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2019

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Articles 961 - 990 of 1389

Full-Text Articles in Mathematics

A Discrete Chaotic Dynamical System On The Sierpinski Gasket, Mustafa Saltan, Ni̇sa Aslan, Bünyami̇n Demi̇r Jan 2019

A Discrete Chaotic Dynamical System On The Sierpinski Gasket, Mustafa Saltan, Ni̇sa Aslan, Bünyami̇n Demi̇r

Turkish Journal of Mathematics

The Sierpinski gasket (also known as the Sierpinski triangle) is one of the fundamental models of self-similar sets. There have been many studies on different features of this set in the last decades. In this paper, initially we construct a dynamical system on the Sierpinski gasket by using expanding and folding maps. We then obtain a surprising shift map on the code set of the Sierpinski gasket, which represents the dynamical system, and we show that this dynamical system is chaotic on the code set of the Sierpinski gasket with respect to the intrinsic metric. Finally, we provide an algorithm …

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On Essential Cohomology Of Powerful $P$-Groups, Fatma Altunbulak Aksu Jan 2019

On Essential Cohomology Of Powerful $P$-Groups, Fatma Altunbulak Aksu

Turkish Journal of Mathematics

For an odd prime $p$, we prove that a finite powerful $p$-group having rank two Frattini quotient has nonzero essential cohomology. We also provide some examples and applications.

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An Asymptotic-Numerical Hybrid Method For Singularly Perturbed System Of Two-Point Reaction-Diffusion Boundary-Value Problems, Süleyman Cengi̇zci̇, Srinivasan Natesan, Mehmet Tarik Atay Jan 2019

An Asymptotic-Numerical Hybrid Method For Singularly Perturbed System Of Two-Point Reaction-Diffusion Boundary-Value Problems, Süleyman Cengi̇zci̇, Srinivasan Natesan, Mehmet Tarik Atay

Turkish Journal of Mathematics

This article focuses on the numerical approximate solution of singularly perturbed systems of second-order reaction-diffusion two-point boundary-value problems for ordinary differential equations. To handle these types of problems, a numerical-asymptotic hybrid method has been used. In this hybrid approach, an efficient asymptotic method, the so-called successive complementary expansion method (SCEM) is employed first, and then a numerical method based on finite differences is applied to approximate the solution of corresponding singularly perturbed reaction-diffusion systems. Two illustrative examples are provided to demonstrate the efficiency, robustness, and easy applicability of the present method with convergence properties.

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Separation Axioms On Neutrosophic Soft Topological Spaces, Çi̇ğdem Gündüz, Taha Yasi̇n Öztürk, Sadi Bayramov Jan 2019

Separation Axioms On Neutrosophic Soft Topological Spaces, Çi̇ğdem Gündüz, Taha Yasi̇n Öztürk, Sadi Bayramov

Turkish Journal of Mathematics

A neutrosophic set, proposed by Smarandache, considers a truth membership function, an indeterminacy membership function, and a falsity membership function. Neutrosophic soft sets combined by Maji have been utilized successfully to model uncertainty in several areas of application such as control, reasoning, pattern recognition, and computer vision. In the present paper, some basic notions of neutrosophic soft sets have been redefined and the neutrosophic soft point concept has been introduced. Later we give the neutrosophic soft $T_{i}$-space and the relationships between them are discussed in detail.

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Young Tableaux And Arf Partitions, Nesri̇n Tutaş, Hali̇l İbrahi̇m Karakaş, Ni̇hal Gümüşbaş Jan 2019

Young Tableaux And Arf Partitions, Nesri̇n Tutaş, Hali̇l İbrahi̇m Karakaş, Ni̇hal Gümüşbaş

Turkish Journal of Mathematics

The aim of this work is to exhibit some relations between partitions of natural numbers and Arf semigroups. We also give characterizations of Arf semigroups via the hook-sets of Young tableaux of partitions.

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A New Class Of Generalized Polynomials Associated With Laguerre And Bernoulli Polynomials, Nabiullah Khan, Talha Usman, Junesang Choi Jan 2019

A New Class Of Generalized Polynomials Associated With Laguerre And Bernoulli Polynomials, Nabiullah Khan, Talha Usman, Junesang Choi

Turkish Journal of Mathematics

Motivated by their importance and potential for applications in certain problems in number theory, combinatorics, classical and numerical analysis, and other fields of applied mathematics, a variety of polynomials and numbers with their variants and extensions have recently been introduced and investigated. In this paper, we aim to introduce generalized Laguerre-Bernoulli polynomials and investigate some of their properties such as explicit summation formulas, addition formulas, implicit formulas, and symmetry identities. Relevant connections of the results presented here with those relatively simple numbers and polynomials are considered.

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Slant Helices: A New Approximation, Pascual Lucas, Jose Antonio Ortega-Yagues Jan 2019

Slant Helices: A New Approximation, Pascual Lucas, Jose Antonio Ortega-Yagues

Turkish Journal of Mathematics

In this paper, we study a weaker version of classic slant helices in Euclidean space $\mathbb{R}^3$ or Minkowski space $\mathbb{R}^3_1$, which will be called general slant helices. We show that any classic slant helix is a general slant helix but the converse is not true. We also obtain equations involving the curvature and torsion that characterize this family of curves.

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Categorical Structures Of Lie-Rinehart Crossed Module, Ali̇ Ayteki̇n Jan 2019

Categorical Structures Of Lie-Rinehart Crossed Module, Ali̇ Ayteki̇n

Turkish Journal of Mathematics

In this paper we give constructions of pullback, finite product, finite limit, coproduct, colimit, pushout, etc. in a special full subcategory $\mathfrak{XMod}/\mathcal{L}$ of the category of Lie-Rinehart crossed modules.

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Some Operator Inequalities Associated With Kantorovich And Hölder-Mccarthyinequalities And Their Applications, Hamdullah Başaran, Mehmet Gürdal, Ayşe Nur Güncan Jan 2019

Some Operator Inequalities Associated With Kantorovich And Hölder-Mccarthyinequalities And Their Applications, Hamdullah Başaran, Mehmet Gürdal, Ayşe Nur Güncan

Turkish Journal of Mathematics

We prove analogs of certain operator inequalities, including Hölder-McCarthy inequality, Kantorovich inequality, and Heinz-Kato inequality, for positive operators on the Hilbert space in terms of the Berezin symbols and the Berezin number of operators on the reproducing kernel Hilbert space.

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Curves Over Finite Fields And Permutations Of The Form $X^K-\Gamma \Mathrm{Tr}(X)$, Nurdagül Anbar Meidl Jan 2019

Curves Over Finite Fields And Permutations Of The Form $X^K-\Gamma \Mathrm{Tr}(X)$, Nurdagül Anbar Meidl

Turkish Journal of Mathematics

We consider the polynomials of the form $P(x)=x^k-\gamma \mathrm{Tr}(x)$ over $\mathbb{F}_{q^n}$ for $n\geq 2$. We show that $P(x)$ is not a permutation of $\mathbb{F}_{q^n}$ in the case $\gcd(k, q^n-1)>1$. Our proof uses an absolutely irreducible curve over $\mathbb{F}_{q^n}$ and the number of rational points on it.

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On The Composition And Exterior Products Of Double Forms And $P$-Pure Manifolds, Abdelhadi Belkhirat, Mohammed Labbi Jan 2019

On The Composition And Exterior Products Of Double Forms And $P$-Pure Manifolds, Abdelhadi Belkhirat, Mohammed Labbi

Turkish Journal of Mathematics

We translate into double forms formalism the basic Greub and Greub-Vanstone identities that were previously obtained in mixed exterior algebras. In particular, we introduce a second product in the space of double forms, namely the composition product, which provides this space with a second associative algebra structure. The composition product interacts with the exterior product of double forms; we show that the resulting relations provide simple alternative proofs to some classical linear algebra identities as well as to recent results in the exterior algebra of double forms. We define and study a refinement of the notion of pure curvature of …

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Rt Distance And Weight Distributions Of Type 1 Constacyclic Codes Of Length\\ $4p^S$ Over $\Frac{\Mathbb F_{P^M}[U]}{\Left\Langle U^A \Right\Rangle}$, Hai Dinh, Bac Nguyen, Songsak Sriboonchitta Jan 2019

Rt Distance And Weight Distributions Of Type 1 Constacyclic Codes Of Length\\ $4p^S$ Over $\Frac{\Mathbb F_{P^M}[U]}{\Left\Langle U^A \Right\Rangle}$, Hai Dinh, Bac Nguyen, Songsak Sriboonchitta

Turkish Journal of Mathematics

For any odd prime $p$ such that $p^m \equiv 1 \pmod{4}$, the class of $\Lambda$-constacyclic codes of length $4p^s$ over the finite commutative chain ring ${\cal R}_a=\frac{\mathbb F_{p^m}[u]}{\left\langle u^a \right\rangle}=\mathbb F_{p^m} + u \mathbb F_{p^m}+ \dots + u^{a-1}\mathbb F_{p^m}$, for all units $\Lambda$ of $\mathcal R_a$ that have the form $\Lambda=\Lambda_0+u\Lambda_1+\dots+u^{a-1}\Lambda_{a-1}$, where $\Lambda_0, \Lambda_1, \dots, \Lambda_{a-1} \in \mathbb F_{p^m}$, $\Lambda_0 \,{\not=}\, 0, \, \Lambda_1 \,{\not=}\, 0$, is investigated. If the unit $\Lambda$ is a square, each $\Lambda$-constacyclic code of length $4p^s$ is expressed as a direct sum of a $-\lambda$-constacyclic code and a $\lambda$-constacyclic code of length $2p^s$. In the …

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Exponential Stabilization Of A Neutrally Delayed Viscoelastic Timoshenko Beam, Sebti Kerbal, Nasser Eddine Tatar Jan 2019

Exponential Stabilization Of A Neutrally Delayed Viscoelastic Timoshenko Beam, Sebti Kerbal, Nasser Eddine Tatar

Turkish Journal of Mathematics

A Timoshenko type beam subject to a viscoelastic damping in the rotational displacement component is considered. Taking into account a neutral type delay, we prove a fast stability result despite the previously observed destabilizing effect due to delays in such systems. The proof relies on the introduction of nine different functionals with which we modify the energy of the system. These functionals are carefully selected and adapted to cope with both the viscoelasticity and the neutral delay.

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Spectral Properties Of Boundary-Value-Transmission Problems With A Constant Retarded Argument, Erdoğan Şen Jan 2019

Spectral Properties Of Boundary-Value-Transmission Problems With A Constant Retarded Argument, Erdoğan Şen

Turkish Journal of Mathematics

In this work, spectra and asymptotics of eigenfunctions of a generalized class of boundary value problems with constant retarded argument are obtained. Contrary to previous works in the literature, the problem has nonclassical transmission conditions.

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Positivity Of Sums And Integrals For $N$-Convex Functions Via The Fink Identity, Asif R. Khan, Josip Pecaric, Marjan Praljak, Sanja Varosanec Jan 2019

Positivity Of Sums And Integrals For $N$-Convex Functions Via The Fink Identity, Asif R. Khan, Josip Pecaric, Marjan Praljak, Sanja Varosanec

Turkish Journal of Mathematics

We consider the positivity of the sum $\sum_{i=1}^n\rho_i\digamma(\xi_i)$, where $\digamma$ is a convex function of higher order, as well as analogous results involving the integral $\int_{a_0}^{b_0}\rho(\xi)\digamma(g(\xi))d\xi$. We use a representation of the function $\digamma$ via the Fink identity and the Green function that leads us to identities from which we obtain conditions for positivity of the above-mentioned sum and integral. We also obtain bounds for the integral remainders which occur in these identities, as well as corresponding mean value results.

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Stability Analysis For A Class Of Nabla $(Q,H)$-Fractional Difference Equations, Xiang Liu, Baoguo Jia, Lynn Erbe, Allan Peterson Jan 2019

Stability Analysis For A Class Of Nabla $(Q,H)$-Fractional Difference Equations, Xiang Liu, Baoguo Jia, Lynn Erbe, Allan Peterson

Turkish Journal of Mathematics

This paper investigates stability of the nabla $(q,h)$-fractional difference equations. Asymptotic stability of the special nabla $(q,h)$-fractional difference equations are discussed. Stability theorems for discrete fractional Lyapunov direct method are proved. Furthermore, we give some new lemmas (including important comparison theorems) related to the nabla $(q,h)$-fractional difference operators that allow proving the stability of the nabla $(q,h)$-fractional difference equations, by means of the discrete fractional Lyapunov direct method, using Lyapunov functions. Some examples are given to illustrate these results.

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$N$-$T$-Torsionfree Modules, Peiyu Zhang, Jie Geng Jan 2019

$N$-$T$-Torsionfree Modules, Peiyu Zhang, Jie Geng

Turkish Journal of Mathematics

As a generalization of the Auslander-Reiten transpose, Xi introduced and studied a more general transpose, called the relative transpose (or, $T$-transpose). Based on this notion, the notion of relative $n$-torsionfree modules (or, $n$-$T$-torsionfree modules) is introduced in this paper, which is a generalization of the $n$-torsionfree modules introduced by Auslander and Bridger. We show that relative $n$-torsionfree modules have many similar properties of $n$-torsionfree modules.

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Inclusion Properties Of Lucas Polynomials For Bi-Univalent Functionsintroduced Through The $\Mathfrak{Q}$-Analogue Of The Noor Integral Operator, Şahsene Altinkaya Jan 2019

Inclusion Properties Of Lucas Polynomials For Bi-Univalent Functionsintroduced Through The $\Mathfrak{Q}$-Analogue Of The Noor Integral Operator, Şahsene Altinkaya

Turkish Journal of Mathematics

In this paper, by using the $(\mathbf{P},\mathbf{Q})$-Lucas polynomials and the $\mathfrak{q}$-analogue of the Noor integral operator, we aim to build a bridge between the theory of geometric functions and that of special functions.

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A Generalization Of $\Pi$-Regular Rings, Peter Danchev Jan 2019

A Generalization Of $\Pi$-Regular Rings, Peter Danchev

Turkish Journal of Mathematics

We introduce the class of so-called { regularly nil clean rings} and systematically study their fundamental characteristic properties accomplished with relationships among certain classical sorts of rings such as exchange rings, Utumi rings etc. These rings of ours naturally generalize the long-known classes of $\pi$-regular and strongly $\pi$-regular rings. We show that the regular nil cleanness possesses a symmetrization which extends the corresponding one for strong $\pi$-regularity that was visualized by Dischinger \cite{Dis}. Likewise, our achieved results substantially improve on establishments presented in two recent papers by Danchev and \v{S}ter \cite{DS} and Danchev \cite{Da}.

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Certain Classes Of Multivalent Functions Defined With Higher-Order Derivatives, Muhamed Kamal Aouf, Abdel Moneim Lashin, Teodor Bulboaca Jan 2019

Certain Classes Of Multivalent Functions Defined With Higher-Order Derivatives, Muhamed Kamal Aouf, Abdel Moneim Lashin, Teodor Bulboaca

Turkish Journal of Mathematics

In this paper we derive some properties of multivalent functions belonging to the classes $R_{p,q}(\alpha)$, $B_{p,q}(\alpha)$, and $M_{p,q}(\alpha)$. The results obtained generalize the related works of some authors, and many other new results are obtained.

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Mannheim Curves With Modified Orthogonal Frame In Euclidean 3-Space, Mohammad Saleem Lone, Hasan Es, Murat Kemal Karacan, Bahaddi̇n Bükcü Jan 2019

Mannheim Curves With Modified Orthogonal Frame In Euclidean 3-Space, Mohammad Saleem Lone, Hasan Es, Murat Kemal Karacan, Bahaddi̇n Bükcü

Turkish Journal of Mathematics

In this paper, we investigate Mannheim pairs, Frenet--Mannheim curves, and weakened Mannheim curves with respect to the modified orthogonal frame in Euclidean 3-space $(E^3)$. We derive some characterization results of these curves.

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Compactness Of The Commutators Of Intrinsic Square Functions On Weighted Lebesgue Spaces, Xiaomei Wu, Xiao Yu Jan 2019

Compactness Of The Commutators Of Intrinsic Square Functions On Weighted Lebesgue Spaces, Xiaomei Wu, Xiao Yu

Turkish Journal of Mathematics

The aim of this paper is to study the compactness for the commutators of intrinsic square functions, including the intrinsic $g_{\lambda}^*$-function and the intrinsic Littlewood-Paley g-function. Using a weighted version of the Frech\'{e}t-Kolmogorov-Riesz theorem, the compactness for their commutators generated with the CMO functions is obtained on the weighted Lebesgue spaces.

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Singly Generated Invariant Subspaces In The Hardy Space On The Unit Ball, Beyaz Başak Koca, Nazim Sadik Jan 2019

Singly Generated Invariant Subspaces In The Hardy Space On The Unit Ball, Beyaz Başak Koca, Nazim Sadik

Turkish Journal of Mathematics

In this paper, we give a complete characterization of singly generated invariant subspaces in the Hardy space on the unit ball. Then we construct a singly generated invariant subspace that cannot be generated by a single inner function, contrary to the one-variable case where every invariant subspace is generated by a single inner function. Some important properties of invariant subspaces are also determined for singly generated invariant subspaces.

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The Twelvefold Way, The Nonintersecting Circles Problem, And Partitions Of Multisets, Daniel Yaqubi, Toufik Mansour, Madjid Mirzavaziri Jan 2019

The Twelvefold Way, The Nonintersecting Circles Problem, And Partitions Of Multisets, Daniel Yaqubi, Toufik Mansour, Madjid Mirzavaziri

Turkish Journal of Mathematics

Let $n$ be a nonnegative integer and $\mathbb{A}=\{a_1,\ldots,a_k\}$ be a multiset with $k$ positive integers such that $a_1\leqslant\cdots\leqslant a_k$. In this paper, we give a recursive formula for partitions and distinct partitions of positive integer $n$ with respect to a multiset $\mathbb{A}$. We also consider the extension of the twelvefold way. By using this notion, we solve the nonintersecting circles problem, which asks to evaluate the number of ways to draw $n$ nonintersecting circles in the plane regardless of their sizes. The latter also enumerates the number of unlabeled rooted trees with $n+1$ vertices.

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On The Number Of $K$-Normal Elements Over Finite Fields, Zülfükar Saygi, Erni̇st Ti̇lenbaev, Çeti̇n Ürti̇ş Jan 2019

On The Number Of $K$-Normal Elements Over Finite Fields, Zülfükar Saygi, Erni̇st Ti̇lenbaev, Çeti̇n Ürti̇ş

Turkish Journal of Mathematics

In this article we give an explicit formula for the number of $k$-normal elements, hence answering Problem 6.1. of Huczynska et al. (Existence and properties of $k$-normal elements over finite fields, Finite Fields Appl 2013; 24: 170-183). Furthermore, for some cases we provide formulas that require the solutions of some linear Diophantine equations. Our results depend on the explicit factorization of cyclotomic polynomials.

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Complete Flat Cone Metrics On Punctured Surfaces, İsmai̇l Sağlam Jan 2019

Complete Flat Cone Metrics On Punctured Surfaces, İsmai̇l Sağlam

Turkish Journal of Mathematics

We prove that each complete flat cone metric on a surface with regular or irregular punctures can be triangulated with finitely many types of triangles. We derive the Gauss-Bonnet formula for this kind of cone metrics. In addition, we prove that each free homotopy class of paths has a geodesic representative.

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On $\Lambda$-Pseudo $Q$-Bi-Starlike Functions, Prakash Kamble, Mallikarjun Shrigan, Şahsene Altinkaya Jan 2019

On $\Lambda$-Pseudo $Q$-Bi-Starlike Functions, Prakash Kamble, Mallikarjun Shrigan, Şahsene Altinkaya

Turkish Journal of Mathematics

Making use of the $\lambda$-pseudo-$q$-differential operator, we aim to investigate a new, interesting class of bi-starlike functions in the conic domain. Furthermore, we obtain certain sharp bounds of the Fekete--Szeg\"{o} functional for functions belonging to this class.

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Jörgensen's Inequality And Purely Loxodromic Two-Generator Free Kleinian Groups, İlker Savaş Yüce Jan 2019

Jörgensen's Inequality And Purely Loxodromic Two-Generator Free Kleinian Groups, İlker Savaş Yüce

Turkish Journal of Mathematics

Let $\xi$ and $\eta$ be two noncommuting isometries of the hyperbolic $3$-space $\mathbb{H}^3$ so that $\Gamma=\langle\xi,\eta\rangle$ is a purely loxodromic free Kleinian group. For $\gamma\in\Gamma$ and $z\in\hyp$, let $d_{\gamma}z$ denote the hyperbolic distance between $z$ and $\gamma(z)$. Let $z_1$ and $z_2$ be the midpoints of the shortest geodesic segments connecting the axis of $\xi$ to the axes of $\eta\xi\eta^{-1}$ and $\eta^{-1}\xi\eta$, respectively. In this manuscript, it is proved that if $d_{\gamma}z_2

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Covariant Differential Calculus On ${\Cal Sp}_H^{2, Sali̇h Çeli̇k, İlknur Temli̇ Jan 2019

Covariant Differential Calculus On ${\Cal Sp}_H^{2, Sali̇h Çeli̇k, İlknur Temli̇

Turkish Journal of Mathematics

The $h$-deformed symplectic superspaces via a contraction of the $q$-deformed symplectic superspaces are introduced and a covariant differential calculus on the quantum symplectic superspace ${\cal SP}_h^{2 1}$ is presented.

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On Strongly Ozaki Bi-Close-To-Convex Functions, Münevver Tezelci̇, Sevtap Sümer Eker Jan 2019

On Strongly Ozaki Bi-Close-To-Convex Functions, Münevver Tezelci̇, Sevtap Sümer Eker

Turkish Journal of Mathematics

In this paper, we introduce and investigate a new subclass of strongly Ozaki bi-close-to-convex functions in the open unit disk. We have also found estimates for the first two Taylor-Maclaurin coefficients for functions belonging to this class. The results presented in this paper have been shown to generalize and improve the work of Brannan and Taha.

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