Mathematics Commons^™

New Topologies And Parallel Algorithms For Static Interconnection Networks., Srabani Sen Gupta Dr.

Doctoral Theses

Many real-life applications in the areas of signal processing, image processing, etc., require a large amount of fast computations to be performed. Although high speed powerful processors are currently available due to the phenomenal advances in VLSI technology, the increasing demand for massive real-time computations can not be met just by a uniprocessor system. One way of achieving the goal of fast computation is through parallel processing. In parallel processing, a problem is broken into several subproblems, which are distributed among different processors so that each of the processors can perform its task simultaneously. Main areas of recent research in …

Some Problems In Estimating Finite Population Total And Variance In Survey Sampling., Saswati Bhattacharya Dr.

Doctoral Theses

The problem of drawing inference concerning the parameters of a finite population of identifiable units has been increasingly engaging the attention of statisticians. The central problem here is to devise a suitable method of selecting a sample from the population and to employ an appropriate estimator to estimate the finite population total or mean. A consider- able progress in this field of study has been made and many authors have contributed towards the development of the theory in this aspect of the problem of statistical inferenceNumerous papers have been written covering the first aspect of the problem, namely, method of …

The Stable Manifold Theorem For Sde's (Stochastic Analysis Seminar, Msri), Salah-Eldin A. Mohammed

Miscellaneous (presentations, translations, interviews, etc)

I gave the following two talks at the Stochastic Analysis Seminar at the Mathematical Sciences Research Institute, Berkeley, California. The two talks describe recent joint work with Michael Scheutzow.

FIRST TALK:

THE STABLE MANIFOLD THEOREM FOR SDE'S , Part I

Wednesday, December 3, 1997, 11:00-12:00 am, MSRI Lecture Hall.

In this talk, we formulate a local stable manifold theorem for stochastic differential equations in Euclidean space, driven by multi-dimensional Brownian motion. We introduce the concept of hyperbolicity for stationary trajectories of a SDE. This is done using the Oseledec muliplicative ergodic theorem on the linearized SDE around the stationary …

An Examination Of The Strengths And Weaknesses Of Newton's Method For Nonlinear Optimization, Renita Demalade

Masters Theses & Specialist Projects

This thesis begins with the history of operations research and introduces two of its major branches, linear and nonlinear optimization. While other methods are mentioned, the focus is on analytical methods used to solve nonlinear optimization problems. We briefly look at some of the most effective constrained methods for nonlinear optimization and then show how unconstrained methods often play a role in developing effective constrained optimization algorithms. In particular we examine Newton and steepest descent methods, focusing primarily on Newton/quasi-Newton methods. Because Newton's method is primarily viewed as a root-finding method, we start with the basic root-finding algorithm for single …

Mathematical Modeling Of Convective Heat Transfer In Mammoth Cave, Jonathan Jernigan

Masters Theses & Specialist Projects

Around two centuries ago, changes were made to the entrances of Mammoth Cave and its passages. Today the Historic Entrance to Mammoth Cave is enlarged and the passage just beyond the entrance known as Houchins' Narrows has been cleared of rubble and filled with sediments. These enlargements have resulted in an increase in airflow throughout the Historic Section of the cave causing environmental conditions such as air temperature and airflow to fluctuate. These fluctuations have negatively impacted inhabitants and contents of the cave system. To restore natural conditions within the cave, Science and Resource Management personnel at Mammoth Cave National …

Invariants Of Twist-Wise Flow Equivalence, Michael C. Sullivan

Articles and Preprints

Twist-wise flow equivalence is a natural generalization of flow equivalence that takes account of twisting in the local stable manifold of the orbits of a flow. Here we announce the discovery of two new invariants in this category.

On Multiple Solutions Of A Nonlinear Dirichlet Problem, Alfonso Castro, Jorge Cossio, John M. Neuberger

All HMC Faculty Publications and Research

We prove that a semilinear elliptic boundary value problem has five solutions when the range of the derivative of the nonlinearity includes at least the first two eigenvalues. We also prove that if the region is a ball the semilinear elliptic problem has two solutions that change sign and are nonradial.

Averaged Motion Of Charged Particles In A Curved Strip, Avner Friedman, Chaocheng Huang

Mathematics and Statistics Faculty Publications

This paper is concerned with the motion of electrically charged particles in a "curved" infinite strip.

The Reform Calculus Debate And The Psychology Of Learning Mathematics, James M. Cargal

Humanistic Mathematics Network Journal

No abstract provided.

Teaching Mathematics Appreciation To Nonscience Majors, Josefina Alvarez

Humanistic Mathematics Network Journal

No abstract provided.

Poems, David L. Finn

Humanistic Mathematics Network Journal

No abstract provided.

Borsuk-Ulam Implies Brouwer: A Direct Construction, Francis E. Su

All HMC Faculty Publications and Research

No abstract provided in this article.

A Situational Pedagogy For Elementary Mathematics, Vincent Haag

Humanistic Mathematics Network Journal

No abstract provided.

The Object And The Study Of Mathematics, Pinar Karaca

Humanistic Mathematics Network Journal

No abstract provided.

Book Review: Ethnomathematics--Challenging Eurocentrism Inmathematics Education, Edited Byarthur B. Powell And Marilyn Frankenstein, Karen Dee Michalowicz

Humanistic Mathematics Network Journal

No abstract provided.

A Tribute To Karl Menger, Seymour Kass

Humanistic Mathematics Network Journal

No abstract provided.

Book Review: Garbage Pizza, Patchwork Quilts, And Math Magic: Stories About Teachers Who Love To Teach And Children Who Love To Learn, By Susan Ohanian, Alvin White

Humanistic Mathematics Network Journal

No abstract provided.

Reflections Of Glenmount Reform Effort, Gail Black, Ruth Miller

Humanistic Mathematics Network Journal

No abstract provided.

Resource Review: Research On Children's Learning As A Tool To Improve Math And Science Teaching, Cynthia Hudley

Humanistic Mathematics Network Journal

No abstract provided.

Helping Students With Attention Deficit Disorder Succeed In A College Mathematics Class, Pamela E. Matthews

Humanistic Mathematics Network Journal

No abstract provided.

John Dewey, The Math And Science Standards, And The Workplace, Bernard A. Fleishman

Humanistic Mathematics Network Journal

No abstract provided.

Inspiration In England, Mary Mcdermott

Humanistic Mathematics Network Journal

No abstract provided.

A Course In Mathematical Ethics, Robert P. Webber

Humanistic Mathematics Network Journal

No abstract provided.

Book Review: Nexus: Architecture And Mathematics, Edited By Kim Williams, Joseph Malkevitch

Humanistic Mathematics Network Journal

No abstract provided.

Orbifolds With Lower Ricci Curvature Bounds, Joseph E. Borzellino

Mathematics

We show that the first betti number of a compact Riemannian orbifold with Ricci curvature and diameter is bounded above by a constant , depending only on dimension, curvature and diameter. In the case when the orbifold has nonnegative Ricci curvature, we show that the is bounded above by the dimension , and that if, in addition, , then is a flat torus .

A Sign-Changing Solution For A Superlinear Dirichlet Problem, Alfonso Castro, Jorge Cossio, John M. Neuberger

All HMC Faculty Publications and Research

We show that a superlinear boundary value problem has at least three nontrivial solutions. A pair are of one sign (positive and negative, respectively), and the third solution changes sign exactly once. The critical level of the sign-changing solution is bounded below by the sum of the two lesser levels of the one-sign solutions. If nondegenerate, the one sign solutions are of Morse index 1 and the signchanging solution has Morse index 2. Our results extend and complement those of Z.Q. Wang [12].

A Unifying Construction For Difference Sets, James A. Davis, Jonathan Jedwab

Department of Math & Statistics Faculty Publications

We present a recursive construction for difference sets which unifies the Hadamard, McFarland, and Spence parameter families and deals with all abelian groups known to contain such difference sets. The construction yields a new family of difference sets with parameters (v, k, λ,n)=(2^2d+4(2^2d+2−1)/3, 2^2d+1(2^2d+3+1)/3, 2^2d+1(2^2d+1+1)/3, 2^4d+2) for d⩾0. The construction establishes that a McFarland difference set exists in an abelian group of order 2^{2 …}

Computational Geometry Column 32, Joseph O'Rourke

Computer Science: Faculty Publications

The proof of Dey's new k-set bound is illustrated.

The Convergence Of The Solutions Of The Navier-Stokes Equations To That Of The Euler Equations, R. Temam, X. Wang

Mathematics and Statistics Faculty Research & Creative Works

In this article, we establish partial results concerning the convergence of the solutions of the Navier-Stokes equations to that of the Euler equations. Convergence is proved in space dimension two under a physically reasonable assumption, namely that the gradient of the pressure remains bounded at the boundary as the Reynolds number converges to infinity.

Attractors For Nonautonomous Nonhomogeneous Navier-Stokes Equations, A. Miranville, X. Wang

Mathematics and Statistics Faculty Research & Creative Works

In this paper our aim is to derive an upper bound on the dimension of the attractor of the family of processes associated to the Navier-Stokes equations with nonhomogeneous boundary conditions depending on time. We consider two-dimensional flows with prescribed quasiperiodic (in time) tangential velocity at the boundary, and obtain an upper bound which is polynomial with respect to the viscosity.