Mathematics Commons^™

A Structural Result Of Irreducible Inclusions Of Type Iii Lambda Factors, Lambda Is An Element Of (0,1), Phan Loi

Mathematics and Statistics Faculty Publications

Given an irreducible inclusion of factors with finite index N ⊂ M, where M is of type III_λ1/m, N of type III_λ1/n, 0 < λ < 1, and m,n are relatively prime positive integers, we will prove that if N ⊂ M satisfies a commuting square condition, then its structure can be characterized by using fixed point algebras and crossed products of automorphisms acting on the middle inclusion of factors associated with N ⊂ M. Relations between N ⊂ M and a certain G-kernel on subfactors are also discussed.

Maximally Disjoint Solutions Of The Set Covering Problem, David J. Rader, Peter L. Hammer

Mathematical Sciences Technical Reports (MSTR)

This paper is concerned with finding two solutions of a set covering problem that have a minimum number of variables in common. We show that this problem is NP­ complete, even in the case where we are only interested in completely disjoint solutions. We describe three heuristic methods based on the standard greedy algorithm for set covering problems. Two of these algorithms find the solutions sequentially, while the third finds them simultaneously. A local search method for reducing the overlap of the two given solutions is then described. This method involves the solution of a reduced set covering problem. Finally, …

Evolution Of Mixed-State Regions In Type-Ii Superconductors, Chaocheng Huang, Tom Svobodny

Mathematics and Statistics Faculty Publications

A mean-field model for dynamics of superconducting vortices is studied. The model, consisting of an elliptic equation coupled with a hyperbolic equation with discontinuous initial data, is formulated as a system of nonlocal integrodifferential equations. We show that there exists a unique classical solution in C^1+α(Ω₀) for all t > Ω, where Ω₀ is the initial vortex region that is assumed to be in C^1+α. Consequently, for any time t, the vortex region Ω_t is of C^1+α, and the vorticity is in C^α(Ω_t).

The Set Of Hemispheres Containing A Closed Curve On The Sphere, Mary Kate Boggiano, Mark Desantis

Department of Math & Statistics Technical Report Series

Suppose you get in your car and take a drive on the sphere of radius R, so that when you return to your starting point the odometer indicates you've traveled less than 2πR. Does your path, γ, have to lie in some hemisphere?

This question was presented to us by Dr. Robert Foote of Wabash College. Previous authors chose two points, A and B, on γ such that these points divided γ into two arcs of equal length. Then they took the midpoint of the great circle arc joining A and B to be the North Pole and showed that …

Lee Weights Of Z/4z-Codes From Elliptic Curves, José Felipe Voloch, Judy L. Walker

Department of Mathematics: Faculty Publications

In [15: J. L. Walker, Algebraic geometric codes over rings], the second author defined algebraic geometric codes over rings. This definition was motivated by two recent trends in coding theory: the study of algebraic geometric codes over finite fields, and the study of codes over rings. In that paper, many of the basic parameters of these new codes were computed. However, the Lee weight, which is very important for codes over the ring Z/4Z, was not considered. In [14: J.-F. Voloch and J. L. Walker, Euclidean weights of codes from elliptic curves over rings], this …

Relationships Among The First Variation, The Convolution Product, And The Fourier-Feynman Transform, Chull Park, David Skough, David Storvick

Department of Mathematics: Faculty Publications

In this paper we examine the various relationships that exist among the first variation, the Fourier- Feynman transform, and the convolution product for functionals on Wiener space that belong to a Banach algebra S.

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.

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

All HMC Faculty Publications and Research

No abstract provided for this article

On C^1 Robust Singular Transitive Sets For Three-Dimensional Flows, Carlos Arnoldo Morales, Maria José Pacífico, Enrique Ramiro Pujals

Publications and Research

Abstract:

The main goal of this paper is to study robust invariant transitive sets containing singularities for C¹ flows on three-dimensional compact boundaryless manifolds:they are partially hyperbolic with volume expanding central direction. Moreover, they are either attractors or repellers. Robust here means that this property cannot be destroyed by small C¹-perturbations of the flow.

Résumé:

Le but de ce travail est d'étudier des ensembles invariants robustes ayant des singularités pour des flots C¹ sur des variétés tridimensionelles : ce sont des ensembles hyperboliques singuliers. << Robuste >> veut dire ici que cette propriété ne peut être détruite par des …

Subiecte Posibile Pentru Examenul De Admitere În Liceu Şi Examenul De Capacitate (In Romanian), Florentin Smarandache, Constantin Coanda, Gheorghe Duta

Branch Mathematics and Statistics Faculty and Staff Publications

Prezenta lucrare" încearcă să pună la dispoziţia elevilor şi profesorilor instrumente de evaluare a cunoştinţelor la toate capitolele din actuala programă de matematică. " În evoluţia adolescenţi/or din ţara noastră etapa admiterii în liceu mobilizează eforturi şi emoţii cu totul speciale. 'Actuala lucrare se doreşte a fi un sfljtuitor permanent În perioada fierbinte dintre e.;wmenul de capacitate şi admiterea În liceu. Testele cuprinse in această culegere au un caracter complementar faţă de multe materiale scrise În vederea sprijinirii celor ce se pregătesc pentru astfel de examene şi se referă la intreaga materie cuprinsă În programele analitice de aritmetică, algebră şi …