Physical Sciences and Mathematics Commons^™

Some Problems Of Continuum Percolation., Anish Sarkar Dr.

Doctoral Theses

The model of continuum percolation can be described as follows. We start with a homogeneous Poisson point process X. At each point of X we centre a ball with a random radius such that the radii corresponding to different points are independent of each other and also independent of the Poisson process X. In this way, the space is divided into two regiorns, the covered region or the occupied region consisting of the region which is covered by at least one ball, and the uncovered region or the vacant region which is complement of the covered region. In this dissertation …

Computer Assistance In Discovering Formulas And Theorems In System Engineering Ii, J. W. Helton, Mark Stankus, Kurt Schneider

Mathematics

[HSWcdc94] focused on procedures for simplifying complicated expressions automatically. [HScdc95] turned to the adventurous pursuit of developing a highly computer assisted method for “discovering” certain types of formulas and theorems.

It is often the case that some variables in the formulation of a problem are not the natural “coordinates” for solution of the problem. Gröbner Basis Algorithms, which lie at the core of our method, are very good at eliminating unknowns, but have no way of finding good changes of variables. This paper gives a way of incorporating changes of variables into our method.

As an example, we “discover” the …

M-Isometric Transformations Of Hilbert Space, Iii, Jim Alger, Mark Stankus

Mathematics

No abstract provided.

A Note On Distributions Of True Versus Fabricated Data, Theodore P. Hill

Research Scholars in Residence

New empirical evidence and statistical derivations of Benford’s Law have led to successful goodness-of fit tests to detect fraud in accounting data. Several recent case studies support the hypothesis that fabricated data does not conform to expected true digital frequencies.

A Stronger Triangle Inequality, Herb Bailey

Mathematical Sciences Technical Reports (MSTR)

The triangle inequality is basic for many results in real and complex analysis. The geometric form states that the sum of any two sides of a triangle is greater than the third. This was included as Proposition XX in the first book of Euclid's Elements. Many geometric triangle inequalities involving sides, angles, altitudes, inscribed circles and circumscribed circles have been found. Hundreds of these inequalities are summarized in [l] and [2]. A nice geometric proof of the triangle inequality is given in [3].

Gender Discourse In Small Learning Groups Of College-Level Developmental Mathematics Students, Allen W. Emerson

Dissertations

This study was motivated by the question as to whether women’s and men’s membership in different gender communicative cultures gives rise to gender differentiated ways of talking that are implicated in the failure of a mixed-sex group to achieve good mathematical discourse when women and men sit face to face engaged in various mathematical tasks. If so, in what ways and to what effect is gender discourse implicated in the failure of a mixed-sex group to achieve good mathematical discourse?

Models of feminine and masculine discourse styles based on the theory of communicative cultural difference, as well as a model …

From The Editor, Issue 14, 1996, Alvin White

Humanistic Mathematics Network Journal

No abstract provided.

What's All The Fuss About?, Sherman K. Stein

Humanistic Mathematics Network Journal

No abstract provided.

The Triex: Explore, Extract, Explain, Sherman K. Stein

Humanistic Mathematics Network Journal

No abstract provided.

Noesis, Lee Goldstein

Humanistic Mathematics Network Journal

No abstract provided.

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.

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 …}

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.

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 …}

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 …