The Relation Between Rough Wijsman Convergence And Asymptotic Cones,
2016
TÜBİTAK
The Relation Between Rough Wijsman Convergence And Asymptotic Cones, Öznur Ölmez, Sali̇h Aytar
Turkish Journal of Mathematics
In this paper, we explore the effect of the asymptotic cone of the limit set of a sequence that is rough Wijsman convergent.
Derivation-Homomorphisms,
2016
TÜBİTAK
Derivation-Homomorphisms, Lingyue Li, Xiaowei Xu
Turkish Journal of Mathematics
In this paper, we introduce notions of $(n,m)$-derivation-homomorphisms and Boolean $n$-derivations. Using Boolean $n$-derivations and $m$-homomorphisms, we describe structures of $(n, m)$-derivation-homomorphisms.
Hom-Lie 2-Superalgebras,
2016
TÜBİTAK
Hom-Lie 2-Superalgebras, Chunyue Wang, Qingcheng Zhang, Jizhu Nan
Turkish Journal of Mathematics
Hom-Lie 2-superalgebras can be considered as the categorification of Hom-Lie superalgebras. We give the definition of Hom-Lie 2-superalgebras and study their superderivations. We obtain the representation, deformation, and abelian extensions related to the 2-cocycle and Hom-Nijenhuis operators. Moreover, we also construct a skeletal (strict) Hom-Lie 2-superalgebra from a Hom-associative Rota--Baxter superalgebra.
Abundance Of $E$-Order-Preserving Transformation Semigroups,
2016
TÜBİTAK
Abundance Of $E$-Order-Preserving Transformation Semigroups, Lei Sun, Xuefeng Han
Turkish Journal of Mathematics
Let ${\cal T}_X$ be the full transformation semigroup on a finite totally ordered set $X=\{1<2<\ldots
Extension Of Refinement Rings,
2016
TÜBİTAK
Extension Of Refinement Rings, Rahman Bahmani Sangesari, Marjan Sheibani Abdulyousefi, Nahid Ashrafi
Turkish Journal of Mathematics
In this paper we prove that a ring $R$ in which every finitely generated projective $R$-module lifts modulo $J(R)$ is a refinement ring if and only if $ \frac{R}{J(R)}$ is a refinement ring. We also prove that the refinement property for rings is Morita invariant. Several examples are constructed as well.
Parameterized Littlewood--Paley Operators And Their Commutators On Herz Spaces With Variable Exponents,
2016
TÜBİTAK
Parameterized Littlewood--Paley Operators And Their Commutators On Herz Spaces With Variable Exponents, Lijuan Wang, Shuangping Tao
Turkish Journal of Mathematics
The aim of this paper is to deal with Littlewood--Paley operators with real parameters, including the parameterized Lusin area integrals and the parameterized Littlewood--Paley $g_{\lambda}^{\ast}$-functions, and their commutators on Herz spaces with two variable exponents $p(\cdot),~q(\cdot)$. By using the properties of the Lebesgue spaces with variable exponents, the boundedness of the parameterized Littlewood--Paley operators and their commutators generated respectively by BMO function and Lipschitz function is obtained on those Herz spaces.
A Note On Gorenstein Projective Complexes,
2016
TÜBİTAK
A Note On Gorenstein Projective Complexes, Bo Lu, Liu Zhongkui
Turkish Journal of Mathematics
As we know, a complex $Q$ is projective if and only if $Q$ is exact and $\mathrm{Z}_n(Q)$ is projective in $R$-$\mathrm{Mod}$ for each $n\in\mathbb{Z}$. In this article, we show that a complex $G$ is Gorenstein projective with Hom$_R(P,G)$ and Hom$_R(G,P)$ exact for any Cartan--Eilenberg projective complex $P$ if and only if $G$ is exact and $\mathrm{Z}_n(G)$ is Gorenstein projective in $R$-$\mathrm{Mod}$ for each $n\in\mathbb{Z}$. Using the above result, a new equivalent characterization of some $\mathcal{A}$ complexes is obtained.
Sparse Sums With Bases Of Chebyshev Polynomials Of The Third And Fourth Kind,
2016
TÜBİTAK
Sparse Sums With Bases Of Chebyshev Polynomials Of The Third And Fourth Kind, Maryam Shams Solary
Turkish Journal of Mathematics
We derive a generalization for the reconstruction of $M$-sparse sums in Chebyshev bases of the third and fourth kind. This work is used for a polynomial with Chebyshev sparsity and samples on a Chebyshev grid of $[-1,1]$. Further, fundamental reconstruction algorithms can be a way for getting M-sparse expansions of Chebyshev polynomials of the third and fourth kind. The numerical results for these algorithms are designed to compare the time effects of doing them.
The Dual Generalized Chernoff Inequality For Star-Shaped Curves,
2016
TÜBİTAK
The Dual Generalized Chernoff Inequality For Star-Shaped Curves, Deyan Zhang, Yunlong Yang
Turkish Journal of Mathematics
In this paper, we first introduce the $k$-order radial function $\rho_k(\theta)$ for star-shaped curves in $\mathbb{R}^2$ and then prove a geometric inequality involving $\rho_k(\theta)$ and the area $A$ enclosed by a star-shaped curve, which can be looked upon as the dual Chernoff--Ou--Pan inequality. As a by-product, we get a new proof of the classical dual isoperimetric inequality. We also prove that $\frac{C^2}{k^2}\leq A
On The Extended Zero Divisor Graph Of Commutative Rings,
2016
TÜBİTAK
On The Extended Zero Divisor Graph Of Commutative Rings, Driss Bennis, Jilali Mikram, Fouad Taraza
Turkish Journal of Mathematics
In this paper we present a new graph that is closely related to the classical zero-divisor graph. In our case two nonzero distinct zero divisors $x$ and $y$ of a commutative ring $R$ are adjacent whenever there exist two nonnegative integers $n$ and $m$ such that $x^ny^m=0$ with $x^n\neq 0$ and $y^m\neq 0$. This yields an extension of the classical zero divisor graph $\Gamma(R)$ of $R$, which will be denoted by $\overline{\Gamma}(R)$. First we distinguish when $\overline{\Gamma}(R)$ and $\Gamma(R)$ coincide. Various examples in this context are given. We show that if $\overline{\Gamma}(R) \not=\Gamma(R)$, then $\overline{\Gamma}(R)$ must contain a cycle. We …
The M[--] And --[M] Functors And Five Short Lemma In $H_V$-Modules,
2016
TÜBİTAK
The M[--] And --[M] Functors And Five Short Lemma In $H_V$-Modules, Yaser Vaziri, Mansour Ghadiri, Bijan Davvaz
Turkish Journal of Mathematics
The largest class of multivalued systems satisfying the module-like axioms are the $H_v$-modules. The main tools concerning the class of $H_v$-modules with the ordinary modules are the fundamental relations. Based on the relation $\varepsilon^*$, exact sequences in $H_v$-modules are defined. In this paper, we introduce the $H_v$-module $M[A]$ and determine its heart and the connection between equivalence relations $\varepsilon^*_{M[A]}$ and $\varepsilon^*_A$. Moreover, we define the $M[-]$ and $-[M]$ functors and investigate the exactness and some concepts related to them. Finally, we prove the five short lemma in $H_v$-modules.
The Sharpening Hölder Inequality Via Abstract Convexity,
2016
TÜBİTAK
The Sharpening Hölder Inequality Via Abstract Convexity, Gülteki̇n Tinaztepe
Turkish Journal of Mathematics
In this work, a new inequality by sharpening the well-known Hölder inequality by means of a theorem based on abstract convexity is derived.
Stability And Data Dependence Results For The Jungck--Khan Iterative Scheme,
2016
TÜBİTAK
Stability And Data Dependence Results For The Jungck--Khan Iterative Scheme, Abdul Rahim Khan, Fai̇k Gürsoy, Vivek Kumar
Turkish Journal of Mathematics
The Jungck--Khan iterative scheme for a pair of nonself operators contains as a special case Jungck--Ishikawa and Jungck--Mann iterative schemes. In this paper, we establish improved results about convergence, stability, and data dependence for the Jungck--Khan iterative scheme.
Point-Wise Slant Submanifolds In Almost Contact Geometry,
2016
TÜBİTAK
Point-Wise Slant Submanifolds In Almost Contact Geometry, Mohammad Bagher Kazemi Balgeshir
Turkish Journal of Mathematics
In this paper, we introduce point-wise slant submanifolds of almost contact and almost contact 3-structure manifolds. We characterize them, give some examples, and obtain necessary and sufficient conditions for a point-wise slant submanifold of a 3-Sasakian manifold to be a slant submanifold. Moreover, we show that there exist no proper Sasakian point-wise 3-slant submanifolds.
Harmonic Functions And Quadratic Harmonic Morphisms On Walker Spaces,
2016
TÜBİTAK
Harmonic Functions And Quadratic Harmonic Morphisms On Walker Spaces, Cornelia-Livia Bejan, Simona-Luiza Druta-Romaniuc
Turkish Journal of Mathematics
Let $(W,q, \mathcal{D})$ be a 4-dimensional Walker manifold. After providing a characterization and some examples for several special $(1,1)$-tensor fields on $(W,q, \mathcal{D})$, we prove that the proper almost complex structure $J$, introduced by Matsushita, is harmonic in the sense of Garcia-Rio et al. if and only if the almost Hermitian structure $(J,q)$ is almost Kahler. We classify all harmonic functions locally defined on $(W,q, \mathcal{D})$. We deal with the harmonicity of quadratic maps defined on $\mathbb{R}^4$ (endowed with a Walker metric $q$) to the $n$-dimensional semi-Euclidean space of index $r$, and then between local charts of two 4-dimensional Walker …
Some Upper Bounds On The Dimension Of The Schur Multiplierof A Pair Of Nilpotent Lie Algebras,
2016
TÜBİTAK
Some Upper Bounds On The Dimension Of The Schur Multiplierof A Pair Of Nilpotent Lie Algebras, Behrouz Edalatzadeh
Turkish Journal of Mathematics
Let $(L,N)$ be a pair of Lie algebras where $N$ is an ideal of the finite dimensional nilpotent Lie algebra $L$. Some upper bounds on the dimension of the Schur multiplier of $(L,N)$ are obtained without considering the existence of a complement for $N$. These results are applied to derive a new bound on the dimension of the Schur multiplier of a nilpotent Lie algebra.
Problems In Matricially Derived Solid Banach Sequence Spaces,
2016
TÜBİTAK
Problems In Matricially Derived Solid Banach Sequence Spaces, Peter D. Johnson, Faruk Polat
Turkish Journal of Mathematics
Let $\mathbb{F}^\mathbb{N}$ denote the vector space of all scalar sequences. If $A$ is an infinite matrix with nonnegative entries and $\lambda$ is a solid subspace of $\mathbb{F}^\mathbb{N}$, then $ sol-A^{-1}(\lambda)=\{x\in \mathbb{F}^\mathbb{N} : A x \in \lambda\} $ is also a solid subspace of $\mathbb{F}^\mathbb{N}$ that, under certain conditions on $A$ and $\lambda$, inherits a solid topological vector space topology from any such topology on $\lambda$. Letting $\Lambda_0=\lambda$ and $\Lambda_m=sol-A^{-1}(\Lambda_{m-1})$ for $m>0$, we derive an infinite sequence $\Lambda_0, \Lambda_1, \Lambda_2,...$ of solid subspaces of $\mathbb{F}^\mathbb{N}$ from the inputs $A$ and $\lambda$. For $A$ and $\lambda$ confined to certain classes, we …
On Generalized Ostrowski-Type Inequalities For Functions Whose First Derivatives Absolute Values Are Convex,
2016
TÜBİTAK
On Generalized Ostrowski-Type Inequalities For Functions Whose First Derivatives Absolute Values Are Convex, Hüseyi̇n Budak, Mehmet Zeki̇ Sarikaya
Turkish Journal of Mathematics
In this paper, we establish some generalized Ostrowski-type inequalities for functions whose first derivatives absolute values are convex.
Invariant Structures And Gauge Transformation Of Almost Contact Metric Manifolds,
2016
TÜBİTAK
Invariant Structures And Gauge Transformation Of Almost Contact Metric Manifolds, Morteza Mirmohammad Rezaii, Mehrnoosh Zandi
Turkish Journal of Mathematics
In this paper, conditions for K-contact, Sasakian, and cosymplectic structures to be invariant under gauge transformation are found. Moreover, the same question is studied for 3-Sasakian, 3-almost contact, and 3-cosymplectic manifolds. Finally, it is shown that a slant submanifold of an almost contact metric manifold is invariant by gauge transformation.
Explicit Estimates On A Mixed Neumann-Robin-Cauchy Problem,
2016
TÜBİTAK
Explicit Estimates On A Mixed Neumann-Robin-Cauchy Problem, Luisa Consiglieri
Turkish Journal of Mathematics
We deal with the existence of weak solutions for a mixed Neumann-Robin-Cauchy problem. The existence results are based on global-in-time estimates of approximating solutions, and the passage to the limit exploits compactness techniques. We investigate explicit estimates for solutions of the parabolic equations with nonhomogeneous boundary conditions and distributional right-hand sides. The parabolic equation is of divergence form with discontinuous coefficients. We consider a nonlinear condition on a part of the boundary such that the power laws (and the Robin boundary condition) appear as particular cases.
