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Articles 1 - 30 of 140
Full-Text Articles in Physical Sciences and Mathematics
Suborbital Graphs For The Atkin-Lehner Group, Tuncay Köroğlu, Bahadir Özgür Güler, Zeynep Şanli
Suborbital Graphs For The Atkin-Lehner Group, Tuncay Köroğlu, Bahadir Özgür Güler, Zeynep Şanli
Turkish Journal of Mathematics
We investigate suborbital graphs for an imprimitive action of the Atkin-Lehner group on a maximal subset of extended rational numbers on which a transitive action is also satisfied. Obtaining edge and some circuit conditions, we examine some combinatorial properties of these graphs.
Topological Entropies Of A Class Of Constrained Systems, Yanni Ma, Bingzhe Hou
Topological Entropies Of A Class Of Constrained Systems, Yanni Ma, Bingzhe Hou
Turkish Journal of Mathematics
In this paper, we consider a class of constrained systems named double upper bounds $(p,q)$-constrained systems ($(p,q)$-DUB systems in brief), which are one-dimensional subshifts of finite type. We determinate the topological entropies (Shannon capacities) $C(p,q)$ of all $(p,q)$-DUB systems and consequently order all $(p,q)$-DUB systems according to the size of topological entropies. In particular, $C(p, \infty)=C(p+1, p+1)$ are the only equalities possible among the topological entropies of $(p,q)$-DUB systems.
$\Mathcal{Vw}$-Gorenstein Complexes, Renyu Zhao, Wei Ren
$\Mathcal{Vw}$-Gorenstein Complexes, Renyu Zhao, Wei Ren
Turkish Journal of Mathematics
Let $\mathcal{V,W}$ be two classes of modules. In this paper, we introduce and study $\mathcal{VW}$-Gorenstein complexes as a common generalization of $\mathcal{W}$-complexes, Gorenstein projective (resp., Gorenstein injective) complexes, and $G_C$-projective (resp., $G_C$-injective) complexes. It is shown that under certain hypotheses a complex $X$ is $\mathcal{VW}$-Gorenstein if and only if each $X^n$ is a $\mathcal{VW}$-Gorenstein module. This result unifies the corresponding results of the aforementioned complexes. As an application, the stability of $\mathcal{VW}$-Gorenstein complexes is explored.
Generalized $\Ast$-Lie Ideal Of $\Ast$-Prime Ring, Seli̇n Türkmen, Neşet Aydin
Generalized $\Ast$-Lie Ideal Of $\Ast$-Prime Ring, Seli̇n Türkmen, Neşet Aydin
Turkish Journal of Mathematics
Let $R$ be a $\ast$-prime ring with characteristic not $2,$ $\sigma, \tau:R\rightarrow R$ be two automorphisms, $U$ be a nonzero $\ast$-$\left( \sigma,\tau\right) $-Lie ideal of $R$ such that $\tau~$commutes with $\ast$, and $a,b$ be in $R.$ $\left( i\right) $ If $a\in S_{\ast}\left( R\right) $ and $\left[ U,a\right] =0$, then $a\in Z\left( R\right) $ or $U\subset Z\left( R\right) .$ $\left( ii\right) $ If $a\in S_{\ast}\left( R\right) $ and $\left[ U,a\right] _{\sigma,\tau}\subset$ $C_{\sigma,\tau}$, then $a\in Z\left( R\right) ~$or$~U\subset Z\left( R\right) .$ $\left( iii\right) $ If $U\not \subset Z\left( R\right) $ and $U\not \subset C_{\sigma,\tau}$, then there exists a nonzero $\ast$-ideal $M$ of …
On Golden Semisymmetric Metric $F$-Connections, Aydin Gezer, Çağri Karaman
On Golden Semisymmetric Metric $F$-Connections, Aydin Gezer, Çağri Karaman
Turkish Journal of Mathematics
In this paper, we construct a golden semisymmetric metric $F$-connection on a locally decomposable golden Riemannian manifold and investigate some properties of its curvature, conharmonic curvature, Weyl projective curvature, and torsion tensors. Moreover, we define the transposed connection of this connection and study its curvature properties.
Singular Dirac Systems In The Sobolev Space, Eki̇n Uğurlu
Singular Dirac Systems In The Sobolev Space, Eki̇n Uğurlu
Turkish Journal of Mathematics
In this paper we construct Weyl's theory for the singular left-definite Dirac systems. In particular, we prove that there exists at least one solution of the system of equations that lies in the Sobolev space. Moreover, we describe the behavior of the solution belonging to the Sobolev space around the singular point.
Some Theorems For A New Type Of Multivalued Contractivemaps On Metric Space, Gonca Durmaz
Some Theorems For A New Type Of Multivalued Contractivemaps On Metric Space, Gonca Durmaz
Turkish Journal of Mathematics
In this paper, taking into account the function $\theta $, we introduce a new type of contraction for multivalued maps on metric space. This new concept includes many known contractions in the literature. We then present some fixed point results for closed and bounded set valued maps on complete metric space. Finally, we provide an example to show the significance of the investigation of this paper.
New Recurrences For Euler's Partition Function, Mircea Merca
New Recurrences For Euler's Partition Function, Mircea Merca
Turkish Journal of Mathematics
In this paper, the author invokes some consequences of the bisectional pentagonal number theorem to derive two linear recurrence relations for Euler's partition function $p(n)$. As a corollary of these results, we obtain an efficient method to compute the parity of Euler's partition function $p(n)$ that requires only the parity of $p(k)$ with $k \leq n/4$.
A New Approach To Uniqueness For Inverse Sturm-Liouville Problems On Finite Intervals, Seyfollah Mosazadeh
A New Approach To Uniqueness For Inverse Sturm-Liouville Problems On Finite Intervals, Seyfollah Mosazadeh
Turkish Journal of Mathematics
In this paper, an approach for studying inverse Sturm--Liouville problems with integrable potentials on finite intervals is presented. We find the relations between Weyl solutions and $m_{j}$-functions of Sturm--Liouville problems, and by finding the connection between these and the solutions of second-order partial differential equations for transformation kernels associated with Sturm--Liouville operators, we prove the uniqueness of the solution of inverse problems.
Corrigendum: On Density Theorems For Rings Of Krull Type With Zero Divisors, Başak Ay Saylam
Corrigendum: On Density Theorems For Rings Of Krull Type With Zero Divisors, Başak Ay Saylam
Turkish Journal of Mathematics
This corrigendum is written to correct some parts of the paper "On density theorems for rings of Krull type with zero divisors". The proofs of Proposition 2.4 and Proposition 4.3 are incorrect and the current note makes the appropriate corrections.
Evaluation Of Euler-Like Sums Via Hurwitz Zeta Values, Ayhan Di̇l, Istvan Mezo, Mehmet Cenkci̇
Evaluation Of Euler-Like Sums Via Hurwitz Zeta Values, Ayhan Di̇l, Istvan Mezo, Mehmet Cenkci̇
Turkish Journal of Mathematics
In this paper we collect two generalizations of harmonic numbers (namelygeneralized harmonic numbers and hyperharmonic numbers) under one roof.Recursion relations, closed-form evaluations, and generating functions of thisunified extension are obtained. In light of this notion we evaluate someparticular values of Euler sums in terms of odd zeta values. We alsoconsider the noninteger property and some arithmetical aspects of this unifiedextension.
Piecewise Asymptotically Almost Periodic Solution Of Neutral Volterra Integro-Differential Equations With Impulsive Effects, Zhinan Xia
Turkish Journal of Mathematics
In this paper, we investigate the existence and uniqueness ofa piecewise asymptotically almost periodic mild solution tononautonomous neutral Volterra integro-differential equations withimpulsive effects in Banach space. The working tools are based onthe Krasnoselskii's fixed point theorem and semigroup theory. Inorder to illustrate our main results, we study the piecewiseasymptotically almost periodic solution of the impulsive partialdifferential equations with Dirichlet conditions.
Warped Product Spaces With Ricci Conditions, Sang Deok Lee, Byung Hak Kim, Jin Hyuk Choi
Warped Product Spaces With Ricci Conditions, Sang Deok Lee, Byung Hak Kim, Jin Hyuk Choi
Turkish Journal of Mathematics
In this paper, we study the Ricci soliton in the Riemannian products$M=R^n \times B$ and warped products $M=R \times _f B$ of theEuclidean space and Riemannian manifolds, and the gradient Riccisoliton in the warped products $M=S^1 \times _f B$ of 1-dimensionalcircle and Riemannian manifolds. Moreover, we introduce the concept ofthe generalized Ricci soliton and we suggest the method of constructionof the Riemannian manifold $(M, g)$ with a Ricci soliton $g$.Finally, we also study the Lorentzian warped products with the Riccisoliton.
Regularity Of Solutions Of The Anisotropic Hyperbolic Heat Equation With Nonregular Heat Sources And Homogeneous Boundary Conditions, Juan Antonio López Molina, Macarena Trujillo
Regularity Of Solutions Of The Anisotropic Hyperbolic Heat Equation With Nonregular Heat Sources And Homogeneous Boundary Conditions, Juan Antonio López Molina, Macarena Trujillo
Turkish Journal of Mathematics
We study regularity properties for the solution of homogeneous boundary value problems for the anisotropic hyperbolic heat equation in the case of infinitely differentiable coefficients but irregular distributions as internal heat sources.
The Most Important Inequalities Of $M$-Convex Functions, Zlatko Pavic, Merve Avci Ardiç
The Most Important Inequalities Of $M$-Convex Functions, Zlatko Pavic, Merve Avci Ardiç
Turkish Journal of Mathematics
The intention of this article is to investigate the most important inequalities of $m$-convex functions without using their derivatives. The article also provides a brief survey of general properties of $m$-convex functions.
Evaluation Of Sums Involving Products Of Gaussian $Q$-Binomial Coefficients With Applications To Fibonomial Sums, Emrah Kiliç, Helmut Prodinger
Evaluation Of Sums Involving Products Of Gaussian $Q$-Binomial Coefficients With Applications To Fibonomial Sums, Emrah Kiliç, Helmut Prodinger
Turkish Journal of Mathematics
Sums of products of two Gaussian $q$-binomial coefficients with a parametric rational weight function are considered. The partial fraction decomposition technique is used to evaluate the sums in closed form. Interesting applications of these results to certain generalized Fibonomial and Lucanomial sums are provided.
$Cc$-Normal Topological Spaces, Lutfi Kalantan, Manal Alhomieyed
$Cc$-Normal Topological Spaces, Lutfi Kalantan, Manal Alhomieyed
Turkish Journal of Mathematics
A topological space $X$ is called \it $CC$-normal \rm if there exist a normal space $Y$ and a bijective function $f:X\longrightarrow Y$ such that the restriction $f_{ _A}:A\longrightarrow f(A)$ is a homeomorphism for each countably compact subspace $A\subseteq X$. We will investigate this property and produce some examples to illustrate the relation between $CC$-normality and other weaker kinds of normality.
Product Of Arbitrary Fibonacci Numbers With Distance 1 To Fibonomial Coefficient, Nuretti̇n Irmak
Product Of Arbitrary Fibonacci Numbers With Distance 1 To Fibonomial Coefficient, Nuretti̇n Irmak
Turkish Journal of Mathematics
In this paper, we solve completely the Diophantine equation \begin{gather} F_{n_{1}}F_{n_{2}}\ldots F_{n_{k}}\pm 1={m\brack t}_{F} \end{gather} for $t=1$ and $t=2$ where $2$ < $n_{1}$ < $n_{2}$ < $\ldots$ < $n_{k}$ positive integers and ${m\brack t}_{F}$ is the Fibonomial coefficient.
On Focal Curves Of Null Cartan Curves, Hakan Şi̇mşek
On Focal Curves Of Null Cartan Curves, Hakan Şi̇mşek
Turkish Journal of Mathematics
The focal curve, which is determined as the locus of centers of osculatingpseudo-spheres of a null Cartan curve, is investigated in Minkowski(n+2)-space $\mathcal{M}^{n+2}.$ Moreover, a curve called \textit{accelerationfocal curve }of a null Cartan curve is introduced by using a new family of functions.
Extension Of The Darboux Frame Into Euclidean 4-Space And Its Invariants, Mustafa Düldül, Bahar Uyar Düldül, Nuri̇ Kuruoğlu, Ertuğrul Özdamar
Extension Of The Darboux Frame Into Euclidean 4-Space And Its Invariants, Mustafa Düldül, Bahar Uyar Düldül, Nuri̇ Kuruoğlu, Ertuğrul Özdamar
Turkish Journal of Mathematics
In this paper, by considering a Frenet curve lying on an oriented hypersurface, we extend the Darboux frame field into Euclidean 4-space $\mathbb{E}^4$. Depending on the linear independency of the curvature vector with the hypersurface's normal, we obtain two cases for this extension. For each case, we obtain some geometrical meanings of new invariants along the curve on the hypersurface. We also give the relationships between the Frenet frame curvatures and Darboux frame curvatures in $\mathbb{E}^4$. Finally, we compute the expressions of the new invariants of a Frenet curve lying on an implicit hypersurface.
A Note On Dynamics In Functional Spaces, Liangxue Peng, Chong Yang
A Note On Dynamics In Functional Spaces, Liangxue Peng, Chong Yang
Turkish Journal of Mathematics
In this note, we study topologically transitive and hypercyclic composition operators on $C_p(X)$ or $C_k(X)$. We prove that if $G$ is a semigroup of continuous self maps of a countable metric space $X$ with the following properties: (1) every element of $G$ is one-to-one on $X$, (2) the action of $G$ is strongly run-away on $X$, then the action of $\hat{G}$ on $C_p(X)$ is topologically transitive and hypercyclic. If $G$ is the set of all one-to-one and continuous self maps of $\mathbb{R}\setminus \mathbb{Z}$, then the action of $\hat{G}$ on $C_k(\mathbb{R}\setminus \mathbb{Z})$ is hypercyclic. We also show that the action of …
On The Volume Of The Indicatrix Of A Complex Finsler Space, Elena Popovici
On The Volume Of The Indicatrix Of A Complex Finsler Space, Elena Popovici
Turkish Journal of Mathematics
Following the study on volume of indicatrices in a real Finsler space, in this paper we are investigating some volume properties of the indicatrix considered in an arbitrary fixed point of a complex Finsler manifold. Since for each point of a complex Finsler space the indicatrix is an embedded CR-hypersurface of the punctured holomorphic tangent bundle, by means of its normal vector, the volume element of the indicatrix is determined. Thus, the volume function is pointed out and its variation is studied. Conditions under which the volume is constant are also determined and some classes of complex Finsler spaces with …
Graph-Directed Fractal Interpolation Functions, Ali̇ Deni̇z, Yunus Özdemi̇r
Graph-Directed Fractal Interpolation Functions, Ali̇ Deni̇z, Yunus Özdemi̇r
Turkish Journal of Mathematics
It is known that there exists a function interpolating a given data set such that the graph of the function is the attractor of an iterated function system, which is called a fractal interpolation function. We generalize the notion of the fractal interpolation function to the graph-directed case and prove that for a finite number of data sets there exist interpolation functions each of which interpolates a corresponding data set in $\mathbb{R}^2$ such that the graphs of the interpolation functions are attractors of a graph-directed iterated function system.
Optimality Conditions Via Weak Subdifferentials In Reflexive Banach Spaces, Sara Hassani, Musa Mammadov, Mina Jamshidi
Optimality Conditions Via Weak Subdifferentials In Reflexive Banach Spaces, Sara Hassani, Musa Mammadov, Mina Jamshidi
Turkish Journal of Mathematics
In this paper the relation between the weak subdifferentials and the directional derivatives, as well as optimality conditions for nonconvex optimization problems in reflexive Banach spaces, are investigated. It partly generalizes several related results obtained for finite dimensional spaces.
Some Fixed Point Theorems For Single Valued Strongly Contractive Mappings In Partially Ordered Ultrametric And Non-Archimedean Normed Spaces, Hamid Mamghaderi, Hashem Parvaneh Masiha, Meraj Hosseini
Some Fixed Point Theorems For Single Valued Strongly Contractive Mappings In Partially Ordered Ultrametric And Non-Archimedean Normed Spaces, Hamid Mamghaderi, Hashem Parvaneh Masiha, Meraj Hosseini
Turkish Journal of Mathematics
Let $ (X,d,\preceq) $ be a partially ordered ultrametric space and $ f:X\to X $ a single valued mapping. We obtain sufficient conditions for the existence of a fixed point for the strongly contractive mapping $ f $. We also investigate the existence of a fixed point for strongly contractive mappings defined on partially ordered non-Archimedean normed spaces under the same conditions. Finally, we give some examples to discuss the assumptions of the theorems.
Extensions Of Quasipolar Rings, Orhan Gürgün
Extensions Of Quasipolar Rings, Orhan Gürgün
Turkish Journal of Mathematics
An associative ring with identity is called quasipolar provided that for each $a\in R$ there exists an idempotent $p\in R$ such that $p\in comm^2(a)$, $a+p\in U(R)$ and $ap\in R^{qnil}$. In this article, we introduce the notion of quasipolar general rings (with or without identity). Some properties of quasipolar general rings are investigated. We prove that a general ring $I$ is quasipolar if and only if every element $a\in I$ can be written in the form $a=s+q$ where $s$ is strongly regular, $s\in comm^2(a)$, $q$ is quasinilpotent, and $sq=qs=0$. It is shown that every ideal of a quasipolar general ring is …
Correcting A Paper On The Randic And Geometric-Arithmetic Indices, Toufik Mansour, Mohammad Ali Rostami, Suresh Elumalai, Britto Antony Xavier
Correcting A Paper On The Randic And Geometric-Arithmetic Indices, Toufik Mansour, Mohammad Ali Rostami, Suresh Elumalai, Britto Antony Xavier
Turkish Journal of Mathematics
The Randic index $(R)$ and the geometric--arithmetic index $(GA)$ are found to be useful tools in QSPR and QSAR studies. In the Journal of Inequalities and Applications 180, 1-7, Lokesha, Shwetha Shetty, Ranjini, Cangul, and Cevik gave "New bounds for Randic and GA indices." In the paper, we first point out that Theorems 1, 2, and 4 are incorrect and in this short note we present the correct inequalities for Randic and GA indices. In the same paper, we provide the equality cases for Theorems 3, 5, and 6.
More Characterizations Of Dedekind Domains And V-Rings, Thuat Van Do, Hai Dinh Hoang, Samruam Baupradist
More Characterizations Of Dedekind Domains And V-Rings, Thuat Van Do, Hai Dinh Hoang, Samruam Baupradist
Turkish Journal of Mathematics
In this paper, cyclic $c-$injective modules are introduced and investigated. It is shown that a commutative Noetherian domain is Dedekind if and only if every simple module is cyclic $c-$injective. Finally, it is shown that injectivity, principal injectivity, mininjectivity, and simple injectivity are all equal to characterize right V-rings, right GV-rings, right pV-rings, and WV-rings.
Maximal Subsemigroups And Finiteness Conditions On Transformation Semigroups With Fixed Sets, Yanisa Chaiya, Preeyanuch Honyam, Jintana Sanwong
Maximal Subsemigroups And Finiteness Conditions On Transformation Semigroups With Fixed Sets, Yanisa Chaiya, Preeyanuch Honyam, Jintana Sanwong
Turkish Journal of Mathematics
Let $Y$ be a fixed subset of a nonempty set $X$ and let $Fix(X,Y)$ be the set of all self maps on $X$ which fix all elements in $Y$. Then under the composition of maps, $Fix(X,Y)$ is a regular monoid. In this paper, we prove that there are only three types of maximal subsemigroups of $Fix\left(X,Y\right)$ and these maximal subsemigroups coincide with the maximal regular subsemigroups when $X\setminus Y$ is a finite set with $ X\setminus Y \geq 2$. We also give necessary and sufficient conditions for $Fix(X,Y)$ to be factorizable, unit-regular, and directly finite.
Dynamic Shum Inequalities, Ravi Agarwal, Martin Bohner, Donal O'Regan, Samir Saker
Dynamic Shum Inequalities, Ravi Agarwal, Martin Bohner, Donal O'Regan, Samir Saker
Turkish Journal of Mathematics
Recently, various forms and improvements of Opial dynamic inequalities have been given in the literature. In this paper, we give refinements of Opial inequalities on time scales that reduce in the continuous case to classical inequalities named after Beesack and Shum. These refinements are new in the important discrete case.