Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
- Keyword
-
- Analytic functions (7)
- Bi-univalent functions (6)
- Coefficient bounds (6)
- Subordination (5)
- Asymptotic behavior (4)
-
- Univalent functions (4)
- Analytic function (3)
- Caputo fractional derivative (3)
- Numerical semigroup (3)
- Stability (3)
- Starlike functions (3)
- Univalent (3)
- Analytic (2)
- Arf semigroup (2)
- Basicity (2)
- Berezin number (2)
- Berezin symbol (2)
- Bi-ideal (2)
- Boundary value problem (2)
- Calculus of variation (2)
- Coefficient estimate (2)
- Commutators (2)
- Compact operators (2)
- Convergence (2)
- Convex function (2)
- Convex functions (2)
- Convolution (2)
- Diophantine equation (2)
- Existence and uniqueness (2)
- Fekete-Szegö problem (2)
Articles 1 - 30 of 223
Full-Text Articles in Physical Sciences and Mathematics
Harmonic Numbers Associated With Inversion Numbers In Terms Of Determinants, Takao Komatsu, Amalia Pizarro-Madariaga
Harmonic Numbers Associated With Inversion Numbers In Terms Of Determinants, Takao Komatsu, Amalia Pizarro-Madariaga
Turkish Journal of Mathematics
It has been known that some numbers, including Bernoulli, Cauchy, and Euler numbers, have such corresponding numbers in terms of determinants of Hessenberg matrices. There exist inversion relations between the original numbers and the corresponding numbers. In this paper, we introduce the numbers related to harmonic numbers in determinants. We also give several of their arithmetical and/or combinatorial properties and applications. These concepts can be generalized in the case of hyperharmonic numbers.
Nonnegative Integer Solutions Of The Equation $F_{N}-F_{M}=5^{A}$, Fati̇h Erduvan, Refi̇k Keski̇n
Nonnegative Integer Solutions Of The Equation $F_{N}-F_{M}=5^{A}$, Fati̇h Erduvan, Refi̇k Keski̇n
Turkish Journal of Mathematics
In this study, we solve the Diophantine equation in the title in nonnegative integers $m,n,$ and $a$. The solutions are given by $F_{1}-F_{0}=F_{2}-F_{0}=F_{3}-F_{2}=F_{3}-F_{1}=F_{4}-F_{3}=5^{0}$ and $F_{5}-F_{0}=F_{6}-F_{4}=F_{7}-F_{6}=5.$ Then we give a conjecture that says that if $a\geq 2$ and $p>7$ is prime, then the equation $F_{n}-F_{m}=p^{a}$ has no solutions in nonnegative integers $m,n.$
A Bernstein-Type Theorem For $\Xi$-Submanifolds Withflat Normal Bundle In The Euclidean Spaces, Xu-Yong Jiang, He-Jun Sun, Peibiao Zhao
A Bernstein-Type Theorem For $\Xi$-Submanifolds Withflat Normal Bundle In The Euclidean Spaces, Xu-Yong Jiang, He-Jun Sun, Peibiao Zhao
Turkish Journal of Mathematics
$\xi$-Submanifolds in the Euclidean spaces are a natural extension of self-shrinkers and a generalization of $\lambda$-hypersurfaces. Moreover, $\xi$-submanifolds are expected to take the place of submanifolds with parallel mean curvature vector. In this paper, we establish a Bernstein-type theorem for $\xi$-submanifolds in the Euclidean spaces. More precisely, we prove that an $n$-dimensional smooth graphic $\xi$-submanifold with flat normal bundle in $\mathbb{R}^{n+p}$ is an affine $n$-plane.
Notes On Certain Analytic Functions, Emel Yavuz Duman, Shigeyoshi Owa
Notes On Certain Analytic Functions, Emel Yavuz Duman, Shigeyoshi Owa
Turkish Journal of Mathematics
Let $\mathcal{A}(n)$ be the class of functions $$f(z)=a_nz^n + a_{n+1}z^{n+1}+\cdots (n\in \mathbb{N}),$$ which are analytic in the open unit disk $\mathbb{U}$, where $a_n \neq 0$. For $f(z)\in \mathcal{A}(n)$, Miller and Mocanu in 1978 showed a very interesting result for $f(z)$. Applying the result due to Miller and Mocanu, we would like to consider some new results for such functions. Our results in this paper are generalizations for results by Nunokawa in 1992.
A Novel Graph-Operational Matrix Method For Solving Multidelay Fractional Differential Equations With Variable Coefficients And A Numerical Comparative Survey Of Fractional Derivative Types, Ömür Kivanç Kürkçü, Ersi̇n Aslan, Mehmet Sezer
A Novel Graph-Operational Matrix Method For Solving Multidelay Fractional Differential Equations With Variable Coefficients And A Numerical Comparative Survey Of Fractional Derivative Types, Ömür Kivanç Kürkçü, Ersi̇n Aslan, Mehmet Sezer
Turkish Journal of Mathematics
In this study, we introduce multidelay fractional differential equations with variable coefficients in a unique formula. A novel graph-operational matrix method based on the fractional Caputo, Riemann-Liouville, Caputo-Fabrizio, and Jumarie derivative types is developed to efficiently solve them. We also make use of the collocation points and matrix relations of the matching polynomial of the complete graph in the method. We determine which of the fractional derivative types is more appropriate for the method. The solutions of model problems are improved via a new residual error analysis technique. We design a general computer program module. Thus, we can explicitly monitor …
On Essential Cohomology Of Powerful $P$-Groups, Fatma Altunbulak Aksu
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.
Singly Generated Invariant Subspaces In The Hardy Space On The Unit Ball, Beyaz Başak Koca, Nazim Sadik
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.
Additive Derivative And Multiplicative Coderivative Operators On Mv-Algebras, Ahmet Hamal
Additive Derivative And Multiplicative Coderivative Operators On Mv-Algebras, Ahmet Hamal
Turkish Journal of Mathematics
In this paper we introduce derivative MV-algebras (or MV-algebras with additive derivative operators). We indicate that the derivative MV-algebras are generalizations of closure MV-algebras. Then we investigate the connection between additive derivative operators on MV-algebras and the derivative operators on the greatest Boolean subalgebras of MV-algebras. Finally, we study some properties of the derivative MV-algebras.
The Differential-Symbol Method Of Constructing The Quasipolynomial Solutions Of Two-Point In Time Problem For Nonhomogeneous Partial Differential Equation, Zinovii Nytrebych, Oksana Malanchuk, Volodymyr Il'kiv, Petro Pukach
The Differential-Symbol Method Of Constructing The Quasipolynomial Solutions Of Two-Point In Time Problem For Nonhomogeneous Partial Differential Equation, Zinovii Nytrebych, Oksana Malanchuk, Volodymyr Il'kiv, Petro Pukach
Turkish Journal of Mathematics
The existence of the solution of nonhomogeneous partial differential equations (PDE) of second order in time and finite or infinite order in spatial variable with quasipolynomial right-hand side is proved. This solution satisfies the homogeneous two-point in time conditions. The differential-symbol method for constructing the solution of the problem is proposed. The examples of applying this method for solving some two-point problems for PDE are suggested.
A Fully Hadamard And Erdelyi-Kober-Type Integral Boundary Value Problem Of Acoupled System Of Implicit Differential Equations, Fatima Zohra Berrabah, Benaouda Hedia, Johnny Henderson
A Fully Hadamard And Erdelyi-Kober-Type Integral Boundary Value Problem Of Acoupled System Of Implicit Differential Equations, Fatima Zohra Berrabah, Benaouda Hedia, Johnny Henderson
Turkish Journal of Mathematics
In this article, we give sufficient conditions for the existence of solutions for a new coupled system of second-order implicit differential equations with Hadamard and Erdelyi-Kober fractional integral boundary conditions and nonlocal conditions at the boundaries in Banach space. The main result is based on a Mönch fixed point theorem combined with the measure of noncompactness of Kuratowski; an example is given to illustrate our approach.
An Involution Of Reals, Discontinuous On Rationals, And Whose Derivative Vanishes A.E., Abdurrahman Muhammed Uludağ, Hakan Ayral
An Involution Of Reals, Discontinuous On Rationals, And Whose Derivative Vanishes A.E., Abdurrahman Muhammed Uludağ, Hakan Ayral
Turkish Journal of Mathematics
We study the involution of the real line, induced by Dyer's outer automorphism of PGL(2,Z). It is continuous at irrationals with jump discontinuities at rationals. We prove that its derivative exists almost everywhere and vanishes almost everywhere.
Categorified Groupoid-Sets And Their Burnside Ring, Laiachi El Kaoutit, Leonardo Spinosa
Categorified Groupoid-Sets And Their Burnside Ring, Laiachi El Kaoutit, Leonardo Spinosa
Turkish Journal of Mathematics
We explore the category of internal categories in the usual category of (right) group-sets, whose objects are referred to as categorified group-sets. More precisely, we develop a new Burnside theory, where the equivalence relation between two categorified group-sets is given by a particular equivalence between the underlying categories. We also exhibit some of the differences between the old Burnside theory and the new one. Lastly, we briefly explain how to extend these new techniques and concepts to the context of groupoids, employing the categories of (right) groupoid-sets, aiming by this to give an alternative approach to the classical Burnside ring …
Unpredictable Solutions Of Linear Differential And Discrete Equations, Marat Akhmet, Mehmet Onur Fen, Madina Tleubergenova, Akylbek Zhamanshin
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.
Near-Vector Spaces Determined By Finite Fields And Their Fibrations, Karin-Therese Howell
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.
Automorphisms Of Free Metabelian Leibniz Algebras Of Rank Three, Tuba Taş Adiyaman, Zeynep Özkurt
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.
Classifying Semisymmetric Cubic Graphs Of Order 20p, Mohsen Shahsavaran, Mohammad Reza Darafsheh
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.
Some Properties Of Riemannian Geometry Of The Tangent Bundle Of Lie Groups, Davood Seifipour, Esmaeil Peyghan
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.
$C$-Paracompactness And $C_2$-Paracompactness, Maha Mohammed, Lutfi Kalantan, Hala Alzumi
$C$-Paracompactness And $C_2$-Paracompactness, Maha Mohammed, Lutfi Kalantan, Hala Alzumi
Turkish Journal of Mathematics
A topological space $X$ is called $C$-paracompact if there exist a paracompact space $Y$ and a bijective function $f:X\longrightarrow Y$ such that the restriction $f _{A}:A\longrightarrow f(A)$ is a homeomorphism for each compact subspace $A\subseteq X$. A topological space $X$ is called $C_2$-paracompact if there exist a Hausdorff paracompact space $Y$ and a bijective function $f:X\longrightarrow Y$ such that the restriction $f _{A}:A\longrightarrow f(A)$ is a homeomorphism for each compact subspace $A\subseteq X$. We investigate these two properties and produce some examples to illustrate the relationship between them and $C$-normality, minimal Hausdorff, and other properties.
Eta Quotients Of Level $\Mathbf{12}$ And Weight $\Mathbf{1}$, Ayşe Alaca, Şaban Alaca, Zafer Selcuk Aygin
Eta Quotients Of Level $\Mathbf{12}$ And Weight $\Mathbf{1}$, Ayşe Alaca, Şaban Alaca, Zafer Selcuk Aygin
Turkish Journal of Mathematics
We find all the eta quotients in the spaces $M_1 \Big(\Gamma_0(12), \left(\frac{d}{\cdot}\right) \Big)$ ($d=-3, -4$) of modular forms and determine their Fourier coefficients, where $\left(\frac{d}{\cdot}\right)$ is the Legendre-Jacobi-Kronecker symbol.
When Do Quasinilpotents Lie In The Jacobson Radical?, Peng Cao, Xin Wang
When Do Quasinilpotents Lie In The Jacobson Radical?, Peng Cao, Xin Wang
Turkish Journal of Mathematics
In this paper, we give some spectral characterizations of the Jacobson radical; that is, we will show that some conditions with $\lambda$-multiplicativity imply that the set of all quasinilpotent elements equals the Jacobson radical. We also give some conditions to make sure the quasinilpotents lie in the Jacobson radical, using the set of elements with singleton spectra.
Sectional Curvatures On Weyl Manifolds With A Special Metric Connection, Fatma Özdemi̇r, Mustafa Deni̇z Türkoğlu
Sectional Curvatures On Weyl Manifolds With A Special Metric Connection, Fatma Özdemi̇r, Mustafa Deni̇z Türkoğlu
Turkish Journal of Mathematics
In this paper, Weyl manifolds, denoted by $WS(g,w,\pi,\mu)$, having a special a semisymmetric recurrent-metric connection are introduced and the uniqueness of this connection is proved. We give an example of $WS(g,w,\pi,\mu)$ with a constant scalar curvature. Furthermore, we define sectional curvatures of $WS(g,w,\pi,\mu)$ and prove that any isotropic Weyl manifold $WS(g,w,\pi,\mu)$ is locally conformal to an Einstein manifold with a semisymmetric recurrent-metric connection, $EWS(g,w,\pi,\mu)$.
Univalent Harmonic Mappings And Hardy Spaces, Ali Ebadian, Saman Azizi, Si̇bel Yalçin Tokgöz
Univalent Harmonic Mappings And Hardy Spaces, Ali Ebadian, Saman Azizi, Si̇bel Yalçin Tokgöz
Turkish Journal of Mathematics
The main purpose of this paper is to establish a relationship between univalent harmonic mappings and Hardy spaces. The main result obtained in this paper improves previously published results. Moreover, we generalize some nice results in the analytic case to the harmonic case.
A Discrete Chaotic Dynamical System On The Sierpinski Gasket, Mustafa Saltan, Ni̇sa Aslan, Bünyami̇n Demi̇r
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 …
Young Tableaux And Arf Partitions, Nesri̇n Tutaş, Hali̇l İbrahi̇m Karakaş, Ni̇hal Gümüşbaş
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.
On The Composition And Exterior Products Of Double Forms And $P$-Pure Manifolds, Abdelhadi Belkhirat, Mohammed Labbi
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 …
Some Operator Inequalities Associated With Kantorovich And Hölder-Mccarthyinequalities And Their Applications, Hamdullah Başaran, Mehmet Gürdal, Ayşe Nur Güncan
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.
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
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 …
Spectral Properties Of Boundary-Value-Transmission Problems With A Constant Retarded Argument, Erdoğan Şen
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.
$N$-$T$-Torsionfree Modules, Peiyu Zhang, Jie Geng
$N$-$T$-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.
On The Number Of $K$-Normal Elements Over Finite Fields, Zülfükar Saygi, Erni̇st Ti̇lenbaev, Çeti̇n Ürti̇ş
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.