Physical Sciences and Mathematics Commons^™

Intersection Homology Of Toric Varieties And A Conjecture Of Kalai, Tom Braden, D. Macpherson

Tom Braden

No abstract provided.

Sensory And Motor Interdependence In Postural Adjustments, Gin Mccollum

Gin McCollum

The sensory reafference from a movement depends upon the movement, and the movement chosen depends upon the available senses, as demonstrated by vestibular patients who abandon certain movements. Often, one variable is assumed to be dependent whereas the other is independent; however, sensory and motor dynamics in posture are interdependent as conditions upon each other. This paper applies conditional dynamics to characterize the global structure of interdependence between sensory states and motor strategies in fast postural adjustments. The mathematical formalism incorporates rich but disparate experimental, clinical, and theoretical results about sensory and motor control of posture.

The control structures presented …

Finding And Characterizing Unstable Fixed Points By Controlling System Dynamics, Daniel Kaplan

Daniel T. Kaplan

No abstract provided.

Extremal Graphs For Weights, Béla Bollobás, Paul Erdös, Amites Sarkar

Mathematics Faculty Publications

Given a graph G = (V,E) and α ∈ R, we write wα(G)=∑_xyϵEdG(x)^αdG(y)^α, and study the function w_α(m) = max {w_α(G): e(G) = m}. Answering a question from Bollobás and Erdös (Graphs of external weights, to appear), we determine w_i(m) for every m, and we also give bounds for the case α ≠ 1.

Recurrence And Ergodicity Of Interacting Particle Systems, J. Theodore Cox, Achim Klenke

Mathematics - All Scholarship

Many interacting particle systems with short range interactions are not ergodic, but converge weakly towards a mixture of their ergodic invariant measures. The question arises whether a.s. the process eventually stays close to one of these ergodic states, or if it changes between the attainable ergodic states infinitely often ("recurrence"). Under the assumption that there exists a convergence--determining class of distributions that is (strongly) preserved under the dynamics, we show that the system is in fact recurrent in the above sense. We apply our method to several interacting particle systems, obtaining new or improved recurrence results. In addition, we answer …

Fisher Information In Weighted Distributions, Satish Iyengar, Paul H. Kvam, Harshinder Singh

Department of Math & Statistics Faculty Publications

Standard inference procedures assume a random sample from a population with density f_μ(x) for estimating the parameter μ. However, there are many applications in which the available data are a biased sample instead. Fisher modeled biased sampling using a weight function w(x) ¸ 0, and constructed a weighted distribution with a density f_μ^w(x) that is proportional to w(x)f_μ(x). In this paper, we assume that f_μ(x) belongs to an exponential family, and study the Fisher information about μ in observations obtained from some commonly arising weighted distributions: (i) the k^th order …

On The Decomposition Of Order-Separable Posets Of Countable Width Into Chains, Gary Gruenhage, Joe Mashburn

Mathematics Faculty Publications

partially ordered set X has countable width if and only if every collection of pairwise incomparable elements of X is countable. It is order-separable if and only if there is a countable subset D of X such that whenever p, q ∈ X and p < q, there is r ∈ D such that p ≤ r ≤ q. Can every order-separable poset of countable width be written as the union of a countable number of chains? We show that the answer to this question is "no" if there is a 2-entangled subset of IR, and "yes" under the Open Coloring Axiom.

Sextic Number Fields With Discriminant -J2A3B, John W. Jones, David P. Roberts

Mathematics Publications

. Complete lists of number fields, of given degree n and unramified outside a given finite set S of primes, are both of intrinsic interest and useful in some applications. For degrees n ≤ 5 and S = {∞, 2, 3}, the complete lists have appeared previously; there are in total 85 such fields. Here we give the complete list for n = 6 and S = {∞, 2, 3}, finding in particular exactly 398 such fields. We use a three-pronged approach to obtain this classification: an exhaustive computer search, sextic twinning, and class field theory. Also we completely identify …

Stability Of A Semilinear Cauchy Problem, Yi Liu, Yi Li, Yinbin Deng

Mathematics and Statistics Faculty Publications

A report of progress in linear and nonlinear partial differential equations, microlocal analysis, singular partial differential operators, spectral analysis and hyperfunction theory. The papers aretaken from a conference on partial differential equations and their applications, held in Wuhan.

On The Exactness Of An S-Shaped Bifurcation Curve, Philip Korman, Yi Li

Mathematics and Statistics Faculty Publications

For a class of two-point boundary value problems we prove exactness of an S-shaped bifurcation curve. Our result applies to a problem from combustion theory, which involves nonlinearities like for .

The Stable Manifold Theorem For Stochastic Differential Equations, Salah-Eldin A. Mohammed, Michael K. R. Scheutzow

Articles and Preprints

We formulate and prove a local stable manifold theorem for stochastic differential equations (SDEs) that are driven by spatial Kunita-type semimartingales with stationary ergodic increments. Both Stratonovich and Itô-type equations are treated. Starting with the existence of a stochastic flow for a SDE, we introduce the notion of a hyperbolic stationary trajectory. We prove the existence of invariant random stable and unstable manifolds in the neighborhood of the hyperbolic stationary solution. For Stratonovich SDEs, the stable and unstable manifolds are dynamically characterized using forward and backward solutions of the anticipating SDE. The proof of the stable manifold theorem is based …

Triple Positive Solutions For Multipoint Conjugate Boundary Value Problems, John M. Davis, Paul W. Eloe, Johnny Henderson

Mathematics Faculty Publications

For the nth order nonlinear differential equation y (n)(t)=f(y(t)), t [0,1], satisfying the multipoint conjugate boundary conditions, y (j)(ai) = 0,1 i k, 0 j n i - 1, 0 =a 1 a 2 a k = 1, and i=1 k n i =n, where f: [0, ) is continuous, growth condtions are imposed on f which yield the existence of at least three solutions that belong to a cone.

Inequalities For Solutions Of Multipoint Boundary Value Problems, Paul W. Eloe, Johnny Henderson

Mathematics Faculty Publications

The concept of concavity is generalized to functions, y, satisfying nth-order differential inequalities. … An analogous inequality for a related Green’s function is also obtained. These inequalities are useful in applications of certain cone theoretic fixed-point theorems.

Reconstructing Subsets Of Reals, A. J. Radcliffe, A. D. Scott

Department of Mathematics: Faculty Publications

We consider the problem of reconstructing a set of real numbers up to translation from the multiset of its subsets of fixed size, given up to translation. This is impossible in general: for instance almost all subsets of Z contain infinitely many translates of every finite subset of Z. We therefore restrict our attention to subsets of R which are locally finite; those which contain only finitely many translates of any given finite set of size at least 2. We prove that every locally finite subset of R is reconstructible from the multiset of its 3-subsets, given up to …

Asupra Unor Noi Functii În Teoria Numerelor, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Performantele matematicii actuale,ca si descoperirile din viitor isi au,desigur, inceputul in cea mai veche si mai aproape de filozofie ramura a matematicii, in teoria numerelor. Matematicienii din toate timpurile au fost, sunt si vor fi atrasi de frumusetea si varietatea problemelor specifice acestei ramuri a matematicii. Regina a matematicii, care la randul ei este regina a stiintelor, dupa cum spunea Gauss, teoria numerelor straluceste cu lumina si atractiile ei, fascinandu-ne si usurandu-ne drumul cunoasterii legitatilor ce guverneaza macrocosmosul si microcosmosul. De la etapa antichitatii, cand teoria numerelor era cuprinsa in aritmetica, la etapa aritmeticii superioare din perioada Renasterii, cand teoria …

Smarandache Type Functions Obtained By Duality, Florentin Smarandache, C Dumitrescu, N Varlan, St Zamfir, E Radescu, N Radescu

Branch Mathematics and Statistics Faculty and Staff Publications

we extend the Smarandache function from the set N* of positive integers to the set Q of rationals

Bounds On A Bug, Arthur T. Benjamin, Matthew T. Fluet '99

All HMC Faculty Publications and Research

In the game of Cootie, players race to construct a "cootie bug" by rolling a die to collect component parts. Each cootie bug is composed of a body, a head, two eyes, one nose, two antennae, and six legs. Players must first acquire the body of the bug by rolling a 1. Next, they must roll a 2 to add the head to the body. Once the body and head are both in place, the remaining body parts can be obtained in any order by rolling two 3s for the eyes, one 4 for the nose, two 5s for the …

On The Number Of Radially Symmetric Solutions To Dirichlet Problems With Jumping Nonlinearities Of Superlinear Order, Alfonso Castro, Hendrik J. Kuiper

All HMC Faculty Publications and Research

This paper is concerned with the multiplicity of radially symmetric solutions u(x) to the Dirichlet problem

Δu+f(u)=h(x)+cφ(x)

on the unit ball Ω⊂R^N with boundary condition u=0 on ∂Ω. Here φ(x) is a positive function and f(u) is a function that is superlinear (but of subcritical growth) for large positive u, while for large negative u we have that f'(u)<μ, where μ is the smallest positive eigenvalue for Δψ+μψ=0 in Ω with ψ=0 on ∂Ω. It is shown that, given any integer k≥0, the value c may be chosen so large that there are 2k+1 solutions with k or less interior nodes. Existence of positive solutions is excluded for large enough values of c.

An Inverse Function Theorem, Alfonso Castro, J. W. Neuberger

All HMC Faculty Publications and Research

In this note we present a local surjectivity result which is applicable to differential equations for which full boundary conditions may not be known. Our method uses continuous steepest descent and Sobolev gradients.

The Bordalo Order On A Commutative Ring, Melvin Henriksen, Frank A. Smith

All HMC Faculty Publications and Research

If R is a commutative ring with identity and ≤ is defined by letting a ≤ b mean ab = a or a = b, then (R,≤) is a partially ordered ring. Necessary and sufficient conditions on R are given for (R,≤) to be a lattice, and conditions are given for it to be modular or distributive. The results are applied to the rings Z_n of integers mod n for n ≥ 2. In particular, if R is reduced, then (R,≤) is a lattice iff R is a weak Baer ring, and (R,≤) is a distributive lattice iff R …

A Lower Bound For The Cyclic Cutwidth Of The N-Cube, James Shigeo Namekata

Theses Digitization Project

No abstract provided.

Algebraic Geometric Codes Over Rings, Judy L. Walker

Department of Mathematics: Faculty Publications

The techniques of algebraic geometry have been widely and successfully applied to the study of linear codes over finite fields since the early 1980’s. Recently, there has been an increased interest in the study of linear codes over finite rings. In this paper, we combine these two approaches to coding theory by introducing the study of algebraic geometric codes over rings. In addition to defining these new codes, we prove several results about their properties.

Conjectures On Partitions Of Integers As Summations Of Primes, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this short note many conjectures on partitions of integers as summations of prime numbers are presented, which are extension of Goldbach conjecture.

Geometrical Models For Grain Dynamics, Giovani L. Vasconcelos, J. J. P. Veerman

Mathematics and Statistics Faculty Publications and Presentations

We study models for the gravity-driven, dissipative motion of a single grain on an inclined rough surface. Imposing some conditions on the momentum loss due to the collisions between the particle and the surface, we arrive at a class of models in which the grain dynamics is described by one-dimensional maps. The dynamics of these maps is studied in detail. We prove the existence of various dynamical phases and show that the presence of these phases is independent of the restitution law (within the class considered).

Lagrangian Systems On Hyperbolic Manifolds, Philip Boyland, Christophe Golé

Mathematics Sciences: Faculty Publications

This paper gives two results that show that the dynamics of a time-periodic Lagrangian system on a hyperbolic manifold are at least as complicated as the geodesic flow of a hyperbolic metric. Given a hyperbolic geodesic in the Poincaré ball, Theorem A asserts that there are minimizers of the lift of the Lagrangian system that are a bounded distance away and have a variety of approximate speeds. Theorem B gives the existence of a collection of compact invariant sets of the Euler-Lagrange flow that are semiconjugate to the geodesic flow of a hyperbolic metric. These results can be viewed as …

The Deconstruction Of Mathematics: A Criticism Of Reuben Hersh's What Is Mathematics, Really? And The Humanist Philosophy Of Mathematics, David J. Stucki

Mathematics Faculty Scholarship

Mathematics, as an academic discipline, has stood for many years as the last bastion against a growing tide of intellectual relativism that has become all but ubiquitous. More recently, however, efforts have been made to "humanize" mathematics by advocating a social-constructivist approach to the philosophy of mathematics, both in practice and education. This paper is intended to serve as a critical response to one advocate of this approach, Reuben Hersh (What Is Mathematics, Really?, 1997), and in the process a defense of Platonism.

Utilization Of Printer Resources Within A Computer Graphics Department: A Print Queue Analysis, Prentice Frazier

Theses and Dissertations

This paper examines print queue management for the graphics department of a financial services company. The current network configuration has proven to be sub-optimal. The IT department is currently undergoing testing of possible alternative network configurations. The objective is to improve performance by leveraging existing resources with new technology. In this paper, the effect of consolidating the queue into one primary queue manager is analyzed, along with prioritizing print jobs, and forecasting future printer needs. Analysis was performed using queuing theory concepts along with an analysis of both steady state and transient behavior using simulation modeling.

Pseudospectral Solution Of The Two-Dimensional Navier{Stokes Equations In A Disk, Evangelos A. Coutsias, David J. Torres

Branch Mathematics and Statistics Faculty and Staff Publications

An efficient and accurate algorithm for solving the two-dimensional (2D) incompressible Navier-Stokes equations on a disk with no-slip boundary conditions is described. The vorticity stream function formulation of these equations is used, and spatially the vorticity and stream functions are expressed as Fourier-Chebyshev expansions. The Poisson and Helmholtz equations which arise from the implicit-explicit time marching scheme are solved as banded systems using a postconditioned spectral tau-method. The polar coordinate singularity is handled by expanding fields radially over the entire diameter using a parity modified Chebyshev series and building partial regularity into the vorticity. The no-slip boundary condition is enforced …

A New Approach To Immersion Theory, Colin Rourke, Brian Sanderson

Turkish Journal of Mathematics

No abstract provided.

Structure Of M-Dimensional Implicitly Defined Surfaces In N-Dimensional Euclidean Space E_N, Alla Borisovna Kotlyar

Turkish Journal of Mathematics

We consider the structure of the surface in the given point, if we vary all its normals in this point.