Mathematics Commons^™

Oscillation Of Third-Order Nonlinear Delay Difference Equations, Mustafa Fahri̇ Aktaş, Aydin Ti̇ryaki̇, Ağacik Zafer

Turkish Journal of Mathematics

Third-order nonlinear difference equations of the form \Delta (c_n\Delta (d_n\Delta x_n))+p_n\Delta x_{n+1}+q_nf(x_{n-\sigma})=0, n\geq n_{0} are considered. Here, {c_n}, {d_n}, {p_n}, and {q_n} are sequences of positive real numbers for n_0 \in N, f is a continuous function such that f(u) /u\geq K > 0 for u \neq 0. By means of a Riccati transformation technique we obtain some new oscillation criteria. Examples are given to illustrate the importance of the results.

Simultaneous Proximinality Of Vector Valued Function Spaces, Mona Khandaqji, Fadi Awawdeh, Jamila Jawdat

Turkish Journal of Mathematics

A characterization of best simultaneous approximation of Köthe spaces of vector-valued functions is given. This characterization is a generalization of some analogous theorems for Orlicz Bochner spaces.

Hypercyclic Tuples Of The Adjoint Of The Weighted Composition Operators, Rahmat Soltani, Bahram Khani Robati, Karim Hedayatian

Turkish Journal of Mathematics

An n-tuple of commuting operators, (T_1,T_2,...,T_n) on a Hilbert space \cal H is said to be hypercyclic, if there exists a vector x \in \cal H such that the set {T_1^{k_1} T_2^{k_2}... T_n^{k_n}x : k_i \geq 0, i=1,2,...n} is dense in \cal H. In this paper, we give sufficient conditions under which the adjoint of an n-tuple of a weighted composition operator on a Hilbert space of analytic functions is hypercyclic.

Contact Cr-Warped Product Submanifolds In Generalized Sasakian Space Forms, Si̇bel Sular, Ci̇han Özgür

Turkish Journal of Mathematics

We consider a contact CR-warped product submanifold M=M_{\top} \times_fM_{\bot} of a trans-Sasakian generalized Sasakian space form \widetilde{M} (f_1,f_2,f_3). We show that M is a contact CR-product under certain conditions.

Bruhat-Chevalley Order On The Rook Monoid, Mahi̇r Bi̇len Can, Lex E. Renner

Turkish Journal of Mathematics

The rook monoid R_n is the finite monoid whose elements are the 0-1 matrices with at most one nonzero entry in each row and column. The group of invertible elements of R_n is isomorphic to the symmetric group S_n. The natural extension to R_n of the Bruhat-Chevalley ordering on the symmetric group is defined in [1]. In this paper, we find an efficient, combinatorial description of the Bruhat-Chevalley ordering on R_n. We also give a useful, combinatorial formula for the length function on R_n.

Lower Bounds For The Maximum Genus Of 4-Regular Graphs, Ding Zhou, Rongxia Hao, Weili He

Turkish Journal of Mathematics

This paper investigates the maximum genus and upper embeddability of connected 4-regular graphs. We obtain lower bounds on the maximum genus of connected 4-regular simple graphs and connected 4-regular graphs without loops in terms of the Betti number. The definition of the Betti number is referred to [Gross and Tucker, Topological Graph Theory, New York, 1987]. Furthermore, we give examples that show that these lower bounds are tight.

Extensions And S-Comparability Of Exchange Rings, Chaoling Huang

Turkish Journal of Mathematics

Let S be a ring extension of R. In this note, for any positive integer s we study s-comparability related to ring extensions. We show that if S is an excellent extension of R, R and S are exchange rings, and R has the n-unperforation property. R satisfies s-comparability if and we only if so does S, and we prove that for a 2-sided ideal J of S, and an exchange subring R of the exchange ring S, which contains J as a direct summand, then R satisfies s-comparability if and only if so does R/J.

Multiplication Modules With Krull Dimension, Mahmood Behboodi, Maryam Molakarimi

Turkish Journal of Mathematics

In ring theory, it is shown that a commutative ring R with Krull dimension has classical Krull dimension and satisfies k.dim(R)=cl.k.dim(R). Moreover, R has only a finite number of distinct minimal prime ideals and some finite product of the minimal primes is zero (see Gordon and Robson [9, Theorem 8.12, Corollary 8.14, and Proposition 7.3]). In this paper, we give a generalization of these facts for multiplication modules over commutative rings. Actually, among other results, we prove that if M is a multiplication R-module with Krull dimension, then: (i) M is finitely generated, (ii) R has finitely many minimal prime …

Structure Theory Of Central Simple Z_D-Graded Algebras, Cemal Koç, Yosum Kurtulmaz

Turkish Journal of Mathematics

This paper investigates the structure theory of Z_d-central simple graded algebras and gives the complete decomposition into building block algebras. The results are also applied to generalized Clifford algebras, which are motivating examples of Z_d-central simple graded algebras.

Best Constants In Second-Order Sobolev Inequalities On Compact Riemannian Manifolds In The Presence Of Symmetries, Mohammed Ali

Turkish Journal of Mathematics

Let (M,g) be a smooth compact 3\leq n-dimensional Riemannian manifold, and G a subgroup of the isometry group of (M,g). We establish the best constants in second-order for a Sobolev inequality when the functions are G-invariant.

On Similarity Of Powers Of Shift Operators, Masoumeh Faghih Ahmadi, Karim Hedayatian

Turkish Journal of Mathematics

Let M_z and B denote, respectively, the multiplication operator and the backward shift operator on a weighted Hardy space. We present sufficient conditions so that M_{z^n} is similar to \bigoplus_1^nM_z, and B^n is similar to \bigoplus_1^nB. The first part generalizes a result obtained by Yucheng Li.

Flat Surfaces In The Minkowski Space E^3_1 With Pointwise 1-Type Gauss Map, Uğur Dursun, Emel Coşkun

Turkish Journal of Mathematics

In this article, we obtain all nonplanar cylindrical surfaces in the Minkowski space E^3_1 with pointwise 1-type Gauss map of the second kind. We also prove that right circular cones and hyperbolic cones in E^3_1 are the only cones in E^3_1 with pointwise 1-type Gauss map of the second kind. We conclude that there is no tangent developable surface fully lying in E^3_1 with pointwise 1-type Gauss map of the second kind.

Pointwise Slant Submanifolds In Almost Hermitian Manifolds, Bang-Yen Chen, Oscar J. Garay

Turkish Journal of Mathematics

An interesting class of submanifolds of almost Hermitian manifolds (\tilde M,\tilde g,J) is the class of slant submanifolds. Slant submanifolds were introduced by the first author in [6] as submanifolds M of (\tilde M,\tilde g,J) such that, for any nonzero vector X \in T_pM, p \in M, the angle \theta(X) between JX and the tangent space T_pM is independent of the choice of p\in M and X \in T_pM. The first results on slant submanifolds were summarized in the book [7]. Since then slant submanifolds have been studied by many geometers. Many nice results on slant submanifolds have been obtained …

An Identity Between The M-Spotty Weight Enumerators Of A Linear Code And Its Dual, İrfan Şi̇ap

Turkish Journal of Mathematics

The m-spotty byte error control codes provide a good source for detecting and correcting errors in semiconductor memory systems using high density RAM chips with wide I/O data (e.g. 8, 16, or 32 bits). m-spotty byte error control codes are very suitable for burst correction. Here, we introduce the m-spotty weights and m-spotty weight enumerator of linear codes over the ring F_2+uF_2 and prove a MacWilliams type identity.

Tensor Products Of Vector Seminormed Spaces, John William Dever

Electronic Theses and Dissertations

A vector seminormed space is a triple consisting of a vector space, a Dedekind complete Riesz space, and a vector valued seminorm, called a vector seminorm, defined on the vector space and taking values in the Riesz space. The collection of vector seminormed spaces with suitably defined morphisms is shown to be a category containing finite products. A theory of vector seminorms on the tensor products of vector seminormed spaces is developed in analogy with the theory of tensor products of Banach spaces. Accordingly, a reasonable cross vector seminorm, or simply tensor seminorm, is defined such that a vector seminorm …

Characterizations Of Zero Divisor Graphs Determined By Equivalence Classes Of Zero Divisors, Amanda Catherine Acosta

Electronic Theses and Dissertations

We study zero divisor graphs of commutative rings determined by equivalence classes of zero divisors, specifically for a Noetherian ring R. We study the classification of these graphs. Specifically, we add more criteria to the list of characterizations that disqualify a graph as the zero divisor graph of a ring. We also briefly discuss Sage, a mathematical software, which was an aid in providing visual pictures for the graphs under study.

Π/2-Angle Yao Graphs Are Spanners, Prosenjit Bose, Mirela Damian, Karim Douïeb, Joseph O'Rourke, Ben Seamone, Michiel Smid, Stefanie Wuhrer

Computer Science: Faculty Publications

We show that the Yao graph Y₄ in the L₂ metric is a spanner with stretch factor 8(29+23√ 2). Enroute to this, we also show that the Yao graph Y^∞₄ in the L_∞ metric is a planar spanner with stretch factor 8.

New Results In Finite Geometries Pertaining To Albert-Like Semifields, Angela Michelle Brown

Mathematics Dissertations - Archive

One of the most widely studied class of semifields are the generalized twisted fields defined by Albert in the 50s and 60s. The collineation groups of generalized twisted field planes have been completely described. In a series of papers Cordero and Figueroa studied semifields with an autotopism that acts transitively on one side of the autotopism triangle, equivalently the plane admits an autotopism which induces a permutation on a side of the autotopism triangle of order a p-primitive divisor of pr - 1. They showed that with some minor exceptions the plane is a generalized twisted field plane. These planes …

Bad Boundary Behavior In Star Invariant Subspaces Ii, William T. Ross, Andreas Hartmann

Department of Math & Statistics Faculty Publications

We continue our study begun in [HR11] concerning the radial growth of functions in the model spaces (IH²)^⊥.

Characterizations Of Certain Continuous Univariate Distributions Based On The Conditional Distribution Of Generalized Order Statistics, M. Ahsanullah, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

The problem of characterizing probability distributions is an interesting problem which has recently attracted the attention of many researchers. Various characterization results have been established in different directions as reported in the literature. We present here, various characterizations of certain univariate continuous distributions based on the conditional distribution of generalized order statistics.

Boundary Values In Range Spaces Of Co-Analytic Truncated Toeplitz Operator, William T. Ross, Andreas Hartmann

Department of Math & Statistics Faculty Publications

Functions in backward shift invariant subspaces have nice analytic continuation properties outside the spectrum of the inner function defining the space. Inside the spectrum of the inner function, Ahern and Clark showed that under some distribution condition on the zeros and the singular measure of the inner function, it is possible to obtain non-tangential boundary values of every function in the backward shift invariant subspace as well as for their derivatives up to a certain order. Here we will investigate, at least when the inner function is a Blaschke product, the non-tangential boundary values of the functions of the backward …

Connected Inverse Limits With A Set-Valued Function, Van C. Nall

Department of Math & Statistics Faculty Publications

In this paper we provide techniques to build set-valued functions whose resulting inverse limits will be connected.

A Direct D-Bar Reconstruction Algorithm For Recovering A Complex Conductivity In 2d, Sarah J. Hamilton, C. N. L. Herrera, J. L. Mueller, A. Von Herrmann

Mathematics, Statistics and Computer Science Faculty Research and Publications

A direct reconstruction algorithm for complex conductivities in W^{2, ∞}(Ω), where Ω is a bounded, simply connected Lipschitz domain in R² , is presented. The framework is based on the uniqueness proof by Francini (2000 Inverse Problems 6 107–19), but equations relating the Dirichlet-to-Neumann to the scattering transform and the exponentially growing solutions are not present in that work, and are derived here. The algorithm constitutes the first D-bar method for the reconstruction of conductivities and permittivities in two dimensions. Reconstructions of numerically simulated chest phantoms with discontinuities at the organ boundaries are included.

Modeling Temporal Pattern And Event Detection Using Hidden Markov Model With Application To A Sludge Bulking Data, Naveen K. Bansal, Xin Feng, Wenjing Zhang, Wutao Wi, Yuanhao Zhao

Mathematics, Statistics and Computer Science Faculty Research and Publications

This paper discusses a method of modeling temporal pattern and event detection based on Hidden Markov Model (HMM) for a continuous time series data. We also provide methods for checking model adequacy and predicting future events. These methods are applied to a real example of sludge bulking data for detecting sludge bulking for a water plant in Chicago.

Composition Operators On A Class Of Analytic Function Spaces Related To Brennan's Conjecture, Valentin Matache, Wayne Smith

Mathematics Faculty Publications

Brennan’s conjecture in univalent function theory states that if τ is any analytic univalent transform of the open unit disk D onto a simply connected domain G and −1/3 < p < 1, then 1/(τ′) p belongs to the Hilbert Bergman space of all analytic square integrable functions with respect to the area measure. We introduce a class of analytic function spaces L2a(μp) on G and prove that Brennan’s conjecture is equivalent to the existence of compact composition operators on these spaces for every simply connected domain G and all p∈(−1/3,1) . Motivated by this result, we study the boundedness and compactness of composition operators in this setting.

A Generalized Cholera Model And Epidemic-Endemic Analysis, Jin Wang, Shu Liao

Mathematics & Statistics Faculty Publications

The transmission of cholera involves both human-to-human and environment-to-human pathways that complicate its dynamics. In this paper, we present a new and unified deterministic model that incorporates a general incidence rate and a general formulation of the pathogen concentration to analyse the dynamics of cholera. Particularly, this work unifies many existing cholera models proposed by different authors. We conduct equilibrium analysis to carefully study the complex epidemic and endemic behaviour of the disease. Our results show that despite the incorporation of the environmental component, there exists a forward transcritical bifurcation at R₀ = 1 for the combined human-environment epidemiological …

Protection By 20-5,14-Hedge Against Surgically-Induced Ischemia Reperfusion Lung Injury In Rats, Irshad Ali, Stephanie Gruenloh, Ying Gao, Anne V. Clough, John R. Falck, Meetha Medhora, Elizabeth R. Jacobs

Mathematics, Statistics and Computer Science Faculty Research and Publications

Background

We previously reported that the cytochrome P450 product 20-hydroxyeicosatetraenoic acid has prosurvival effects in pulmonary artery endothelial cells and ex vivo pulmonary arteries. We tested the potential of a 20-hydroxyeicosatetraenoic acid analog N-[20-hydroxyeicosa-5(Z),14(Z)-dienoyl]glycine (20-5,14-HEDGE) to protect against lung ischemic reperfusion injury in rats. Furthermore, we examined activation of innate immune system components, high mobility group box 1 (HMGB1) and toll-like receptor 4 (TLR4), in this model as well as the effect of 20-5,14-HEDGE on this signaling pathway.

Methods

Sprague-Dawley rats treated with 20-5,14-HEDGE or vehicle were subjected to surgically induced, unilateral lung ischemia for 60 minutes followed by reperfusion …

Abel Dynamic Equations Of The First And Second Kind, Sabrina Heike Streipert

Masters Theses

"In this work, we study Abel dynamic equations of the first and the second kind. After a brief introduction to time scales, we introduce the Abel differential equations of the first and the second kind, as well as the canonical Abel form in the continuous case. Using the existing information, we derive novel results for time scales. We provide formulas for the Abel dynamic equations of the second kind and present a solution method. We furthermore achieve a special class of Abel equations of the first kind and discuss the canonical Abel equation. We get relations between common dynamic equations …

Homogeneous Besov Spaces On Stratified Lie Groups And Their Wavelet Characterization, Hartmut Fuhr, Azita Mayeli

Publications and Research

We establish wavelet characterizations of homogeneous Besov spaces on stratified Lie groups, bothin terms of continuous and discrete wavelet systems. We first introduce a notion of homogeneous Besov space ̇Bsp,qin terms of a Littlewood-Paley-type decomposition, in analogy to the well-known characterization of the Euclidean case. Such decompositions can be defined via the spectral measure of a suitably chosen sub-Laplacian. We prove that the scale of Besov spaces is independent of the precise choice of Littlewood-Paley decomposition. In particular, different sub-Laplacians yield the same Besov spaces. We then turn to wavelet characterizations, first via continuous wavelet transforms which can be viewed …

Equivariant Degenerations Of Spherical Modules For Groups Of Type A, Stavros Argyrios Papadakis, Bart Van Steirteghem

Publications and Research

Let G be a complex reductive algebraic group. Fix a Borel subgroup B of G and a maximal torus T in B. Call the monoid of dominant weights L+ and let S be a finitely generated submonoid of L+. V. Alexeev and M. Brion introduced a moduli scheme MS which classifies affine G-varieties X equipped with a T-equivariant isomorphism SpecC[X]U → SpecC[S], where U is the unipotent radical of B. Examples of MS have been obtained by S. Jansou, P. Bravi and S. Cupit-Foutou. In this paper, we prove that MS is isomorphic to an affine space when S is …