Mathematics Commons^™

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.

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).

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.

A Fractal Example Of A Continuous Monotone Function With Vanishing Derivatives On A Dense Set And Infinite Derivatives On Another Dense Set, Bünyami̇n Demi̇r, Vakif Dzhafarov, Şahi̇n Koçak, Mehmet Üreyen

Turkish Journal of Mathematics

Inspired by the theory of analysis on fractals, we construct an example of a continuous, monotone function on an interval, which has vanishing derivatives on a dense set and infinite derivatives on another dense set. Although such examples could be constructed by classical means of probability and measure theory, this one is more elementary and emerges naturally as a byproduct of some new fractal constructions.

On The Power Subgroups Of The Extended Modular Group \Overline{\Gamma} (Corrigendum - Turk. J. Math. 28,143-151, 2004), Recep Şahi̇n, Sebahatti̇n İki̇kardeş, Özden Koruoğlu

Turkish Journal of Mathematics

No abstract provided.

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

Turkish Journal of Mathematics

In this paper we first review the definitions of crossed module [10], pullback crossed module and cat^1-object in the category of commutative algebras. We then describe a certain pullback of cat^1- commutative algebras.

Connectedness In Isotonic Spaces, Eissa D. Habil, Khalid A. Elzenati

Turkish Journal of Mathematics

An isotonic space (X,cl) is a set X with isotonic operator cl:P(X) \to P(X) which satisfies cl(\emptyset) = \emptyset and cl(A)\subseteq cl(B) whenever A\subseteq B\subseteq X. Many properties which hold in topological spaces hold in isotonic spaces as well. The notion of connectedness that is familiar from topological spaces generalizes to isotonic spaces. We further extend the notions of Z-connectedness and strong connectedness to isotonic spaces, and we indicate the intimate relationship between these notions.

The Restriction And The Continuity Properties Of Potentials Depending On \Lambda-Distance, M. Zeki̇ Sarikaya, Hüseyi̇n Yildirim

Turkish Journal of Mathematics

In this study we establish theorems on the restriction and continuity of the generalized Riesz potentials with the non-isotropic kernels depending on \lambda-distance.

The Radius Of Starlikeness P-Valently Analytic Functions In The Unit Disc, Yaşar Polatoğlu, Meti̇n Bolcal, Arzu Şen, H. Esra Özkan

Turkish Journal of Mathematics

In the present paper we shall give the radius of starlikeness for the classes of p-valent analytic functions in the unit disc D = { z z < 1 }.

On Reduced And Semicommutative Modules, Muhi̇tti̇n Başer, Nazim Agayev

Turkish Journal of Mathematics

In this paper, various results of reduced and semicommutative rings are extended to reduced and semicommutative modules. In particular, we show: (1) For a principally quasi-Baer module, M_R is semicommutative if and only if M_R is reduced. (2) If M_R is a p.p.-module then M_R is nonsingular.

Existence Of Linear-Quadratic Regulator For Degenerate Diffusions, Md. Azizul Baten

Turkish Journal of Mathematics

This paper studies a linear regulatory quadratic control problem for degenerate Hamilton-Jacobi-Bellman (HJB) equation. We establish the existence of a unique viscosity and a classical solution of the degenerate HJB equation associated with this problem by the technique of viscosity solutions, and, hence, derive an optimal control from the optimality conditions in the HJB equation.

Two-Weight Norm Inequalities For Some Anisotropic Sublinear Operators, Yusuf Zeren, V. S. Guliyev

Turkish Journal of Mathematics

In this paper, we establish several general theorems for the boundedness of the anisotropic sublinear operators on a weighted Lebesgue space. Conditions of these theorems are satisfied by many important operators in analysis. We also give some applications the boundedness of the parabolic singular integral operators, and the maximal operators associated with them from one weighted Lebesgue space to another one. Using this results, we prove weighted embedding theorems for the anisotropic Sobolev spaces W_{\omega_0,\omega_1,...,\omega_n}^{l_1,...,l_n}(\Rn).

On Graded Weakly Prime Ideals, Shahabaddin Ebrahimi Atani

Turkish Journal of Mathematics

Let G be an arbitrary group with identity e, and let R be a G-graded commutative ring. Weakly prime ideals in a commutative ring with non-zero identity have been introduced and studied in [1]. Here we study the graded weakly prime ideals of a G-graded commutative ring. A number of results concerning graded weakly prime ideals are given. For example, we give some characterizations of graded weakly prime ideals and their homogeneous components.

Some Random Fixed Point Theorems For Non-Self Nonexpansive Random Operators, Poom Kumam, Somyot Plubtieng

Turkish Journal of Mathematics

Let (\Omega, \Sigma) be a measurable space, with \sum a sigma-algebra of subsets of \Omega, and let E be a nonempty bounded closed convex and separable subset of a Banach space X, whose characteristic of noncompact convexity is less than 1. We prove that a multivalued nonexpansive, non-self operator T: \Omega \times E \rightarrow KC(X) satisfying an inwardness condition and itself being a 1-\chi-contractive nonexpansive mapping has a random fixed point. We also prove that a multivalued nonexpansive, non-self operator T:\Omega\times E\rightarrow KC(X) with a uniformly convex X satisfying an inwardness condition has a random fixed point.

Weighted Norm Inequalities For A Class Of Rough Maximal Operators, Hussain Al-Qassem

Turkish Journal of Mathematics

We consider maximal singular integral operators arising from rough kernels satisfying an H^1-type condition on the unit (n-1)-sphere and prove weighted L^p estimates for certain radial weights. We also prove weighted L^p estimates with A_p-weights where in this case the H^1 -type condition is replaced by an L^q-type condition with q > 1. Some applications of these results are also obtained regarding singular integrals and Marcinkiewicz integrals. Our results are essential extensions and improvements of some known results.

A Note On Kaehlerian Manifolds, Nejmi̇ Cengi̇z, Ö. Tarakçi, A. A. Sali̇mov

Turkish Journal of Mathematics

The main purpose of the present paper is to study nearly Kaehlerian manifolds. We give the condition for an almost Hermitian manifold to be nearly Kaehlerian.

Local Fourier Bases And Modulation Spaces, Salti Samarah, Rania Salman

Turkish Journal of Mathematics

It is shown that local Fourier bases are unconditional bases for modulation spaces. We prove first a version of the Schur test for double sequence with mixed norm and then use it to show boundedness of the analysis operator on the modulation space M_{p,q}^w

Adaptive Finite Element Methods For Elliptic Pdes Based On Conforming Centroidal Voronoi-Delaunay Triangulations, Lili Ju, Max Gunzburger, Weidong Zhao

Faculty Publications

A new triangular mesh adaptivity algorithm for elliptic PDEs that combines a posteriori error estimation with centroidal Voronoi–Delaunay tessellations of domains in two dimensions is proposed and tested. The ability of the first ingredient to detect local regions of large error and the ability of the second ingredient to generate superior unstructured grids result in a mesh adaptivity algorithm that has several very desirable features, including the following. Errors are very well equidistributed over the triangles; at all levels of refinement, the triangles remain very well shaped, even if the grid size at any particular refinement level, when viewed globally, …

Countable Short Recursively Saturated Models Of Arithmetic, Erez Shochat

Dissertations, Theses, and Capstone Projects

Short recursively saturated models of arithmetic are exactly the elementary initial segments of recursively saturated models of arithmetic. Since any countable recursively saturated model of arithmetic has continuum many elementary initial segments which are already recursively saturated, we turn our attention to the (countably many) initial segments which are not recursively saturated. We first look at properties of countable short recursively saturated models of arithmetic and show that although these models cannot be cofinally resplendent (an expandability property slightly weaker than resplendency), these models have non-definable expansions which are still short recursively saturated.

A Solidification Phenomenon In Random Packings, L. Bowen, R. Lyons, C. Radin, P. Winkler

Dartmouth Scholarship

We prove that uniformly random packings of copies of a certain simply connected figure in the plane exhibit global connectedness at all sufficiently high densities, but not at low densities.

The Sonic Representation Of Mathematical Data, Charlie Cullen

Doctoral

Conveying data and information using non-speech audio is an ever growing field of research. Existing work has been performed investigating sonfication and its applications, and this research seeks to build upon these ideas while also suggesting new areas of potential. In this research, initial work focused on the sonification of DNA and RNA nucleotide base sequences for analysis. A case study was undertaken into the potential of rhythmic parsing of such data sequences, with test results indicating that a more effective method of representing data in a sonification was required. Sonification of complex data such as DNA and RNA was …

Multi-Dimensional Seismic Imaging Using The Inverse Scattering Series, Fang Liu, Arthur B. Weglein, Kristopher A. Innanen, Bogdan Nita

Department of Mathematics Faculty Scholarship and Creative Works

The inverse scattering series (ISS) is a comprehensive multidimensional theory for processing and inverting seismic reflection data, that may be task-separated such that meaningful sub-problems of the seismic inverse problem may be accomplished individually, each without an accurate velocity model. We describe a task-separated subseries of the ISS geared towards accurate location in depth of reflectors, in particular the mechanisms of the series that act in multiple dimensions. We show that some 2D ISS imaging terms have analogs in previously developed 1D ISS imaging theory (e.g., Weglein et al., 2002; Shaw, 2005) and others do not; the former are used …

Maldi-Tof Baseline Drift Removal Using Stochastic Bernstein Approximation, Joseph Kolibal, Daniel Howard

Faculty Publications

Stochastic Bernstein (SB) approximation can tackle the problem of baseline drift correction of instrumentation data. This is demonstrated for spectral data: matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOF) data. Two SB schemes for removing the baseline drift are presented: iterative and direct. Following an explanation of the origin of the MALDI-TOF baseline drift that sheds light on the inherent difficulty of its removal by chemical means, SB baseline drift removal is illustrated for both proteomics and genomics MALDI-TOF data sets. SB is an elegant signal processing method to obtain a numerically straightforward baseline shift removal method as it includes a …

Specific Antibodies To Recombinant Allergens Of Aspergillus Fumigatus In Cystic Fibrosis Patients With Abpa, Viswanath P. Kurup, Alan P. Knutsen, Richard B. Moss, Naveen K. Bansal

Mathematics, Statistics and Computer Science Faculty Research and Publications

Background

Aspergillus fumigatus, a widely distributed fungus, has been implicated in causing life threatening infections as well as severe asthma and allergic diseases in man. Allergic affliction like allergic bronchopulmonary aspergillosis (ABPA) is a disabling lung disease frequently seen in patients with asthma and cystic fibrosis. Immunodiagnosis of the former is comparatively easier due to the availability of purified antigens and sensitive methods. However, this is not true with cystic fibrosis patients where the prevalence of ABPA is fairly high and the morbidity and mortality are significant.

Methods

In the present study, we have evaluated purified recombinant allergens from …

The Chang-Los-Suszko Theorem In A Topological Setting, Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

The Chang-Łoś-Suszko theorem of first-order model theory characterizes universal-existential classes of models as just those elementary classes that are closed under unions of chains. This theorem can then be used to equate two model-theoretic closure conditions for elementary classes; namely unions of chains and existential substructures. In the present paper we prove a topological analogue and indicate some applications.