Mathematics Commons^™

Sharp Bounds For The First Nonzero Steklov Eigenvalues For$F$-Laplacians, Guangyue Huang, Bingqing Ma

Turkish Journal of Mathematics

Let $M$ be an $n$-dimensional compact Riemannian manifold with a boundary. In this paper, we consider the Steklov first eigenvalue with respect to the $f$-divergence form: $$ e^{f}{\rm div}(e^{-f}A\nabla u)=0\ {\rm in}\ \ M, \ \ \ \ \ \langle A(\nabla u),\nu\rangle-\eta u=0 \ \ {\rm on}\ \partial M,$$ where $A$ is a smooth symmetric and positive definite endomorphism of $TM$, and the following three fourth order Steklov eigenvalue problems: $$ (\Delta_f)^2u=0\ \ {\rm in}\ M, \ \ \ \ \ u=\Delta_f u-q\frac{\partial u}{\partial \nu}=0\ \ {\rm on}\ \partial M; $$ $$ (\Delta_f)^2u=0\ {\rm in}\ \ M, \ \ \ …

A Remark On Singularity Of Homeomorphisms And Hausdorff Dimension, Chun Wei, Shengyou Wen

Turkish Journal of Mathematics

We prove that there is a homeomorphism of the unit interval onto itself that is so singular that it maps some set $E$ of $\dim_HE=0$ onto a set $F$ of $\dim_H[0,1]\setminus F=0$.

Idempotents Of The Green Algebras Of Finite Dimensionalpointed Rank One Hopf Algebras Of Nilpotent Type, Zhihua Wang

Turkish Journal of Mathematics

In this paper, we intend to study idempotents of the Green algebra (complexified Green ring) of any finite dimensional pointed rank one Hopf algebra of nilpotent type over the complex number field. We first determine all one dimensional representations of the quotient algebra of the Green algebra modulo its Jacobson radical. This gives rise to all primitive idempotents of the quotient algebra. Then we present explicitly primitive idempotents of the Green algebra by lifting the ones of the quotient algebra. Finally, as an example, we describe all primitive idempotents of the Green algebra of the Taft algebra $T_3$.

A New Aspect To Picard Operators With Simulation Functions, Murat Olgun, Tuğçe Alyildiz, Özge Bi̇çer

Turkish Journal of Mathematics

In the present paper, considering the simulation function, we give a new class of Picard operators on complete metric spaces. We also provide a nontrivial example that shows the aforementioned class properly contains some earlier such classes.

On The Zero-Divisor Graphs Of Finite Free Semilattices, Kemal Toker

Turkish Journal of Mathematics

Let $SL_{X}$ be the free semilattice on a finite nonempty set $X$. There exists an undirected graph $\Gamma(SL_{X})$ associated with $SL_{X}$ whose vertices are the proper subsets of $X$, except the empty set, and two distinct vertices $A$ and $B$ of $\Gamma(SL_{X})$ are adjacent if and only if $A\cup B=X$. In this paper, the diameter, radius, girth, degree of any vertex, domination number, independence number, clique number, chromatic number, and chromatic index of $\Gamma(SL_{X})$ have been established. Moreover, we have determined when $\Gamma(SL_{X})$ is a perfect graph and when the core of $\Gamma(SL_{X})$ is a Hamiltonian graph.

New Oscillation Tests And Some Refinements For First-Order Delay Dynamic Equations, Başak Karpuz, Özkan Öcalan

Turkish Journal of Mathematics

In this paper, we present new sufficient conditions for the oscillation of first-order delay dynamic equations on time scales. We also present some examples to which none of the previous results in the literature can apply.

Veronese Transform And Castelnuovo-Mumford Regularity Of Modules, Marcel Morales, Nguyen Thi Dung

Turkish Journal of Mathematics

Veronese rings, Segre embeddings, or more generally Segre--Veronese embeddings are very important rings in algebraic geometry. In this paper we present an original, elementary way to compute the Hilbert--Poincar\'e series of these rings; as a consequence we compute their Castelnuovo--Mumford regularity and also the highest graded Betti number. Moreover, using the Castelnuovo--Mumford regularity of a Cohen--Macaulay finitely generated graded module, we compute that of its Veronese transforms.

An Improved Singular Trudinger-Moser Inequality In Dimension Two, Anfeng Yuan, Zhiyong Huang

Turkish Journal of Mathematics

Let $\Omega\subset\mathbb{R}^2$ be a smooth bounded domain and $W_0^{1,2}(\Omega)$ be the usual Sobolev space. Let $\beta$, $0\leq\beta1$, $$\lambda_{p,\beta}(\Omega)=\inf_{u\in W_0^{1,2}(\Omega),\,u\not\equiv 0}{\ \nabla u\ _2^2}/{\ u\ _{p,\beta}^2},$$ where $\ \cdot\ _2$ denotes the standard $L^2$-norm in $\Omega$ and $\ u\ _{p,\beta}=({\int_{\Omega} x ^{-\beta} u ^pdx})^{1/p}$. Suppose that $\gamma$ satisfies $\f{\gamma}{4\pi}+\f{\beta}{2}=1$. Using a rearrangement argument, the author proves that $$\sup_{u\in W_0^{1,2}(\Omega), \ \nabla u\ _2\leq 1}\int_{\Omega} x ^{-\beta}e^{\gamma u^2 \le(1+\alpha\ u\ _{p,\beta}^2\ri) }dx$$ is finite for any $\alpha$, $0\leq\alpha

On $*$-Commuting Mappings And Derivations In Rings With Involution, Nadeem Ahmad Dar, Shakir Ali

Turkish Journal of Mathematics

Let $R$ be a ring with involution $*$. A mapping $f:R\rightarrow R$ is said to be $*$-commuting on $R$ if $[f(x),x^*]=0$ holds for all $x\in R$. The purpose of this paper is to describe the structure of a pair of additive mappings that are $*$-commuting on a semiprime ring with involution. Furthermore, we study the commutativity of prime rings with involution satisfying any one of the following conditions: (i) $[d(x),d(x^*)]=0,$ (ii) $d(x)\circ d(x^*)=0$, (iii) $d([x,x^*])\pm [x,x^*]=0$ (iv) $d(x\circ x^*)\pm (x\circ x^*)=0,$ (v) $d([x,x^*])\pm (x\circ x^*)=0$, (vi) $d(x\circ x^*)\pm [x,x^*]=0$, where $d$ is a nonzero derivation of $R$. Finally, an example …

Overall Approach To Mizoguchi--Takahashi Type Fixed Point Results, Gülhan Minak, İshak Altun

Turkish Journal of Mathematics

In this work, inspired by the recent technique of Jleli and Samet, we give a new generalization of the well-known Mizoguchi--Takahashi fixed point theorem, which is the closest answer to Reich's conjecture about the existence of fixed points of multivalued mappings on complete metric spaces. We also provide a nontrivial example showing that our result is a proper generalization of the Mizoguchi--Takahashi result.

On The Comaximal Ideal Graph Of A Commutative Ring, Mehrdad Azadi, Zeinab Jafari, Changiz Eslahchi

Turkish Journal of Mathematics

Let $R$ be a commutative ring with identity. We use $\Gamma ( R )$ to denote the comaximal ideal graph. The vertices of $\Gamma ( R )$ are proper ideals of R that are not contained in the Jacobson radical of $R$, and two vertices $I$ and $J$ are adjacent if and only if $I + J = R$. In this paper we show some properties of this graph together with the planarity and perfection of $\Gamma ( R )$.

A Contribution To The Analysis Of A Reduction Algorithm For Groups With An Extraspecial Normal Subgroup, Abdullah Çağman, Nurullah Ankaralioğlu

Turkish Journal of Mathematics

Reduction algorithms are an important tool for understanding structural properties of groups. They play an important role in algorithms designed to investigate matrix groups over a finite field. One such algorithm was designed by Brooksbank et al. for members of the class $C_6$ in Aschbacher's theorem, namely groups $N$ that are normalizers in $GL(d,q)$ of certain absolutely irreducible symplectic-type $r$-groups $R$, where $r$ is a prime and $d=r^n$ with $n>2$. However, the analysis of this algorithm has only been completed when $d=r^2$ and when $d=r^n$ and $n>2$, in the latter case under the condition that $G/RZ(G)\cong N/RZ(N)$. We …

Bell-Shaped Curve For Productivity Growth: An Explanation, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

A recent analysis of the productivity growth data shows, somewhat surprisingly, that the dependence of the 20-century productivity growth on time can be reasonably well described by a Gaussian formula. In this paper, we provide a possible theoretical explanation for this observation.

A Generalization Of The Difference Of Slopes Test To Poisson Regression With Three-Way Interaction, Melinda Bierhals

Theses, Dissertations and Capstones

Linear regression models involving interaction can use the difference of slopes test to compare slopes for various situations. We will be generalizing this process to develop a procedure to compare rates in a Poisson regression model, allowing us to consider unbounded count data as opposed to continuous data. We will apply this process to an educational data set from a sample of students located in two different Los Angeles high schools. Our model will include a three-way interaction and address the following questions:

• Does language ability impact the relationship between math ability and attendance in the same way for …

Arithmetic Local Constants For Abelian Varieties With Extra Endomorphisms, Sunil Chetty

Mathematics Faculty Publications

This work generalizes the theory of arithmetic local constants, introduced by Mazur and Rubin, to better address abelian varieties with a larger endomorphism ring than ℤ. We then study the growth of the p^∞- Selmer rank of our abelian variety, and we address the problem of extending the results of Mazur and Rubin to dihedral towers k ⊂ K ⊂ F in which [F : K] is not a p-power extension.

Sphere Representations, Stacked Polytopes, And The Colin De Verdière Number Of A Graph, Lon Mitchell, Lynne Yengulalp

Mathematics Faculty Publications

We prove that a k-tree can be viewed as a subgraph of a special type of (k + 1)- tree that corresponds to a stacked polytope and that these “stacked” (k + 1)-trees admit representations by orthogonal spheres in R k+1. As a result, we derive lower bounds for Colin de Verdi`ere’s µ of complements of partial k-trees and prove that µ(G) + µ(G) > |G| − 2 for all chordal G.

Serre Weights And Wild Ramification In Two-Dimensional Galois Representations, Lassina Dembélé, Fred Diamond, David P. Roberts

Mathematics Publications

A generalization of Serre’s Conjecture asserts that if F is a totally real field, then certain characteristic p representations of Galois groups over F arise from Hilbert modular forms. Moreover, it predicts the set of weights of such forms in terms of the local behaviour of the Galois representation at primes over p. This characterization of the weights, which is formulated using p-adic Hodge theory, is known under mild technical hypotheses if p > 2. In this paper we give, under the assumption that p is unramified in F, a conjectural alternative description for the set of weights. …

Generalized Eulerian Numbers And Multiplex Juggling Sequences, Esther M. Banaian

All College Thesis Program, 2016-2019

We consider generalizations of both juggling sequences and non-attacking rook placements. We demonstrate the important connection between these objects, and also propose a generalization of the Eulerian numbers. These generalizations give rise to several interesting counting problems, which we explore.

On Coprimely Structured Rings, Nesli̇han Ayşen Özki̇ri̇şci̇, Kürşat Hakan Oral, Ünsal Teki̇r

Turkish Journal of Mathematics

In this paper, we define coprimely structured rings, which are the generalization of strongly 0-dimensional rings. Furthermore, we investigate coprimely structured rings and give some relations between other rings such as Artinian rings, strongly 0-dimensional rings, and h-local domains.

Almost Co-K\"{A}Hler Manifolds Satisfying Some Symmetry Conditions, Yaning Wang

Turkish Journal of Mathematics

Let $M^{2n+1}$ be an almost co-K\"{a}hler manifold of dimension $>3$ with K\"{a}hlerian leaves. In this paper, we first prove that if $M^{2n+1}$ is locally symmetric, then either it is a co-K\"{a}hler manifold with locally symmetric K\"{a}hlerian leaves, or the Reeb vector field $\xi$ is harmonic and in this case $M^{2n+1}$ is non-co-K\"{a}hler. We also prove that any almost co-K\"{a}hler manifold of dimension $3$ is $\phi$-symmetric if and only if it is locally isometric to either a flat Euclidean space $\mathbb{R}^3$ or a Riemannian product $\mathbb{R}\times N^2(c)$, where $N^2(c)$ denotes a K\"{a}hler surface of constant curvature $c\neq0$.