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2019

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Articles 1051 - 1080 of 1389

Full-Text Articles in Mathematics

A New Subclass Of Starlike Functions, Hesam Mahzoon, Rahim Kargar, Janusz Sokol Jan 2019

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

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On Operator Systems Generated By Reducible Projective Unitary Representations Of Compact Groups, Grigori Amosov Jan 2019

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.

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On The $J$-Reflexive Sequences, Parviz Sadat Hosseini, Bahmann Yousefi Jan 2019

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.

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Unpredictable Solutions Of Linear Differential And Discrete Equations, Marat Akhmet, Mehmet Onur Fen, Madina Tleubergenova, Akylbek Zhamanshin Jan 2019

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.

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Quasi-Idempotent Ranks Of Some Permutation Groups And Transformation Semigroups, Leyla Bugay Jan 2019

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.

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On Congruence Equations Arising From Suborbital Graphs, Bahadir Özgür Güler, Murat Beşenk, Serkan Kader Jan 2019

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.

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Subclasses Of Uniformly Convex And Starlike Functions Associated Withbessel Functions, Muhammad Naeem, Saqib Hussain, Fethi̇ye Müge Sakar, Tahir Mahmood, Akhter Rasheed Jan 2019

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.

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The Eternal Solution To The Cross Curvature Flow Exists In 3-Manifolds Of Negative Sectional Curvature, Weihung Liao Jan 2019

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.

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Existence Of Solutions Of Bvps For Impulsive Fractional Langevin Equations Involving Caputo Fractional Derivatives, Yuji Liu, Ravi Agarwal Jan 2019

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.

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Some Properties For A Class Of Analytic Functions Defined By A Higher-Order Differential Inequality, Oqlah Alrefai Jan 2019

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.

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A Remark On A Paper Of P. B. Djakov And M. S. Ramanujan, Eli̇f Uyanik, Murat Hayretti̇n Yurdakul Jan 2019

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.

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The Generalized Picard Groups For Finite Dimensional $C^*$-Hopf Algebra Coactions On Unital $C^*$-Algebras, Kazunori Kodaka Jan 2019

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.

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A Geometric Description For Simple And Damped Harmonic Oscillators, Zahi̇de Ok Bayrakdar, Tuna Bayrakdar Jan 2019

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.

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Near-Vector Spaces Determined By Finite Fields And Their Fibrations, Karin-Therese Howell Jan 2019

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.

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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 Jan 2019

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 $(x,y,z)=(1,1,2)$.

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Fekete-Szegö Problem For A General Subclass Of Analytic Functions, Nesli̇han Uyanik Jan 2019

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.

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On Factorials In Perrin And Padovan Sequences, Nuretti̇n Irmak Jan 2019

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.

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Ricci-Yamabe Maps For Riemannian Flows And Their Volume Variation And Volume Entropy, Si̇nem Güler, Mircea Crasmareanu Jan 2019

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 …

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On Congruences For $Q$-Analogues Of Ballot Numbers, Si̇bel Koparal Jan 2019

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) $.

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Radii Of Starlikeness And Convexity Of $Q$-Mittag-Leffler Functions, Evri̇m Toklu Jan 2019

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.

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Derivations Of Generalized Quaternion Algebra, Eyüp Kizil, Yasemi̇n Alagöz Jan 2019

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.

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Automorphisms Of Free Metabelian Leibniz Algebras Of Rank Three, Tuba Taş Adiyaman, Zeynep Özkurt Jan 2019

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.

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On The N-Strong Drazin Invertibility In Rings, Honglin Zou, Dijana Mosic, Kezheng Zuo, Yinlan Chen Jan 2019

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 = …

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Sherman's Inequality And Its Converse For Strongly Convex Functions Withapplications To Generalizedf-Divergences, Slavica Ivelic Bradanovic Jan 2019

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 …

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Study On The Q-Analogue Of A Certain Family Of Linear Operators, Shujaat Ali Shah, Khalida Inayat Noor Jan 2019

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.

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Unbounded Absolutely Weak Dunford-Pettis Operators, Nazi̇fe Erkurşun Özcan, Ni̇yazi̇ Anil Gezer, Omid Zabeti Jan 2019

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.

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The Intrinsic Metric And Geodesics On The Sierpinski Gasket Sg(3), Yunus Özdemi̇r Jan 2019

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.

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On The Regularity Of The Solution Map Of The Euler-Poisson System, Hasan İnci̇ Jan 2019

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 $\mathbb{R}^3$.

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Classifying Semisymmetric Cubic Graphs Of Order 20p, Mohsen Shahsavaran, Mohammad Reza Darafsheh Jan 2019

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.

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Minimal Free Resolutions Of The Tangent Cones For Gorenstein Monomial Curves, Pinar Mete, Esra Emi̇ne Zengi̇n Jan 2019

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.

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