Mathematics Commons^™

Formula For The Highly Regularized Trace Of The Sturm-Liouville Operator With Unbounded Operator Coefficients Having Singularity, İnci̇ Albayrak, Oya Baykal, Erdal Gül

Turkish Journal of Mathematics

In this work, a formula for the n^{th} regularized trace of the Sturm-Liouville operator with unbounded operator coefficients having singularity is obtained

Inequalities For The Vibrating Clamped Plate Problem, Kimberley Mchale, Ünal Ufuktepe

Turkish Journal of Mathematics

We study the eigenvalues of the vibrating clamped plate problem. We have made improvements on the bounds of the ratios of the eigenvalues of the biharmonic operator (clamped plate) using the methods of Payne, Polya, and Weinberger. The difference in our proof lies mainly with the trial functions and the orthogonality arguments. While Payne, Polya, and Weinberger and Hile and Yeh project away components along u_1,u_2,...,u_k to meet the orthogonality conditions,we use a translation/rotation argument to meet these conditions.

On The Expansions In Eigenfunctions Of Hill's Operator, Fi̇li̇z Aras, Gusei̇n Sh Gusei̇nov

Turkish Journal of Mathematics

In this paper we show how one can deduce the Titchmarsh expansion formula in eigenfunctions of Hill's operator from the Gel'fand expansion formula.

Global Convergence For Discrete Dynamical Systems And Forward Neural Networks, Asuman G. Aksoy, Mario Martelli

Turkish Journal of Mathematics

Using a theoretical result regarding the global stability of discrete dynamical systems of lower triangular form, we establish convergence properties of forward neural networks when the neuron response functions fail to be continuous.

On Modified Baskakov Operators On Weighted Spaces, Nurhayat İspi̇r

Turkish Journal of Mathematics

The author presents a modification of the Baskakov operator for the intervals [0,b_{n}], where b_{n} is an increasing sequence of positive numbers with either finite or infinite limit. Convergence properties of such an operator for continuous and differentiable functions in weighted space are established.

On The Centroid Of The Prime Gamma Rings Ii, Mehmet Ali̇ Öztürk, Young Bae Jun

Turkish Journal of Mathematics

The aim of this paper is to study the properities of the extended centroid of the prime \Gamma-rings. Main results are the following theorems: (1) Let M be a simple \Gamma-ring with unity. Suppose that for some a\neq 0 in M we have a\gamma_{1} x\gamma_{2} a\beta_{1} y\beta_{2}a = a\beta_{1} y\beta_{2} a\gamma_{1} x\gamma_{2}a for all x, y\in M and \gamma_{1} ,\gamma_{2} ,\beta_{1} ,\beta_{2} \in \Gamma. Then M is isomorphic onto the \Gamma-ring D_{n,m}, where D_{n,m} is the additive abelian group of all rectangular matrices of type n\times m over a division ring D and \Gamma is a nonzero subgroup of the …

A Perturbed Version Of The Ostrowski Inequality For Twice Differentiable Mappings, A. Sofo, S. S. Dragomir

Turkish Journal of Mathematics

A generalisation of a perturbed version of the Ostrowski inequality for twice differentiable mappings is studied. It is shown that the error bounds are better than those obtained previously. Applications for general quadrature formulae are also given.

On Qr-Submanifolds Of A Quaternionic Space Form, Bayram Şahi̇n

Turkish Journal of Mathematics

In this paper, we investigate mixed QR-submanifolds in a quaternionic space form and pseudo umbilical QR-submanifold of a quaternionic space form under some additional condition. Finally we give a necessary condition for QR-submanifold of a quaternion Kaehler manifold such that \dim \upsilon ^{\perp }=1 to be a 3-quasi Sasakian Manifold.

Characterizations Of Matroid Via Ofr-Sets, Talal Ali̇ Al-Hawary

Turkish Journal of Mathematics

The aim of this paper is to introduce the class of OFR-sets as the sets that are the intersection of an open set and a feeble-regular set. Several classes of matroids are studied via the new concept. New decompositions of strong maps are provided.

Fuzzy Maximal Ideals Of Gamma Near-Rings, Young Bae Yun, Kyung Ho Kim, Mehmet Ali̇ Öztürk

Turkish Journal of Mathematics

Fuzzy maximal ideals and complete normal fuzzy ideals in \Gamma-near-rings are considered, and related properties are investigated.

A General Fixed Point Theorem For Weakly Compatible Mappings In Compact Metric Spaces, Valeriu Popa

Turkish Journal of Mathematics

A general fixed point theorem for weakly compatible mappings satisfying an implicit relation in compact metric spaces is proved generalizing the results by [1],[3],[13],[14] and others.

Some Applications Of The Lattice Finite Representability In Spaces Of Measurable Functions, P. Gomez Palaci̇o, J. A. Lopez Molina, M. J. Rivera

Turkish Journal of Mathematics

We study the lattice finite representability of the Bochner space L_p(\mu_1,L_q(\mu_2)) in \ell_p{\ell_q}, 1 \le p,q < \infty, and then we characterize the ideal of the operators which factor through a lattice homomorphism between L_{\infty}(\mu) and L_p(\mu_1,L_q(\mu_2)).

Diagonal Lift In The Cotangent Bundle And Its Applications, Sezgi̇n Akbulut, Murat Özdemi̇r, Ari̇f A. Salimov

Turkish Journal of Mathematics

The purpose of this paper is to define a diagonal lift ^{\mathcal{D }}g of a Riemannian metric g of a manifold M_{n} to the cotangent bundle T^{*}(M_{n}) of M_{n}, to associate with ^{\mathcal{D}}g an Levi-Civita connection of T^{*}(M_{n}) in a natural way and to investigate applications of the diagonal lifts.

Absolutely Representing Systems Of Exponentials In The Spaces Of Infinitely-Differentiable Functions And Extendability In The Sense Of Whitney, Yu. F. Korobeinik

Turkish Journal of Mathematics

Let Q be a compactum in~\mathbb{R}^p, p\geqslant1, such that int Q\neq\varnothing and Q=\overline{ int Q}. Denote by C^{\infty}[Q] the space of functions from C^{\infty}( int Q) uniformly continuous in int Q together with all their partial derivatives. The conditions of the existence of absolutely representing systems of exponentials with purely imaginary exponents in the space C^{\infty}[Q] and some of its subspaces of Denjoy--Carleman type are investigated. It is also proved under rather general assumptions that there is no such absolutely representing systems in the space E(G)=\operatornamewithlimits{proj}\limits_ {\overleftarrow {Q\in \mathcal{F}_G}}E[Q] where G is an arbitrary open set in~\mathbb{R}^p, E[Q] is C^{\infty}[Q] …

L^P Boundedness Of A Class Of Singular Integral Operators With Rough Kernels, Ahmad Al-Salman, Hussain Al-Quassem

Turkish Journal of Mathematics

In this paper, we study the L^p mapping properties of singular integral operators with kernels belonging to certain block spaces. These operators have singularities along sets of the form {x=\Phi ( y )y^'} where \Phi satisfies certain growth conditions. Our results improve as well as extend previously known results on singular integrals.

On The Lebesgue Measure Of Self-Affine Sets, İbrahi̇m Kirat

Turkish Journal of Mathematics

Flaherty and Wang studied Haar-type multiwavelets and multi-tiles. The information on what digit sets give multi-attractors with positive Lebesgue measure is very limited. In this note, we give a few classes of digit sets leading to multi-attractors with positive measure. The attractors we obtain include the Haar-type multi-tiles of Flaherty and Wang.

On An Application Of The Hardy Classes To The Riemann Zeta-Function, K. Ilgar Eroglu, Iossif V. Ostrovskii

Turkish Journal of Mathematics

We show that the function f(z) : = \frac{z}{1-z} \zeta (\frac{1}{1-z}), z < 1, belongs to the Hardy class H_{p} if and only if 0 < p < 1.

Tangent Lines Of Generalized Regular Curves Parametrized By Time Scales, Gusei̇n Gusei̇nov, Emi̇n Özyilmaz

Turkish Journal of Mathematics

In this paper a generalization of the notion of regular curve is introduced. For such curves the concept of tangent line is investigated.

Locally 1-To-1 Maps And 2-To-1 Retractions, Jo Heath, Van C. Nall

Department of Math & Statistics Faculty Publications

This paper considers the question of which continua are 2-to-1 retracts of continua.

The Multiplicities Of A Dual-Thin Q-Polynomial Association Scheme, Bruce E. Sagen, John S. Caughman Iv

Mathematics and Statistics Faculty Publications and Presentations

Let Y=(X,{Ri}1≤i≤D) denote a symmetric association scheme, and assume that Y is Q-polynomial with respect to an ordering E₀,...,E_D of the primitive idempotents. Bannai and Ito conjectured that the associated sequence of multiplicities mi (0≤i≤D) of Yis unimodal. Talking to Terwilliger, Stanton made the related conjecture that mi≤mi+1 and mi≤mD−i for i<D/2. We prove that if Y is dual-thin in the sense of Terwilliger, then the …

Biharmonic Maps On V-Manifolds, Yuan-Jen Chiang, Hongan Sun

Mathematics Articles

We generalize biharmonic maps between Riemannian manifolds into the case of the domain being V-manifolds. We obtain the first and second variations of biharmonic maps on V-manifolds. Since a biharmonic map from a compact V-manifold into a Riemannian manifold of nonpositive curvature is harmonic, we construct a biharmonic non-harmonic map into a sphere. We also show that under certain condition the biharmonic property of f implies the harmonic property of f. We finally discuss the composition of biharmonic maps on V-manifolds.

Nested Balanced Incomplete Block Designs, J. P. Morgan, D. A. Preece, D. H. Rees

Mathematics & Statistics Faculty Publications

If the blocks of a balanced incomplete block design (BIBD) with v treatments and with parameters (v; b₁;r;k₁) are each partitioned into sub-blocks of size k₂, and the b₂ =b₁k₁=k2 sub-blocks themselves constitute a BIBD with parameters (v; b₂;r;k₂), then the system of blocks, sub-blocks and treatments is, by de4nition, a nested BIBD (NBIBD). Whist tournaments are special types of NBIBD with k₁ =2k₂= 4. Although NBIBDs were introduced in the statistical literature in 1967 and have subsequently received occasional attention there, …

Numerical Ranges Of Composition Operators, Valentin Matache

Mathematics Faculty Publications

Composition operators on the Hilbert Hardy space of the unit disk are considered. The shape of their numerical range is determined in the case when the symbol of the composition operator is a monomial or an inner function fixing 0. Several results on the numerical range of composition operators of arbitrary symbol are obtained. It is proved that 1 is an extreme boundary point if and only if 0 is a fixed point of the symbol. If 0 is not a fixed point of the symbol 1 is shown to be interior to the numerical range. Some composition operators whose …

Iteration Of Λ-Complete Forcing Notions Not Collapsing Λ+, Andrzej Roslanowski

Mathematics Faculty Publications

We look for a parallel to the notion of “proper forcing” among λ-complete forcing notions not collapsing λ+. We suggest such a definition and prove that it is preserved by suitable iterations.

Scintillation Behind The Collecting Lens Of A Receiver, Clarissa A. Fleming Russell

Retrospective Theses and Dissertations

One of the negative effects that a laser beam experiences as it propagates through the atmosphere is intensity fluctuations or scintillation. Because scintillation-- as it pertains to laser radar and laser satellite communication systems-- is the main subject of this research, the assumption of an optical element ( such as a Gaussian lens) along the propagation path in front of the detector is valid. The mathematical addition of optical elements to the propagation path is treated using the ABCD ray matrix method. The expression for scintillation is derived, analyzed, and numerically calculated for positions to the left and right of …

The Problem Of A Viscoelastic Cylinder Rolling On A Rigid Half-Space, John Murrough Golden, G.A.C. Graham

Articles

The problem of a viscoelastic cylinder rolling on a rigid base, propelled by a line force acting at its centre, is solved in the noninertial approximation. The method used is based on a decomposition of hereditary integrals developed by the authors in previous work, and on the viscoelastic Kolosov-Muskhelishvili equations which are used to generate a Hilbert problem. In this formulation, the problem reduces to a nonsingular integral equation in space and time, which simplifies under steady-state conditions and for exponential decay materials, to algebraic form. There are also two subsidiary conditions.

In the case of a standard linear model, …

Topologically Pure Extensions, Peter Loth

Mathematics Faculty Publications

A proper short exact sequence 0→H →G→K→0 (*) in the category of locally compact abelian groups is said to be topologically pure if the induced sequence 0→nH→nG→nK→0 is proper short exact for all positive integers n. Some characterizations of topologically pure sequences in terms of direct decompositions, pure extensions and tensor products are established. A simple proof is given for a theorem on pure subgroups by Hartman and Hulanickl. Using topologically pure extensions, we characterize those splitting locally compact abelian groups whose torsion part is a direct sum of a compact …

Asymptotic Inference In Censored Regression Models Revisited, Chihwa Kao

Center for Policy Research

This paper establishes that regressors in the models with censored dependent variables need not be bounded for the standard asymptotic results to apply. Thus, regressors that grow monotonically with the observation index may be acceptable. It also purports to provide an upper bound on the rate at which regressors may grow.

Heckman's Methodology For Correcting Selectivity Bias : An Application To Road Crash Costs, Margaret Giles

Research outputs pre 2011

Aggregate road crash costs are traditionally determined using average costs applied to incidence figures found in Police-notified crash data. Such data only comprise a non-random sample of the true population of road crashes, the bias being due to the existence of crashes that are not notified to the Police. The traditional approach is to label the Police-notified sample as 'non-random' thereby casting a cloud over data analyses using this sample. Heckman however viewed similar problems as 'omitted variables' problems in that the exclusion of some observations in a systematic manner (so-called selectivity bias) has inadvertently introduced the need for an …

On The Evolution Of Probability-Weighting Function And Its Impact On Gambling, Steven Li, Yun Hsing Cheung

Research outputs pre 2011

It is well known that individuals treat losses and gains differently and there exists non-linearity in probability. The asymmetry between gains and losses is highlighted by the reflection effect. The non-linearity in probability is described by the curvature of the probability-weighting function. This paper studies the evolution of the probability-weighting function. It is assumed that the probability weighting for an individual follows a mean-reverting stochastic process. The Monte Carlo simulation technique is employed to study the evolution of the weighting function. The evolution of the probability- weighting function implies that an individual does not treat gains or losses consistently over …