Digital Commons Network^™

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.

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.

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.

Mathematical Rebuses, Florentin Smarandache

Humanistic Mathematics Network Journal

No abstract provided.

Fibonacci Melodies, Robert Lewand

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.

Glial Cell Line-Derived Neurotrophic Factor Signals Through The Ret Receptor And Activates Mitogen-Activated Protein Kinase, Carolyn A. Worby, Quinn C. Vega, Yi Zhao, Hanna H. Chao, Audrey F. Seasholtz, Jack E. Dixon

Department of Mathematics Faculty Scholarship and Creative Works

Glial cell line-derived neurotrophic factor (GDNF), a member of the transforming growth factor-β family of growth factors, was first identified by its ability to promote the survival of midbrain dopaminergic neurons in culture. We demonstrate that GDNF treatment of several neuroblastoma cell lines leads to dose-dependent tyrosine phosphorylation of the RET receptor and that other transforming growth factor-β family members are not able to activate the RET receptor. GDNF treatment of neuroblastoma cells also results in increased transcription of an Elk luciferase reporter gene, suggesting that GDNF activates the mitogen-activated protein kinase signal transduction pathway.

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.

Glial Cell Line-Derived Neurotrophic Factor Activates The Receptor Tyrosine Kinase Ret And Promotes Kidney Morphogenesis, Quinn Vega, Carolyn A. Worby, Mark S. Lechner, Jack E. Dixon, Gregory R. Dressler

Department of Mathematics Faculty Scholarship and Creative Works

The receptor tyrosine kinase RET functions during the development of the kidney and the enteric nervous system, yet no ligand has been identified to date. This report demonstrates that the glial cell line-derived neurotrophic factor (GDNF) activates RET, as measured by tyrosine phosphorylation of the intracellular catalytic domain. GDNF also binds RET with a dissociation constant of 8 nM, and 125I-labeled GDNF can be coimmunoprecipitated with anti-RET antibodies. In addition, exogenous GDNF stimulates both branching and proliferation of embryonic kidneys in organ culture, whereas neutralizing antibodies against GDNF inhibit branching morphogenesis. These data indicate that RET and GDNF are components …

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 …}

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.

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 Capstones

No abstract provided.

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.

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.

Wheels On Wheels On Wheels-Surprising Symmetry, Frank A. Farris

Mathematics and Computer Science

While designing a computer laboratory exercise for my calculus students, I happened to sketch the curve defined by this vector equation: (x, y) = (cos(t), sin(t)) + 1/2(cos(7t), sin(7t)) + 1/3(sin(17t), cos(17t)). I was thinking of the curve traced by a particle on a wheel mounted on a wheel mounted on a wheel, each turning at a different rate. The first term represents the largest wheel, of radius 1, turning counter-clockwise at one radian per second. The second term represents a smaller wheel centered at the edge of the first, turning 7 times as fast. The third term is for …

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 …

A Graph Theoretic Study Of The Similarity Of Discrete Structures, Heather D. Gavlas

Dissertations

A basic problem in drug design consists of finding a compound that satisfies a spectrum of biological and chemical properties. Although drug design problems are central to pharmaceutical research, statisticians have yet to become involved in this area as these problems are viewed statistically as optimization problems. Before statistical optimization procedures can be defined on these spaces whose points are structures and not vectors, very basic mathematical notions of distance must be defined. Graphs have been used as mathematical models to represent the bonding arrangements of molecules for quite some time. In fact, if some of the methodology used by …