Mathematics Commons^™

The Difference Between Pure And Applied Mathematics, Adrian Riskin

Humanistic Mathematics Network Journal

No abstract provided.

Music Of The Spheres, Lawrence Mark Lesser

Humanistic Mathematics Network Journal

No abstract provided.

The Prospects For Mathematics In A Multi-Media Civilization, Philip J. Davis

Humanistic Mathematics Network Journal

No abstract provided.

A New Family Of Irrational Numbers With Curious Properties, Vera W. De Spinadel, José M. Paz University Of Buenos Aires

Humanistic Mathematics Network Journal

No abstract provided.

The Möbius Metaphor, Julian Fleron

Humanistic Mathematics Network Journal

No abstract provided.

Leibniz: His Philosophy And His Calculi, Eric Ditwiler

Humanistic Mathematics Network Journal

No abstract provided.

Classroom Capsules: Additivity ⊕ Homogeneity, Michael J. Bradley, Michael St. Vincent, David L. Finn

Mathematics Faculty Publications

A Classroom Capsule is a short article that contains a new insight on a topic taught in the earlier years of undergraduate mathematics.

Molecular Mechanics Simulations Of The Three Dimensional Cavity Problem, Donald Greenspan

Mathematics Technical Papers - Archive

The rapid development of computer technology has resulted in broad interest in three dimensional fluid simulation, which is known to have more complex force interactions than occur in two dimensions (see, e.g., refs. [1-6], [9], [11-15], [17], [18] and the additional references therein). In this paper we develop and analyze some molecular mechanics simulations of the three dimensional cavity problem. The fluid considered is water at 15° C.

Tennis, Geometric Progression, Probability And Basketball, Mostafa Ghandehari

Mathematics Technical Papers - Archive

The following problem about a tennis match is well—known. See Halmos [1, 2]. Consider 2n tennis players playing a single elimination match. Ask the question: what are the number of games played? The answer can be obtained in two ways. First using the geometric progression 2n-1 + 2n-2 + • • • -2+1 we find that the answer is 2n — 1. We can also explain the answer as follows: for each game played there is a loser. Thus the total number of games played is equal to the number of losers. Since there is only one winner the total …

Nontoric Hamiltonian Circle Actions On Four-Dimensional Symplectic Orbifolds, S. F. Singer, Janet Talvacchia, N. Watson

Mathematics & Statistics Faculty Works

We construct four-dimensional symplectic orbifolds admitting Hamiltonian circle actions with isolated fixed points, but not admitting any Hamiltonian action of a two-torus. One example is linear, and one example is compact.

Prestructuring Neural Networks Via Extended Dependency Analysis With Application To Pattern Classification, George G. Lendaris, Thaddeus T. Shannon, Martin Zwick

Complex Systems Faculty Publications and Presentations

We consider the problem of matching domain-specific statistical structure to neural-network (NN) architecture. In past work we have considered this problem in the function approximation context; here we consider the pattern classification context. General Systems Methodology tools for finding problem-domain structure suffer exponential scaling of computation with respect to the number of variables considered. Therefore we introduce the use of Extended Dependency Analysis (EDA), which scales only polynomially in the number of variables, for the desired analysis. Based on EDA, we demonstrate a number of NN pre-structuring techniques applicable for building neural classifiers. An example is provided in which EDA …

Some Studies On Shape Of Dot Patterns., Anirban Ray Chaudhuri Dr.

Doctoral Theses

The important visual characteristics of an object are shape, size, color, brightness, contrast and texture. Of them, shape is a multidimensional concept that is difficult to define. It takes different meanings in different contexts. We try to explain it in terms of their attributes like elongation, roundness, and symmetry: although these terms do not capture the complete notion of shape.Perhaps Gestalt theory Koffka 351 is the first attempt to study the principles of visual perception in a systematic manner. The central concept of this theory is Gestalt' which means form or configuration. In this theory form is examined from physical. …

Time-Space Harmonic Polynomials For Stochastic Processes., Arindam Sengupta Dr.

Doctoral Theses

The sequence of polynomials of a single variable known as the Hermite polynomialshala) = ), k21, (-1)* ha(z) =has many close links with the Normal distribution. Their association goes very doep, and extends to several connections bet ween the two-variable Hermite polynomialsHll, 2) = the(z/t), . k21.and the prime example of Gaussian processes, that is Brownian motion, as well. Much of this connection stems from what we term the time-space harmonic property of these polynomials for the Brownian motion process. An exact definition of this property follows later. A natural question that arises is, for stochastic processes in general, when …

Studies Of Supply Responses In Indian Agriculture: Some Models For Planning Rational Food Supply., Nilabja Ghosh Dr.

Doctoral Theses

This thesis deals with food supply in a less developed country.In a world where social awareness together with technical progress is offering advances in all spheres of life, the persisting presence of hunger and malnutrition in any corner of the earth casts a shadow on all human achievements. It is said that over 800 million human beings in this world are suffering from hunger and a great majority of them live in Asia. Food problem has many dimensions (Timmer et al, 1983), but the solution lies mostly in adequate supply of foodgrains and proper distribution of the same. Any shortfall …

Pattern Classification Using Genetic Algorithms., Sanghamitra Bandyopadhyay Dr.

Doctoral Theses

Pattern recognition and machine learning form a major area of research and develop- ment activity that encompasses the processing of pictorial and other non-numerical information obtained from the interaction between science, technology and society. A motivation for the spurt of activity in this field is the need for people to com- municate with the computing machines in their natural mode of communication. Another important motivation is that the scientists are also concerned with the idea of designing and making intelligent machines that can carry out certain tasks that we human beings do. The most salient outcome of these is the …

Muyltivariate And Regression Analysis Based On The Geometry Of Data Clouds., Biman Chakraborty Dr.

Doctoral Theses

Median is a natural estimate of location of a data set, and there are several versions of inultivariate median studied in the literature, each of which is an interesting descriptive statistic for multivariate data and provides some nice geometric insights into the data cloud. One would expect that multidimensional median will be a natural estimate for the center of symmetry of a multivariate distribution. However, there is no unique concept of symmetry in multivariate problems. The center of symmetry can be defined in several ways there. For example, the d-dimensional random variable X is spherically symmetric about e €Rd if …

A Priori Lρ Error Estimates For Galerkin Approximations To Porous Medium And Fast Diffusion Equations, Dongming Wei, Lew Lefton

Mathematics Faculty Publications

Galerkin approximations to solutions of a Cauchy-Dirichlet prob-

lem governed by a generalized porous medium equation.

Woven Rope Friezes, Frank A. Farris, Nils Kristian Rossing

Mathematics and Computer Science

Here we present a complete set of recipes showing how to construct smooth curves with any desired frieze symmetry; we provide examples woven by Rossing for many of the pattern types, and invite readers to make others. We review the concept of frieze symmetry, develop the formulas for parametric equations with given symmetries, and pose some open questions raised by our analysis.

Computer Assistance For "Discovering'' Formulas In System Engineering And Operator Theory, J. W. Helton, Mark Stankus

Mathematics

The objective of this paper is two-fold. First we present a methodology for using a combination of computer assistance and human intervention to discover highly algebraic theorems in operator, matrix, and linear systems engineering theory. Since the methodology allows limited human intervention, it is slightly less rigid than an algorithm. We call it a strategy. The second objective is to illustrate the methodology by deriving four theorems. The presentation of the methodology is carried out in three steps. The first step is introducing an abstraction of the methodology which we call an idealized strategy. This abstraction facilitates a high level …

Single-Change Circular Covering Designs, John P. Mcsorley

Articles and Preprints

A single-change circular covering design (scccd) based on the set [v] = {1, . . . ,v} with block size k is an ordered collection of b blocks, B = {B₁, . . . ,B_b}, each B_i ⊂ [v], which obey: (1) each block differs from the previous block by a single element, as does the last from the first, and, (2) every pair of [v] is covered by some Bi. The object is to minimize b for a fixed v and k. …

Invariant Measure For Diffusions With Jumps, Jose-Luis Menaldi, Maurice Robin

Mathematics Faculty Research Publications

Our purpose is to study an ergodic linear equation associated to diffusion processes with jumps in the whole space. This integro-differential equation plays a fundamental role in ergodic control problems of second order Markov processes. The key result is to prove the existence and uniqueness of an invariant density function for a jump diffusion, whose lower order coefficients are only Borel measurable. Based on this invariant probability, existence and uniqueness (up to an additive constant) of solutions to the ergodic linear equation are established.

Magic "Squares" Indeed, Arthur T. Benjamin, Kan Yasuda '97

All HMC Faculty Publications and Research

No abstract provided in this article.

A Quadratic Fredholm Integral Equation And Its Solution For Various Kernels, Merlynd K. Nestell, Mostafa Ghandehari

Mathematics Technical Papers - Archive

Consider the Fredholm integral equation [see pdf for notation], a parameter. The solution of this equation is discussed for separable, difference and distribution kernels. Existence, uniqueness and bifurcation questions are explored for various assumptions on the kernel.

Heating Water Vapor In A Square Cavity Using Molecular And Particle Mechanics, Donald Greenspan

Mathematics Technical Papers - Archive

This paper explores the computer simulation of heating water vapor in a square cavity. Both molecular and particle mechanics are applied. A particular parameter called vel, found on the micro level, is shown to be applicable on the macro level in generating both laminar and turbulent flows.

Structure-Function Relationships In The Pulmonary Arterial Tree, Christopher A. Dawson, Gary S. Krenz, Kelly Lynn Karau, Steven Thomas Haworth, Christopher C. Hanger, John H. Linehan

Mathematics, Statistics and Computer Science Faculty Research and Publications

Knowledge of the relationship between structure and function of the normal pulmonary arterial tree is necessary for understanding normal pulmonary hemodynamics and the functional consequences of the vascular remodeling that accompanies pulmonary vascular diseases. In an effort to provide a means for relating the measurable vascular geometry and vessel mechanics data to the mean pressure-flow relationship and longitudinal pressure profile, we present a mathematical model of the pulmonary arterial tree. The model is based on the observation that the normal pulmonary arterial tree is a bifurcating tree in which the parent-to-daughter diameter ratios at a bifurcation and vessel distensibility are …

A Theoretical Study Of Bubble Motion In Surfactant Solutions, Yanping Wang

Dissertations

We examine the effect of surfactants on a spherical gas bubble rising steadily in an infinite fluid at low and order one Reynolds number with order one and larger Peclet numbers. Our mathematical model is based on the Navier-Stokes equations coupled with a convection-diffusion equation together with appropriate interfacial conditions. The nonlinearity of the equations and boundary conditions, and the coupling between hydrodynamics and surfactant transport make the problem very challenging.

When a bubble rises in a fluid containing surface-active agents, surfactant adsorbs onto the bubble surface at the leading edge, convects to the trailing edge by the surface flow …

Some Recent Developments In Difference Sets, James A. Davis, Jonathan Jedwab

Department of Math & Statistics Faculty Publications

There are five known parameter families for (v, k, λ, n)- difference sets satisfying gcd(v, n)>1: the Hadamard, McFarland, Spence, Davis-Jedwab, and Chen families. The authors recently gave a recursive unifying construction for difference sets from the first four families which relies on relative difference sets. We give an overview of this construction and show that, by modifying it to use divisible difference sets in place of relative difference sets, the recent difference set discoveries of Chen can be brought within the unifying framework. We also demonstrate the recursive use of an auxiliary construction for …

Composition Operators On Hardy Spaces Of A Half-Plane, Valentin Matache

Mathematics Faculty Publications

We consider composition operators on Hardy spaces of a half-plane. We mainly study boundedness and compactness. We prove that on these spaces there are no compact composition operators.

Elementary Inversion Of The Laplace Transform, Kurt M. Bryan

Mathematical Sciences Technical Reports (MSTR)

This paper provides an elementary derivation of a very simple "closed-form"

inversion formula for the Laplace Transform.

Relations In The Homotopy Of Simplicial Abelian Hopf Algebras, James M. Turner

University Faculty Publications and Creative Works

In this paper, we analyze the structure possessed by the homotopy groups of a simplicial abelian Hopf algebra over the field F2. Specifically, we review the higher-order structure that the homotopy groups of a simplicial commutative algebra and simplicial cocommutative coalgebra possess. We then demonstrate how these structures interact under the added conditions present in a Hopf algebra.