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1997

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Articles 31 - 60 of 240

Full-Text Articles in Mathematics

Legendrian Circular Helix Links, Lisa Traynor Sep 1997

Legendrian Circular Helix Links, Lisa Traynor

Mathematics Faculty Research and Scholarship

Examples are given of legendrian links in the manifold of cooriented contact elements of the plane, or equivalently, in the 1-jet space of the circle which are not equivalent via an isotopy of contact diffeomorphisms. These examples have generalizations to linked legendrian spheres in contact manifolds diffeomorphic to R-n x Sn-1. These links are distinguished by applying the theory of generating functions to contact manifolds.

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Asymptotics Of Zeros Of Relativistic Hermite Polynomials, Matthew He, K. Pan, Paolo E. Ricci Sep 1997

Asymptotics Of Zeros Of Relativistic Hermite Polynomials, Matthew He, K. Pan, Paolo E. Ricci

Mathematics Faculty Articles

The relativistic Hermite polynomial (RHP) is a class of orthogonal polynomials associated with varying weights. We study the asymptotics of the zeros of the RHP when both degree $n$ of polynomials and relativistic parameter $N$ approach infinity.

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Complexity And Decomposability Of Relations, Martin Zwick Sep 1997

Complexity And Decomposability Of Relations, Martin Zwick

Complex Systems Faculty Publications and Presentations

A discrete multivariate relation, defined set-theoretically, is a subset of a cartesian product of sets which specify the possible values of a number of variables. Where three or more variables are involved, the highest order relation, namely the relation between all the variables, may or may not be decomposable without loss into sets of lower order relations which involve subsets of the variables. In a completely parallel manner, the highest order relation defined information-theoretically, namely the joint probability distribution involving all the variables, may or may not be decomposed without loss into lower-order distributions involving subsets of the variables. Decomposability …

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On The Product Of Two Generalized Derivations, Mohamed Barraa, Steen Pedersen Sep 1997

On The Product Of Two Generalized Derivations, Mohamed Barraa, Steen Pedersen

Mathematics and Statistics Faculty Publications

Two elements A and B in a ring R determine a generalized derivation deltaA,B on R by setting δA,B(X) = AX - XA for any X in R. We characterize when the product δC,DδA,B is a generalized derivation in the cases when the ring R is the algebra of all bounded operators on a Banach space epsilon, and when R is a C*-algebra U. We use the se characterizations to compute the commutant of the range of δA,B.

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Pompeiu Problem And Analogues Of The Weiner-Tauberian Theorem For Certain Homogeneous Spaces., Rama Rawat Dr. Aug 1997

Pompeiu Problem And Analogues Of The Weiner-Tauberian Theorem For Certain Homogeneous Spaces., Rama Rawat Dr.

Doctoral Theses

Let G be a connected locally compact unimodular group acting transitively on a locally compact space X. For a function f on X and g € G, define of by 9f(x) = fA 9.a), a € X. One of the recurring themes in analysis is the question of when a function f in a given function space F(X) will have property that Span{gf : g € G} is dense in F(X). If X = R and G = R, the celebrated Wiener-Tauberian theorem answers this question completely for the space L1(R): The span of the translates of fE L1(R) is …

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Oval Intersections In Tilings On Surfaces, Dennis A. Schmidt Aug 1997

Oval Intersections In Tilings On Surfaces, Dennis A. Schmidt

Mathematical Sciences Technical Reports (MSTR)

A tiling is a covering by polygons, without gaps or overlapping, of a compact, orientable surface. We are particularly interested in tilings by triangles that generate a large symmetry group of the surface. An oval of the tiling is a simple, closed curve that is a union of edges of the tiling. We investigate the number of points of intersection of two ovals. We have found that the number of intersections is bounded when the subgroup of orientation preserving symmetries is abelian. However, there is no upper bound on the number of intersections in the non-abelian case.

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Invariant Subspaces And Hyper-Reflexivity For Free Semigroup Algebras, Kenneth R. Davidson, David R. Pitts Aug 1997

Invariant Subspaces And Hyper-Reflexivity For Free Semigroup Algebras, Kenneth R. Davidson, David R. Pitts

Department of Mathematics: Faculty Publications

In this paper, we obtain a complete description of the invariant subspace structure of an interesting new class of algebras which we call free semigroup algebras. This enables us to prove that they are reflexive, and moreover to obtain a quantitative measure of the distance to these algebras in terms of the invariant subspaces. Such algebras are called hyper-reflexive. This property is very strong, but it has been established in only a very few cases. Moreover the prototypes of this class of algebras are the natural candidate for a non-commutative analytic Toeplitz algebra on n variables. The case we make …

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Counting Ovals On A Symmetric Riemann Surface, Sean A. Broughton Aug 1997

Counting Ovals On A Symmetric Riemann Surface, Sean A. Broughton

Mathematical Sciences Technical Reports (MSTR)

Let S be a compact Riemann surface without boundary. A symmetry of S is an anti-conformal, involutary automorphism. Its fixed point set is a disjoint union of circles, each of which is called an oval. A method is presented for counting the ovals of a symmetry when S admits a large group G of automorphisms. The method involves only calculations in G, based on the geometric description of S/G, and the knowledge of the action of the symmetry on G.

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Pseudocontinuations And The Backward Shift, Alexandru Aleman, Stefan Richter, William T. Ross Aug 1997

Pseudocontinuations And The Backward Shift, Alexandru Aleman, Stefan Richter, William T. Ross

Department of Math & Statistics Technical Report Series

In this paper, we will examine the backward shift operator Lƒ = (ƒ – ƒ(0))/z on certain Banach spaces of analytic functions on the open unit disk D. In particular, for a (closed) subspace M for which LM ⊂ M, we wish to determine the spectrum, the point spectrum, and the approximate point spectrum of L|M. In order to do this, we will use the concept of "pseudocontinuation" of functions across the unit circle ∏.

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A Generalized Mahonian Statistic On Absorption Ring Mappings, Don Rawlings Aug 1997

A Generalized Mahonian Statistic On Absorption Ring Mappings, Don Rawlings

Mathematics

Based on a coin-tossing scheme, a generalized Mahonian statistic is defined on absorption ring mappings and applied in obtaining combinatorial interpretations of the coefficient ofqjin the expansion of ∏ki=1 (1+q+q2+…+qmi). In the permutation case, the statistic coincides with one studied by Han that specializes many known Mahonian statistics.

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Hypersurfaces In R-D And The Variance Of Exit Times For Brownian Motion, Kimberly Kinateder, Patrick Mcdonald Aug 1997

Hypersurfaces In R-D And The Variance Of Exit Times For Brownian Motion, Kimberly Kinateder, Patrick Mcdonald

Mathematics and Statistics Faculty Publications

Using the first exit time for Brownian motion from a smoothly bounded domain in Euclidean space, we define two natural functionals on the space of embedded, compact, oriented, unparametrized hypersurfaces in Euclidean space. We develop explicit formulas for the first variation of each of the functionals and characterize the critical points.

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Infinite-Dimensional Hamilton-Jacobi-Bellman Equations In Gauss-Sobolev Spaces, Pao-Liu Chow, Jose-Luis Menaldi Aug 1997

Infinite-Dimensional Hamilton-Jacobi-Bellman Equations In Gauss-Sobolev Spaces, Pao-Liu Chow, Jose-Luis Menaldi

Mathematics Faculty Research Publications

We consider the strong solution of a semi linear HJB equation associated with a stochastic optimal control in a Hilbert space H: By strong solution we mean a solution in a L2(μ,H)-Sobolev space setting. Within this framework, the present problem can be treated in a similar fashion to that of a finite-dimensional case. Of independent interest, a related linear problem with unbounded coefficient is studied and an application to the stochastic control of a reaction-diffusion equation will be given.

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Quasi-Steady Monopole And Tripole Attractors In Relaxing Vortices, Louis F. Rossi, Joseph F. Lingevitch, Andrew J. Bernoff Aug 1997

Quasi-Steady Monopole And Tripole Attractors In Relaxing Vortices, Louis F. Rossi, Joseph F. Lingevitch, Andrew J. Bernoff

All HMC Faculty Publications and Research

Using fully nonlinear simulations of the two-dimensional Navier–Stokes equations at large Reynolds number (Re), we bracket a threshold amplitude above which a perturbed Gaussian monopole will relax to a quasi-steady, rotating tripole, and below which will relax to an axisymmetric monopole. The resulting quasi-steady structures are robust to small perturbations. We propose a means of measuring the decay rate of disturbances to asymptotic vortical structures wherein streamlines and lines of constant vorticity correspond in some rotating or translating frame. These experiments support the hypothesis that small or moderate deviations from asymptotic structures decay through inviscid and viscous mixing.

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Lyapunov Exponents, Singularities, And A Riddling Bifurcation, Lora Billings, James H. Curry, Eric Phipps Aug 1997

Lyapunov Exponents, Singularities, And A Riddling Bifurcation, Lora Billings, James H. Curry, Eric Phipps

Department of Mathematics Faculty Scholarship and Creative Works

There are few examples in dynamical systems theory which lend themselves to exact computations of macroscopic variables of interest. One such variable is the Lyapunov exponent which measures the average attraction of an invariant set. This article presents .a family of noninvertible transformations of the plane for which such computations are possible. This model sheds additional insight into the notion of what it can mean for an attracting invariant set to have a riddled basin of attraction.

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Using The Quantum Computer To Break Elliptic Curve Cryptosystems, Jodie Eicher, Yaw Opoku Jul 1997

Using The Quantum Computer To Break Elliptic Curve Cryptosystems, Jodie Eicher, Yaw Opoku

Department of Math & Statistics Technical Report Series

This article gives an introduction to Elliptic Curve Cryptography and Quantum Computing. It includes an analysis of Peter Shor’s algorithm for the quantum computer breakdown of Discrete Log Cryptosystems and an analog to Shor’s algorithm for Elliptic Curve Cryptosystems. An extended example is included which illustrates how this modified Shor’s algorithm will work.

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Magneto-Optic Trapping Of Β-Decaying 38km, 37k From An On-Line Isotope Separator, J. A. Behr, A. Gorelov, T. Swanson, O. Hausser, K. P. Jackson, M. Trinczek, U. Giesen, J. M. D'Auria, R. Hardy, T. Wilson, P. Choboter, F, Leblond, L. Buchmann, M. Dombsky, C. D.P. Levy, G. Roy, B. A. Brown, J. Dilling Jul 1997

Magneto-Optic Trapping Of Β-Decaying 38km, 37k From An On-Line Isotope Separator, J. A. Behr, A. Gorelov, T. Swanson, O. Hausser, K. P. Jackson, M. Trinczek, U. Giesen, J. M. D'Auria, R. Hardy, T. Wilson, P. Choboter, F, Leblond, L. Buchmann, M. Dombsky, C. D.P. Levy, G. Roy, B. A. Brown, J. Dilling

Mathematics

A magneto-optic trap (MOT) can provide a well-polarized, backing-free, localized source of radioactive atoms for β-decay experiments. We have trapped approximately 6000 atoms of 38Km ( t1/2 = 0.925s) and 2000 atoms of 37K (1.226 s) produced at the TRIUMF on-line separator TISOL in a vapor-cell MOT. We have measured optical isotope shifts and deduced the nuclear charge radii, which show an unusual lack of change at the neutron number N = 20 shell closure. Plans include a search for scalar contributions to the β+- ν correlation in the 0+→0+ decay …

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Nested Hadamard Difference Sets, James A. Davis, Jonathan Jedwab Jul 1997

Nested Hadamard Difference Sets, James A. Davis, Jonathan Jedwab

Department of Math & Statistics Faculty Publications

A Hadamard difference set (HDS) has the parameters (4N2, 2N2 − N, N2 − N). In the abelian case it is equivalent to a perfect binary array, which is a multidimensional matrix with elements ±1 such that all out-of-phase periodic autocorrelation coefficients are zero. We show that if a group of the form H × Z2pr contains a (hp2r, √hpr(2√hpr − 1), √hpr(√hpr − 1)) HDS (HDS), p a prime not dividing |H| …

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What Kind Of Thing Is A Number?: A Talk With Reuben Hersh, Reuben Hersh Jul 1997

What Kind Of Thing Is A Number?: A Talk With Reuben Hersh, Reuben Hersh

Humanistic Mathematics Network Journal

No abstract provided.

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Math Lingo Vs. Plain English: Multiple Entendre, Stephen I. Brown Jul 1997

Math Lingo Vs. Plain English: Multiple Entendre, Stephen I. Brown

Humanistic Mathematics Network Journal

No abstract provided.

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Book Review: The Crest Of The Peacock: Non-European Roots Of Mathematics,By George Gheverghese Joseph, Bernadette Anne Berken Jul 1997

Book Review: The Crest Of The Peacock: Non-European Roots Of Mathematics,By George Gheverghese Joseph, Bernadette Anne Berken

Humanistic Mathematics Network Journal

No abstract provided.

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Algebra Anyone?, Leslie Jones, Ted Panitz, Walter Burlage Jul 1997

Algebra Anyone?, Leslie Jones, Ted Panitz, Walter Burlage

Humanistic Mathematics Network Journal

No abstract provided.

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Abe Shenitzer At 75, Hardy Grant Jul 1997

Abe Shenitzer At 75, Hardy Grant

Humanistic Mathematics Network Journal

No abstract provided.

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Illumination And Geometry In Islamic Art, Salma Marani Jul 1997

Illumination And Geometry In Islamic Art, Salma Marani

Humanistic Mathematics Network Journal

No abstract provided.

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Curriculum Development Via Literary And Musical Forms, Joel K. Haack Jul 1997

Curriculum Development Via Literary And Musical Forms, Joel K. Haack

Humanistic Mathematics Network Journal

No abstract provided.

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A Brief Tribute To Π, J. D. Phillips Jul 1997

A Brief Tribute To Π, J. D. Phillips

Humanistic Mathematics Network Journal

No abstract provided.

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Reminiscences Of Paul Erdös (1913-1996), Melvin Henriksen Jul 1997

Reminiscences Of Paul Erdös (1913-1996), Melvin Henriksen

Humanistic Mathematics Network Journal

No abstract provided.

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Sand Songs: The Formal Languages Of Warlpiri Iconography, James V. Rauff Jul 1997

Sand Songs: The Formal Languages Of Warlpiri Iconography, James V. Rauff

Humanistic Mathematics Network Journal

No abstract provided.

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Al-Khawarizmi's Algebra: The First Paradigm In Algebra, Murad Jurdak Jul 1997

Al-Khawarizmi's Algebra: The First Paradigm In Algebra, Murad Jurdak

Humanistic Mathematics Network Journal

No abstract provided.

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See-Duction: How Scientists And Artists Are Creating A Third Way Of Knowing, Howard Levine Jul 1997

See-Duction: How Scientists And Artists Are Creating A Third Way Of Knowing, Howard Levine

Humanistic Mathematics Network Journal

No abstract provided.

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Mathematical Rebuses, Arthur V. Johnson Ii Jul 1997

Mathematical Rebuses, Arthur V. Johnson Ii

Humanistic Mathematics Network Journal

No abstract provided.

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