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.
Highly Non-Concurrent Longest Paths In Lattices,
2016
TÜBİTAK
Highly Non-Concurrent Longest Paths In Lattices, Yasir Bashir, Faisal Nadeem, Ayesha Shabbir
Turkish Journal of Mathematics
In this paper we consider graphs in which any pair of vertices is missed by some longest path. We are proving the existence of such graphs in the infinite triangular, square and hexagonal lattices in the plane. Moreover, we extend our investigation to lattices on several surfaces such as the torus, the M\"obius strip and the Klein bottle.
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
Note On The Divisoriality Of Domains Of The Form $K[[X^{P}, X^{Q}]]$, $K[X^{P}, X^{Q}]$, $K[[X^{P}, X^{Q}, X^{R}]]$, And $K[X^{P}, X^{Q}, X^{R}]$, Abdeslam Mimouni
Turkish Journal of Mathematics
Let $k$ be a field and $X$ an indeterminate over $k$. In this note we prove that the domain $k[[X^{p}, X^{q}]]$ (resp. $k[X^{p}, X^{q}]$) where $p, q$ are relatively prime positive integers is always divisorial but $k[[X^{p}, X^{q}, X^{r}]]$ (resp. $k[X^{p}, X^{q}, X^{r}]$) where $p, q, r$ are positive integers is not. We also prove that $k[[X^{q}, X^{q+1}, X^{q+2}]]$ (resp. $k[X^{q}, X^{q+1}, X^{q+2}]$) is divisorial if and only if $q$ is even. These are very special cases of well-known results on semigroup rings, but our proofs are mainly concerned with the computation of the dual (equivalently the inverse) of the …
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.
On The Twisted Modules For Finite Matrix Groups,
2016
TÜBİTAK
On The Twisted Modules For Finite Matrix Groups, Kübra Gül, Nurullah Ankaralioğlu
Turkish Journal of Mathematics
Suppose that $W$ is an irreducible $F_{q}G$-module of dimension $n$ $% (d^{2}
An Extension Of Cline''S Formula For A Generalized Drazin Inverse,
2016
TÜBİTAK
An Extension Of Cline''S Formula For A Generalized Drazin Inverse, Haifeng Lian, Qingping Zeng
Turkish Journal of Mathematics
In this note we give an answer to a question recently posed by Zeng and Zhong, to note that Cline's formula for a generalized Drazin inverse extends to the case when $aba=aca$. Cline's formula for a pseudo Drazin inverse is also presented in this case.
Quenching Behavior Of A Semilinear Reaction-Diffusion System With Singularboundary Condition,
2016
TÜBİTAK
Quenching Behavior Of A Semilinear Reaction-Diffusion System With Singularboundary Condition, Burhan Selçuk
Turkish Journal of Mathematics
In this paper, we study the quenching behavior of the solution of a semilinear reaction-diffusion system with singular boundary condition. We first get a local exisence result. Then we prove that the solution quenches only on the right boundary in finite time and the time derivative blows up at the quenching time under certain conditions. Finally, we get lower bounds and upper bounds for quenching time.
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.
Fixed Point Theory In Wc--Banach Algebras,
2016
TÜBİTAK
Fixed Point Theory In Wc--Banach Algebras, Aref Jeribi, Bilel Krichen, Bilel Mefteh
Turkish Journal of Mathematics
In this paper, we will prove some fixed point theorems for the sum and the product of nonlinear weakly sequentially continuous operators acting on a WC--Banach algebra. Our results improve and correct some recent results given by Banas and Taoudi, and extend several earlier works using the condition $(\mathcal{P})$.
Construction Of Biorthogonal Wavelet Packets On Local Fields Of Positive Characteristic,
2016
TÜBİTAK
Construction Of Biorthogonal Wavelet Packets On Local Fields Of Positive Characteristic, Firdous Ahmad Shah, Mohammad Younus Bhat
Turkish Journal of Mathematics
Orthogonal wavelet packets lack symmetry, which is a much desired property in image and signal processing. The biorthogonal wavelet packets achieve symmetry where the orthogonality is replaced by biorthogonality. In the present paper, we construct biorthogonal wavelet packets on local fields of positive characteristic and investigate their properties by means of Fourier transforms. We also show how to obtain several new Riesz bases of the space $L^2(K)$ by constructing a series of subspaces of these wavelet packets. Finally, we provide algorithms for the decomposition and reconstruction using these biorthogonal wavelet packets.
Solving An Initial Boundary Value Problem On Thesemiinfinite Interval,
2016
TÜBİTAK
Solving An Initial Boundary Value Problem On Thesemiinfinite Interval, Feri̇he Atalan, Gusein Sh. Guseinov
Turkish Journal of Mathematics
We explore the sign properties of eigenvalues and the basis properties of eigenvectors for a special quadratic matrix polynomial and use the results obtained to solve the corresponding linear system of differential equations on the half line subject to an initial condition at $t=0$ and a condition at $t=\infty$.
The $Q$-Analogue Of The $E_{2;1}$-Transform And Its Applications,
2016
TÜBİTAK
The $Q$-Analogue Of The $E_{2;1}$-Transform And Its Applications, Ahmed Salem, Faruk Uçar
Turkish Journal of Mathematics
In this paper, we introduce a new integral transform $\ _{q}\mathcal{E}_{2;1}$, which is the $q$-analogue of the $\mathcal{E}_{2;1}$-transform and can be regarded as a $\mathit{q}$-extension of the $\mathcal{E}_{2;1}$-transform. Some identities involving $~_{q}L_{2}$-transfom, $~_{q}\mathcal{L}_{2}$-transfom, and $\mathcal{P}_{q}$-transform are given. By making use of these identities and $\ _{q}\mathcal{E}_{2;1}$-transform, a new Parseval--Goldstein type theorem is obtained. Some examples are also given as an illustration of the main results presented here.
A Note On Riesz Space Valued Measures,
2016
TÜBİTAK
A Note On Riesz Space Valued Measures, Neşet Özkan Tan
Turkish Journal of Mathematics
In this paper, some properties of Riesz space valued measures that are defined on an algebra of sets are obtained. The question of under what conditions $oba(\mathcal{F},E)$ =$a(\mathcal{F},E)$ for a given Dedekind complete Riesz space $E$ is answered under natural conditions. The outer measure, which is generated by order bounded Riesz space valued measure, is obtained and its properties are investigated. The concept of hazy convergence that is valid for real valued signed measures is extended to Riesz space valued measures. The consequences of order convergence of $f:X\rightarrow E$, which implies hazy convergence, are given.
Evaluation Of Spectrum Of 2-Periodic Tridiagonal-Sylvester Matrix,
2016
TÜBİTAK
Evaluation Of Spectrum Of 2-Periodic Tridiagonal-Sylvester Matrix, Emrah Kiliç, Talha Arikan
Turkish Journal of Mathematics
The Sylvester matrix was first defined by JJ Sylvester. Some authors have studied the relationships between certain orthogonal polynomials and the determinant of the Sylvester matrix. Chu studied a generalization of the Sylvester matrix. In this paper, we introduce its $2$-periodic generalization. Then we compute its spectrum by left eigenvectors with a similarity trick.
Notes On Cotorsion Dimension Of Hopf--Galois Extensions,
2016
TÜBİTAK
Notes On Cotorsion Dimension Of Hopf--Galois Extensions, Xiaoyan Zhou, Min Wei
Turkish Journal of Mathematics
Let $H$ be a finite dimensional Hopf algebra over a field $k$ and $A/B$ be a right $H$-Galois extension. In this note the relationship of cotorsion dimensions between $A$ and $B$ will be studied. We prove that $\mbox{r.cot.D}(A)\leq\mbox{r.cot.D}(B)+\mbox{l.D}(H)$. Moreover, we give some sufficient conditions for which $\mbox{r.cot.D}(A)=\mbox{r.cot.D}(B)$. As applications, we obtain some results about cotorsion dimension of the smash product.
Shellability Of Simplicial Complexes And Simplicial Complexes With The Free Vertex Property,
2016
TÜBİTAK
Shellability Of Simplicial Complexes And Simplicial Complexes With The Free Vertex Property, Guangjun Zhu
Turkish Journal of Mathematics
To a simplicial complex $\Delta$, we associate a square-free monomial ideal $\mathcal{F}(\Delta)$ in the polynomial ring generated by its facet over a field. Furthermore, we could consider $\mathcal{F}(\Delta)$ as the Stanley--Reisner ideal of another simplicial complex $\delta_{N}(\mathcal{F}(\Delta))$ from facet ideal theory and Stanley--Reisner theory. In this paper, we determine what families of simplicial complexes $\Delta$ have the property that their Stanley--Reisner complexes $\delta_{N}(\mathcal{F}(\Delta))$ are shellable. Furthermore, we show that the simplicial complex with the free vertex property is sequentially Cohen--Macaulay. This result gives a new proof for a result of Faridi on the sequentially Cohen--Macaulayness of simplicial forests.
Zero-Divisor Graph Of Matrix Rings And Hurwitz Rings,
2016
TÜBİTAK
Zero-Divisor Graph Of Matrix Rings And Hurwitz Rings, Ci̇hat Abdi̇oğlu
Turkish Journal of Mathematics
Let $R$ be ring a with identity $1\neq 0$, $S_n(R)$ be a subring of the ring $T_n(R)$ of $n\times n$ upper triangular matrices over $R$, and $H_n(R)$ be the ring defined in the next section using $HR$, the ring of the Hurwitz series over $R$. In this paper, we introduce the zero-divisor graph $\overset{\rightarrow}{\Gamma}(S_n(R))$ and its underlying undirected graph $\Gamma(S_n(R))$ of $S_n(R)$. We give some basic graph theory properties of $\overset{\rightarrow}{\Gamma}(S_n(R))$. Moreover, we obtain some results of the zero-divisor directed graph of $\overset{\rightarrow}{\Gamma}(H_n(R))$.
Rectifying Curves In The $N$-Dimensional Euclidean Space,
2016
TÜBİTAK
Rectifying Curves In The $N$-Dimensional Euclidean Space, Stijn Cambie, Wendy Goemans, Iris Van Den Bussche
Turkish Journal of Mathematics
In this article, we study the so-called rectifying curves in an arbitrary dimensional Euclidean space. A curve is said to be a rectifying curve if, in all points of the curve, the orthogonal complement of its normal vector contains a fixed point. If this fixed point is chosen to be the origin, then this condition is equivalent to saying that the position vector of the curve in every point lies in the orthogonal complement of its normal vector. Here we characterize rectifying curves in the $n$-dimensional Euclidean space in different ways: using conditions on their curvatures, with an expression for …
