Some Higher-Order Identities For Generalized Bi-Periodic Horadam Sequences,
2020
TÜBİTAK
Some Higher-Order Identities For Generalized Bi-Periodic Horadam Sequences, Ho-Hon Leung, Eli̇f Tan
Turkish Journal of Mathematics
In this paper, we derive higher-order identities for the generalized bi-periodic Horadam sequences. Some of our results generalize the identities for the classical Fibonacci sequences and Horadam sequences obtained by Hoggatt, Horadam and Waddill. As an application, we derive some congruence properties satisfied by the generalized bi-periodic Horadam sequences.
Extension Of Montgomery Identity Via Taylor Polynomial On Time Scales,
2020
TÜBİTAK
Extension Of Montgomery Identity Via Taylor Polynomial On Time Scales, Khuram Ali Khan, Khalid Mahmood Awan, Sumaiya Malik, Ammara Nosheen
Turkish Journal of Mathematics
An extension in Montgomery identity with the help of Taylor?s formula on time scales is provided in the paper, which is used to establish Ostrowski type inequality, midpoint inequality and trapezoid type inequality on time scales in generalized forms. The weighted version of obtained Montgomery identity and respective Ostrowski inequality are also addressed at the end of the paper.
An Algorithm To Check The Equality Of Total Domination Number And Double Of Domination Number In Graphs,
2020
TÜBİTAK
An Algorithm To Check The Equality Of Total Domination Number And Double Of Domination Number In Graphs, Seli̇m Bahadir
Turkish Journal of Mathematics
In graph theory, domination number and its variants such as total domination number are studied by many authors. Let the domination number and the total domination number of a graph $G$ without isolated vertices be $\gamma(G)$ and $\gamma_t(G)$, respectively. Based on the inequality $\gamma_t(G) \leq 2\gamma(G)$, we investigate the graphs satisfying the upper bound, that is, graphs $G$ with $\gamma_t(G) = 2\gamma(G)$. In this paper, we present some new properties of such graphs and provide an algorithm which can determine whether $\gamma_t(G) = 2\gamma(G)$ or not for a family of graphs not covered by the previous results in the literature.
Benedicks And Donoho-Stark Type Theorems,
2020
TÜBİTAK
Benedicks And Donoho-Stark Type Theorems, Lotfi Kamoun, Raoudha Laffi
Turkish Journal of Mathematics
In this paper, we prove a Benedicks type theorem and a Donoho-Stark type theorem, for the generalized Fourier transform $\mathcal{F}_\alpha$ associated to some differential operators that we call Flensted-Jensen operators, in various spaces such $\mathrm{L}^1_\alpha(\mathbb{K})$, $\mathrm{L}^2_\alpha(\mathbb{K})$ and $\mathrm{L}^1_\alpha(\mathbb{K})\cap\mathrm{L}^2_\alpha(\mathbb{K})$, where $\mathbb{K}=\mathbb{R}_+\times\mathbb{R}$
Some Characterizations Of Kb-Operators On Banach Lattices And Ordered Banach Spaces,
2020
TÜBİTAK
Some Characterizations Of Kb-Operators On Banach Lattices And Ordered Banach Spaces, Bi̇rol Altin, Nabil Machrafi
Turkish Journal of Mathematics
We determine that two recent classes of KB-operators and weak KB-operators and the well-known class of b-weakly compact operators, from a Banach lattice into a Banach space, are the same. We extend our study to the ordered Banach space setting by showing that a weak chain-preserving operator between two ordered Banach spaces is a KB-operator if and only if it is a weak KB-operator.
The Generalized Inverses Of The Products Of Two Elements In A Ring,
2020
TÜBİTAK
The Generalized Inverses Of The Products Of Two Elements In A Ring, Kai Yan, Qingping Zeng
Turkish Journal of Mathematics
In this paper, new extensions of Jacobson's lemma and Cline's formula for Drazin inverses, generalized Drazin inverses, and ($m,n$)-pseudo-inverses are given. As applications, we provide a formula for the powers of the products of two elements and establish connections between two B-Fredholm elements through the canonical map.
On Hausdorff-Young Inequalities In Generalized Lebesgue Spaces,
2020
TÜBİTAK
On Hausdorff-Young Inequalities In Generalized Lebesgue Spaces, Miqdad Ismailov
Turkish Journal of Mathematics
Lebesgue spaces with the variable rate of summability are considered in this work. Generalizations of Riesz and Paley theorems are proved in these spaces. The obtained results are applied, in particular, to a classical exponential system.
On $\Mathcal{X}$-Gorenstein Projective Dimensions And Precovers,
2020
TÜBİTAK
On $\Mathcal{X}$-Gorenstein Projective Dimensions And Precovers, Bin Yu
Turkish Journal of Mathematics
For a class of $R$-modules $\mathcal{X}$ containing all projective $R$-modules, the $\mathcal{X}$-Gorenstein projective $R$-modules vary from projective to Gorenstein projective $R$-modules. We characterize the rings over which the left global $\mathcal{X}$-Gorenstein projective dimensions are finite. If further $\mathcal{Y}$ contains all injective $R$-modules, we show the existence of a new left global Gorenstein dimension of $R$ with respect to $\mathcal{X}$ and $\mathcal{Y}$ satisfying proper conditions. As an application we characterize Ding-Chen rings by this new global Gorenstein dimension and show the existence of Ding-Chen rings with infinite global Gorenstein dimension. We also show the existence of $\mathcal{X}$-Gorenstein projective precovers for a …
On The Autocentralizer Subgroups Of Finite $P$--Groups,
2020
TÜBİTAK
On The Autocentralizer Subgroups Of Finite $P$--Groups, Parisa Seifizadeh, Ali Gholamian, Amirali Farokhniaee, Mohammad Mehdi Nasrabadi
Turkish Journal of Mathematics
Let $G$ be a finite group and ${\rm Aut}(G)$ be the group of automorphisms of $G.$ Then, the autocentralizer of an automorphism $\alpha\in {\rm Aut}(G)$ in $G$ is defined as $C_{G}(\alpha)= \lbrace g \in G\vert \alpha(g)=g\rbrace.$ Let $Acent(G)=\lbrace C_{G}(\alpha)\vert \alpha \in {\rm Aut}(G) \rbrace.$ If $\vert Acent(G)\vert= n,$ then $G$ is an $n$--autocentralizer group. In this paper, we classify all $n$--autocentralizer abelian groups for $n=$ 6, 7 and 8. We also obtain a lower bound on the number of autocentralizer subgroups for $p$--groups, where $p$ is a prime number. We show that if $p\neq 2,$ there is no $n$--autocentralizer $p$--group …
Application Of Spectral Mapping Method To Dirac Operator,
2020
TÜBİTAK
Application Of Spectral Mapping Method To Dirac Operator, Rauf Ami̇rov, Merve Arslantaş
Turkish Journal of Mathematics
In the present study, theorems related to the uniqueness of the solution of inverse problems for Dirac equations system are proved by applying spectral mapping method. With the help of this method, the inverse problem is reduced to the so-called main equation, which corresponds to the problem of existence and uniqueness of the solution of the system of linear equations in the Banach space.
Lattice Ordered Semigroups And $\Gamma$-Hypersemigroups,
2020
TÜBİTAK
Lattice Ordered Semigroups And $\Gamma$-Hypersemigroups, Niovi Kehayopulu
Turkish Journal of Mathematics
As we have already seen in Turkish Journal of Mathematics (2019) 43: 2592-2601 many results on hypersemigroups do not need any proof as they can be obtained from lattice ordered semigroups. The present paper goes a step further, to show that many results on $\Gamma$-hypersemigroups as well can be obtained from lattice ordered semigroups. It can be instructive to prove them directly, but even in that case the proofs go along the lines of lattice ordered semigroups (or $poe$-semigroups). In the investigation, we faced the problem to correct the definition of $\Gamma$-hypersemigroups given in the existing bibliography.
Dynamics Of A Fluid Equation With Neumann Boundary Conditions,
2020
TÜBİTAK
Dynamics Of A Fluid Equation With Neumann Boundary Conditions, Limin Chen, Shengjun Li, Yumei Zou
Turkish Journal of Mathematics
We study the dynamics of a Neumann boundary value problem arising in fluid dynamics. We prove the nonexistence, existence and uniqueness of positive solutions under suitable conditions. At the same time, under stricter conditions, we also obtain the dynamic properties of the Neumann boundary value problem, such as the stability and instability of positive solutions. The methods of proof mainly involve the upper and lower solutions method, eigenvalue theory and some analysis techniques.
Hypergeometric Distribution Of The Number Of Draws From An Urn With Two Types Of Items Before One Of The Counts Reaches A Threshold, J. L. Gonzalez-Santander
Turkish Journal of Mathematics
We consider an urn with $R$ elements of one type and $B$ elements of other type. We calculate the probability distribution $P_{n_{R},n_{B}}^{R,B}\left( s\right) $ wherein the random variable $s$ is the number of draws from the urn until we reach $n_{R}$ elements of type $R$ or $n_{B}$ elements of type $B$. We calculate the mean value $\left\langle s\right\rangle $ and the standard deviation $\sigma $ of $P_{n_{R},n_{B}}^{R,B}\left( s\right) $ in terms of hypergeometric functions. For $n_{R}=n_{B}$ and $B=R$ , we reduce $\left\langle s\right\rangle $ and $\sigma $ in terms of elementary functions. Also, the normalization condition leads to a new …
Classification Of Some Subclasses Of 6-Dimensional Nilpotent Leibniz Algebras,
2020
TÜBİTAK
Classification Of Some Subclasses Of 6-Dimensional Nilpotent Leibniz Algebras, Ismail Demir
Turkish Journal of Mathematics
This article is a contribution to the improvement of classification theory in Leibniz algebras. We extend the method of congruence classes of matrices of bilinear forms that was used to classify complex nilpotent Leibniz algebras with one dimensional derived algebra. In this work we focus on applying this method to the classification of 6-dimensional complex nilpotent Leibniz algebras with two dimensional derived algebra.
Vacuum Isolating And Blow-Up Analysis For Edge Hyperbolic System On Edge Sobolev Spaces,
2020
TÜBİTAK
Vacuum Isolating And Blow-Up Analysis For Edge Hyperbolic System On Edge Sobolev Spaces, Morteza Koozehgar Kalleji, Nematollah Kadkhoda
Turkish Journal of Mathematics
This paper deals with the study of the initial-boundary value problem of edge-hyperbolic system with damping term on the manifold with edge singularity. More precisely, it is analyzed the invariance and vacuum isolating of the solution sets to the edge-hyperbolic systems on edge Sobolev spaces. Then, by using a family of modified potential wells and concavity methods, it is obtained existence and nonexistence results of global solutions with exponential decay and is shown the blow-up in finite time of solutions on the manifold with edge singularities.
The Third Logarithmic Coefficient For The Class $\Mathcal{S}$,
2020
TÜBİTAK
The Third Logarithmic Coefficient For The Class $\Mathcal{S}$, Milutin Obradovic, Nikola Tuneski
Turkish Journal of Mathematics
In this paper we give an upper bound of the third logarithmic coefficient for the class $\mathcal{S}$ of univalent functions in the unit disc.
Representation Numbers Of Seven Quaternary Quadratic Forms Each In A Genus Consisting Of Only Two Classes,
2020
TÜBİTAK
Representation Numbers Of Seven Quaternary Quadratic Forms Each In A Genus Consisting Of Only Two Classes, Ayşe Alaca, Şaban Alaca, Kenneth Williams
Turkish Journal of Mathematics
The purpose of this paper is to present some examples of positive-definite integral nondiagonal quaternary quadratic forms whose representation numbers can be determined explicitly using the theory of modular forms. Very few such examples appear in the literature. The seven forms presented were selected because they each belong to a genus containing exactly two form classes for which the single genus mate is a diagonal form whose representation number has been determined recently.
On Certain Subclasses Of Starlike And Convex Functions Associated With Pascal Distribution Series,
2020
TÜBİTAK
On Certain Subclasses Of Starlike And Convex Functions Associated With Pascal Distribution Series, Bi̇lal Şeker, Sevtap Sümer Eker
Turkish Journal of Mathematics
In this article, we introduced a new power series whose coefficients are probabilities of the Pascal distribution. We investigated new approaches between the Pascal distribution series and some subclasses of normalized analytic functions. Also, we defined some mappings containing these functions the Alexander type integral operator. Moreover, we obtained sufficient conditions such that these mappings belong to some subclass of univalent functions.
Generalized $\Pi$-Baer Rings,
2020
TÜBİTAK
Generalized $\Pi$-Baer Rings, Ali Shahidikia, Hamid Haj Seyyed Javadi, Ahmad Moussavi
Turkish Journal of Mathematics
We call a ring $R$ generalized right $\pi$-Baer, if for any projection invariant left ideal $Y$ of $R$, the right annihilator of $Y^n$ is generated, as a right ideal, by an idempotent, for some positive integer $n$, depending on $Y$. In this paper, we investigate connections between the \g $\pi$-Baer rings and related classes of rings (e.g., $\pi$-Baer, generalized Baer, generalized quasi-Baer, etc.) In fact, generalized right $\pi$-Baer rings are special cases of generalized right quasi-Baer rings and also are a generalization of $\pi$-Baer and generalized right Baer rings. The behavior of the generalized right $\pi$-Baer condition is investigated with …
Some Deformations Of The Fibred Biset Category,
2020
TÜBİTAK
Some Deformations Of The Fibred Biset Category, Laurence Barker, İsmai̇l Alperen Öğüt
Turkish Journal of Mathematics
We prove the well-definedness of some deformations of the fibred biset category in characteristic zero. The method is to realize the fibred biset category and the deformations as the invariant parts of some categories whose compositions are given by simpler formulas. Those larger categories are constructed from a partial category of subcharacters by linearizing and introducing a cocycle.
