Physical Sciences and Mathematics Commons^™

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 …

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.

Difference Method For A Singularly Perturbed Initial Value Problem, Gabi̇l Muhammadoğlu Amiraliyev

Turkish Journal of Mathematics

In this paper we construct a completely exponentially fitted finite difference scheme for the initial value problem with small parameter by first and second derivatives. We prove the first order uniform convergence of the scheme in the sense of discrete maximum norm. Numerical results are presented.

Molecular Cavity Flow, Donald Greenspan

Mathematics Technical Papers

Using molecular mechanics, cavity flow is studied in a basin of 4235 water molecules at 15°C. Primary vortices are generated with wallspeeds [see pdf for notation]. The vortex motions agree with experimental results in the large. Fully turbulent flow is generated with wallspeed .V = 3000°A/ps. The mechanisms for primary vortex generation are clearly delineated, as are those for turbulent flow.

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

Department of Math & Statistics Faculty Publications

In this paper, we will examine the backward shift operator Lf = (f −f(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 Ϲ 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 T.

We will first discuss the backward shift on a general Banach space of analytic functions and then for the weighted …

Hadamard Difference Sets In Nonabelian 2-Groups With High Exponent, James A. Davis, Joel E. Iiams

Department of Math & Statistics Faculty Publications

Nontrivial difference sets in groups of order a power of 2 are part of the family of difference sets called Hadamard difference sets. In the abelian case, a group of order 2^{2t + 2} has a difference set if and only if the exponent of the group is less than or equal to 2^{t + 2}. In a previous work (R. A. Liebler and K. W. Smith, in “Coding Theory, Design Theory, Group Theory: Proc. of the Marshall Hall Conf.,” Wiley, New York, 1992), the authors constructed a difference set in a nonabelian group of order …

Games To Teach Mathematical Modelling, James A. Powell, J. Cangelosi, A. M. Harris

James A. Powell

We discuss the use of in-class games to create realistic situations for mathematical modelling. Two games are presented which are appropriate for use in post-calculus settings. The first game reproduces predator{prey oscillations and the second game simulates disease propagation in a mixing population. When used creatively these games encourage students to model realistic data and apply mathematical concepts to understanding the data.

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 …

Teachers And Students Investigating And Communicating About Geometry: The Math Forum, K. Ann Renninger, S. A. Weimar, Eugene A. Klotz

Educational Studies Faculty Works

No abstract provided.

Potential And Consistency For Semivalues Of Finite Cooperative Tu Games, Irinel C. Dragan

Mathematics Technical Papers

A new axiomatic characterization of the semivalues of finite cooperative n-person games with transferable utilities is given, by using a potential function. The semivalues are proved to be the unique functionals on the space of such games, which are consistent relative to a Hart/Mas Colell type of reduced game and weighted standard for two person games. The potential is also used to prove the validity of a recursive definition of semivalues, as well as the fact that the semivalues are Shapley values of the so called Power Game.

Computational Geometry Column 34, Pankaj K. Agarwal, Joseph O'Rourke

Computer Science: Faculty Publications

Problems presented at the open-problem session of the 14th Annual ACM Symposium on Computational Geometry are listed.

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.

A New Integrable Reduction Of The Coupled Nls Equation, Mehmet Naci̇ Özer

Turkish Journal of Mathematics

The method of multiple scales is used to derive a new integrable coupled nonlinear Schr\\"odinger equation (CNLS) as an amplitude equation from the coupled nonlinear Klein-Gordon Equation (CNKG). We also give the corresponding spectral problem and further reduce the derived equation into a finite dimensional integrable Hamiltonian system. Finally the integrability of the reduced system is deduced by using a perturbation analysis.

On The Discrete Squeezing Property For Semilinear Wave Equations, A. Eden, V. K. Kalantarov

Turkish Journal of Mathematics

No abstract provided.

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.

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. …

On The Cohomology Ring Of The Infinite Flag Manifold Lg/D, Cenap Özel

Turkish Journal of Mathematics

In this work, we discuss the calculation of cohomology rings of LG / T. First we describe the root system and Weyl group of LG, then we give some homotopy equivalences on the loop groups and homogeneous spaces, and investigate the cohomology ring structures of LSU_2 /T and \Omega SU_2. Also we prove that BGG-type operators correspond to partial derivation operators on the divided power algebras.

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.

Using Symbolic Dynamical Systems: A Search For Knot Invariants, Russell Clark Wheeler

Theses Digitization Project

No abstract provided.

Chief Factors And The Principal Block Of A Restricted Lie Algebra, Jorg Feldvoss

University Faculty and Staff Publications

This paper is part of the conference proceedings from the conference titled The Monster and Lie Algebras that took place during a special research quarter at the Ohio State University in the spring of 1996. This conference was sponsored by the Ohio State University Mathematical Research Institute and the National Science Foundation. The focus of the conference was groups, Lie algebras, and the Monster, with emphasis on presenting the various aspects of group theory and Lie algebra theory from a modern perspective.

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 …

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.

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

Articles

No abstract available

[Introduction To] Schaum's Outlines Fundamentals Of Computing With C++, John R. Hubbard

Bookshelf

This book is intended to be used primarily for self study, preferably in conjunction with a regular course in the fundamentals of computer science using the new ANSI/ISO Standard C++. The book covers topics from the fundamental units of the 1991 A.C.M. computing curricula.

Operations And Spectral Sequences. I, James M. Turner

University Faculty Publications and Creative Works

Using methods developed by W. Singer and J. P. May, we describe a systematic approach to showing that many spectral sequences, determined by a filtration on a complex whose homology has an action of operations, possess a compatible action of the same operations. As a consequence, we obtain \V. Singer's result for Steenrod operations on Serre spectral sequence and extend A. Bahri's action of Dyer-Lashof operations on the second quadrant Eilenberg-Moore spectral sequence.

Theorems On Three-Term Relations For Hardy Sum, Y. Şi̇mşek

Turkish Journal of Mathematics

Some three-term and mixed three-term relations for Hardy sums were given by Goldberg [7]. His proofs are based on Bernd's transformation formulae for the logarithms of the classical Theat-functions. Pettet and Sitaramachandararo [9] proved elementary proofs for all of Goldberg's results and also proved some three-term relations of Dedekind sums. In this paper, some new theorems on three-term relations for hardy sums were found by applying derivative operator to three-term polynomial relation. Furthermore, proofs of the reciprocity relations for Hardy sums are presented in a more concise way from the original proofs of Berndt [2, 3, 4] and Goldberg [7].

Dold-Kan Type Theorems For N-Types Of Simplicitial Commutative Algebras, Z. Arvasi̇, M. Koçak

Turkish Journal of Mathematics

A functor from simplicial algebras to crossed \( n \)-cubes is shown to be an embedding on a reflexive subcategory of the category of simplicial algebras that contains representatives for all \( n \) types.

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.

On Certain Varieties Of Semigroups, A. Tiefenbach

Turkish Journal of Mathematics

In this paper we generalize the class of completely regular semigroups (unions of groups) to the class of local monoids, that is the class of all semigroups where the local subsemigroups \( aSa \) are local submonoids. The sublattice of this variety \( (\mathbf{L}(\caL(\cam)) \) covers another lattice isomorphic to the lattice of all bands \( ([x^2 = x]). \) Every bundvariety \( \cau \) has as image the variety \( \Phi - \cau, \) which is the class of all semigroups, where \( \Phi \) is a \( \cau \)-congruence \( (a \Phi b \Leftrightarrow aSa = bSb). \) …

Locally Volume-Minimizing Codimension-One Foliation Of The Solid Torus, İ. Kocayusufoğlu, D. L. Jhonson

Turkish Journal of Mathematics

The aim of this paper is to construct a specific codimension-1 foliation of \( D^2 \times S^1 \) with one Reeb component, and to show that this foliation locally minimizes the volume among foliations with the boundary torus as a leaf.