Physical Sciences and Mathematics Commons^™

Puzzles, Patterns Drums: The Dawn Of Mathematics In Rwanda And Burundi., D. Huylebrouck

Humanistic Mathematics Network Journal

No abstract provided.

Music And Mathematics, Roxanne Kitts

Humanistic Mathematics Network Journal

No abstract provided.

Book Review: Emblems Of Mind, The Inner Life Of Music And Mathematics, By Edward Rothstein, Sandra Z. Keith

Humanistic Mathematics Network Journal

No abstract provided.

Book Review: Emblems Of Mind, The Inner Life Of Music And Mathematics, By Edward Rothstein, Dan Fitzgerald, Joel Haack

Humanistic Mathematics Network Journal

No abstract provided.

Mathematical Rebuses, Florentin Smarandache

Humanistic Mathematics Network Journal

No abstract provided.

Fibonacci Melodies, Robert Lewand

Humanistic Mathematics Network Journal

No abstract provided.

Book Review: Ethnomathematics: A Multicultural View Of Mathematical Ideas, By Marcia Ascher, Bernadette Anne Berken

Humanistic Mathematics Network Journal

No abstract provided.

The Folktale: Linking Story To Mathematical Principles, Audrey Kopp

Humanistic Mathematics Network Journal

No abstract provided.

Psychosis, Lee Goldstein

Humanistic Mathematics Network Journal

No abstract provided.

On The Use Of Intelligent Tutoring Systems For Teaching And Learning Mathematics, M.D. C. Mendes, M.G. V. Nunes, C. A. Andreucci

Humanistic Mathematics Network Journal

No abstract provided.

Note: On The Degree Of Lp Approximation With Positive Linear Operators, J. J. Swetits, B. Wood

Mathematics & Statistics Faculty Publications

The degree of approximation in L_p-spaces by positive linear operators is estimated in terms of the integral modulus of smoothness. It is shown that the conjectured optimal degree of approximation is not attained in the class of functions having a second derivative belonging to L_p.

Some Global Bifurcation Results For Variational Inequalities, Vy Khoi Le

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.

Murnaghan-Nakayama Rules For Characters Of Iwahori-Hecke Algebras Of Classical Type, Thomas Halverson, A. Ram

Thomas M. Halverson

No abstract provided.

On The Homology Spectral Sequence For Topological Hochschild Homology, Thomas J. Hunter

Mathematics & Statistics Faculty Works

Marcel Bokstedt has computed the homotopy type of the topological Hochschild homology of Z/p using his definition of topological Hochschild homology for a functor with smash product. Here we show that easy conceptual proofs of his main technical result of are possible in the context of the homotopy theory of S-algebras as introduced by Elmendorf, Kriz, Mandell and May. We give algebraic arguments based on naturality properties of the topological Hochschild homology spectral sequence. In the process we demonstrate the utility of the unstable ''lower'' notation for the Dyer-Lashof algebra.

Existence And Bifurcation Of The Positive Solutions For A Semilinear Equation With Critical Exponent, Yinbin Deng, Yi Li

Yi Li

In this paper, we consider the semilinear elliptic equation[formula]Forp=2N/(N−2), we show that there exists a positive constantμ*>0 such that (∗)_μpossesses at least one solution ifμ∈(0, μ*) and no solutions ifμ>μ*. Furthermore, (∗)_μpossesses a unique solution whenμ=μ*, and at least two solutions whenμ∈(0, μ*) and 2<NN⩾6, under some monotonicity conditions onf((1.6)) we show that there exist two constants 0<μ_**⩽μ**<μ* such that problem (∗)_{μ …}

Existence And Bifurcation Of The Positive Solutions For A Semilinear Equation With Critical Exponent, Yinbin Deng, Yi Li

Mathematics and Statistics Faculty Publications

In this paper, we consider the semilinear elliptic equation[formula]Forp=2N/(N−2), we show that there exists a positive constantμ*>0 such that (∗)_μpossesses at least one solution ifμ∈(0, μ*) and no solutions ifμ>μ*. Furthermore, (∗)_μpossesses a unique solution whenμ=μ*, and at least two solutions whenμ∈(0, μ*) and 2<NN⩾6, under some monotonicity conditions onf((1.6)) we show that there exist two constants 0<μ_**⩽μ**<μ* such that problem (∗)_{μ …}

Automatic Realizability Of Galois Groups Of Order 16, Helen G. Grundman, Tara L. Smith

Mathematics Faculty Research and Scholarship

This article examines the realizability of small groups of order 2(k), k less than or equal to 4, as Galois groups over arbitrary fields of characteristic not 2. In particular we consider automatic realizability of certain groups given the realizability of others.

Computational Algebra Applications In Reliability, G Hartless, Lawrence Leemis

Arts & Sciences Articles

Reliability analysts are typically forced to choose between using an 'algorithmic programming language' or a 'reliability package' for analyzing their models and lifetime data. This paper shows that computational languages can be used to bridge the gap to combine the flexibility of a programming language with the ease of use of a package. Computational languages facilitate the development of new statistical techniques and are excellent teaching tools. This paper considers three diverse reliability problems that are handled easily with a computational algebra language: system reliability bounds; lifetime data analysis; and model selection.

Strongly-Consistent, Distribution-Free Confidence Intervals For Quantiles, David Gilat, Theodore P. Hill

Research Scholars in Residence

Strongly-consistent, distribution-free confidence intervals are derived to estimate the fixed quantiles of an arbitrary unknown distribution, based on order statistics of an iid sequence from that distribution. This new method, unlike classical estimates, works for totally arbitrary (including discontinuous) distributions, and is based on recent one-sided strong laws of large numbers.

Some Applications Of Sophisticated Mathematics To Randomized Computing, Ronald I. Greenberg

Computer Science: Faculty Publications and Other Works

No abstract provided.

Self-Consistency: A Fundamental Concept In Statistics, Thaddeus Tarpey, Bernard Flury

Mathematics and Statistics Faculty Publications

The term ''self-consistency'' was introduced in 1989 by Hastie and Stuetzle to describe the property that each point on a smooth curve or surface is the mean of all points that project orthogonally onto it. We generalize this concept to self-consistent random vectors: a random vector Y is self-consistent for X if E[X|Y] = Y almost surely. This allows us to construct a unified theoretical basis for principal components, principal curves and surfaces, principal points, principal variables, principal modes of variation and other statistical methods. We provide some general results on self-consistent random variables, give …

Positive Solutions For A Semilinear Elliptic Problem With Critical Exponent, Ismail Ali, Alfonso Castro

All HMC Faculty Publications and Research

No abstract provided in article.

Extensions Of Commutative Rings With Linearly Ordered Intermediate Rings, Michael Scott Gilbert

Doctoral Dissertations

This work concerns λ-extensions of (commutative) rings, which are defined as ring extensions R ⊆ T whose set of intermediate rings is linearly ordered by inclusion. λ-extensions from a subclass of the ∆-extensions of Gilmer-Huckaba and generalize the adjacent extensions of Ferrand-Oliver, Modica, and Dechene.

In Chapter I, we characterize λ-domains (i.e., integral domains R with quotient field K such that R ⊆ K is a λ-extension), showing that they form a subclass of quasilocal i-domains. These results parallel results of Gilmer-Huckaba for ∆-domains. We relate λ-domains to divided domains and pseudovaluation domains.

Chapter II concerns λ-extensions R ⊆ T …

On Three Dimensional Digital Topology And Its Application To Image Processing., Punam Kumar Saha Dr.

Doctoral Theses

Digital topology provides a sound mathematical basis for object classification, counting and labeling, border tracking, contour filling, thinning, segmentation and many other image processing applications. An important characteristic of topo- logical properties is that they are invariant under translation, rotation, and more generally under any elastic deformation. The analysis of three dimensional (3D) digital images has generated increasing interest with the rapid growth of 3D image processing applications including computer vision. 3D digital images are common input/output media in the several application domains of image processing, pattern recognition and computer vision among which 3D medical imaging is of particular interest. …

Design,Analysis And Routing In Static Interconnection Networks., Rajib Kumar Das Dr.

Doctoral Theses

Many real-life applications such as image processing, weather forecasting, digital signal processing, etc., require large amount of computations. By distributing the task among several processors, one can appreciably reduce the computation time. To solve complex problems, several computer architectures using multiple processors have been introduced. Recent developments in IC technology have made it economically feasible to construct multiple processor systems consisting of hundreds or thousands of processors.There are two types of multiprocessor systems (PS87). One is tightly coupled, where the processors share a common clock and/or memory. The other is loosely coupled, where each processor runs independently with a local …

A Problem Set In Conditional Probability Using Martingales With A Derivation Of The Gambler’S Ruin Formula, Michael Everett Theriot Jr

Honors Theses

No abstract provided.

Strong Laws For L- And U-Statistics, J. Aaronson, R. Burton, H. Dehling, D. Gilat, Theodore P. Hill, B. Weiss

Research Scholars in Residence

Strong laws of large numbers are given for L-statistics (linear combinations of order statistics) and for U-statistics (averages of kernels of random samples) for ergodic stationary processes, extending classical theorems of Hoeffding and of Helmers for iid sequences. Examples are given to show that strong and even weak convergence may fail if the given sufficient conditions are not satisfied, and an application is given to estimation of correlation dimension of invariant measures.

A Combinatorial Interpretation Of Lommel Polynomials And Their Derivatives, Philip J. Feinsilver, John P. Mcsorley, René Schott

Articles and Preprints

In this paper we present interpretations of Lommel polynomials and their derivatives. A combinatorial interpretation uses matchings in graphs. This gives an interpretation for the derivatives as well. Then Lommel polynomials are considered from the point of view of operator calculus. A step-3 nilpotent Lie algebra and finite-difference operators arise in the analysis.

Characters Of The Centralizer Algebras Of Mixed Tensor Representations Of Gl(R,C) And The Quantum Group U-Q(Gl(R,C)), Thomas Halverson

Thomas M. Halverson

No abstract provided.

A Mathematician Among The Molasses Barrels: Maclaurin's Unpublished Memoir On Volumes, Judith V. Grabiner

Pitzer Faculty Publications and Research

Suppose we are given a solid of revolution generated by a conic section. Slice out a frustum of the solid [14, diagrams pp. 77, 80]. Then, construct a cylinder, with the same height as the frustum, whose diameter coincides with the diameter of the frustum at the midpoint of its height. What is the difference between the volume of the frustum and the volume of this cylinder? Does this difference depend on where in the solid the frustum is taken?

The beautiful theorems which answer these questions first appear in a 1735 manuscript by Colin Maclaurin (1698–1746). This …