The Exponential Diophantine Equation $(3am^2-1)^X+(A(A-3)M^2+1)^Y=(Am)^Z$,
2019
TÜBİTAK
The Exponential Diophantine Equation $(3am^2-1)^X+(A(A-3)M^2+1)^Y=(Am)^Z$, Nai-Juan Deng, Dan-Yao Wu, Ping-Zhi Yuan
Turkish Journal of Mathematics
Let $a,\ m$ be positive integers such that $am\not\equiv0\pmod{3}, 2\nmid a$, and $a>3$. We prove that the exponential Diophantine equation $(3am^2-1)^x+(a(a-3)m^2+1)^y=(am)^z$ has only the positive integer solution $(x,y,z)=(1,1,2)$.
Fekete-Szegö Problem For A General Subclass Of Analytic Functions,
2019
TÜBİTAK
Fekete-Szegö Problem For A General Subclass Of Analytic Functions, Nesli̇han Uyanik
Turkish Journal of Mathematics
In this present investigation, we introduced a certain subclass of starlike and convex functions of complex order $b$, using a linear multiplier differential operator $D_{\lambda ,\mu }^{m}f(z)$. For this class, the Fekete-Szegö problem is completely solved. Various new special cases are considered.
On Factorials In Perrin And Padovan Sequences,
2019
TÜBİTAK
On Factorials In Perrin And Padovan Sequences, Nuretti̇n Irmak
Turkish Journal of Mathematics
Assume that $w_n$ is the $n$th term of either Padovan or Perrin sequence. In this paper, we solve the equation $w_n=m!$ completely.
Ricci-Yamabe Maps For Riemannian Flows And Their Volume Variation And Volume Entropy,
2019
TÜBİTAK
Ricci-Yamabe Maps For Riemannian Flows And Their Volume Variation And Volume Entropy, Si̇nem Güler, Mircea Crasmareanu
Turkish Journal of Mathematics
The aim of this short note is to produce new examples of geometrical flows associated to a given Riemannian flow $g(t)$. The considered flow in covariant symmetric $2$-tensor fields will be called Ricci-Yamabe map since it involves a scalar combination of Ricci tensor and scalar curvature of $g(t)$. Due to the signs of considered scalars the Ricci-Yamabe flow can be also a Riemannian or semi-Riemannian or singular Riemannian flow. We study the associated function of volume variation as well as the volume entropy. Finally, since the two-dimensional case was the most commonly addressed situation we express the Ricci flow equation …
On Congruences For $Q$-Analogues Of Ballot Numbers,
2019
TÜBİTAK
On Congruences For $Q$-Analogues Of Ballot Numbers, Si̇bel Koparal
Turkish Journal of Mathematics
In this paper, we examine some congruences with $q$-analogues of ballot numbers. For example, for $n>1$ and $% d=0,1,...,n-1$, \begin{eqnarray*} &&\sum\limits_{k=1}^{n-d}q^{k}B_{k,d}^{q}\equiv -2+\left( -1\right) ^{n-d}\left( \frac{n-d+1}{3}\right) q^{-\frac{1}{3}\binom{n-d}{2}}-\left( \frac{n-d-1% }{3}\right) q^{d+1-\frac{1}{3}\binom{n-d-2}{2}} \pmod{\Phi _{n}\left( q\right)} , \end{eqnarray*}% with the Legendre symbol $\left( \frac{.}{3}\right) ,~$the$~q$-analogue of ballot number $B_{n,d}^{q}$, and the $n$th cyclotomic polynomial $% \Phi _{n}\left( q\right) $.
Radii Of Starlikeness And Convexity Of $Q$-Mittag-Leffler Functions,
2019
TÜBİTAK
Radii Of Starlikeness And Convexity Of $Q$-Mittag-Leffler Functions, Evri̇m Toklu
Turkish Journal of Mathematics
In this paper we deal with the radii of starlikeness and convexity of the $q$-Mittag-Leffler function for three different kinds of normalization by making use of their Hadamard factorization in such a way that the resulting functions are analytic in the unit disk of the complex plane. By applying Euler-Rayleigh inequalities for the first positive zeros of these functions tight lower and upper bounds for the radii of starlikeness of these functions are obtained. The Laguerre-P\'olya class of real entire functions plays a pivotal role in this investigation.
Derivations Of Generalized Quaternion Algebra,
2019
TÜBİTAK
Derivations Of Generalized Quaternion Algebra, Eyüp Kizil, Yasemi̇n Alagöz
Turkish Journal of Mathematics
The purpose of this paper is to determine derivations of the algebra $H_{\alpha ,\beta }$ of generalized quaternions over the reals and hence to obtain the algebra $Der(H_{\alpha ,\beta })$ of derivations of $H_{\alpha ,\beta }$. Once we know derivations we might decompose $Der(H_{\alpha ,\beta })$ in terms of its inner and/or central derivations whenever they exist. Apart from $Der(H_{\alpha ,\beta })$ we would also be able to obtain generalized derivations, which have been studied by analysts in the context of algebras of some normed spaces, and of prime and semiprime rings.
Automorphisms Of Free Metabelian Leibniz Algebras Of Rank Three,
2019
TÜBİTAK
Automorphisms Of Free Metabelian Leibniz Algebras Of Rank Three, Tuba Taş Adiyaman, Zeynep Özkurt
Turkish Journal of Mathematics
In this work, we determine the structure of the automorphism group of the free metabelian Leibniz algebra of rank three over a field K of characteristic zero.
On The N-Strong Drazin Invertibility In Rings,
2019
TÜBİTAK
On The N-Strong Drazin Invertibility In Rings, Honglin Zou, Dijana Mosic, Kezheng Zuo, Yinlan Chen
Turkish Journal of Mathematics
Let R be a ring and n be a positive integer. In this paper, further results on the n-strong Drazin inverse are obtained in a ring. We prove that a ∈ R is n-strongly Drazin invertible if and only if a-an+1 is nilpotent. In terms of this characterization, the extensions of Cline's formula and Jacobson's lemma for this inverse are proved. Moreover, the n-strong Drazin invertibility for the sums of two elements is considered. We prove that a,b ∈ R are n-strongly Drazin invertible if and only if a + b is n-strongly Drazin invertible, under the condition ab = …
Sherman's Inequality And Its Converse For Strongly Convex Functions Withapplications To Generalizedf-Divergences,
2019
TÜBİTAK
Sherman's Inequality And Its Converse For Strongly Convex Functions Withapplications To Generalizedf-Divergences, Slavica Ivelic Bradanovic
Turkish Journal of Mathematics
Considering the weighted concept of majorization, Sherman obtained generalization of majorization inequality for convex functions known as Sherman's inequality. We extend Sherman's result to the class of n-strongly convex functions using extended idea of convexity to the class of strongly convex functions. We also obtain upper bound for Sherman's inequality, called the converse Sherman inequality, and as easy consequences we get Jensen's as well as majorization inequality and their conversions for strongly convex functions. Obtained results are stronger versions for analogous results for convex functions. As applications, we introduced a generalized concept of f-divergence and derived some reverse relations for …
Study On The Q-Analogue Of A Certain Family Of Linear Operators,
2019
TÜBİTAK
Study On The Q-Analogue Of A Certain Family Of Linear Operators, Shujaat Ali Shah, Khalida Inayat Noor
Turkish Journal of Mathematics
Inthispaper, weintroducetheq-analogueofacertainfamilyoflinearoperatorsingeometricfunctiontheory. Our main purpose is to define some subclasses of analytic functions by means of the q-analogue of linear operators and investigate various inclusion relationships with integral preserving properties.
Unbounded Absolutely Weak Dunford-Pettis Operators,
2019
TÜBİTAK
Unbounded Absolutely Weak Dunford-Pettis Operators, Nazi̇fe Erkurşun Özcan, Ni̇yazi̇ Anil Gezer, Omid Zabeti
Turkish Journal of Mathematics
In the present article, we expose various properties of unbounded absolutely weak Dunford?Pettis and unbounded absolutely weak compact operators on a Banach lattice E. In addition to their topological and lattice properties, we investigate relationships between M-weakly compact operators, L-weakly compact operators, and order weakly compact operators with unbounded absolutely weak Dunford-Pettis operators. We show that the square of any positive uaw-Dunford-Pettis (M-weakly compact) operator on an order continuous Banach lattice is compact. Many examples are given to illustrate the essential conditions.
The Intrinsic Metric And Geodesics On The Sierpinski Gasket Sg(3),
2019
TÜBİTAK
The Intrinsic Metric And Geodesics On The Sierpinski Gasket Sg(3), Yunus Özdemi̇r
Turkish Journal of Mathematics
We give an explicit expression for the intrinsic metric on the Sierpinski gasket SG(3) (the mod-3 Sierpinski gasket) via code representation of its points. We also investigate the geodesics of SG(3) and determine the number of geodesics between two points.
On The Regularity Of The Solution Map Of The Euler-Poisson System,
2019
TÜBİTAK
On The Regularity Of The Solution Map Of The Euler-Poisson System, Hasan İnci̇
Turkish Journal of Mathematics
In this paper we consider the Euler--Poisson system (describing a plasma consisting of positive ions with a negligible temperature and massless electrons in thermodynamical equilibrium) on the Sobolev spaces $H^s(\mathbb{R}^3)$, $s > 5/2$. Using a geometric approach we show that for any time $T > 0$ the corresponding solution map, $(\rho_0,u_0) \mapsto (\rho(T),u(T))$, is nowhere locally uniformly continuous. On the other hand it turns out that the trajectories of the ions are analytic curves in $\mathbb{R}^3$.
Classifying Semisymmetric Cubic Graphs Of Order 20p,
2019
TÜBİTAK
Classifying Semisymmetric Cubic Graphs Of Order 20p, Mohsen Shahsavaran, Mohammad Reza Darafsheh
Turkish Journal of Mathematics
A simple graph is called semisymmetric if it is regular and edge-transitive but not vertex-transitive. In this paper we classify all connected cubic semisymmetric graphs of order 20p, p prime.
Minimal Free Resolutions Of The Tangent Cones For Gorenstein Monomial Curves,
2019
TÜBİTAK
Minimal Free Resolutions Of The Tangent Cones For Gorenstein Monomial Curves, Pinar Mete, Esra Emi̇ne Zengi̇n
Turkish Journal of Mathematics
We study the minimal free resolution of the tangent cone of Gorenstein monomial curves in affine 4-space. We give the explicit minimal free resolution of the tangent cone of noncomplete intersection Gorenstein monomial curve whose tangentcone has fiveminimal generators and showthat the possible Betti sequences are (1,5,6,2) and (1,5,5,1). Moreover, we compute the Hilbert function of the tangent cone of these families as a result.
The Relation Between B-Weakly Compact Operator And Kb-Operator,
2019
TÜBİTAK
The Relation Between B-Weakly Compact Operator And Kb-Operator, Bahri̇ Turan, Bi̇rol Altin
Turkish Journal of Mathematics
Our aim is to solve the problem asked by Bahramnezhad and Azar in "KB-operators on Banach lattices and their relationships with Dunford-Pettis and order weakly compact operators". We show that a continuous operators R from a Banach lattice N into a Banach space M is a b-weakly compact operator if and only if R is a KB-operator.
Extended S-Supplement Submodules,
2019
TÜBİTAK
Extended S-Supplement Submodules, Yilmaz Durğun
Turkish Journal of Mathematics
In this paper, we introduced and studied extended S-supplement submodules. A submodule U of a module V is called extended S-supplement submodule in V if there exists a submodule T of V such that V = T + U and U ∩ T is Goldie torsion. Extended S-supplement submodule is a dual notion of extended S-closed submodule. The class of extended S-supplement sequences is a proper class which is generated by nonsingular modules injectively. We studied coinjective objects of this class. Moreover, extended S-supplemented modules are also investigated. We present new characterizations of Z2(RR) -semiperfect rings and SI-rings by extended …
Some Properties Of Riemannian Geometry Of The Tangent Bundle Of Lie Groups,
2019
TÜBİTAK
Some Properties Of Riemannian Geometry Of The Tangent Bundle Of Lie Groups, Davood Seifipour, Esmaeil Peyghan
Turkish Journal of Mathematics
We consider a bi-invariant Lie group (G, g) and we equip its tangent bundle TG with the left invariant Riemannian metric introduced in the paper of Asgari and Salimi Moghaddam. We investigate Einstein-like, Ricci soliton, and Yamabe soliton structures on TG. Then we study some geometrical tensors on TG such as Cotton, Schouten, Weyl, and Bach tensors, and we also compute projective and concircular and m-projective curvatures on TG. Finally, we compute the Szabo operator and Jacobi operator on the tangent Lie group TG.
Coefficient Estimates For A New Subclasses Of Λ-Pseudo Biunivalent Functions Withrespect To Symmetrical Points Associated With The Horadam Polynomials, Adnan Alamoush
Turkish Journal of Mathematics
In the present article, we introduce two new subclasses of λ-pseudo biunivalent functions with respect to symmetrical points in the open unit disk U defined by means of the Horadam polynomials. For functions belonging to these subclasses, estimates on the Taylor -Maclaurin coefficients ja2j and ja3j are obtained. Fekete-Szegö inequalities of functions belonging to these subclasses are also founded. Furthermore, we point out several new special cases of our results.
