Physical Sciences and Mathematics Commons^™

On (\Sigma,\Tau) Derivations With Module Values, M. Soytürk

Turkish Journal of Mathematics

Let R be a ring, X\neq (0) an R-bi-module, d: R\ra X a(\sigma,\tau)- derivation with module value such that d\sigma=\sigma d, d\tau=\tau d and U\neq (0) an ideal of R. Furthermore the following properties are also satisfied. \begin{eqnarray*} && \mbox{For }x\in X, a\in R\quad x Ra=0 \mbox{ implies } x=0 \mbox{ or } a=0 \ldots\ldots (G_{1})\\ && \mbox{For }a\in R, x\in X \quad a Rx=0 \mbox{ implies } a=0 \mbox{ or } x=0 \ldots\ldots (G_{2}) \end{eqnarray*} \noindent In this paper we have proved the following results; (1) If (G_{1}) (or (G_{2})) is satisfied and for a \in R, d(U) a=0 …

Sturm-Liouville Theory, Lycretia Englang Ting

Theses Digitization Project

No abstract provided.

Detecting Trends And Patterns In Reliability Data Over Time Using Exponentially Weighted Moving-Averages, Harry F. Martz, Paul H. Kvam

Department of Math & Statistics Faculty Publications

A simple, easy-to-use graphical method is presented for use in determining if there is any statistically significant trend or pattern over time in an underlying Poisson event rate of occurrence or binomial failure on demand probability. The method is based on the combined use of both an exponentially weighted moving-average (EWMA) and a Shewhart chart. Two nuclear power plant examples are introduced and used to illustrate the method. The false alarm probability and power when using the combined procedure are also determined for both cases using Monte Carlo simulation. The results indicate that the combined procedure is quite effective in …

Bergman Spaces On Disconnected Domains, William T. Ross, Alexandru Aleman, Stefan Richter

Department of Math & Statistics Faculty Publications

For a bounded region G C C and a compact set K C G, with area measure zero, we will characterize the invariant subspaces M (under f -> zf)of the Bergman space L^p_a(G \ K), 1 ≤ p < ∞, which contain L^p_a(G) and with dim(M/(z - λ)M) = 1 for all λϵ G \ K. When G \ K is connected, we will see that di\m(M /(z — λ)M) = 1 for all λ ϵ G \ K and thus in this case we will have a complete …

Exponent Bounds For A Family Of Abelian Difference Sets, K. T. Arasu, James A. Davis, Jonathan Jedwab, Siu Lun Ma, Robert L. Mcfarland

Department of Math & Statistics Faculty Publications

Which groups G contain difference sets with the parameters (v, k, λ)= (q³ + 2q² , q² + q, q), where q is a power of a prime p? Constructions of K. Takeuchi, R.L. McFarland, and J.F. Dillon together yield difference sets with these parameters if G contains an elementary abelian group of order q² in its center. A result of R.J. Turyn implies that if G is abelian and p is self-conjugate modulo the exponent of G, then a necessary condition for existence is that the exponent …

The Backward Shift Of Weighted Bergman Spaces, William T. Ross, Alexandru Aleman

Department of Math & Statistics Faculty Publications

No abstract provided.

Topological Classification Of Non-Degenerate Quadratic System, Aleksandr Voldman

Theses Digitization Project

No abstract provided.

Homological Topics In The Representation Theory Of Restricted Lie Algebras, Jorg Feldvoss

University Faculty and Staff Publications

We present some recent developments in the application of homological methods to the representation theory of finite dimensional restricted Lie algebras.

Dynamical Generation Of Electron Motions In Ground State H2+, In Ground State H2, And In The First Excited State Of H2, Donald Greenspan

Mathematics Technical Papers

Using the recent formulation of Gell-Mann and Hartle for approximating quantum dynamical phenomena by means of classical equations, we simulate electron motions in ground state H2+, in ground state H2, and in the first excited state of H2. The approach develops approximate initial data first by mathematical bisection. The dynamical calculations are then carried out over short time intervals only, which is consistent with the Gell-Mann and Hartle theory and which is applicable because the phenomena to be studied are periodic. An energy conserving numerical scheme is used so that the energy of a given system will be a numerical …

Conservative Motion Of Discrete, Tetrahedral Tops And Gyroscopes, Donald Greenspan

Mathematics Technical Papers

Tetrahedral tops and gyroscopes are simulated as discrete, rigid bodies in rotation by introducing a molecular mechanics formulation. The conservative, dynamical differential equations are solved numerically in such a fashion that all the system invariants are preserved. Examples which include precession and nutation are described and discussed.

Self-Circumference Of Rotors, Edward J. O'Neill, Mostafa Ghandehari

Mathematics Technical Papers

The law of cosines from trigonometry is used to obtain elliptic integrals of the second kind to calculate the "self-circumference" of a Reuleaux triangle and the self-circumference of a rotor in an equilateral triangle. The Euclidean lengths of the polar duals of these sets with respect to their centers are expressed in terms of elliptic integrals of the second kind. Geometric inequalities for the polar duals of rotors in the plane are discussed.

Tests Of Random Number Generators Using Ising Model Simulations, Paul D. Coddington

Northeast Parallel Architecture Center

Large-scale Monte Carlo simulations require high-quality random number generators to ensure correct results. The contrapositive of this statement is also true – the quality of random number generators can be tested by using them in large-scale Monte Carlo simulations. We have tested many commonly used random number generators with high precision Monte Carlo simulations of the 2-d Ising model using the Metropolis, Swendsen-Wang, and Wolff algorithms. This work is being extended to the testing of random number generators for parallel computers. The results of these tests are presented, along with recommendations for random number generators for high-performance computers, particularly for …

The B-Spline Wavelet Recurrence Relation And B-Spline Wavelet Interpolation, Patrick J. Crowley '96

Honors Projects

In most signal processing applications, a given range of data is best described by a set of local characteristics as opposed to a single global characteristic. In image processing, for example, a region of an image that contains numerous edges is best described as a region whose pixel color values change abruptly, i.e., they are not continuous values of color. A region of constant color, or gradually changing color, is best described as a region whose pixel values are constant, or whose values increase linearly by some factor. It is advantageous to represent this data with signals capable of adapting …

Macroelements And Orthogonal Multiresolutional Analysis, Jonathan M. Corbett '96

Honors Projects

Orthogonal multiresolutional wavelet analysis in a two dimension setting furnishes a basis for wavelet analysis. Bernstein-Bezier polynomials over simplexes provide elegant expressions of the necessary and sufficient conditions for a shift invariant space generating an orthogonal multiresolution analysis.

On Non-Holonomic Second-Order Connections With Applications To Continua With Microstructure, Marek Elźanowski, Serge Preston

Mathematics and Statistics Faculty Publications and Presentations

Motivated by the theory of uniform elastic structures we try to determine the conditions for the local flatness of locally integrable connections on non-holonomic frame bundles of order 2. Utilizing the results of Yuen as well as our results for the holonomic case, we show that the locally integrable non-holonomic 2-connection is locally flat if, and only if, its projection to the bundle of linear frames is symmetric and the so-called inhomogeneity tensor vanishes. In the last section of this short paper we show how these results can be interpreted in the framework of the theory of uniformity of simple …

Structured Eigenvectors, Interlacing, And Matrix Completions, Brenda K. Kroschel

Dissertations, Theses, and Masters Projects

This dissertation presents results from three areas of applicable matrix analysis: structured eigenvectors, interlacing, and matrix completion problems. Although these are distinct topics, the structured eigenvector results provide connections.;It is a straightforward matrix calculation that if {dollar}\lambda{dollar} is an eigenvalue of A, x an associated structured eigenvector and {dollar}\alpha{dollar} the set of positions in which x has nonzero entries, then {dollar}\lambda{dollar} is also an eigenvalue of the submatrix of A that lies in the rows and columns indexed by {dollar}\alpha{dollar}. We present a converse to this statement and apply the results to interlacing and to matrix completion problems. Several corollaries …

A Multiple-Precision Division Algorithm, David M. Smith

Mathematics, Statistics and Data Science Faculty Works

The classical algorithm for multiple-precision division normalizes digits during each step and sometimes makes correction steps when the initial guess for the quotient digit turns out to be wrong. A method is presented that runs faster by skipping most of the intermediate normalization and recovers from wrong guesses without separate correction steps.

On Functions That Are Trivial Cocycles For A Set Of Irrationals. Ii, Lawrence W. Baggett, Herbert A. Medina, Kathy D. Merrill

Mathematics, Statistics and Data Science Faculty Works

Two results are obtained about the topological size of the set of irrationals for which a given function is a trivial cocycle. An example of a continuous function which is a coboundary with non-L(1) cobounding function is constructed.

On The \Ell_{P} Norms Of Almost Cauchy-Toeplitz Matrices, D. Bozkurt

Turkish Journal of Mathematics

In this study, we have given the definition of almost Cauchy-Toeplitz matrix. i.e. its elements are t_{ij}= a(i=j) and t_{ij}=1/(i-j)\, (i\neq j) such that a is a real number. We have found a lower and upper bounds for the \ell_{p} norm of this matrix. Furthermore, we have done the proof of the conjecture that were given by myself for the spectral norm of this matrix.

An Analysis Of Shewhart Quality Control Charts To Monitor Both The Mean And Variability, Keith Jacob Barrs

Legacy ETDs

When monitoring the mean of a continuous quality measure it is often recommended a separate chart be used to monitor the variability. These charts are traditionally designed separately. This project considers them together as a combined charting procedure and gives recommendations for their design. This is based on an average run length (ARL) analysis. The run length distribution is determined using two methods both based on a Markov chain approach.

Decidability Of The Two-Quantifier Theory Of The Recursively Enumerable Weak Truth-Table Degrees And Other Distributive Upper Semi-Lattices, Klaus Ambos-Spies, Peter A. Fejer, Steffen Lempp, Manuel Lerman

Computer Science Faculty Publication Series

We give a decision procedure for the ∀∃-theory of the weak truth-table (wtt) degrees of the recursively enumerable sets. The key to this decision procedure is a characterization of the finite lattices which can be embedded into the r.e. wtt-degrees by a map which preserves the least and greatest elements: a finite lattice has such an embedding if and only if it is distributive and the ideal generated by its cappable elements and the filter generated by its cuppable elements are disjoint. We formulate general criteria that allow one to conclude that a distributive upper semi-lattice has a decidable two-quantifier …

Data Compression Based On The Cubic B-Spline Wavelet With Uniform Two-Scale Relation, S. K. Yang, C. H. Cooke

Mathematics & Statistics Faculty Publications

The aim of this paper is to investigate the potential artificial compression which can be achieved using an interval multiresolution analysis based on a semiorthogonal cubic B-spline wavelet. The Chui-Quak [1] spline multiresolution analysis for the finite interval has been modified [2] so as to be characterized by natural spline projection and uniform two-scale relation. Strengths and weaknesses of the semiorthogonal wavelet as regards artificial compression and data smoothing by the method of thresholding wavelet coefficients are indicated.

Sums Of Powers And The Bernoulli Numbers, Laura Elizabeth S. Coen

Masters Theses

This expository thesis examines the relationship between finite sums of powers and a sequence of numbers known as the Bernoulli numbers. It presents significant historical events tracing the discovery of formulas for finite sums of powers of integers, the discovery of a single formula by Jacob Bernoulli which gives the Bernoulli numbers, and important discoveries related to the Bernoulli numbers. A method of generating the sequence by means of a number theoretic recursive formula is given. Also given is an application of matrix theory to find a relation, first given by Johannes Faulhaber, between finite sums of odd powers and …

Secrets Of The Madelung Constant, Stan Wagon

Stan Wagon, Retired

No abstract provided.

Polynomials For Radicals, Stan Wagon

Stan Wagon, Retired

No abstract provided.

The Magic Of Imaginary Factoring, Stan Wagon

Stan Wagon, Retired

No abstract provided.

Animating Calculus: Mathematica Notebooks For The Laboratory, E. Packel, Stan Wagon

Stan Wagon, Retired

No abstract provided.

An Almost Periodic Function Of Several Variables With No Local Minimum, Gregory S. Spradlin

Gregory S. Spradlin

Su(1,1) Algebraic Description Of One-Dimensional Potentials Within The R-Matrix Theory, Andrei Ludu

Andrei Ludu

No abstract provided.

Generalization Kdv Equation For Fluid Dynamics And Quantum Algebras, Andrei Ludu

Andrei Ludu

No abstract provided.