Digital Commons Network^™

A Study In Geometric Construction, Nichola Sue Mcclain

Theses Digitization Project

No abstract provided.

Using Symbolic Dynamical Systems: A Search For Knot Invariants, Russell Clark Wheeler

Theses Digitization Project

No abstract provided.

Spatial Estimates For Stochastic Flows In Euclidean Space, Salah-Eldin A. Mohammed, Michael K. R. Scheutzow

Articles and Preprints

We study the behavior for large |x| of Kunita-type stochastic flows φ(t, ω, x) on R^d, driven by continuous spatial semimartingales. For this class of flows we prove new spatial estimates for large |x|, under very mild regularity conditions on the driving semimartingale random field. It is expected that the results would be of interest for the theory of stochastic flows on noncompact manifolds as well as in the study of nonlinear filtering, stochastic functional and partial differential equations. Some examples and counterexamples are given.

Further Properties Of An Extremal Set Of Uniqueness, David E. Grow, Matt Insall

Mathematics and Statistics Faculty Research & Creative Works

Consider the circle group T = R mod 2_ as the interval [0, 1). Then each x 2 T has a binary expansion: x =P1 k=1 xk2−k where each xk is 0 or 1. Let S be the set of x with a binary expansionsuch that the number of 1's does not exceed the number of the leading zeros by more than one. The authors prove that the countable compact set S cannot be expressed as the union of a finite number of Dirichlet sets.

Interactions Of Topological Kinks In Two Coupled Rings Of Nonlinear Oscillators, A E. Duwel, C P. Heij, J C. Weisenfeld, Stephen M.K. Yeung, E Trias, S. J.K. Vardy, H. S.J. Van Der Zant, S H. Strogatz, T P. Orlando

Mathematics

Two discrete rings of nonlinear oscillators with topologically trapped kinks exhibit features due to coupling interactions between the rings. These interaction effects include phase locking between kinks in different rings, precession of the kink/antikink collision region, excitation of kink/antikink pairs, and time-dependent switching. We study these phenomena in simulations of two coupled discrete sine-Gordon equations, and in experiments on two inductively coupled rings of niobium Josephson junctions.

A Minmax Principle, Index Of The Critical Point, And Existence Of Sign Changing Solutions To Elliptic Boundary Value Problems, Alfonso Castro, Jorge Cossio, John M. Neuberger

All HMC Faculty Publications and Research

In this article we apply the minmax principle we developed in [6] to obtain sign-changing solutions for superlinear and asymptotically linear Dirichlet problems.

We prove that, when isolated, the local degree of any solution given by this minmax principle is +1. By combining the results of [6] with the degree-theoretic results of Castro and Cossio in [5], in the case where the nonlinearity is asymptotically linear, we provide sufficient conditions for:

i) the existence of at least four solutions (one of which changes sign exactly once),

ii) the existence of at least five solutions (two of which change sign), and …

Newton's Cubic Roots, Lisette G. De Pillis

All HMC Faculty Publications and Research

No abstract included in this article

Teachers And Students Investigating And Communicating About Geometry: The Math Forum, K. Ann Renninger, S. A. Weimar, Eugene A. Klotz

Educational Studies Faculty Works

No abstract provided.

Torus Embedding And Its Applications, Rick Hung Nguyenhuu

Theses Digitization Project

No abstract provided.

Cahit Arf's Contribution To Algebraic Number Theory And Related Fields, Masatoshi G. İkeda

Turkish Journal of Mathematics

No abstract provided.

Validating A Health Questionnaire For Predicting Neuropathy In Patients With Insulin-Dependent Diabetes Mellitus, Matthew J. Maurer

Honors Theses, 1963-2015

Questionnaires are a cost-effective method for screening large numbers of people for health problems. More expensive clinical follow-up can focus on people whose responses to the questionnaire suggest they are most at risk. To my knowledge, no questionnaire has ever been developed to screen for neuropathy in diabetics. Using the questionnaire developed by Dr. Peter Cavanagh and Dr. Robert Van Deursen at the Center for Locomotion Studies (CELOS) at Penn State University, I was able to create a model from the questionnaire that predicts the presence of neuropathy.

Counting Cards: Combinatorics, Group Theory, And Probability In War, Angela J. Chappell

Honors Theses, 1963-2015

My project involved taking a look at the card game War, searching for patterns which develop in the game, and then looking for Mathematical explanations for those patterns. The project began when my advisor, Professor Marc Brodie, was playing War with his children and began to notice patterns and ask questions about them. The questions I set out to answer were: What is the probability of playing a game of war in which a loop develops? If we know the size of the deck we are using, can we determine what loop lengths are possible? How are cards cycling between …

Operations And Spectral Sequences. I, James M. Turner

University Faculty Publications and Creative Works

Using methods developed by W. Singer and J. P. May, we describe a systematic approach to showing that many spectral sequences, determined by a filtration on a complex whose homology has an action of operations, possess a compatible action of the same operations. As a consequence, we obtain \V. Singer's result for Steenrod operations on Serre spectral sequence and extend A. Bahri's action of Dyer-Lashof operations on the second quadrant Eilenberg-Moore spectral sequence.

A Manifold That Does Not Contain A Compact Core, Gerard A. Venema

University Faculty Publications and Creative Works

A core of a (noncompact) manifold is a submanifold with the property that the inclusion of the submanifold into the manifold is a homotopy equivalence. It is shown by example that a manifold may fail to contain a compact core even though the manifold has the homotopy type of a finite complex.

A Homotopy Equivalence That Is Not Homotopic To A Topological Embedding, Vo Thanh Liem, Yukio Matsumoto, Gerard A. Venema

University Faculty Publications and Creative Works

An open subset W of Sn, n ≥ 6 or n = 4, and a homotopy equivalence f : S2 × Sn-4 → W are constructed having the property that f is not homotopic to any topological embedding.

Some Root Invariants And Steenrod Operations In Ext_A(F2,F2), Robert R. Bruner

Mathematics Faculty Research Publications

We give the results of computations of root invariants in Ext over the Steenrod algebra through the 25-stem, with partial information through the 45-stem. This allows the computation of some new Steenrod operations as well.

Some Remarks On The Root Invariant, Robert R. Bruner

Mathematics Faculty Research Publications

We show how the root invariant of a product depends upon the product of the root invariants, give some examples of the equivariant definition of the root invariant, and verify a weakened form of the algebraic Bredon-Löffler conjecture.

A Yoneda Description Of The Steenrod Operations, Robert R. Bruner

Mathematics Faculty Research Publications

No abstract provided.

Potential And Consistency For Semivalues Of Finite Cooperative Tu Games, Irinel C. Dragan

Mathematics Technical Papers - Archive

A new axiomatic characterization of the semivalues of finite cooperative n-person games with transferable utilities is given, by using a potential function. The semivalues are proved to be the unique functionals on the space of such games, which are consistent relative to a Hart/Mas Colell type of reduced game and weighted standard for two person games. The potential is also used to prove the validity of a recursive definition of semivalues, as well as the fact that the semivalues are Shapley values of the so called Power Game.

Difference Method For A Singularly Perturbed Initial Value Problem, Gabi̇l Muhammadoğlu Amiraliyev

Turkish Journal of Mathematics

In this paper we construct a completely exponentially fitted finite difference scheme for the initial value problem with small parameter by first and second derivatives. We prove the first order uniform convergence of the scheme in the sense of discrete maximum norm. Numerical results are presented.

Average-Case Lower Bounds For Noisy Boolean Decision Trees, William Evans, Nicholas Pippenger

All HMC Faculty Publications and Research

We present a new method for deriving lower bounds to the expected number of queries made by noisy decision trees computing Boolean functions. The new method has the feature that expectations are taken with respect to a uniformly distributed random input, as well as with respect to the random noise, thus yielding stronger lower bounds. It also applies to many more functions than do previous results. The method yields a simple proof of the result (previously established by Reischuk and Schmeltz) that almost all Boolean functions of n arguments require $\Me(n \log n)$ queries, and strengthens this bound from the …

Positive Solutions For A Concave Semipositone Dirichlet Problem, Alfonso Castro, Ratnasingham Shivaji

All HMC Faculty Publications and Research

No abstract provided for this article

Convergence Of Random Walks On The Circle Generated By An Irrational Rotation, Francis E. Su

All HMC Faculty Publications and Research

Fix . Consider the random walk on the circle which proceeds by repeatedly rotating points forward or backward, with probability , by an angle . This paper analyzes the rate of convergence of this walk to the uniform distribution under ``discrepancy'' distance. The rate depends on the continued fraction properties of the number . We obtain bounds for rates when is any irrational, and a sharp rate when is a quadratic irrational. In that case the discrepancy falls as (up to constant factors), where is the number of steps in the walk. This is the first example of a sharp …

Tree-Based Multicasting In Wormhole-Routed Irregular Topologies, Ran Libeskind-Hadas, Dominic Mazzoni '99, Ranjith Rajagopalan '99

All HMC Faculty Publications and Research

A deadlock-free tree-based multicast routing algorithm is presented for all direct networks, regardless of interconnection topology. The algorithm delivers a message to any number of destinations using only a single startup phase. In contrast to existing tree-based schemes, this algorithm applies to all interconnection topologies, requires only fixed-sized input buffers that are independent of maximum message length, and uses a single asynchronous flit replication mechanism. The theoretical basis of the technique used here is sufficiently general to develop other tree-based multicasting algorithms for regular and irregular topologies. Simulation results demonstrate that this tree-based algorithm provides a very promising means of …

Molecular Cavity Flow, Donald Greenspan

Mathematics Technical Papers - Archive

Using molecular mechanics, cavity flow is studied in a basin of 4235 water molecules at 15°C. Primary vortices are generated with wallspeeds [see pdf for notation]. The vortex motions agree with experimental results in the large. Fully turbulent flow is generated with wallspeed .V = 3000°A/ps. The mechanisms for primary vortex generation are clearly delineated, as are those for turbulent flow.

Orthogonal Harmonic Analysis Of Fractal Measures, Palle Jorgensen, Steen Pedersen

Mathematics and Statistics Faculty Publications

We show that certain iteration systems lead to fractal measures admitting an exact orthogonal harmonic analysis.

Gn.3(C) Is Prime If N Is Odd, John Ferdinands

University Faculty Publications and Creative Works

A finite CW complex X is said to be prime if for every Hurewicz fibration F → E → B with E homotopy equivalent to X, and B and F homotopically equivalent to finite CW complexes, either B or F is contractible. We show that the 3-plane complex Grassmannian Gn.3(C) is prime if n is odd.

Variational Lyapunov Method And Stability Theory, V. Lakshmikantham, Xinzhi Liu, S. G. Leela

Mathematics and System Engineering Faculty Publications

By unifying the method of variation of parameters and Lyapunov's second method, we develop a fruitful technique which we call variational Lyapunov method. We then consider the stability theory in this new framework showing the advantage of this unification.

An Embedding Of Schwartz Distributions In The Algebra Of Asymptotic Functions, Michael Oberguggenberger, Todor D. Todorov

Mathematics

We present a solution of the problem of multiplication of Schwartz distributions by embedding the space of distributions into a differential algebra of generalized functions, called in the paper "asymptotic function," similar to but different from J. F Colombeau's algebras of new generalized functions.

On A Certain Subclass Of Analytic Functions With Negative Cefficients, M. K. Aouf, Nak Eun Cho

Turkish Journal of Mathematics

The object of the present paper is to derive several interesting properties of the class $T_n\lam$ consisting of analytic and univalent functions with negative coefficients. Coefficient inequalities, distortion theorems and closure theorems of functions in the class $T_n\lam$ are determined. Also radii of close-to-convexity, starlikeness and convexity are determined. Furthermore, integral operators and modified Hadamard products of several functions belonging to the class $Tn\lam$ are studied here.