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2016

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Articles 1021 - 1050 of 1329

Full-Text Articles in Mathematics

Isometric $N$-Jordan Weighted Shift Operators, Saeed Yarmahmoodi, Karim Hedayatian Jan 2016

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.

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Regularity And Projective Dimension Of Some Class Of Well-Covered Graphs, Esfandiyar Lashani, Ali Soleyman Jahan Jan 2016

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.

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$Q$-Riordan Array For $Q$-Pascal Matrix And Its Inverse Matrix, Nai̇m Tuğlu, Fatma Yeşi̇l, Maciej Dziemianczuk, E. Gökçen Koçer Jan 2016

$Q$-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.

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On A Factorization Of Operators On Finite Dimensional Hilbert Spaces, Jiawei Luo, Juexian Li, Geng Tian Jan 2016

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

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High-Order Uniformly Convergent Method For Nonlinear Singularly Perturbed Delay Differential Equations With Small Shifts, Abdelhay Salama, Dirhem Al-Amery Jan 2016

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 …

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Pseudospectral Operational Matrix For Numerical Solution Of Single And Multiterm Time Fractional Diffusion Equation, Saeid Gholami, Esmail Babolian, Mohammad Javidi Jan 2016

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.

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On Generalized Ostrowski-Type Inequalities For Functions Whose First Derivatives Absolute Values Are Convex, Hüseyi̇n Budak, Mehmet Zeki̇ Sarikaya Jan 2016

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.

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Some Properties Of Concave Operators, Lotfollah Karimi, Masoumeh Faghih Ahmadi, Karim Hedayatian Jan 2016

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.

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On Hermite-Hadamard Type Inequalities Via Generalized Fractional Integrals, Mohamed Jleli, Donal O'Regan, Bessem Samet Jan 2016

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.

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Mixed Modulus Of Continuity In The Lebesgue Spaces With Muckenhouptweights And Their Properties, Ramazan Akgün Jan 2016

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.

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Structural Stability Analysis Of Solutions To The Initial Boundary Value Problem For A Nonlinear Strongly Damped Wave Equation, Şevket Gür, İpek Güleç Jan 2016

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 $H^1(\Omega)$.

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Perturbational Self-Similar Solutions For The 2-Component Degasperis-Procesi System Via A Characteristic Method, Hongli An, Ka-Luen Cheung, Manwai Yuen Jan 2016

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.

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Some Normality Criteria, Gopal Datt, Sanjay Kumar Jan 2016

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.

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Invariant Structures And Gauge Transformation Of Almost Contact Metric Manifolds, Morteza Mirmohammad Rezaii, Mehrnoosh Zandi Jan 2016

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.

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Approximation Of $B$-Continuous And $B$-Differentiable Functions By Gbs Operators Of $Q$-Bernstein-Schurer-Stancu Type, Manjari Sidharth, Nurhayat İspi̇r, Purshottam Narain Agrawal Jan 2016

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 …

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Explicit Estimates On A Mixed Neumann-Robin-Cauchy Problem, Luisa Consiglieri Jan 2016

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.

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The Moore-Penrose Inverse Of Differences And Products Of Projectors In A Ring With Involution, Huihui Zhu, Jianlong Chen, Pedro Patricio Jan 2016

The Moore-Penrose Inverse Of Differences And Products Of Projectors In A Ring With Involution, Huihui Zhu, Jianlong Chen, Pedro Patricio

Turkish Journal of Mathematics

In this paper, we study the Moore-Penrose inverses of differences and products of projectors in a ring with involution. Some necessary and sufficient conditions for the existence of the Moore-Penrose inverse are given. Moreover, the expressions of the Moore-Penrose inverses of differences and products of projectors are presented.

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Uniqueness Of Entire Graphs In Riemannian Warped Products, Junhong Dong, Ximin Liu Jan 2016

Uniqueness Of Entire Graphs In Riemannian Warped Products, Junhong Dong, Ximin Liu

Turkish Journal of Mathematics

In this paper, by applying the generalized Omori-Yau maximum principle for complete spacelike hypersurfaces in warped product spaces, we obtain the sign relationship between the derivative of warping function and support function. Afterwards, by using this result and imposing suitable restrictions on the higher order mean curvatures, we establish uniqueness results for the entire graph in a Riemannian warped product space, which has a strictly monotone warping function. Furthermore, applications to such a space are given.

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On The Nphss-Kpik Iteration Method For Low-Rank Complex Sylvester Equations Arising From Time-Periodic Fractional Diffusion Equations, Min-Li Zeng, Guo-Feng Zhang Jan 2016

On The Nphss-Kpik Iteration Method For Low-Rank Complex Sylvester Equations Arising From Time-Periodic Fractional Diffusion Equations, Min-Li Zeng, Guo-Feng Zhang

Turkish Journal of Mathematics

Based on the Hermitian and skew-Hermitian (HS) splitting for non-Hermitian matrices, a nonalternating preconditioned Hermitian and skew-Hermitian splitting-Krylov plus inverted Krylov subspace (NPHSS-KPIK) iteration method for solving a class of large and low-rank complex Sylvester equations arising from the two-dimensional time-periodic fractional diffusion problem is established. The local convergence condition is proposed and the optimal parameter is given. Numerical experiments are used to show the efficiency of the NPHSS-KPIK iteration method for solving the Sylvester equations arising from the time-periodic fractional diffusion equations.

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The Relation Between Rough Wijsman Convergence And Asymptotic Cones, Öznur Ölmez, Sali̇h Aytar Jan 2016

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.

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Rings Associated To Coverings Of Finite $P$-Groups, Gary Walls, Linhong Wang Jan 2016

Rings Associated To Coverings Of Finite $P$-Groups, Gary Walls, Linhong Wang

Turkish Journal of Mathematics

In general the endomorphisms of a nonabelian group do not form a ring under the operations of addition and composition of functions. Several papers have dealt with the ring of functions defined on a group, which are endomorphisms when restricted to the elements of a cover of the group by abelian subgroups. We give an algorithm that allows us to determine the elements of the ring of functions of a finite $p$-group that arises in this manner when the elements of the cover are required to be either cyclic or elementary abelian of rank $2$. This enables us to determine …

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Every Norm Is A Restriction Of An Order-Unit Norm, Mert Çağlar, Zafer Ercan Jan 2016

Every Norm Is A Restriction Of An Order-Unit Norm, Mert Çağlar, Zafer Ercan

Turkish Journal of Mathematics

We point out the equivalence of the fact that every norm on a vector space is a restriction of an order-unit norm to that of Paulsen's construction concerning generalization of operator systems.

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Coefficient Estimates For General Subclasses Of $M$-Foldsymmetric Analytic Bi-Univalent Functions, Serap Bulut Jan 2016

Coefficient Estimates For General Subclasses Of $M$-Foldsymmetric Analytic Bi-Univalent Functions, Serap Bulut

Turkish Journal of Mathematics

In this work, we introduce and investigate two new subclasses of the bi-univalent functions in which both $f$ and $f^{-1}$ are $ m$-fold symmetric analytic functions. For functions in each of the subclasses introduced in this paper, we obtain the coefficient bounds for $ \left\vert a_{m+1}\right\vert $ and $\left\vert a_{2m+1}\right\vert .$

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Erratum To "The Geometry Of Hemi-Slant Submanifolds Of A Locally Product Riemannian Manifold", Hakan Mete Taştan, Fatma Özdemi̇r Jan 2016

Erratum To "The Geometry Of Hemi-Slant Submanifolds Of A Locally Product Riemannian Manifold", Hakan Mete Taştan, Fatma Özdemi̇r

Turkish Journal of Mathematics

No abstract provided.

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$\V\W$-Gorenstein Categories, Guoqiang Zhao, Juxiang Sun Jan 2016

$\V\W$-Gorenstein Categories, Guoqiang Zhao, Juxiang Sun

Turkish Journal of Mathematics

Let $\A$ be an abelian category, and $\V$,$\W$ two additive full subcategories of $\A$. We introduce and study the $\V\W$-Gorenstein subcategory of $\A$, which unifies many known notions, such as the Gorenstein category and the category consisting of $G_C$-projective (injective) modules, although they were defined in a different way. We also prove that the Bass class with respect to a semidualizing module is one kind of $\V\W$-Gorenstein category. The connections between $\V\W$-Gorenstein categories and Gorenstein categories are discussed. Some applications are given.

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On The Extended Zero Divisor Graph Of Commutative Rings, Driss Bennis, Jilali Mikram, Fouad Taraza Jan 2016

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 …

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Primary And Biprimary Class Sizes Implying Nilpotency Of Finite Groups, Qinhui Jiang, Changguo Shao Jan 2016

Primary And Biprimary Class Sizes Implying Nilpotency Of Finite Groups, Qinhui Jiang, Changguo Shao

Turkish Journal of Mathematics

Let $G$ be a finite group. We prove that $G$ is nilpotent if the set of conjugacy class sizes of primary and bipirimary elements is $\{1,m,n,mn\}$ with $m$ and $n$ coprime. Moreover, $m$ and $n$ are distinct primes power.

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Li--Yorke Chaos For Invertible Mappings On Noncompact Spaces, Bingzhe Hou, Lvlin Luo Jan 2016

Li--Yorke Chaos For Invertible Mappings On Noncompact Spaces, Bingzhe Hou, Lvlin Luo

Turkish Journal of Mathematics

In this paper, we give two examples to show that an invertible mapping being Li--Yorke chaotic does not imply its inverse being Li--Yorke chaotic, in which one is an invertible bounded linear operator on an infinite dimensional Hilbert space and the other is a homeomorphism on the unit open disk. Moreover, we use the last example to prove that Li--Yorke chaos is not preserved under topological conjugacy.

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The M[--] And --[M] Functors And Five Short Lemma In $H_V$-Modules, Yaser Vaziri, Mansour Ghadiri, Bijan Davvaz Jan 2016

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.

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Popoviciu Type Inequalities Via Green Function And Taylor Polynomial, Saad Ihsan Butt, Khuram Ali Khan, Josip Pecaric Jan 2016

Popoviciu Type Inequalities Via Green Function And Taylor Polynomial, Saad Ihsan Butt, Khuram Ali Khan, Josip Pecaric

Turkish Journal of Mathematics

The well-known Taylor polynomial is used to construct the identities coming from Popoviciu type inequalities for convex functions via the Green function. The bounds for the new identities are found using the Çebyşev functional to develop the Grüss and Ostrowski type inequalities. Further, more exponential convexity together with Cauchy means is presented for linear functionals associated with the obtained inequalities.

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