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Parameterized Littlewood--Paley Operators And Their Commutators On Herz Spaces With Variable Exponents, Lijuan Wang, Shuangping Tao
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, Kübra Gül, Nurullah Ankaralioğlu
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, Haifeng Lian, Qingping Zeng
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, Burhan Selçuk
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, Bo Lu, Liu Zhongkui
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, Aref Jeribi, Bilel Krichen, Bilel Mefteh
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, Firdous Ahmad Shah, Mohammad Younus Bhat
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, Feri̇he Atalan, Gusein Sh. Guseinov
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, Ahmed Salem, Faruk Uçar
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, Neşet Özkan Tan
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, Emrah Kiliç, Talha Arikan
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, Xiaoyan Zhou, Min Wei
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, Guangjun Zhu
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, Ci̇hat Abdi̇oğlu
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, Stijn Cambie, Wendy Goemans, Iris Van Den Bussche
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 …
Isometric $N$-Jordan Weighted Shift Operators, Saeed Yarmahmoodi, Karim Hedayatian
Isometric $N$-Jordan Weighted Shift Operators, Saeed Yarmahmoodi, Karim Hedayatian
Turkish Journal of Mathematics
A bounded linear operator $T$ on a Hilbert space is an isometric $N$-Jordan operator if it can be written as $A+Q$, where $A$ is an isometry and $Q$ is a nilpotent of order $N$ such that $AQ= QA$. In this paper, we will show that the only isometric $N$-Jordan weighted shift operators are isometries. This answers a question recently raised.
Regularity And Projective Dimension Of Some Class Of Well-Covered Graphs, Esfandiyar Lashani, Ali Soleyman Jahan
Regularity And Projective Dimension Of Some Class Of Well-Covered Graphs, Esfandiyar Lashani, Ali Soleyman Jahan
Turkish Journal of Mathematics
In this paper we study the Castelnuovo--Mumford regularity of an edge ideal associated with a graph in a special class of well-covered graphs. We show that if $G$ belongs to the class $\mathcal {SQ}$, then the Castelnuovo-Mumford regularity of $R/I(G)$ will be equal to induced matching number of $G$. For this class of graphs we also compute the projective dimension of the ring $R/I(G)$. As a corollary we describe these invariants in well-covered forests, well-covered chordal graphs, Cohen-Macaulay Cameron-Walker graphs, and simplicial graphs.
$Q$-Riordan Array For $Q$-Pascal Matrix And Its Inverse Matrix, Nai̇m Tuğlu, Fatma Yeşi̇l, Maciej Dziemianczuk, E. Gökçen Koçer
$Q$-Riordan Array For $Q$-Pascal Matrix And Its Inverse Matrix, Nai̇m Tuğlu, Fatma Yeşi̇l, Maciej Dziemianczuk, E. Gökçen Koçer
Turkish Journal of Mathematics
In this paper, we prove the $q$-analogue of the fundamental theorem of Riordan arrays. In particular, by defining two new binary operations $\ast_{q} $ and $\ast _{1/q}$, we obtain a $q$-analogue of the Riordan representation of the $q$-Pascal matrix. In addition, by aid of the $q$-Lagrange expansion formula we get $q$-Riordan representation for its inverse matrix.
On A Factorization Of Operators On Finite Dimensional Hilbert Spaces, Jiawei Luo, Juexian Li, Geng Tian
On A Factorization Of Operators On Finite Dimensional Hilbert Spaces, Jiawei Luo, Juexian Li, Geng Tian
Turkish Journal of Mathematics
As is well known, for any operator $T$ on a complex separable Hilbert space, $T$ has the polar decomposition $T=U T $, where $U$ is a partial isometry and $ T $ is the nonnegative operator $(T^*T)^{\frac{1}{2}}$. In 2014, Tian et al. proved that on a complex separable infinite dimensional Hilbert space, any operator admits a polar decomposition in a strongly irreducible sense. More precisely, for any operator $T$ and any $\varepsilon>0$, there exists a decomposition $T=(U+K)S$, where $U$ is a partial isometry, $K$ is a compact operator with $ K
High-Order Uniformly Convergent Method For Nonlinear Singularly Perturbed Delay Differential Equations With Small Shifts, Abdelhay Salama, Dirhem Al-Amery
High-Order Uniformly Convergent Method For Nonlinear Singularly Perturbed Delay Differential Equations With Small Shifts, Abdelhay Salama, Dirhem Al-Amery
Turkish Journal of Mathematics
In this paper, we propose and analyze a high-order uniform method for solving boundary value problems (BVPs) for singularly perturbed nonlinear delay differential equations with small shifts (delay and advance). Such types of BVPs play an important role in the modeling of various real life phenomena, such as the variational problem in control theory and in the determination of the expected time for the generation of action potentials in nerve cells. To obtain parameter-uniform convergence, the present method is constructed on a piecewise-uniform Shishkin mesh. The error estimate is discussed and it is shown that the method is uniformly convergent …
Pseudospectral Operational Matrix For Numerical Solution Of Single And Multiterm Time Fractional Diffusion Equation, Saeid Gholami, Esmail Babolian, Mohammad Javidi
Pseudospectral Operational Matrix For Numerical Solution Of Single And Multiterm Time Fractional Diffusion Equation, Saeid Gholami, Esmail Babolian, Mohammad Javidi
Turkish Journal of Mathematics
This paper presents a new numerical approach to solve single and multiterm time fractional diffusion equations. In this work, the space dimension is discretized to the Gauss$-$Lobatto points. We use the normalized Grunwald approximation for the time dimension and a pseudospectral successive integration matrix for the space dimension. This approach shows that with fewer numbers of points, we can approximate the solution with more accuracy. Some examples with numerical results in tables and figures displayed.
On Generalized Ostrowski-Type Inequalities For Functions Whose First Derivatives Absolute Values Are Convex, Hüseyi̇n Budak, Mehmet Zeki̇ Sarikaya
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.
Some Properties Of Concave Operators, Lotfollah Karimi, Masoumeh Faghih Ahmadi, Karim Hedayatian
Some Properties Of Concave Operators, Lotfollah Karimi, Masoumeh Faghih Ahmadi, Karim Hedayatian
Turkish Journal of Mathematics
A bounded linear operator $T$ on a Hilbert space $\mathcal{H}$ is concave if, for each $x\in\mathcal{H}$, $\ T^2x\ ^2-2\ Tx\ ^2 +\ x\ ^2 \leq 0$. In this paper, it is shown that if $T$ is a concave operator then so is every power of $T$. Moreover, we investigate the concavity of shift operators. Furthermore, we obtain necessary and sufficient conditions for N-supercyclicity of co-concave operators. Finally, we establish necessary and sufficient conditions for the left and right multiplications to be concave on the Hilbert-Schmidt class.
On Hermite-Hadamard Type Inequalities Via Generalized Fractional Integrals, Mohamed Jleli, Donal O'Regan, Bessem Samet
On Hermite-Hadamard Type Inequalities Via Generalized Fractional Integrals, Mohamed Jleli, Donal O'Regan, Bessem Samet
Turkish Journal of Mathematics
New Hermite-Hadamard type inequalities are obtained for convex functions via generalized fractional integrals. The results presented here are generalizations of those obtained in earlier works.
Mixed Modulus Of Continuity In The Lebesgue Spaces With Muckenhouptweights And Their Properties, Ramazan Akgün
Mixed Modulus Of Continuity In The Lebesgue Spaces With Muckenhouptweights And Their Properties, Ramazan Akgün
Turkish Journal of Mathematics
Main properties of the mixed modulus of continuity in the Lebesgue spaces with Muckenhoupt weights are investigated. We use the mixed modulus of continuity to obtain Potapov type direct and inverse estimates of angular trigonometric approximation of functions in these spaces. We prove an equivalence between the mixed modulus of continuity and K -functional and realization functional.
Structural Stability Analysis Of Solutions To The Initial Boundary Value Problem For A Nonlinear Strongly Damped Wave Equation, Şevket Gür, İpek Güleç
Structural Stability Analysis Of Solutions To The Initial Boundary Value Problem For A Nonlinear Strongly Damped Wave Equation, Şevket Gür, İpek Güleç
Turkish Journal of Mathematics
In this paper the initial-boundary value problem for a nonlinear strongly damped wave equation is considered. We analyze the structural stability of solutions of the nonlinear strongly damped wave equation with coefficients from $H^1(\Omega)$.
Perturbational Self-Similar Solutions For The 2-Component Degasperis-Procesi System Via A Characteristic Method, Hongli An, Ka-Luen Cheung, Manwai Yuen
Perturbational Self-Similar Solutions For The 2-Component Degasperis-Procesi System Via A Characteristic Method, Hongli An, Ka-Luen Cheung, Manwai Yuen
Turkish Journal of Mathematics
In this paper, the two-component Degasperis-Procesi system arising in shallow water theory is investigated. By using a special transformation and the characteristic method, a class of perturbational self-similar solutions is constructed. Such solutions are not only more general than those obtained by Yuen in 2011, but also they may have potential applications in the modeling of tsunamis. In addition, the method proposed can be extended to other mathematical physics models like the two-component Camassa-Holm equations.
Some Normality Criteria, Gopal Datt, Sanjay Kumar
Some Normality Criteria, Gopal Datt, Sanjay Kumar
Turkish Journal of Mathematics
In this article, we prove some normality criteria for a family of meromorphic functions, which involves sharing of a nonzero value by certain differential monomials generated by the members of the family. These results generalize some of the results of Schwick.
Invariant Structures And Gauge Transformation Of Almost Contact Metric Manifolds, Morteza Mirmohammad Rezaii, Mehrnoosh Zandi
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.
Approximation Of $B$-Continuous And $B$-Differentiable Functions By Gbs Operators Of $Q$-Bernstein-Schurer-Stancu Type, Manjari Sidharth, Nurhayat İspi̇r, Purshottam Narain Agrawal
Approximation Of $B$-Continuous And $B$-Differentiable Functions By Gbs Operators Of $Q$-Bernstein-Schurer-Stancu Type, Manjari Sidharth, Nurhayat İspi̇r, Purshottam Narain Agrawal
Turkish Journal of Mathematics
B&acaron;rbosu and Muraru (2015) introduced the bivariate generalization of the $q$-Bernstein-Schurer-Stancu operators and constructed a GBS operator of $q$-Bernstein-Schurer-Stancu type. The concern of this paper is to obtain the rate of convergence in terms of the partial and complete modulus of continuity and the degree of approximation by means of Lipschitz-type class for the bivariate operators. In the last section we estimate the degree of approximation by means of Lipschitz class function and the rate of convergence with the help of mixed modulus of smoothness for the GBS operator of $q$-Bernstein-Schurer-Stancu type. Furthermore, we show comparisons by some illustrative graphics …