Mathematics Commons^™

A Multigrid Method For Variable Coefficient Maxwell's Equations, Jim E. Jones, Barry Lee

Mathematics and System Engineering Faculty Publications

This paper presents a multigrid method for solving variable coefficient Maxwell's equations. The novelty in this method is the use of interpolation operators that do not produce multilevel commutativity complexes that lead to multilevel exactness. Rather, the effects of multilevel exactness are built into the level equations themselves-on the finest level using a discrete T -V formulation and on the coarser grids through the Galerkin coarsening procedure of a T - V formulation. These built-in structures permit the levelwise use of an effective hybrid smoother on the curl-free near-nullspace components and permit the development of interpolation operators for handling the …

The Dynamics Of Newton's Method On Cubic Polynomials, Shannon N. Miller

Theses, Dissertations and Capstones

The field of dynamics is itself a huge part of many branches of science, including the motion of the planets and galaxies, changing weather patterns, and the growth and decline of populations. Consider a function f and pick x0 in the domain of f . If we iterate this function around the point x0, then we will have the sequence x0, f (x0), f (f (x0)), f (f (f (x0))), ..., which becomes our dynamical system. We are essentially interested in the end behavior of this system. Do …

Probabilisticmodel-Based Cell Tracking, Nezamoddin Nezamoddini-Kachouie, Paul Fieguth, Eric Jervis

Mathematics and System Engineering Faculty Publications

The study of cell behavior is of crucial importance in drug and disease research. The fields of bioinformatics and biotechnology rely on the collection, processing, and analysis of huge numbers of biocellular images, including cell features such as cell size, shape, and motility. However manual methods of inferring these values are so onerous that automated methods of cell tracking and segmentation are in high demand. In this paper, a novel model-based cell tracker is designed to locate and track individual cells. The proposed cell tracker has been successfully applied to track hematopoietic stem cells (HSCs) based on identified cell locations …

On A Class Of Two-Point Boundary Value Problems With Singular Boundary Conditions, Ravi P. Agarwal, To Fu Ma

Mathematics and System Engineering Faculty Publications

A new existence theory for a class of second order two-point boundary value problems with nonlinear boundary conditions which can blow up in finite intervals is established. The proofs are based on the dual variational principle and the critical point theory.

Generalized Flow Invariance For Differential Inclusions, Tarun Gnana Bhaskar, V. Lakshmikantham

Mathematics and System Engineering Faculty Publications

We introduce a generalized notion of invariance for differential inclusions, using a proximal aiming condition in terms of proximal normals. A set of sufficient conditions for the weak and strong invariance in the generalized sense are presented.

Coalgebras And Their Logics, Alexander Kurz

Engineering Faculty Articles and Research

"Transition systems pervade much of computer science. This article outlines the beginnings of a general theory of specification languages for transition systems. More specifically, transition systems are generalised to coalgebras. Specification languages together with their proof systems, in the following called (logical or modal) calculi, are presented by the associated classes of algebras (e.g., classical propositional logic by Boolean algebras). Stone duality will be used to relate the logics and their coalgebraic semantics."

Prediction In The Panel Data Model With Spatial Correlation: The Case Of Liquor, Badi H. Baltagi, Dong Li

Center for Policy Research

This paper considers the problem of prediction in a panel data regression model with spatial autocorrelation in the context of a simple demand equation for liquor. This is based on a panel of 43 states over the period 1965-1994. The spatial autocorrelation due to neighboring states and the individual heterogeneity across states is taken explicitly into account. We compare the performance of several predictors of the states demand for liquor for one year and five years ahead. The estimators whose predictions are compared include OLS, fixed effects ignoring spatial correlation, fixed effects with spatial correlation, random effects GLS estimator ignoring …

On The Existence Of Infinitely Many Closed Geodesics On Orbifolds Of Revolution, Joseph Borzellino, Christopher R. Jordan-Squire, Gregory C. Petrics, D. Mark Sullivan

Mathematics

Using the theory of geodesics on surfaces of revolution, we introduce the period function. We use this as our main tool in showing that any two-dimensional orbifold of revolution homeomorphic to S2 must contain an infinite number of geometrically distinct closed geodesics. Since any such orbifold of revolution can be regarded as a topological two-sphere with metric singularities, we will have extended Bangert’s theorem on the existence of infinitely many closed geodesics on any smooth Riemannian two-sphere. In addition, we give an example of a two-sphere cone-manifold of revolution which possesses a single closed geodesic, thus showing that Bangert’s result …

Classifying E-Algebras Over Dedekind Domains, Brendan Goldsmith, R. Gobel

Articles

An R-algebra A is said to be a generalized E-algebra if A is isomorphic to the algebra EndR(A). Generalized E-algebras have been extensively investigated. In this work they are classified ‘modulo cotorsion-free modules’ when the underlying ring R is a Dedekind domain.

Poisson Structure And Action-Angle Variables For The Camassa-Holm Equation, Adrian Constantin, Rossen Ivanov

Articles

The Poisson brackets for the scattering data of the Camassa-Holm equation are computed. Consequently, the action-angle variables are expressed in terms of the scattering data.

Decentralized Convex-Type Equilibrium In Nonconvex Models Of Welfare Economics Via Nonlinear Prices, Boris S. Mordukhovich

Mathematics Research Reports

The paper is devoted to applications of modern tools of variational analysis to equilibrium models of welfare economics involving nonconvex economies with infinite-dimensional commodity spaces. The main results relate to generalized/ extended second welfare theorems ensuring an equilibrium price support at Pareto optimal allocations. Based on advanced tools of generalized differentiation, we establish refined results of this type with the novel usage of nonlinear prices at the three types to optimal allocations: weak Pareto, Pareto, and strong Pareto. The usage of nonlinear (vs. standard linear) prices allow us to decentralized price equilibria in fully nonconvex models similarly to linear prices …

Inverse Scattering Transform For The Camassa-Holm Equation, Adrian Constantin, Vladimir Gerdjikov, Rossen Ivanov

Articles

An Inverse Scattering Method is developed for the Camassa-Holm equation. As an illustration of our approach the solutions corresponding to the reflectionless potentials are constructed in terms of the scattering data. The main difference with respect to the standard Inverse Scattering Transform lies in the fact that we have a weighted spectral problem. We therefore have to develop different asymptotic expansions.

Bass Series For Small Witt Rings, Robert W. Fitzgerald

Articles and Preprints

No abstract provided.

The Stable Manifold Theorem For Semilinear Stochastic Evolution Equations And Stochastic Partial Differential Equations, Salah-Eldin A. Mohammed, Tusheng Zhang, Huaizhong Zhao

Articles and Preprints

The main objective of this paper is to characterize the pathwise local structure of solutions of semilinear stochastic evolution equations (see’s) and stochastic partial differential equations (spde’s) near stationary solutions. Such characterization is realized through the long-term behavior of the solution field near stationary points. The analysis falls in two parts 1, 2.

In Part 1, we prove general existence and compactness theorems for C^k-cocycles of semilinear see’s and spde’s. Our results cover a large class of semilinear see’s as well as certain semilinear spde’s with Lipschitz and non-Lipschitz terms such as stochastic reaction diffusion equations and the …

On The Generalized Möbius Inversion Formulas, Tian-Xiao He, Peter Shiue3, Leetsch Hsu

Scholarship

We provide a wide class of M¨obius inversion formulas in terms of the generalized M¨obius functions and its application to the setting of the Selberg multiplicative functions.

The Pitch And The Pseudo Angle Of Pitch Of A Closed Piece Of (K+1)-Dimensional Ruled Surface In R_\Nu^N, Ayşe Altin

Turkish Journal of Mathematics

In this paper, we define the closed piece of ruled surface, the pitch and the pseudo angle of pitch of a closed piece of ruled surface and calculate these values in Minkowski space R_\nu^n= (R ^n,-\sum^{\nu}_{i=1}dx_i+\sum^n_{i=\nu+1}dx_i).

Second-Order Nonlinear Three Point Boundary-Value Problems On Time Scales, S. Gülşan Topal

Turkish Journal of Mathematics

We consider a second order three point boundary value problem for dynamic equations on time scales and establish criteria for the existence of at least two positive solutions of an eigenvalue problem by an application of a fixed point theorem in cones. Existence result for non-eigenvalue problem is also given by the monotone method.

P-Elastica In The 3-Dimensional Lorentzian Space Forms, Nevi̇n Gürbüz

Turkish Journal of Mathematics

R Huang worked the p-elastic in a Riemannian manifold with constant sectional curvature [1]. In this work, we solve the Euler-Lagrange equation by quadrature and study the Frenet equation of the p-elastica by using the Killing field in the three dimensional Lorentzian space forms

Inequality For Ricci Curvature Of Slant Submanifolds In Cosymplectic Space Forms, Dae Won Yoon

Turkish Journal of Mathematics

In this article, we establish inequalities between the Ricci curvature and the squared mean curvature, and also between the k-Ricci curvature and the scalar curvature for a slant, semi-slant and bi-slant submanifold in a cosymplectic space form of constant \varphi-sectional curvature with arbitrary codimension.

Existence Of Periodic Solutions For Second Order Rayleigh Equations With Piecewise Constant Argument, Gen-Qiang Wang, Sui Sun Cheng

Turkish Journal of Mathematics

Based on a continuation theorem of Mawhin, periodic solutions are found for the second-order Rayleigh equation with piecewise constant argument.

On Irregular Semi Strong P-Adic U Numbers, Hülya Duru

Turkish Journal of Mathematics

The concept of the ``relation of comparability'' was introduced by Maillet in [7], who showed that if \alpha,\beta are comparable Liouville numbers then each of the numbers \alpha +\beta, \alpha -\beta, \alpha \beta and \alpha /\beta is either a rational or Lioville number. Moreover those which are Liouville numbers are comparable aamong theem and to \alpha and \beta. Maillet's proof uses in an essential way the transitivity of the comparability relation. Unfortunately, as the comparability relation is not transitive, his proof is defective. In this paper, without using the comparability relation, we obtain some uncountable subfields of p-adic numbers field, …

A Connected Sum Of Knots And Fintushel-Stern Knot Surgery On 4-Manifolds, Manabu Akaho

Turkish Journal of Mathematics

We give some new examples of smooth 4-manifolds which are diffeomorphic although they are obtained by Fintushel-Stern knot surgeries on a smooth 4-manifold with different knots; the first such examples are given by Akbulut [1]. In the proof we essentially use the monodromy of a cusp.

On Cauchy's Bound For Zeros Of A Polynomial, V. K. Jain

Turkish Journal of Mathematics

In this note, we improve upon Cauchy's classical bound, and upon some recent bounds for the moduli of the zeros of a polynomial.

On Finitary Permutation Groups, Ali̇ Osman Asar

Turkish Journal of Mathematics

In this work we give some sufficient conditions under which the structure of a transitive group of finitary permutations on an infinite set can be determined from the structure of a point stabilizer. Also, we give some sufficient conditions for the existence of a proper subgroup having an infinite orbit in a totally imprimitive p-group of finitary permutations. These results, with the help of some known results, give sufficient conditions for the nonexistence of a perfect locally finite minimal non FC - (p-group).

On Certain Modified Meyer-König And Zeller Operators, Lucyna Rempulska, Karolina Tomczak

Turkish Journal of Mathematics

We introduce certain modified Meyer-König and Zeller operators and we study their approximation properties. The similar results for modified Bernstein polynomials were given in [6].

The Homological Theory Of Degree Of Fql-Mappings, Aki̇f Abbasov

Turkish Journal of Mathematics

In this article the homological theory is specially worked out, ìadaptedî for definition of the degree of mapping from one of the classes of infinite-dimensional mappings, exactly FQL-mappings, introduced in [7].

Finite Groups All Of Whose Abelian Subgroups Of Equal Order Are Conjugate, Sezgi̇n Sezer, Robert W. Van Der Waall

Turkish Journal of Mathematics

In this paper we classify the finite groups whose abelian subgroups of equal order (B^*-groups) are conjugate. The classification has been achieved by means of a lot of general structure properties of B^*-groups, provided in the course of the paper.

Quasi-Dual Modules, M. Tamer Koşan

Turkish Journal of Mathematics

Let R be a ring, M be a right R-module and S = End_R(M). M is called a quasi-dual module if, for every R-submodule N of M, N is a direct summand of r_M(X) where X \subseteq S. In this article, we study and provide several characterizations of this module classes. We show that if M is quasi-dual module, then, for all m \in M, r_M \ell_S(m) = mR \oplus K for some submodule K of M. We also show that every quasi-dual module is a Kasch module and Z(_SM) \subseteq Rad (M_R).

Decompositions Of Continuity, Talal Al-Hawary, Ahmad Al-Omari

Turkish Journal of Mathematics

In 2004, Al-Hawary and Al-Omari introduced and explored the class of \omega^o-open sets which is strictly stronger than the class of \omega-open sets and weaker than that of open sets. In this paper, we introduce what we call \omega^o-continuity and \omega_X^o-continuity and we give several characterizations and two decompositions of \omega ^o-continuity. Finally, new decompositions of continuity are provided.

On Lifts Of Paracomplex Structures, Mehmet Tekkoyun

Turkish Journal of Mathematics

In this paper, we obtain vertical, complete and horizontal lifts of paracomplex geometric structures on paracomplex manifolds to its tangent bundle. Also, we obtain integrability on paracomplex tangent bundle.