Digital Commons Network^™

Quadratic Convergence Of Approximate Solutions Of Two-Point Boundary Value Problems With Impulse, Vidya Doddaballapur, Paul W. Eloe, Yongzhi Zhang

Mathematics Faculty Publications

The method of quasilinearization, coupled with the method of upper and lower solutions, is applied to a boundary value problem for an ordinary differential equation with impulse that has a unique solution. The method generates sequences of approximate solutions which converge monotonically and quadratically to the unique solution. In this work, we allow nonlinear terms with respect to velocity; in particular, Nagumo conditions are employed.

Splitting In Locally Compact Abelian Groups, Peter Loth

Mathematics Faculty Publications

No abstract provided.

Finite Rank Zᵈ Actions And The Loosely Bernoulli Property, Aimee S.A. Johnson, A. A. Şahin

Mathematics & Statistics Faculty Works

We define finite rank for Zᵈ actions and show that those finite rank actions with a certain tower shape are loosely Bernoulli for d ≥ 1.

The Tachibana Operator And Transfer Of Lifts, Abdullah Mağden, Muhammet Kamali, Arif A. Salimov

Turkish Journal of Mathematics

The main purpose of this paper is to investigate, using the Tachibana operator, transfer of the complete lifts of affinor structures along the cross-sections of the tangent and cotangent bundles.

On Circulant Weighing Matrices, K. T. Arasu, Jennifer Seberry

Mathematics and Statistics Faculty Publications

Algebraic techniques are employed to obtain necessary conditions for the existence of certain circulant weighing matrices. As an application we rule out the existence of many circulant weighing matrices. We study orders n = 82 +8+1, for 10 ~ 8 ~ 25. These orders correspond to the number of points in a projective plane of order 8.

Timelike Ruled Surfaces In The Minkowski 3-Space-Ii, A. Turgut, H. H. Hacisali̇oğlu

Turkish Journal of Mathematics

This paper is devoted to a study of timelike ruled surfaces in three dimensional Minkowski space obtained by a spacelike straight line moving along a timelike curve. The central point, the curve of striction and the distribution parameter of a timelike ruled surface in Minkowski 3-space are considered, and some theorems relating to their structure are obtained. In addition, some results about developable timelike ruled surfaces are also given.

About Some Classical Functional Equations, Nicolae Neamtu

Turkish Journal of Mathematics

The purpose of this paper is to give a new method of finding the solution of Lobashevsky's functional equation and those of other classical functional equations. At the beginning we present the properties of solution $f, \; f \neq 0$, of Lobachevsky's functional equation. Using only the boundedness property on $(-r, r)$, we deduce the continuity, convexity and differentiability properties of the solution.

An Improper Integral Representation Of Linnik's Probability Densities, A. (Bastiyali) Hayfavi̇

Turkish Journal of Mathematics

A representation of Linnik's Probability Densities by a contour integral distinct than the one given in [2] is obtained. An Improper integral representation of the same density functions is derived. An investigation into the exceptional set is achieved as well.

Isospectral Deformations Of Closed Riemannian Manifolds With Different Scalar Curvature, Carolyn S. Gordon, Ruth Gornet, Dorothee Schueth, David L. Webb

Dartmouth Scholarship

No abstract provided.

On Unit Sum Number Of Rings And Modules, Brendan Goldsmith, S. Pabst, A. Scott

Articles

No abstract available

Κ-To-1 Darboux-Like Functions, Krzysztof Ciesielski

Faculty & Staff Scholarship

We examine the existence of κ-to-1 functions f : R → R in the class of continuous functions, Darboux functions, functions with perfect roads, and functions with the Cantor intermediate value property. In this setting κ denotes a cardinal number (finite or infinite). We also consider different variations on this theme.

Some Additive Darboux-Like Functions, Krzysztof Ciesielski

Faculty & Staff Scholarship

In this note we will construct several additive Darboux-like functions f : R → R answering some problems from (an earlier version of) [4]. In particular, in Section 2 we will construct, under different additional set theoretical assumptions, additive almost continuous (in sense of Stallings) functions f : R → R whose graph is either meager or null in the plane. In Section 3 we will construct an additive almost continuous function f : R → R which has the Cantor intermediate value property but is discontinuous on any perfect set. In particular, such an f does not have the …

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 …

A Tour Of Mistakes, Paul H. Edelman

Vanderbilt Law School Faculty Publications

In these pages, Steven Lubet recently reviewed A Tour of the Calculus, by David Berlinski. Inspired by both the beauty of calculus and Berlinski's description of it, Lubet waxes poetic on the many parallels between the law and calculus. It is completely understandable--even admirable that one might be led to ruminations on the relationship between calculus and one's own discipline. There is little doubt that the subject of calculus stands as one of the great intellectual feats of Western thought. It has had profound implications for physics, engineering, economics and many other disciplines-so why not law? Alas, these philosophical musings …

On The Differential Prime Radical Of A Differential Ring, Djavvat Khadjiev, Fethi̇ Çallialp

Turkish Journal of Mathematics

In this paper we have obtained the following results for a differential ring (associative or nonassociative): (1) For a differential ring ({\cal D}-ring) we introduce definitions of a {\cal D}-prime {\cal D}-ideal, {\cal D}-semiprime {\cal D}-ideal and a strongly {\cal D}-nilpotent element. We define the {\cal D}-prime radical as the intersection of all {\cal D}-prime {\cal D}-ideals. For any {\cal D}-ring the {\cal D}-prime radical, the intersection of all {\cal D}-semiprime {\cal D}-semiprime {\cal D}-ideals and the set of all strongly {\cal D}-nilpotent elements are equal. (2) For a {\cal D}-ring we introduce a definition of an s-nilpotent {\cal D}-ideal. …

Normal Subgroups Of Hecke Groups On Sphere And, İsmai̇l Naci̇ Cangül, Osman Bi̇zi̇m

Turkish Journal of Mathematics

We use regular map theory to obtain all normal subgroups of Hecke groups of genus 0 and 1. The existence of a regular map corresponding uniquely to every normal subgroup of Hecke groups H(\lambda_q) is a result of Jones and Singerman, and it is frequently used here to obtain normal subgroups. It is found that when q is even, H(\lambda_q) has infinitely many normal subgroups on the sphere, while for odd q, this number is finite. The total number of normal subgroups of H(\lambda_q) on a torus is found to be either 0 or infinite. The latter case appears iff …

Fuzzy Ideals In Gamma Near-Rings, Young Bae Jun, Mehmet Sapanci, Mehmet Ali̇ Öztürk

Turkish Journal of Mathematics

The aim of this paper is to introduce the notion of fuzzy left (resp. right) ideals of \Gamma-near-rings, and to study the related properties.

A Berry-Esseen Bound For Empty Boxes Statistic On The Scheme An Allocations Of Several Type Balls, S.A. Mirakhmedov, O. Saidova

Turkish Journal of Mathematics

A Berry-Esseen bound for the number of empty cells in the scheme of independent and random allocation of balls of $s$ type into different cells is obtained.

Finite Direct Sums Of (D1)-Modules, Derya Keskin

Turkish Journal of Mathematics

In this paper we give necessary conditions for a finite direct sum of (D1)--modules to be a (D1)--module.

On Derived Equivalences And Local Structure Of Blocks Of Finite Groups, Markus Linckelmann

Turkish Journal of Mathematics

No abstract provided.

Crossed N-Cubes And N-Crossed Complexes Of Commutative Algebras, Z. Arvasi̇, M. Koçak

Turkish Journal of Mathematics

In this paper we will define crossed $\Bbb N$-cubes and n-crossed complexes of commutative algebras and construct a functor from the category of simplicial algebras to that of n-crossed complexes.

Pullbacks Of Crossed Modules And Cat^1-Groups, Murat Alp

Turkish Journal of Mathematics

In this paper, wer define the pullback cat$^{1}$-groups and we showed that the category of bullback cat$^{1}$-group is equivalent to the category of pullback crossed modules. 1991 A. M. S. C.: 13D99, 16A99, 17B99, 18D35.

Derivation Of Separable Amplitude Equations By Multiple Scales Method, Mehmet Naci̇ Özer, Dursun Eser

Turkish Journal of Mathematics

The method of multiple scales is used to derive separable nonlinear Schrödinger equations as amplitude equation from three component 2D nonlinear Klein-Gordon Equation. We further discuss the integrability of the derived separable amplitude equations and reduce them into finite dimensional Hamiltonian systems. Finally we give first integrals for the reduced systems.

The Dual Of The Bochner Space L^P(\Mu,E) For Arbitrary \Mu, Bahatti̇n Cengi̇z

Turkish Journal of Mathematics

Let $\mu$ be a finite measure, $E$ a Banach space, and $1\leq p

Direct Sums And The Schur Property, Betül Tanbay

Turkish Journal of Mathematics

It is a known fact that $\ell^1$, the dual space of the null sequences $c_0$, has the Schur property, that is, weakly convergent sequences in $\ell^1$ are norm convergent. In this paper, we prove that if $(X_{\alpha})_{\alpha\in I}$ are Banach spaces and $X=(\oplus_{\alpha\in I}X_{\alpha})_1$ their $l_1$-sum, then the space $X$ has the Schur property iff each factor $X_{\alpha}$ has it.

Random Fractals And Multifractal Measures, Kenneth E. Sunderland

Theses, Dissertations and Capstones

Much of what we call fractal geometry today can be traced to the critical years around the turn of the 19th/20th century. One of the cracks in what some had considered to be a virtually complete mathematical edifice may have been the publication in 1883 of Georg Cantor's famous "perfect and dense-in-itself' set. This set, a set of points on the real line everywhere dense in itself but nowhere dense on the line, was considered at best paradoxical and at worst monstrous. It challenged standard notions of continuity since Cantor was able to prove that there existed a one-to-one and …

Characterisations Of Slender Groups, Thomas Kelly

Masters

Chapter 1 summarises some necessary results concerning free, divisible, algebraically compact and cotorsion groups. A detailed proof of the well-known result that the Specker group P is ℵ1 free but not free is included and the structure of the quotient group P/S is determined. The basic properties of slender groups are examined and cotorsion groups of cardinality less than or equal to that of the continuum are shown to be epimorphic images of P. Chapter II presents Nunke’s characterisation of slender groups. This approach establishes that homomorphic images of the Specker group P are the direct sum of a cotorsion …

Transitive And Fully Transitive Groups, Steve Files, Brendan Goldsmith

Articles

The notions of transitivity and full transitivity for abelian p-groups were introduced by Kaplansky in the 1950s. Important classes of transitive and fully transitive p-groups were discovered by Hill, among others. Since a 1976 paper by Corner, it has been known that the two properties are independent of one another. We examine how the formation of direct sums of p-groups affects transitivity and full transitivity. In so doing, we uncover a far-reaching class of p-groups for which transitivity and full transitivity are equivalent. This result sheds light on the relationship between the two properties for all p-groups.

Stochastic Analysis Of Quality Control Charts Using Integral Equations, Kenneth Adam Scharnagl

College of Graduate Studies: Theses & Dissertations (1964–2006)

No abstract provided.

Error-Correcting Codes Associated With Generalized Hadamard Matrices Over Groups, Iem H. Heng

Mathematics & Statistics Theses & Dissertations

Classical Hadamard matrices are orthogonal matrices whose elements are ±1. It is well-known that error correcting codes having large minimum distance between codewords can be associated with these Hadamard matrices. Indeed, the success of early Mars deep-space probes was strongly dependent upon this communication technology.

The concept of Hadamard matrices with elements drawn from an Abelian group is a natural generalization of the concept. For the case in which the dimension of the matrix is q and the group consists of the p-th roots of unity, these generalized Hadamard matrices are called “Butson Hadamard Matrices BH(p, q)”, …