Digital Commons Network^™

Weighted Ergodic Averages, M.D. Ha

Turkish Journal of Mathematics

Let $(X, {\cal F}, \lambda)$ be the unit circle $\Bbb S^1 = \{z \in \Bbb C : z = 1\}$ with the usual $\sigma$-algebra ${\cal F}$ of Lebesgue measurable subsets and the normalized Lebesgue measure $\lambda$. Consider a sequence $\nu_n: \Bbb N \ra \Bbb R, \;\; \nu_n(k) \geq 0, \;\; \Sigma^{\infty}_{k=1} \nu_n(k) = 1$. For any measure-preserving $\tau : X \ra X$, this sequence induces a sequence $(T_n)^{\infty}_1$ of bounded, linear operators on $L^p(X), \;\; 1 \leq p \leq \infty$, by defining \[ T_n f = \sum^{\infty}_{k=1} \nu_n(k) \; f \circ \tau^k, \quad n = 1, 2, \ldots . \] …

Cess-Modules, Cesim Çelik

Turkish Journal of Mathematics

In this paper, we investigate generalizations of CS-modules, namely CESS-modules, weak CS-modules and modules satisfying a condition (P). Several results are given to show the relationships between the classes of these modules.

The Non Uniform Bounds Of Remainder Term In Clt For The Sum Of Functions Of Uniform Spacings, S. Mirakhmedov, U. Kalandarov

Turkish Journal of Mathematics

The non uniform bound of the remainder in the central limit theorem for the sums of functions of uniform spacings is established. The bound depend on the moments of functions of the standard exponential random variables.

A Combinatorial Definition Of N-Types Of Simplicial Commutative Algebras, Z. Arvasi, M. Koçak, M. Alp

Turkish Journal of Mathematics

In this paper, we will give a description of the functor from the category of crossed $n$-cubes to that of simplicial commutative algebras and study a commutative algebra version of Loday's theorem on $n$-types of simplicial groups.

The Norm In Taxicab Geometry, Cumali̇ Eki̇ci̇, I. Kocayusufoğlu, Z. Akça

Turkish Journal of Mathematics

In this paper, we will define the inner-product and the norm in taxicab geometry and then we will discuss this inner-product geometrically.

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.

Error Estimation Of The Padé Approximation Of Transfer Functions Via The Lanczos Process, Zhaojun Bai, Qiang Ye

Mathematics Faculty Publications

Krylov subspace based moment matching algorithms, such as PVL (Padé approximation Via the Lanczos process), have emerged as popular tools for efficient analyses of the impulse response in a large linear circuit. In this work, a new derivation of the PVL algorithm is presented from the matrix point of view. This approach simplifies the mathematical theory and derivation of the algorithm. Moreover, an explicit formulation of the approximation error of the PVL algorithm is given. With this error expression, one may implement the PVL algorithm that adaptively determines the number of Lanczos steps required to satisfy a prescribed error tolerance. …

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 \( (a \Phi b \Leftrightarrow aSa = bSb). \) …

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].

On The Action Of Steenrod Operations On Polynomial Algebras, İ. Karaca

Turkish Journal of Mathematics

Let \( \bba \) be the mod-\( p \) Steenrod Algebra. Let \( p \) be an odd prime number and \( Z_{p} = Z/pZ \). Let \( P_{s} = Z_{p} [x_{1},x_{2},\ldots,x_{s}]. \) A polynomial \( N \in P_{s} \) is said to be hit if it is in the image of the action \( A \otimes P_{s} \ra P_{s}. \) In [10] for \( p=2, \) Wood showed that if \( \a(d+s) > s \) then every polynomial of degree \( d \) in \( P_{s} \) is hit where \( \a(d+s) \) denotes the number of ones in the …

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.

From Simplicial Groups To Crossed Complexes, Z. Arvasi̇

Turkish Journal of Mathematics

In this paper, we will give a short proof of the construction of the crossed complex of groups by using the higher order Peiffer elements.

On The Validity Of The Borel-Hirzebruch Formula For Topological Actions, D. Dönmez

Turkish Journal of Mathematics

We defined an equivalence among group actions and find sufficient conditions for actions of compact connected Lie groups on Euclidean spaces for which the topological version of the Borel-Hirzebruch formula holds.

On The Parabolic Class Number Of Some Subgroups Of Hecke Groups, R. Keski̇n

Turkish Journal of Mathematics

In this paper we calculate the parabolic class number of subgroups of Hecke groups ( H(\sqrt{2}), H (\sqrt{3}) ).

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.

Codes On Superelliptic Curves, F. Özbudak, M. Glukhov

Turkish Journal of Mathematics

The purpose of this paper is to apply superelliptic curves with a lot of rational points to construct rather good geometric Goppa codes.

Dynamical System Topology Preserved In The Presence Of Noise, Judy A. Kennedy, James A. Yorke

Turkish Journal of Mathematics

We first give a precise definition of the terms ``topological horseshoe'' and ``generalized quadrilateral'' and then examine the behavior of a homeomorphism F on a locally compact, separable, locally connected metric space X (X is usually a manifold in applications) such that F restricted to some generalized quadrilateral Q in X is a topological horseshoe map. For a set Q \subset X we define and describe (1) the permanent set Z of Q to be \{x\in X:F^n(x)\in Q for all integers n\}, and (2) the entrainment set of Q to be E(Q)=\{x\in X: F^{-n} (x)\in Q for all sufficiently large …

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.

On 3 Dimensional Isotropic Submaniolds Of A Space From, Takehiro Itoh, Koichi Ogiue

Turkish Journal of Mathematics

We study 3-dimensional isotropic submanifolds of a space form with low-dimensional first normal space

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.

A Version Of A Theorem Of Dahlberg For The Subelliptic Dirichlet Problem, Luca Capogna, Nicola Garofalo, Duy Minh Nhieu

Mathematics Sciences: Faculty Publications

No abstract provided.

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.

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 …

A Comparison Of Advanced Time Series Models For Environmental Dependent Stock Recruitment Of The Western Rock Lobster, Saarah A. Farag

Theses: Doctorates and Masters

Time series models have been applied in many areas including economics, stuck recruitment and the environment. Most environmental time series involve highly correlated dependent variables, which makes it difficult to apply conventional regression analysis, Traditionally, regression analysis has been applied to the environmental dependent stock and recruitment relationships for crustacean species in Western Australian fisheries. Alternative models, such as transfer function models and state space models have the potential to provide unproved forecasts for these types of data sets. This dissertation will explore the application of regression models, transfer function models, and state space models to modelling the puerulus stage …

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 …

Generalized Inverse Estimator And Comparison With Least Squares Estimator, S. Sakallıoğlu, F. Akdeniz

Turkish Journal of Mathematics

Trenkler [13] described an iteration estimator. This estimator is defined as follows: for $0 < \gamma < 1/\lambda_i \max$ \[ \hat{\beta}_{m, \gamma} = \gamma \sum^m_{i=0} (1-\gamma X'X)^i X'y , \] where $\lambda_i$ are eigenvalues of $X'X$. In this paper a new estimator (generalized inverse estimator) is introduced based on the results of Tewarson [11]. A sufficient condition for the difference of mean square error matrices of least squares estimator and generalized inverse estimator to be positive definite (p.d.) is derived.

Cyclic Cutwidth Of Three Dimensional Cubes, Ray N. Gregory

Theses Digitization Project

No abstract provided.

The Eigenfunctions Of A Certain Composition Operator, Valentin Matache

Mathematics Faculty Publications

The composition operator on the classical Hardy space H2, induced by a hyperbolic disk automorphism is considered. It is investigated when a H2-function induces under the given operator a minimal invariant cyclic subspace. Theorems where we use the behaviour of this function in the neighbourhood of the fixed points of the hyperbolic automorphism in order to decide if the cyclic subspace mentioned above is minimal invariant or not, are obtained. The inner eigenfunctions of the operator under consideration are characterized.