i) is a cyclic diagonal operator if its restriction to each X(,i) is a diagonal operator into X(,i+1) (if i = n into X(,1)). Certain eigenspaces of these operators have important applications to Banach space theory. Finally, in Chapter 6, we use a recently discovered space of G. Pisier to answer affirmatively a long outstanding question of. Pe l cynski and Saphar which is converse to Grothendieck's result: Given a (nonzero) sequence ((lamda)(,n)) in l(,2), is there a Banach space X and a nuclear operator on X whose eigenvalue sequence is ((lamda)(,n))?

On Valuation Rings As Homomorphic Images Of Valuation Domains., J. Paul Vicknair

LSU Historical Dissertations and Theses

A number of years ago, I. Kaplansky raised informally the question of whether every valuation ring could be expressed as a homomorphic image of a valuation domain. By a valuation ring, we mean a commutative ring with identity whose ideals are linearly ordered by inclusion. The classical notion of a valuation ring included the assumption that the ring is a domain. For two cases an affirmative answer to Kaplansky's question is known: for 0-dimensional valuation rings; and, for valuation rings which are monoid rings. In the early 40's, Kaplansky obtained structure theorems for a large class of (maximally complete) valuation …

On A Conjugate Class Of Subgroups Determined By A Formation, Mark Challis Hofmann

Doctoral Dissertations

This thesis is an investigation of the interrelationships between a formation f, a finite solvable group G, and G(,f) the residual of f in G. This study is developed by introducing the f-subgroups. It is proven that the f-subgroups of G form a characteristic conjugacy class of CAR-subgroups of G. Moreover these subgroups generate G(,f). As a result, G is an element of the formation f if and only if an f-subgroup is equal to the identity subgroup.

It is established that an f-subgroup is a product of known subgroups of the f-residual. The covering and avoidance properties of f-subgroups …

Richard Whately And The Revival Of Syllogistic Logic In Great Britain In The Early Nineteenth Century, Calvin Jongsma

Faculty Work Comprehensive List

Richard Whately's Elements of Logic in 1826 marked the end of a dismal era in the history of British logic. His work sparked a revival in Britain, culminating in several distinct developments, none of which, however, Whately contributed to. Yet his work laid the foundation for them by providing a spirited defense of the syllogism and of deductive reasoning generally.

The first chapter begins with a systematic synopsis of the criticisms and responses which were made from the seventeenth to the early nineteenth century. These related primarily to the nature of logic and the epistemic utility of syllogistic reasoning, but …

Combinatorics And Diagonals Of Matrices., K. Balasubramanian Dr.

Doctoral Theses

This theale maindy desie with conbinatoriel aspocte of diayonale of natelees. or enurne, there are aleo eosulte which are nat sunbinatorial in naturos but thase ara neroly by-producta. Chapter-0 gives e very short nary ot the cnntenta of the theete. The raeulte aro ofr tuo kinde. (1) complately rev and (2) old results through rew rethude.Thịa thasle, wholly or pertly, has not baon subnittad to any othor Univerdity or Inatitute for e degree.I exprees hoceby ry doopost sonse of grotitude to br. KA. PARTHASARATHY, Haed of the Doparteant af Mathemties, Indian Inatituta of Tochmlogy, Redras, under uhana bonign guidance thie …

Metrizability And The Frechet-Urysohn Property In Topological Groups, Peter J. Nyikos

Faculty Publications

A question of Arhangel'skii, whether weakly first countable topological groups are metrizable, is answered in two ways: if the Hausdorff axiom is assumed, the answer is yes, but in general a weakly first countable topological group need not be pseudometrizable. The former result is obtained as a corollary of a more general sufficient condition for a sequential group to be Fr&chet-Urysohn. A general necessary and sufficient condition for a sequential group to be Frechet-Urysohn is given, and a number of questions are raised. Examples are given to show in what respect the theorems of the paper are the "best possible".

Electron Transport And Energy Degradation : On The Numerical Solution To The Two-Stream Equations, Knut Stamnes

GI Reports

A new numerical solution to the two-stream equations for electron transport and thermalization is presented and discussed. The numerical code is verified by comparing computed results with the analytic results of Stamnes (1981) and with the Nagy-Banks code (Nagy and Banks, 1970). Further verification is provided by carefully testing for energy conservation. The computational speed depends primarily on the number of grid points in altitude utilized. It is demonstrated that useful results can be obtained with as little as 20-40 altitude grid points. The present numerical code represents an extension of the Nagy-Banks code to high electron energies appropriate for …

Sufficiency Pairwise Sufficiency And Bayes Sufficiency In Undominanted Experiments., R. V. Ramamoorthi Dr.

Doctoral Theses

An experiment or a statiatical structure consists of a set X and a family of probability measures P on , indexod by a set (. The set I together with a g-algebra of subsets of X is the sample space and the set (H ith a -algebra g of subsets of (D is the parameter space, To avoid trivialities ve consider only situations where the para- sotrization is one-one, i,e, if Ø1, and Ø2, are distinct then s0 are PØ1. and PØ2. Various notions of aufficiency of a -lgebra 3 is considered in statistical literature, Anong the se are the …

Studies In Multipartite Self-Complementary Graphs., T. Gangopadhyay Dr.

Doctoral Theses

The class of self-complenentary egraphs has been extensively etudied by nany people, among others by C.R.J. Clephan, S.B, Rao, G, Ringel and H. Sache, and nany problems have been solved for this class, such as the Haniltonian problen and the characterisati on of potentially and forcibly self-complenentary dogree sequences (see [1], [2], [12), [13), [14, [15)). Thus self-complenentary graphs form an interesting class and this has been generalised by Hebbare [8] into the class of multipartite self-conplementary graphs.An r-partite self-complenentary graph is an r-partite graph G which is isomorphic to its r-partite complement where H has the sane vertex set …

Estimation Of Spectral Variation., Rajendra Bhatia Dr.

Doctoral Theses

The study of spectra occupies a central place in the theory of linear operators. One part of this study consists of obtaining a detailed and complete knowledge of the spectrum of a given lincar operator. The other part - perturbation theory - consists of using this knowledge to obtain information about the spectra of nearby operators.Apart from the intrinsic mathematical interest it has, perturbation theory is of great importance in the study of several physical problems. In fact, the theory came into existence with the work of Rayleigh on sound waves and that of Schrodinger on quantum mechanics. Later, their …

Some Singular Measures On The Circle Which Improve L('P) Spaces., David Lawrence Ritter

LSU Historical Dissertations and Theses

Let (mu) be a positive Borel measure on the circle group T. If, for P (GREATERTHEQ) 1, there is a q > p such that (mu) defines a bounded convolution operator from L('p)(T) to L('q)(T), then (mu) is L('p)-improving or (mu) improves L('p). Here a result of Oberlin is extended. It is shown that a large class of Cantor-Lebesgue measures improve L('p)(T) for p > 1. Also, for the members of a particular sequence of Lebesgue measures associated with some homogeneous Cantor sets, which includes the middle-third Cantor-Lebesgue measure studied by Oberlin, estimates are obtained for the amount of improvement. These results …

The Effects Of A Role Model Intervention Program On The Attitudes Of Junior High School Students Towards Mathematics And Sex-Role Orientation, Linda Fritz Havins

UNLV Retrospective Theses & Dissertations

Bureau of Labor Statistics information indicated 55 percent of all women in the labor force in 1980 were employed in traditional clerical and service occupations. The limited participation of women in certain sectors of the labor force represented a great loss of human potential, particularly in the case of academically talented women. This exploratory study focused on two potential barriers that may keep capable women from realizing their full potential: sex-role orientation and attitudes toward mathematics course-taKing Another area of focus determined what effect stability factors had on the population under study and how stability might affect future studies. A …

Bilin: A Bilinear Transformation Computer Program And Its Applications, John Dana Greer

Retrospective Theses and Dissertations

Given a transfer function for a differential equation model, an approach for obtaining a solution is by way of bilinear transformation. The bilinear transform approach is a numerical integration scheme which gives a discrete approximation to the differential equation solution. BILIN applies a series of polynomial transformations to the transfer function H(s). As a result, H(s) is mapped into the complex z plane obtaining the discrete transfer function H(z). From H(z), the difference equation is obtained whose solution y(nT) approximates the actual differential solution y(t). Hence, BILIN provides a means for obtaining discrete transfer functions for the design of digital …

Optimum Monotonic Step Response Filters, Peter H. Halpern

Retrospective Theses and Dissertations

The problem of designing sharp cutoff filters with monotonic step responses is addressed. The impulse responses of the filters are expanded in terms of finite duration trigonometric polynomials. The coefficients of the trigonometric polynomials are obtained, for arbitrary frequency penalty functions, by solving a generalized eigenvalue problem. Once the trigonometric polynomial is specified the network can be synthesized with known techniques. Two theorems which assist in the numerical solution are proven.

Contribution To Theories Of Repetitive Sampling Strategies., Raghunath Arnab Dr.

Doctoral Theses

A common practical problem to whlch a survey - sampler has frequently to address himself 1s one of sampling a given finite population on successive occasions. One of the relevant issues requiring one's attention then 1s to adopt a suitable sampling strategy to estimate the population total of a variate of interest an the current occasion in an optimal manner. Here one has of necessity to take care to utilize the accumalated data on that variate procured in course of the survey along with other auxdliary information on one or more additional variables that may also incidentally be available, Several …