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Explicit Estimates On A Mixed Neumann-Robin-Cauchy Problem, Luisa Consiglieri
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.
The Moore-Penrose Inverse Of Differences And Products Of Projectors In A Ring With Involution, Huihui Zhu, Jianlong Chen, Pedro Patricio
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.
Uniqueness Of Entire Graphs In Riemannian Warped Products, Junhong Dong, Ximin Liu
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.
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
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.
The Relation Between Rough Wijsman Convergence And Asymptotic Cones, Öznur Ölmez, Sali̇h Aytar
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.
Rings Associated To Coverings Of Finite $P$-Groups, Gary Walls, Linhong Wang
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 …
Every Norm Is A Restriction Of An Order-Unit Norm, Mert Çağlar, Zafer Ercan
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.
Coefficient Estimates For General Subclasses Of $M$-Foldsymmetric Analytic Bi-Univalent Functions, Serap Bulut
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 $\left\vert a_{2m+1}\right\vert .$
Erratum To "The Geometry Of Hemi-Slant Submanifolds Of A Locally Product Riemannian Manifold", Hakan Mete Taştan, Fatma Özdemi̇r
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.
$\V\W$-Gorenstein Categories, Guoqiang Zhao, Juxiang Sun
$\V\W$-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.
On The Extended Zero Divisor Graph Of Commutative Rings, Driss Bennis, Jilali Mikram, Fouad Taraza
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 …
Primary And Biprimary Class Sizes Implying Nilpotency Of Finite Groups, Qinhui Jiang, Changguo Shao
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.
Li--Yorke Chaos For Invertible Mappings On Noncompact Spaces, Bingzhe Hou, Lvlin Luo
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.
The M[--] And --[M] Functors And Five Short Lemma In $H_V$-Modules, Yaser Vaziri, Mansour Ghadiri, Bijan Davvaz
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.
Popoviciu Type Inequalities Via Green Function And Taylor Polynomial, Saad Ihsan Butt, Khuram Ali Khan, Josip Pecaric
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.
Representations For Generalized Drazin Inverse Of Operator Matrices Over A Banach Space, Daochang Zhang
Representations For Generalized Drazin Inverse Of Operator Matrices Over A Banach Space, Daochang Zhang
Turkish Journal of Mathematics
In this paper we give expressions for the generalized Drazin inverse of a (2,2,0) operator matrix and a $2\times2$ operator matrix under certain circumstances, which generalizes and unifies several results in the literature.
Some Results And Examples On Difference Cordial Graphs, Mohammed Seoud, Shakir Salman
Some Results And Examples On Difference Cordial Graphs, Mohammed Seoud, Shakir Salman
Turkish Journal of Mathematics
In this paper we introduce some results on difference cordial graphs and describe the difference cordial labeling for some families of graphs.
Quadraticeigenparameter-Dependent Quantum Difference Equations, Yelda Aygar Küçükevci̇li̇oğlu
Quadraticeigenparameter-Dependent Quantum Difference Equations, Yelda Aygar Küçükevci̇li̇oğlu
Turkish Journal of Mathematics
The main aim of this paper is to construct quantum extension of the discrete Sturm--Liouville equation consisting of second-order difference equation and boundary conditions that depend on a quadratic eigenvalue parameter. We consider a boundary value problem (BVP) consisting of a second-order quantum difference equation and boundary conditions that depend on the quadratic eigenvalue parameter. We present a condition that guarantees that this BVP has a finite number of eigenvalues and spectral singularities with finite multiplicities.
G-Frames For Operators In Hilbert $C^{\Ast}$-Modules, Zhongqi Xiang, Yongming Li
G-Frames For Operators In Hilbert $C^{\Ast}$-Modules, Zhongqi Xiang, Yongming Li
Turkish Journal of Mathematics
We present a generalization of g-frames related to an adjointable operator $K$ on a Hilbert $C^{\ast}$-module, which we call $K$-g-frames. We obtain several characterizations of $K$-g-frames and we also give conditions under which the removal of an element from a $K$-g-frame leaves again a $K$-g-frame. In addition, we define a concept of dual, and using it we study the relation between a $K$-g-frame and a g-Bessel sequence with respect to different sequences of Hilbert $C^{\ast}$-modules.
The Sharpening Hölder Inequality Via Abstract Convexity, Gülteki̇n Tinaztepe
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.
Combining Euclidean And Adequate Rings, Huanyin Chen, Marjan Sheibani
Combining Euclidean And Adequate Rings, Huanyin Chen, Marjan Sheibani
Turkish Journal of Mathematics
We combine Euclidean and adequate rings, and introduce a new type of ring. A ring $R$ is called an E-adequate ring provided that for any $a,b\in R$ such that $aR+bR=R$ and $c\neq 0$ there exists $y\in R$ such that $(a+by,c)$ is an E-adequate pair. We shall prove that an E-adequate ring is an elementary divisor ring if and only if it is a Hermite ring. Elementary matrix reduction over such rings is also studied. We thereby generalize Domsha, Vasiunyk, and Zabavsky's theorems to a much wider class of rings.
Multiple Positive Solutions Of Nonlinear $M$-Point Dynamic Equations For $P$-Laplacian On Time Scales, Abdülkadi̇r Doğan
Multiple Positive Solutions Of Nonlinear $M$-Point Dynamic Equations For $P$-Laplacian On Time Scales, Abdülkadi̇r Doğan
Turkish Journal of Mathematics
In this paper, we study the existence of positive solutions of a nonlinear $ m $-point $p$-Laplacian dynamic equation $$(\phi_p(x^\Delta(t)))^\nabla+w(t)f(t,x(t),x^\Delta(t))=0,\hspace{2cm} t_1< t 1.$ Sufficient conditions for the existence of at least three positive solutions of the problem are obtained by using a fixed point theorem. The interesting point is the nonlinear term $f$ is involved with the first order derivative explicitly. As an application, an example is given to illustrate the result.
The Generalized Reciprocal Super Catalan Matrix, Emrah Kiliç, Talha Arikan
The Generalized Reciprocal Super Catalan Matrix, Emrah Kiliç, Talha Arikan
Turkish Journal of Mathematics
The reciprocal super Catalan matrix studied by Prodinger is further generalized, introducing two additional parameters. Explicit formulae are derived for the $LU$-decomposition and their inverses, as well as the Cholesky decomposition. The approach is to use $q$-analysis and to leave the justification of the necessary identities to the $q$-version of Zeilberger's celebrated algorithm.
On Congruences Related To Central Binomial Coefficients, Harmonic And Lucasnumbers, Si̇bel Koparal, Neşe Ömür
On Congruences Related To Central Binomial Coefficients, Harmonic And Lucasnumbers, Si̇bel Koparal, Neşe Ömür
Turkish Journal of Mathematics
In this paper, using some combinatorial identities, we present new congruences involving central binomial coefficients and harmonic, Catalan, and Fibonacci numbers. For example, for an odd prime $p$, we have \begin{eqnarray*} \sum\limits_{k=1}^{\left( p-1\right) /2}\left( -1\right) ^{k}\binom{2k}{k}% H_{k-1} &\equiv &\frac{2^{p}}{p}\left( 2F_{p+1}-5^{\left( p-1\right) /2}-1\right) ({\rm mod\ }p), \\ \sum\limits_{k=0}^{\left( p-1\right) /2}\frac{H_{k}C_{k}}{\left( -4\right) ^{k}} &\equiv &2\frac{Q_{p+1}}{p}-\frac{2^{p+1}}{p}\left( 1+2^{\left( p+1\right) /2}\right) ({\rm mod\ }p), \end{eqnarray*}% and for $\left( \frac{5}{p}\right) =1,$% \begin{equation*} \sum\limits_{k=1}^{\left( p-1\right) /2}\binom{2k}{k}\frac{H_{k-1}F_{k}}{% \left( -4\right) ^{k}}\equiv \frac{1}{p}\left( F_{2p+1}-F_{p+2}\right) -% \frac{2^{p}}{p}F_{p-1}({\rm mod\ }p), \end{equation*} where $\left\{ F_{n}\right\} $ is the Fibonacci sequence and $\left\{ Q_{n}\right\} $ is the Pell-Lucas sequence.
Factorizations Related To The Reciprocal Pascal Matrix, Helmut Prodinger
Factorizations Related To The Reciprocal Pascal Matrix, Helmut Prodinger
Turkish Journal of Mathematics
The reciprocal Pascal matrix has entries $\binom{i+j}{j}^{-1}$. Explicit formul$\ae{}$ for its LU-decomposition, the LU-decomposition of its inverse, and some related matrices are obtained. For all results, $q$-analogues are also presented.
Lagrangian Description, Symplectization, And Eulerian Dynamics Of Incompressible Fluids, Hasan Gümral
Lagrangian Description, Symplectization, And Eulerian Dynamics Of Incompressible Fluids, Hasan Gümral
Turkish Journal of Mathematics
Eulerian dynamical equations in a three-dimensional domain are used to construct a formal symplectic structure on time-extended space. Symmetries, invariants, and conservation laws are related to this geometric structure. The symplectic structure incorporates dynamics of helicities as identities. The generator of the infinitesimal dilation for symplectic two-form can be interpreted as a current vector for helicity. Symplectic dilation implies the existence of contact hypersurfaces. In particular, these include contact structures on the space of streamlines and on the Bernoulli surfaces.
Some Upper Bounds On The Dimension Of The Schur Multiplierof A Pair Of Nilpotent Lie Algebras, Behrouz Edalatzadeh
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, Peter D. Johnson, Faruk Polat
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 …
Existence Of Positive Solutions For Difference Systems Coming From A Model For Burglary, Tianlan Chen, Ruyun Ma
Existence Of Positive Solutions For Difference Systems Coming From A Model For Burglary, Tianlan Chen, Ruyun Ma
Turkish Journal of Mathematics
In this paper, we use the Brouwer degree to prove existence results of positive solutions for the following difference systems: $$\aligned &{D}_k\Delta^2(A_{k-1}-A^0_{k-1})-(A_{k}-A^0_{k})+N_kf(k, A_{k})=0,\ \ k\in[2, n-1]_\mathbb{Z},\\ &\Delta^2N_{k-1}+\Delta[g(k, A_{k}, \Delta A_{k-1})N_k]-w^2(N_k-1)=0,\ \ k\in[2, n-1]_\mathbb{Z},\\ &\Delta A_{1}=0=\Delta A_{n-1},\ \ \Delta N_{1}=0=\Delta N_{n-1}, \endaligned\eqno $$ where the assumptions on $w,\ D_k, A_k^0, f$, and $g$ are motivated by some mathematical models for the burglary of houses.
Further Results On Edge - Odd Graceful Graphs, Mohammed Seoud, Maher Salim
Further Results On Edge - Odd Graceful Graphs, Mohammed Seoud, Maher Salim
Turkish Journal of Mathematics
wheel $W_n$, for $n\equiv 1,\ 2$ and $3\ mod\ 4$; $C_n\bigodot\bar{K}_{2m-1}$; even helms; $P_n\bigodot\bar{K}_{2m}$ and $K_{2,s}$. Also we present two theorems of non edge - odd graceful graphs and an idea to label complete graphs.