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A Note On T, Topologies, Wilson R. Crisler, Troy L. Hicks

Mathematics and Statistics Faculty Research & Creative Works

Let t be a T. topology for a set X. The problem of representing t as the lattice product (intersection) of stronger topologies is considered. © 1974 American Mathematical Society.

Fields Medals And Nevanlinna Prize Presented At Icm-94 In Zurich, Nicholas Pippenger, J. Lindenstrauss, L.C. Evans, A. Douady, A. Shalev

All HMC Faculty Publications and Research

The Notices solicited the following five articles describing the work of the Fields Medalists and Nevanlinna Prize winner.

Stability And Transversality, Robert D. May

Mathematics & Computer Science Faculty Publications

No abstract provided.

Lipschitz Spaces On The Surface Of Unit Sphere In Euclidean N-Space, Harvey Greenwald

Mathematics

This paper is concerned with defining Lipschitz spaces on Σn-1 the surface of the unit sphere in Rn. The importance of this example is that Σn-1 is not a group but a symmetric space. One begins with functions in Lp(Σn-1),1≤p≤∞. Σn-1 is a symmetric space and is related in a natural way to the rotation group SO(n). One can then use the group SO(n) to define first and second differences for functions in Lp(Σn-1). Such a function is the boundary value of its Poisson integral. This enables one to work with functions which are harmonic. Differences can then be replaced …

Faces, Edges, Vertices Of Some Polyhedra, Charles H. Harbison

Journal of the Arkansas Academy of Science

A proof that: for any given polyhedron so shaped that every closed non-self intersecting broken line composed of edges of the polyhedron divides the surface of the polyhedron into precisely two disjoint regions each of which is bounded by the closed broken line, v - e + f = 2, where v is the number of vertices of the polyhedron, e the number of edges and f the number of faces.

Graphs With 1-Factors, David Sumner

Faculty Publications

In this paper it is shown that if G is a connected graph of order 2n (n > 1) not containing a 1-factor, then for each k, 1

Symmetric Groups And Their Automorphism Groups, Harold Lyle Madison

All Master's Theses

This paper presents an account of the relationship between the symmetric group on n symbols, S_n, and its automorphism group for each natural number n. For n ≠ 2, S_n is isomorphic to its inner automorphism group. S₂ has only the identity automorphism. For n ≥ 3, n ≠ 6, each automorphism of S_n is an inner automorphism. An illustration shows where this proof fails when n = 6. S₆ has outer automorphism. An example of an outer automorphism for S₆ is given.

The Effect Of An Administration Of Audio-Visual Aids On The Attitudes Of Geometry Students Toward Mathematics, Kirk Quistorff

All Master's Theses

This paper presents an experiment to determine the effect of an administration of audio-visual aids on the attitudes of geometry students. It was hypothesized that the experimental group would make a significant improvement in their attitude toward mathematics. The control group had eight-two students and the experimental group had forty-six students. In the control class no audio-visual aids other than the overhead projector were used. The results did not verify the hypothesis and the author concluded that more research was needed.

The Completions Of Local Rings And Their Modules., Christopher Scott Taber

Masters Theses

"This paper gives a generally self-contained introduction to the completions of local rings and their modules. The '.Fbrmal Power Series, the Ideal-adic, and the Projective Limit completions are established, and the conditions under which they are equivalent are also given. In addition, two methods of obtaining the completion of an R-module from the completion of the ring Rare supplied. As an ideal of R may also be taken as an R-module, a discussion of obtaining its completion from the completed ring is also provided. Two well-known examples are furnished in this paper"--- Abstract, p. ii

Linear Geometry, Phyllis L. Thomas

Masters Theses

"This paper contains material suitable for a one semester course in linear geometry where the student has had a one semester course in linear algebra previously. It compiles information in the areas of affine sets, affine geometry, convex sets, and a few applications. Also included are Caratheodory's theorem and the well-known theorem by Helly as proved by Radon"--Abstract, page ii.

On Integrability And L¹ Convergence Of Certain Cosine Sums, John William Garrett

Doctoral Dissertations

"Rees and Stanojevic altered the standard cosine series and obtained a necessary and sufficient condition for integrability of the altered sum. Here these sums are generalized, and it is shown that such sums converge in L¹-norm"--Abstract, page iv.

Solvability Of Differential Systems Near Singular Points, Leon M. Hall

Doctoral Dissertations

"Functional analysis techniques are used to prove a theorem, analogous to the Harris-Sibuya-Weinberg theorem for ordinary differential equations, which yields as corollaries a number of existence theorems for holomorphic solutions of linear functional differential systems of the form z^Dy'(z) = A(z)y(z) + B(z)y(αz) + C(z)y'(αz) in the neighborhood of the singularity at z = 0"--Abstract, page 2.

On Interaction In The Two-Way Aov Model Without Replication Including Power Comparisons Of Two Tests For Non-Additivity, Victor John Hegemann

Doctoral Dissertations

"Data analysts have long been concerned with the problem of giving a complete analysis of the two-way crossed classification design with one observation per cell when interaction is present in the data. Conventional tests of hypotheses and statistical inferences are not applicable in this case since an estimate of the error variance is not available. Transformation of the data to additive data has been one solution to this problem; however, interpretation of the physical units of the transformed data is difficult. Recent contributions to the analysis of this design include a test for interaction, a test for testing differences in …

Methods And Applications Of The Mean-Variance Portfolio Selection Model, John W. Marsh

Doctoral Dissertations

"The Mean-Variance portfolio selection model, or Efficient Market model, is examined in terms of the small investor. The performance is first tested on the small sample space of the thirty Dow Jones Industrials. The results show that it is possible to outperform the market by investing in the minimum-variance, or safest, portfolio. The Critical-Line algorithm as developed by Markowitz and modified by Sharpe is used in this analysis.

Since the Critical-Line algorithm is very time-consuming and does not always converge to a solution, an alternate algorithm is developed. This algorithm, referred to as the “Simplified Algorithm”, is designed to find …

Maintaining Topological Properties On The Brink Of Destruction, Kay J. Hamm

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Throughout the paper we consider the setting where f is a continuous function (a mapping) whose domain X and range Y are both Hausdorff spaces. Our object is to determine conditions on the map f which insure that when X has a certain topological property Q, then Y will also have property Q. For example, if X is metrizable, then it does not necessarily follow that Y is a metric space; but if f is a perfect map, then metrizability is preserved. Chapter III is devoted to the study of this metrizability problem. In particular, we present Frink's [ 2] …

Functional Analysis Techniques In Numerical Analysis, Kenneth D. Schoenfeld

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

In this paper we will consider the problem of selecting the best, or optimal, numerical method of solution to a given mathematical problem. The admissible numerical methods will be a clearly defined set for each problem. Obviously, in order to find the best method in this set, we must have a clear mathematical formulation of just what "best" means; this will be the intent of Theorem 0.1. Intuitively, the best method will be understood to be the one which minimizes the maximum possible error where this error will be measured in terms of the norm of a given Hilbert space. …

A Study Of Vector And Matrix Norms, Alvena Weiskircher

Theses & Honors Papers

A vector or matrix can be associated with a single nonnegative scalar . Basically this is the concept of a vector or matrix norm. While the study of these norms may be classified as numerical analysis , a limited background in linear algebra , matrix theory , and advanced calculus is sufficient to pursue the study of norms.

In this paper many of the properties and theorems concerning norms have been proven . It is thought that the most important results deal with the use of vector and matrix norms in testing for convergence of sequences and series of matrices …

Truncated Circular Normal Distribution With Applications In Ballistics And Meteorology, Danny D. Dyer

Mathematics Technical Papers - Archive

The use of the circular normal distribution (CND) to describe the behavior of random phenomena of a geophysical nature has been discussed by Crutcher [7, p. 9]. Based on the Mauchly [17] - Hsu [12] test, the harmonic dial points (the Fourier coefficients obtained from harmonic analysis of observations of periodic phenomena) representing i.) lunar semidiurnal atmospheric tides (Chapman and Lindzen [5, p. 66]), ii.) the westerly component of wind in the study of tidal oscillations in the upper atmosphere (Haurwitz [10]), and iii.) terrestrial-magnetic activity relative to solar activity (Bartels [2]) may be treated as observations from a CND. …

Existence Md Estimates For Solutions Of Nonlinear Equations Near A Branch Point, Jerome Eisenfeld, V. Lakshmikantham

Mathematics Technical Papers - Archive

Consider the equation (1.1) [see pdf for notation] on a Hilbert space H. Here n is a scalar and [see pdf for notation] is a linear Fredholm operator. That is: (a) L is closed; (b) The domain, D(L) is dense in H; (c) The range, R(L) is closed in H; (d) The dimension of the null space, dim n(L) <= (e) The dimension of the null space of the adjoint dim n(L*) <= The operator N, which may be nonlinear, is defined for sufficiently small and appropriately restricted [see pdf for notation], and [see pdf for notation] Using the method of Lyapunov-Schmidt (cf., e.g. [4] or [5]) we express w in the form (1.2) [see pdf for notation] where [see pdf for notation] denotes the orthogonal complement of n(L) in H. Suppose (u,v) satisfy the simultaneous equations (1.3) [see pdf for notation] (1.4) [see pdf for notation] where P is the orthogonal projection operator of H onto R(L), I is the identity operator on H, and J is a right inverse of L on R(L), i.e.

An Analytic Study Of A System Of Nonlinear Ordinary Differential Equations At An Irregular Type Singularity, James M. Lamb

Masters Theses

No abstract provided.

Decompositions Of Modules And Matrices, Thomas Shores, Roger Wiegand

Department of Mathematics: Faculty Publications

A canonical form for a module M over a commutative ring R is a decomposition M ≈ R/I₁ Ο … Ο R/I_n, where the I_j are ideals of R and 1₁ ≤ . . . ≤ I_n. A complete structure theory is developed for those rings for which every finitely generated module has a canonical form. The (possibly larger) class of rings, for which every finitely generated module is a direct sum of cyclics, is also considered, and partial results are obtained for rings with fewer than 2^{c …}

On A Boundary Value Problem For A Class Of Differential Equations With A Deviating Argument, V. Lakshmikantham, Jerome Eisenfeld

Mathematics Technical Papers - Archive

Recently, J. Chandra [1] obtained comparison estimates for differential equations with deviating argument (1) [see pdf for notation] on the interval I: to [see pdf for notation] , where [see pdf for notation] is a given continuous function defined on a suitable interval (containing I ), together with the boundary conditions (2) [see pdf for notation] for [see pdf for notation] The class of BVP (1) - (2) is incorporated in a larger class discussed in [3]. The introduction in [1] of a maximal solution has furnished comparison results and an iterative procedure for obtaining solutions. The use of the …

Comparison Principle And Non Linear Contract In Abstract Spaces, V. Lakshmikantham, Jerome Eisenfeld

Mathematics Technical Papers - Archive

The theory of differential and integral equations exploits comparison and iterative techniques which do not fall under the Contractive Mapping Principle. For they make use of partial orderings and maximal solutions; concepts which have no significance in a metric space. These methods take their proper place in the theory of cones [1], [2]. In this paper, Banach's Contraction Mapping Principle and comparison and iterative methods are brought together under a single roof which houses various results from the theory of differential equations [3], in addition to an interesting generalization of Banach's Theorem [4]. One 'It thus led, in a natural …

On Hamiltonian - Connected Graphs, James E. Williamson

Dissertations

No abstract provided.

Linear Operators Between Nonarchimedean Banach Spaces, Krishnamachari S. Nadathur

Dissertations

I Preliminaries

The purpose of this dissertation is to extend some classical results on compact and Fredholm operators to the case in which the linear spaces involved are non-archimedean normed linear spaces over a valued field.

In Section I are listed some definitions and basic concepts that are needed for a study of non-archimedean valuation theory. The concepts of tensor products of nonarchimedean Banach spaces over a spherically complete field F, and of the tensor product of operators, are also dealt with in this section.

The proofs of most of the results in Section II are based on the known …

Study Of Dynamic Programming And Gambling Systems., N. D. Prabhakar Dr.

Doctoral Theses

The body of methods known as Dynamic Programming (d.p.) was developed by Bellman and was successfully applied by him to solve practical problems in diverse fields (see 12] and the pa pers cited there.). These methods revolved around an intuitively appealing principle which Bellman called the principle of optimatity. A general formulation of d.p. problem was given by Blackwell (3, s] which is narrower in scope than Bollman's but includes many important applications i12) and offers a proper framework for asking the many inte- resting and mathematically sophisticated questions that arise in d.p.. Strauch, Brown, Maitra, Furukawa, Dantas, Hinderer etc., …

A Method Of Moments Applied To An Invariant Imbedding Solution Of A Certain Class Of Fredholm Integral Equations., Grenfell Paul Boicourt

Mathematics & Statistics ETDs

This dissertation first develops a method for solving the integral equation when y(z') is a constant and then extends it to the case where y(z') is a step function. The solution of the integral equation is achieved by solving the integro differential invariant imbedding equations derived from the integral equation by varying the limits of integration. The imbedding equations are solved using a moment method which reduces the calculation to an initial value problem. Proofs of the existence and convergence of the method are given. In the case where y(z') is a constant, the solution of the integral equation is …

Line Critical Point Determining And Point Distinguishing Graphs.Geodetic Orientations Of Complete K-Partite Graphs., Larry Dean Gassman

Mathematics & Statistics ETDs

I. Sumner defined a graph to be point determining if and only if distinct points have distinct neighborhoods and he has characterized connected line-critical point determining graphs. Here a short alternate proof of his characterization is provided and arbitrary line-critical point determining graphs are then characterized. Next line-critical point distinguishing graphs are considered; a graph is point distinguishing if and only if it is the complement of a point determining graph. Finally line-critical graphs that are both point determining and point distinguishing are characterized.

II. Ore defined a graph to be geodetic if and only if there is a unique …

Estimation Of Probability Functions Using Splines., Douglas Wade Hill

Mathematics & Statistics ETDs

In this paper, three classes of spline functions are applied to the problem of estimating probability distribution and density functions. In each case, it is shown that the spline function approximating the sample cumulative distribution function converges almost surely to the unknown distribution, F, given that F has at least two continuous derivatives. If F has three or more continuous derivatives, the derivative of the spline converges to the density function. For polynomial splines of sufficiently high degree if F has k continuous derivative, the rate of convergence for the j-th derivative is shown to be 0(hk-j-1/2) where h is …

Nonlinear Stochastic Integral-Equation Of Hammerstein Type, William J. Padgett

Faculty Publications

No abstract provided.