A Certain Subclass Of Bi-Univalent Analytic Functions Introduced Bymeans Of The $Q$-Analogue Of Noor Integral Operator And Horadam Polynomials, Arzu Akgül, Fethi̇ye Müge Sakar
Turkish Journal of Mathematics
In the present study, by using the Horadam Polnomials and $q-$analogue of Noor integral oprerator, we target to construct an interesting connection between the geometric function theory and that of special functions. Also, by defining a new class of bi-univalent analytic functions, we investigate coefficient estimates and famous Fekete-Szegö inequality for functions belonging to this interesting class.
Rational Maps From Euclidean Configuration Spaces To Spheres,
2019
TÜBİTAK
Rational Maps From Euclidean Configuration Spaces To Spheres, Urtzi Buijs, Antonio Garvin, Aniceto Murillo
Turkish Journal of Mathematics
In this note we give an algorithm to determine the rational homotopy type of the free and pointed mapping spaces $\map(F(\br^m,k),\bs^n)$ and $\map^*(F(\br^m,k),\bs^n)$. An explicit description of these spaces is given for $k=3$. The general case for $n$ odd is also presented as an immediate consequence of the rational version of a classical result of Thom.
On Walker 4-Manifolds With Pseudo Bi-Hermitian Structures,
2019
TÜBİTAK
On Walker 4-Manifolds With Pseudo Bi-Hermitian Structures, Si̇bel Turanli
Turkish Journal of Mathematics
$\left(M_{2n},g^w,D\right)$ is a 4-dimensional Walker manifold and this triple is also a pseudo-Riemannian manifold $\left(M_{2n},g^w\right)$ of signature $(++--$) (or neutral), which is admitted a field of null 2-plane. In this paper, we consider bi-Hermitian structures $({\varphi }_1,{\ \varphi }_2)$ on 4-dimensional Walker manifolds. We discuss when these structures are integrable and when the bi-Kahler forms are symplectic.
Spectral Analysis Of Some Classes First-Order Normal Differential Operators,
2019
TÜBİTAK
Spectral Analysis Of Some Classes First-Order Normal Differential Operators, Pembe Ipek Al
Turkish Journal of Mathematics
In this paper, the general form of all normal differential operators generated by first-order linear singular differential expressions in the weighted Hilbert spaces of vector-functions on right semiaxis has been found. Later on, the spectrum set of these type extensions is investigated. Finally, the asymptotical behavior of the singular numbers of any normal extension is studied.
Modules In Which Semisimple Fully Invariant Submodules Are Essential In Summands,
2019
TÜBİTAK
Modules In Which Semisimple Fully Invariant Submodules Are Essential In Summands, Ramazan Yaşar
Turkish Journal of Mathematics
One of the useful generalization of extending notion is $FI$-extending property. A module is called $FI$-extending if every fully invariant submodule is essential in a direct summand. In this paper, we explore Weak $FI$-extending concept by considering only semisimple fully invariant submodules rather than all fully invariant submodules. To this end, we call such a module Weak $FI$-extending. We obtain that $FI$-extending modules are properly contained in this new class of modules. Amongst other structural properties, we also deal with direct sums and direct summands of Weak $FI$-extending modules.
An Approach To Negative Hypergeometric Distribution By Generatingfunction For Special Numbers And Polynomials,
2019
TÜBİTAK
An Approach To Negative Hypergeometric Distribution By Generatingfunction For Special Numbers And Polynomials, İrem Küçükoğlu, Burçi̇n Şi̇mşek, Yilmaz Şi̇mşek
Turkish Journal of Mathematics
The aim of this paper is to not only provide a definition of a new family of special numbers and polynomials of higher-order with their generating functions, but also to investigate their fundamental properties in the spirit of probabilistic distributions. By applying generating functions methods, we derive miscellaneous novel identities and formulas involving the Chu--Vandermonde-type convolution formulas, combinatorial sums, Bernstein basis functions, and the other well-known special numbers and polynomials. Moreover, we provide a computational algorithm which returns special values of these numbers and polynomials. In addition, we show that our new identities and formulas are connected with the interpolation …
A New Subclass Of Starlike Functions,
2019
TÜBİTAK
A New Subclass Of Starlike Functions, Hesam Mahzoon, Rahim Kargar, Janusz Sokol
Turkish Journal of Mathematics
Motivated by the Ronning-starlike class [Proc Amer Math Soc {\bf118}, no. 1, 189-196, 1993], we introduce new class $\mathcal{S}^*_c$ includes of analytic and normalized functions $f$ which satisfy the inequality $$ {\rm Re}\left\{\frac{zf'(z)}{f(z)}\right\}\geq\left \frac{f(z)}{z}-1\right \quad( z 1/2$ in $ z
On Operator Systems Generated By Reducible Projective Unitary Representations Of Compact Groups,
2019
TÜBİTAK
On Operator Systems Generated By Reducible Projective Unitary Representations Of Compact Groups, Grigori Amosov
Turkish Journal of Mathematics
We study reducible projective unitary representations $(U_g)_{g\in G}$ of a compact group $G$ in separable Hilbert spaces $H$. It is shown that there exist the projections $Q$ and $P$ for which ${\mathcal V}=\overline {span(U_gQU_g^*,\ g\in G)}$ is the operator system and $P{\mathcal V}P=\{{\mathbb C}P\}$. As an example, a bipartite Hilbert space $H={\mathfrak {H}}\otimes {\mathfrak {H}}$ is considered. In this case, the action of $(U_g)_{g\in G}$ has the property of transforming separable vectors to entangled.
On The $J$-Reflexive Sequences,
2019
TÜBİTAK
On The $J$-Reflexive Sequences, Parviz Sadat Hosseini, Bahmann Yousefi
Turkish Journal of Mathematics
We call a sequence $\mathcal{T}=(T_n)_n$ of bounded operators on a Banach space $X$, $J$-reflexive if every bounded operator on $X$ that leaves invariant, the $J$-sets of $\mathcal{T}$ is contained in the closure of $\{I, T_1, T_2, ... \}$ in the strong operator topology. We discuss some properties of $J$-reflexive sequences. We also give and prove some sufficient conditions under which an operator sequence is $J$-reflexive. Some examples are considered. Indeed, weakly $J^{mix}$-reflexivity is also defined. Finally, we extend the $J$-reflexive property in terms of subsets.
Unpredictable Solutions Of Linear Differential And Discrete Equations,
2019
TÜBİTAK
Unpredictable Solutions Of Linear Differential And Discrete Equations, Marat Akhmet, Mehmet Onur Fen, Madina Tleubergenova, Akylbek Zhamanshin
Turkish Journal of Mathematics
The existence and uniqueness of unpredictable solutions in the dynamics of nonhomogeneous linear systems of differential and discrete equations are investigated. The hyperbolic cases are under discussion. The presence of unpredictable solutions confirms the existence of Poincaré chaos. Simulations illustrating the chaos are provided.
Quasi-Idempotent Ranks Of Some Permutation Groups And Transformation Semigroups,
2019
TÜBİTAK
Quasi-Idempotent Ranks Of Some Permutation Groups And Transformation Semigroups, Leyla Bugay
Turkish Journal of Mathematics
Let $S_{n}$, $A_{n}$, $I_{n}$, $T_{n}$, and $P_{n}$ be the symmetric group, alternating group, symmetric inverse semigroup, (full) transformations semigroup, and partial transformations semigroup on $X_{n}=\{1,\dots ,n\}$, for $n\geq 2$, respectively. A non-idempotent element whose square is an idempotent in $P_{n}$ is called a quasi-idempotent. In this paper first we show that the quasi-idempotent ranks of $S_{n}$ (for $n\geq 4$) and $A_{n}$ (for $n\geq 5$) are both $3$. Then, by using the quasi-idempotent rank of $S_{n}$, we show that the quasi-idempotent ranks of $I_{n}$, $T_{n}$, and $P_{n}$ (for $n\geq 4$) are $4$, $4$, and $5$, respectively.
On Congruence Equations Arising From Suborbital Graphs,
2019
TÜBİTAK
On Congruence Equations Arising From Suborbital Graphs, Bahadir Özgür Güler, Murat Beşenk, Serkan Kader
Turkish Journal of Mathematics
In this paper we deal with congruence equations arising from suborbital graphs of the normalizer of $\Gamma _{0}(m)$ in $PSL(2,\mathbb{R})$. We also propose a conjecture concerning the suborbital graphs of the normalizer and the related congruence equations. In order to prove the existence of solution of an equation over prime finite field, this paper utilizes the Fuchsian group action on the upper half plane and Farey graphs properties.
Subclasses Of Uniformly Convex And Starlike Functions Associated Withbessel Functions,
2019
TÜBİTAK
Subclasses Of Uniformly Convex And Starlike Functions Associated Withbessel Functions, Muhammad Naeem, Saqib Hussain, Fethi̇ye Müge Sakar, Tahir Mahmood, Akhter Rasheed
Turkish Journal of Mathematics
In recent years, applications of Bessel differential equations have been commonly used in univalent functions theory. The main object of the present paper is to give some characteristic properties for some subclasses of uniformly starlike and convex functions which are defined here by means of the normalized form of the generalized Bessel function to be univalent in the open unit disc. Furthermore, we also establish some results of these subclasses related to a particular integral operator. Some corresponding consequences of our main results are also considered.
The Eternal Solution To The Cross Curvature Flow Exists In 3-Manifolds Of Negative Sectional Curvature,
2019
TÜBİTAK
The Eternal Solution To The Cross Curvature Flow Exists In 3-Manifolds Of Negative Sectional Curvature, Weihung Liao
Turkish Journal of Mathematics
Given a closed 3-manifold $M^3$ endowed with a radial symmetric metric of negative sectional curvature, we define the cross curvature flow on $M^3$; using the maximum principle theorem, we demonstrated that the solution to the cross curvature flow exists for all time and converges pointwise to a hyperbolic metric.
Existence Of Solutions Of Bvps For Impulsive Fractional Langevin Equations Involving Caputo Fractional Derivatives,
2019
TÜBİTAK
Existence Of Solutions Of Bvps For Impulsive Fractional Langevin Equations Involving Caputo Fractional Derivatives, Yuji Liu, Ravi Agarwal
Turkish Journal of Mathematics
The standard Caputo fractional derivative is generalized for the piecewise continuous functions. A more general boundary value problem for the impulsive Langevin fractional differential equation involving the Caputo fractional derivatives is studied. New existence results for solutions of concerned problems are established.
Some Properties For A Class Of Analytic Functions Defined By A Higher-Order Differential Inequality,
2019
TÜBİTAK
Some Properties For A Class Of Analytic Functions Defined By A Higher-Order Differential Inequality, Oqlah Alrefai
Turkish Journal of Mathematics
Let $\mathcal{B}_p(\alpha,\beta, \lambda;j)$ be the class consisting of functions $f(z)= z^p+\sum_{k=p+1}^{\infty}a_k z^{k},\; p\in \mathbb{N}$ which satisfy $ \mathrm{Re}\left\{\alpha\frac{f^{(j)}(z)}{z^{p-j}}+\beta\frac{f^{(j+1)}(z)}{z^{p-j-1}}+\left(\frac{\beta-\alpha}{2}\right)\frac{f^{(j+2)}(z)}{z^{p-j-2}}\right\}>\lambda,\;\;(z\in \mathbb{U}=\{z:\; z (5-12\ln 2)/(44-48\ln 2)\approx -0.309$ is sufficient condition for any normalized analytic function $f$ to be starlike in $\mathbb{U}$. The results improve and include a number of known results as their special cases.
A Remark On A Paper Of P. B. Djakov And M. S. Ramanujan,
2019
TÜBİTAK
A Remark On A Paper Of P. B. Djakov And M. S. Ramanujan, Eli̇f Uyanik, Murat Hayretti̇n Yurdakul
Turkish Journal of Mathematics
Let $\ell$ be a Banach sequence space with a monotone norm in which the canonical system $(e_{n})$ is an unconditional basis. We show that if there exists a continuous linear unbounded operator between $\ell$-Köthe spaces, then there exists a continuous unbounded quasidiagonal operator between them. Using this result, we study the corresponding Köthe matrices when every continuous linear operator between $\ell$-Köthe spaces is bounded. As an application, we observe that the existence of an unbounded operator between $\ell$-Köthe spaces, under a splitting condition, causes the existence of a common basic subspace.
The Generalized Picard Groups For Finite Dimensional $C^*$-Hopf Algebra Coactions On Unital $C^*$-Algebras,
2019
TÜBİTAK
The Generalized Picard Groups For Finite Dimensional $C^*$-Hopf Algebra Coactions On Unital $C^*$-Algebras, Kazunori Kodaka
Turkish Journal of Mathematics
We shall generalize the notion of the strong Morita equivalence for coactions of a finite dimensional $C^*$-Hopf algebra on a unital $C^*$-algebra and define the Picard groups with respect to the generalized strong Morita equivalence. We call them the generalized Picard groups for coactions of a finite dimensional $C^*$-Hopf algebra on a unital $C^*$-algebra. We shall investigate basic properties of the generalized Picard groups and clarify the relation between the generalized Picard groups and the Picard groups for unital inclusions of unital $C^*$-algebras.
A Geometric Description For Simple And Damped Harmonic Oscillators,
2019
TÜBİTAK
A Geometric Description For Simple And Damped Harmonic Oscillators, Zahi̇de Ok Bayrakdar, Tuna Bayrakdar
Turkish Journal of Mathematics
In this work we consider the Riemannian geometry associated with the differential equations of one dimensional simple and damped linear harmonic oscillators. We show that the sectional curvatures are completely determined by the oscillation frequency and the friction coefficient and these physical constants can be thought as obstructions for the manifold to be flat. Moreover, equations of simple and damped harmonic oscillators describe nonisomorphic solvable Lie groups with nonpositive scalar curvature.
Near-Vector Spaces Determined By Finite Fields And Their Fibrations,
2019
TÜBİTAK
Near-Vector Spaces Determined By Finite Fields And Their Fibrations, Karin-Therese Howell
Turkish Journal of Mathematics
In this paper we study near-vector spaces constructed from copies of finite fields. We show that for these near-vector spaces regularity is equivalent to the quasikernel being the entire space. As a second focus, we study the fibrations of near-vector spaces. We define the pseudo-projective space of a near-vector space and prove that a special class of near-vector spaces, namely those constructed using finite fields, always has a fibration associated with them. We also give a formula for calculating the cardinality of the pseudo-projective space for this class of near-vector spaces.
