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2019

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Articles 1261 - 1290 of 1387

Full-Text Articles in Mathematics

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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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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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 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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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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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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Almost Symmetric Numerical Semigroups With High Type, Pedro A. Garcia-Sanchez, Ignacio Ojeda Jan 2019

Almost Symmetric Numerical Semigroups With High Type, Pedro A. Garcia-Sanchez, Ignacio Ojeda

Turkish Journal of Mathematics

We establish a one-to-one correspondence between numerical semigroups of genus $g$ and almost symmetric numerical semigroups with Frobenius number $F$ and type $F-2g$, provided that $F$ is greater than or equal to $4g-1$.

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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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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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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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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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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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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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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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Principal Parts Of A Vector Bundle On Projective Line And The Fractional Derivative, Hafiz Syed Husain, Mariam Sultana Jan 2019

Principal Parts Of A Vector Bundle On Projective Line And The Fractional Derivative, Hafiz Syed Husain, Mariam Sultana

Turkish Journal of Mathematics

This work is an exposition on computational aspects of principal parts of a vector bundle on projective line over the field of characteristic zero. Principal parts help determine the possibility of algebraically formalizing infinitesimal-neighborhoods of subschemes inside some ambient scheme. The purpose of this study is to look for the possibility of formalizing the algebraic geometric interpretation of fractional derivative. For the latter, this study follows theapproachproposedbyVasilyTarasov. The difference is that Tarasov proposeda geometric interpretation using finite order jet bundles from differential geometry. Present study proposes finite-order principal parts of the structure-sheaf of real projective line as its formal algebraic …

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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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Nonexistence Of Global Solutions For A Fractional System Of Strongly Coupled Integro-Differential Equations, Ahmad Mugbil Ahmad, Nasser Eddine Tatar Jan 2019

Nonexistence Of Global Solutions For A Fractional System Of Strongly Coupled Integro-Differential Equations, Ahmad Mugbil Ahmad, Nasser Eddine Tatar

Turkish Journal of Mathematics

In this paper, we study the nonexistence of nontrivial global solutions for a system of two strongly coupled fractional differential equations. Each equation involves two fractional derivatives and a nonlinear source term. The fractional derivatives are of Caputo type of subfirst orders. The nonlinear sources are nonlocal in time. They have the form of a convolution of a polynomial of the state with a (possibly singular) kernel. The system under consideration is a generalization of many interesting special systems of equations whose solutions do not exist globally in time. We establish some criteria under which no nontrivial global solutions exist. …

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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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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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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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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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Fixed-Disc Results Via Simulation Functions, Ni̇hal Özgür Jan 2019

Fixed-Disc Results Via Simulation Functions, Ni̇hal Özgür

Turkish Journal of Mathematics

In this paper, our aim is to obtain new fixed-disc results on metric spaces. To do this, we present a new approach using the set of simulation functions and some known fixed-point techniques. We do not need to have some strong conditions such as completeness or compactness of the metric space or continuity of the self-mapping in our results. Taking only one geometric condition, we ensure the existence of a fixed disc of a new type contractive mapping.

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A Circulant Functional Equation For The Additive Function And Its Stability, Vichian Laohakosol, Watcharapon Pimsert, Kanet Ponpetch Jan 2019

A Circulant Functional Equation For The Additive Function And Its Stability, Vichian Laohakosol, Watcharapon Pimsert, Kanet Ponpetch

Turkish Journal of Mathematics

A general solution of a matrix functional equation involving circulant matrices of the additive function is determined, and its stability is established.

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Extended S-Supplement Submodules, Yilmaz Durğun Jan 2019

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 …

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Some Properties Of Riemannian Geometry Of The Tangent Bundle Of Lie Groups, Davood Seifipour, Esmaeil Peyghan Jan 2019

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.

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Coefficient Estimates For A New Subclasses Of Λ-Pseudo Biunivalent Functions Withrespect To Symmetrical Points Associated With The Horadam Polynomials, Adnan Alamoush Jan 2019

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.

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A Metric Invariant Of Möbius Transformations, Teerapong Suksumran, Oğuzhan Demi̇rel Jan 2019

A Metric Invariant Of Möbius Transformations, Teerapong Suksumran, Oğuzhan Demi̇rel

Turkish Journal of Mathematics

The complex unit disk $\mathbb{D} = \{z\in\mathbb{C}\colon z < 1\}$ is endowed with Möbius addition $\oplus_M$ defined by $$ w\oplus_M z = \dfrac{w+z}{1+\overline{w}z}. $$ We prove that the metric $d_T$ defined on $\mathbb{D}$ by $d_T(w, z) = \tan^{-1} -w\oplus_M z $ is an invariant of Möbius transformations carrying $\mathbb{D}$ onto itself. We also prove that $(\mathbb{D}, d_T)$ and $(\mathbb{D}, d_P)$, where $d_P$ denotes the Poincaré metric, have the same isometry group and then classify the isometries of $(\mathbb{D}, d_T)$.

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Multiplicative Lie Algebras, Gary L. Walls Jan 2019

Multiplicative Lie Algebras, Gary L. Walls

Turkish Journal of Mathematics

A multiplicative Lie algebra is a group together with a "bracket function" that satisfies the basic properties of the commutator function. This paper investigates the construction of such functions.

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Tauberian Conditions Under Which Convergence Follows From Summability By Thediscrete Power Series Method, Sefa Anil Sezer, İbrahi̇m Çanak Jan 2019

Tauberian Conditions Under Which Convergence Follows From Summability By Thediscrete Power Series Method, Sefa Anil Sezer, İbrahi̇m Çanak

Turkish Journal of Mathematics

In this paper, we obtain Tauberian conditions to recover convergence of a series from its discrete power series summability under certain conditions. As special cases of our main results, we get discrete analogues of some well-known Tauberian theorems in the literature.

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Null Scrolls As B-Scrolls In Lorentz-Minkowski 3-Space, Zeljka Milin Sipus, Ljiljana Primorac Gajcic, Ivana Protrka Jan 2019

Null Scrolls As B-Scrolls In Lorentz-Minkowski 3-Space, Zeljka Milin Sipus, Ljiljana Primorac Gajcic, Ivana Protrka

Turkish Journal of Mathematics

Null scrolls, i.e. ruled surfaces whose base curve and rulings are both lightlike (null), are Lorentzian surfaces having no Euclidean counterparts. In this work we present reparametrization of nondegenerate null scroll as a B-scroll, i.e. as a ruled surface whose rulings correspond to the binormal vectors of a base curve. We prove that the curvature of a base curve, which determines the Gaussian and mean curvature of a null scroll, is invariant under such a reparametrization. We also determine a one-parameter family of null curves on null scroll which serve as base curves for this kind of reparametrization.

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