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On A Fifth-Order Nonselfadjoint Boundary Value Problem, Eki̇n Uğurlu, Kenan Taş
On A Fifth-Order Nonselfadjoint Boundary Value Problem, Eki̇n Uğurlu, Kenan Taş
Turkish Journal of Mathematics
In this paper we aim to share a way to impose some nonselfadjoint boundary conditions for the solutions of a formally symmetric fifth-order differential equation. Constructing a dissipative operator related with the problem we obtain some informations on spectral properties of the problem. In particular, using coordinate-free approach we construct characteristic matrix-function related with the contraction which is obtained with the aid of the dissipative operator.
Completeness Conditions Of Systems Of Bessel Functions In Weighted $L^2$-Spaces In Terms Of Entire Functions, Ruslan Khats'
Completeness Conditions Of Systems Of Bessel Functions In Weighted $L^2$-Spaces In Terms Of Entire Functions, Ruslan Khats'
Turkish Journal of Mathematics
Let $J_{\nu}$ be the Bessel function of the first kind of index $\nu\ge 1/2$, $p\in\mathbb R$ and $(\rho_k)_{k\in\mathbb N}$ be a sequence of distinct nonzero complex numbers. Sufficient conditions for the completeness of the system $\big\{x^{-p-1}\sqrt{x\rho_k}J_{\nu}(x\rho_k):k\in\mathbb N\big\}$ in the weighted space $L^2((0;1);x^{2p} dx)$ are found in terms of an entire function with the set of zeros coinciding with the sequence $(\rho_k)_{k\in\mathbb N}$.
Oscillation Tests For Nonlinear Differential Equations With Nonmonotone Delays, Nurten Kiliç
Oscillation Tests For Nonlinear Differential Equations With Nonmonotone Delays, Nurten Kiliç
Turkish Journal of Mathematics
In this paper, our aim is to investigate a class of first-order nonlinear delay differential equations with several deviating arguments. In addition, we present some sufficient conditions for the oscillatory solutions of these equations. Differing from other studies in the literature, delay terms are not necessarily monotone. Finally, we give examples to demonstrate the results.
Generating Finite Coxeter Groups With Elements Of The Same Order, Sarah B. Hart, Veronica Kelsey, Peter Rowley
Generating Finite Coxeter Groups With Elements Of The Same Order, Sarah B. Hart, Veronica Kelsey, Peter Rowley
Turkish Journal of Mathematics
Supposing $G$ is a group and $k$ a natural number, $d_k(G)$ is defined to be the minimal number of elements of $G$ of order $k$ which generate $G$ (setting $d_k(G)=0$ if $G$ has no such generating sets). This paper investigates $d_k(G)$ when $G$ is a finite Coxeter group either of type $B_n$ or $D_n$, or of exceptional type. Together with the work of Garzoni and Yu, this determines $d_k(G)$ for all finite irreducible Coxeter groups $G$ when $2 \leq k \leq (G)$ ($(G)+1$ when $G$ is of type A$_{n}$).
A Classification Of 1-Well-Covered Graphs, Zaki̇r Deni̇z
A Classification Of 1-Well-Covered Graphs, Zaki̇r Deni̇z
Turkish Journal of Mathematics
A graph is well-covered if all its maximal independent sets have the same size. If a graph is well-covered and remains well-covered upon removal of any vertex, then it is called 1-well-covered graph. It is well-known that $[\frac{n}{2}]+1\leq \alpha(G) + \mu(G) \leq n$ for any graph $G$ with $n$ vertices where $\alpha(G)$ and $\mu(G)$ are the independence and matching numbers of $G$, respectively. A graph $G$ satisfying $\alpha(G) + \mu(G) = n$ is known as König-Egervary graph, and such graphs are characterized by Levit and Mandrescu [14] under the assumption that $G$ is 1-well-covered. In this paper, we investigate connected …
Some Properties Of Second-Order Weak Subdifferentials, Gonca İnceoğlu
Some Properties Of Second-Order Weak Subdifferentials, Gonca İnceoğlu
Turkish Journal of Mathematics
This article deals with second-order weak subdifferential. Firstly, the concept of second-order weak subdifferential is defined. Next, some of its properties are investigated. The necessary and sufficient condition for a second-order weakly subdifferentiable function to have a global minimum has been proved. It has been proved that a second-order weakly subdifferentiable function is both lower semicontinuous and lower Lipschitz.
Fekete-Szegö Problem For A New Subclass Of Analytic Functions Satisfying Subordinate Condition Associated With Chebyshev Polynomials, Muhammet Kamali̇, Murat Çağlar, Erhan Deni̇z, Mirzaolim Turabaev
Fekete-Szegö Problem For A New Subclass Of Analytic Functions Satisfying Subordinate Condition Associated With Chebyshev Polynomials, Muhammet Kamali̇, Murat Çağlar, Erhan Deni̇z, Mirzaolim Turabaev
Turkish Journal of Mathematics
In this paper,we define a class of analytic functions $F_{\left( \beta ,\lambda \right) }\left( H,\alpha ,\delta ,\mu \right) ,$ satisfying the following subordinate condition associated with Chebyshev polynomials \begin{equation*} \left\{ \alpha \left[ \frac{zG^{^{\prime }}\left( z\right) }{G\left( z\right) }\right] ^{\delta }+\left( 1-\alpha \right) \left[ \frac{% zG^{^{\prime }}\left( z\right) }{G\left( z\right) }\right] ^{\mu }\left[ 1+% \frac{zG^{^{\prime \prime }}\left( z\right) }{G^{^{\prime }}\left( z\right) }% \right] ^{1-\mu }\right\} \prec H\left( z,t\right) , \end{equation*}% where $G\left( z\right) =\lambda \beta z^{2}f^{^{\prime \prime }}\left( z\right) +\left( \lambda -\beta \right) zf^{^{\prime }}\left( z\right) +\left( 1-\lambda +\beta \right) f\left( z\right) ,$ $0\leq \alpha \leq 1,$ $% 1\leq \delta \leq …
Second Hankel Determinant For Mocanu Type Bi-Starlike Functionsrelated To Shell-Shaped Region, Ni̇zami̇ Mustafa, Gangadharan Murungusundaramoorthy
Second Hankel Determinant For Mocanu Type Bi-Starlike Functionsrelated To Shell-Shaped Region, Ni̇zami̇ Mustafa, Gangadharan Murungusundaramoorthy
Turkish Journal of Mathematics
In this paper, we investigate the coefficient bound estimates, second Hankel determinant, and Fekete-Szegö inequality for the analytic bi-univalent function class, which we call Mocanu type bi-starlike functions, related to a shell-shaped region in the open unit disk in the complex plane. Some interesting special cases of the results are also discussed.
General Rotational $\Xi -$Surfaces In Euclidean Spaces, Kadri̇ Arslan, Yilmaz Aydin, Betül Bulca
General Rotational $\Xi -$Surfaces In Euclidean Spaces, Kadri̇ Arslan, Yilmaz Aydin, Betül Bulca
Turkish Journal of Mathematics
The general rotational surfaces in the Euclidean 4-space $\mathbb{R}^{4}$ was first studied by Moore (1919). The Vranceanu surfaces are the special examples of these kind of surfaces. Self-shrinker flows arise as special solution of the mean curvature flow that preserves the shape of the evolving submanifold. In addition, $\xi -$surfaces are the generalization of self-shrinker surfaces. In the present article we consider $\xi -$surfaces in Euclidean spaces. We obtained some results related with rotational surfaces in Euclidean $4-$space $\mathbb{R}^{4}$ to become self-shrinkers. Furthermore, we classify the general rotational $\xi -$surfaces with constant mean curvature. As an application, we give some …
Weak C-Ideals Of A Lie Algebra, Zeki̇ye Çi̇loğlu Şahi̇n, David Anthony Towers
Weak C-Ideals Of A Lie Algebra, Zeki̇ye Çi̇loğlu Şahi̇n, David Anthony Towers
Turkish Journal of Mathematics
A subalgebra $B$ of a Lie algebra $L$ is called a weak c-ideal of $L$ if there is a subideal $C$ of $L$ such that $L=B+C$ and $B\cap C\leq B_{L} $ where $B_{L}$ is the largest ideal of $L$ contained in $B.$ This is analogous to the concept of weakly c-normal subgroups, which has been studied by a number of authors. We obtain some properties of weak c-ideals and use them to give some characterisations of solvable and supersolvable Lie algebras. We also note that one-dimensional weak c-ideals are c-ideals.
Some New Uniqueness And Ulam Stability Results For A Class Of Multi-Terms Fractional Differential Equations In The Framework Of Generalized Caputo Fractional Derivative Using The $\Phi$-Fractional Bielecki-Type Norm, Choukri Derbazi, Zidane Baitiche, Michal Feckan
Some New Uniqueness And Ulam Stability Results For A Class Of Multi-Terms Fractional Differential Equations In The Framework Of Generalized Caputo Fractional Derivative Using The $\Phi$-Fractional Bielecki-Type Norm, Choukri Derbazi, Zidane Baitiche, Michal Feckan
Turkish Journal of Mathematics
In this research article, a novel $\Phi$-fractional Bielecki-type norm introduced by Sousa and Oliveira [23] is used to obtain results on uniqueness and Ulam stability of solutions for a new class of multiterms fractional differential equations in the framework of generalized Caputo fractional derivative. The uniqueness results are obtained by employing Banach' and Perov's fixed point theorems. While the $\Phi$-fractional Gronwall type inequality and the concept of the matrices converging to zero are implemented to examine different types of stabilities in the sense of Ulam-Hyers (UH) of the given problems. Finally, two illustrative examples are provided to demonstrate the validity …
Axes In Non-Associative Algebras, Louis Rowen, Yoav Segev
Axes In Non-Associative Algebras, Louis Rowen, Yoav Segev
Turkish Journal of Mathematics
Fusion rules are laws of multiplication among eigenspaces of an idempotent. This terminology is relatively new and is closely related to axial algebras, introduced recently by Hall, Rehren and Shpectorov. Axial algebras, in turn, are closely related to $3$-transposition groups and Vertex operator algebras. In this paper we consider fusion rules for semisimple idempotents, following Albert in the power-associative case. We examine the notion of an axis in the non-commutative setting and show that the dimension $d$ of any algebra $A$ generated by a pair $a,b$ of (not necessarily Jordan) axes of respective types $(λ,δ)$ and $(λ',δ')$ must be at …
Linear Stability Of Periodic Standing Waves Of The Kgz System, Sevdzhan Ahmedov Hakkaev, Fati̇h Hunutlu
Linear Stability Of Periodic Standing Waves Of The Kgz System, Sevdzhan Ahmedov Hakkaev, Fati̇h Hunutlu
Turkish Journal of Mathematics
In this work we consider the periodic standing wave solutions for a Klein-Gordon-Zakharov system. We find the conditions on the parameters, for which the periodic waves of dnoidal type are linear stable/unstable.
A Gompertz Distribution For Time Scales, Tom Cuchta, Robert Jon Niichel, Sabrina Streipert
A Gompertz Distribution For Time Scales, Tom Cuchta, Robert Jon Niichel, Sabrina Streipert
Turkish Journal of Mathematics
We investigate a family of probability distributions, with three parameters associated with the dynamic Gompertz function. We prove its existence for various parameter sets and discuss the existence of its time scale moments. Afterwards, we investigate the special case of discrete time scales, where it is shown that the discrete Gompertz distribution is a $q$-geometric distribution of the second kind. Further, we find their $q$-binomial moments, we bound their expected value, and we show how a classical Gompertz distribution is obtained from them.
Number Fields And Divisible Groups Via Model Theor, Şermi̇n Çam Çeli̇k, Haydar Göral
Number Fields And Divisible Groups Via Model Theor, Şermi̇n Çam Çeli̇k, Haydar Göral
Turkish Journal of Mathematics
In this note, we first show that solutions of certain equations classify the number fields lying in imaginary quadratic number fields. Then, we study divisible groups with a predicate. We show that these structures are not simple and have the independence property under some natural assumptions.
Polyhedral Optimization Of Second-Order Discrete And Differential Inclusions With Delay, Sevi̇lay Demi̇r Sağlam, Eli̇mhan N. Mahmudov
Polyhedral Optimization Of Second-Order Discrete And Differential Inclusions With Delay, Sevi̇lay Demi̇r Sağlam, Eli̇mhan N. Mahmudov
Turkish Journal of Mathematics
he present paper studies the optimal control theory of second-order polyhedral delay discrete and delay differential inclusions with state constraints. We formulate the conditions of optimality for the problems with the second-order polyhedral delay discrete $(PD_d)$ and the delay differential $(PC_d)$ in terms of the Euler-Lagrange inclusions and the distinctive ''transversality'' conditions. Moreover, some linear control problem with second-order delay differential inclusions is given to illustrate the effectiveness and usefulness of the main theoretic results.
A New Gauss--Newton-Like Method For Nonlinear Equations, Haijun Wang, Qi Wang
A New Gauss--Newton-Like Method For Nonlinear Equations, Haijun Wang, Qi Wang
Turkish Journal of Mathematics
In this paper, a new Gauss-Newton-like method that is based on a rational approximation model with linear numerator is proposed for solving nonlinear equations. The new method revises the $J_k^\mathrm{T}J_k$ matrix by a rank-one matrix at each iteration. Furthermore, we design a new iterative algorithm for nonlinear equations and prove that it is locally q-quadratically convergent. The numerical results show that the new proposed method has better performance than the classical Gauss-Newton method.
Self-Adjoint Extensions For A Class Of Singular Operators, Rauf Ami̇rov, Hidayat Mehmetoğlu Huseynov, Sevi̇m Durak
Self-Adjoint Extensions For A Class Of Singular Operators, Rauf Ami̇rov, Hidayat Mehmetoğlu Huseynov, Sevi̇m Durak
Turkish Journal of Mathematics
In this study, we consider the domains of the minimal and maximal operators generated of singular differential-expression-type Sturm-Liouville and obtain all self-adjoint extensions of the operator in terms of boundary conditions.
Peiffer Pairings In Multisimplicial Groups And Crossed $N$-Cubes And Applications For Bisimplicial Groups, Özgün Gürmen Alansal, Erdal Ulualan
Peiffer Pairings In Multisimplicial Groups And Crossed $N$-Cubes And Applications For Bisimplicial Groups, Özgün Gürmen Alansal, Erdal Ulualan
Turkish Journal of Mathematics
We explore the Peiffer pairings within the Moore complex of multisimplicial groups, and as an application, we give a detailed construction of a crossed $n$- cube from an $n$-simplicial group in terms of these pairings. We also give explicit calculations of Peiffer pairings in the Moore bicomplex of a bisimplicial group to see the role of these pairings in the relationship between bisimplicial groups and crossed squares.
On $F$-Kenmotsu $3$-Manifolds With Respect To The Schouten-Van Kampen Connection, Selcen Yüksel Perktaş, Ahmet Yildiz
On $F$-Kenmotsu $3$-Manifolds With Respect To The Schouten-Van Kampen Connection, Selcen Yüksel Perktaş, Ahmet Yildiz
Turkish Journal of Mathematics
In this paper we study some semisymmetry conditions and some soliton types on $f$-Kenmotsu $3$-manifolds with respect to the Schouten-van Kampen connection.
Crossed Product Of Infinite Groups And Complete Rewriting Systems, Esra Kirmizi Çeti̇nalp, Eylem Güzel Karpuz
Crossed Product Of Infinite Groups And Complete Rewriting Systems, Esra Kirmizi Çeti̇nalp, Eylem Güzel Karpuz
Turkish Journal of Mathematics
The aim of this paper is to obtain a presentation for crossed product of some infinite groups and then find its complete rewriting system. Hence, we present normal form structure of elements of crossed product of infinite groups which yield solvability of the word problem.
Notes On Multivalent Bazilevic Functions Defined By Higher Order Derivatives, Mohamed K. Aouf, Adela O. Mostafa, Teodor Bulboaca
Notes On Multivalent Bazilevic Functions Defined By Higher Order Derivatives, Mohamed K. Aouf, Adela O. Mostafa, Teodor Bulboaca
Turkish Journal of Mathematics
In this paper we consider two subclasses $B(p,q,\alpha,\beta)$ and $B_{1}(p,q,\alpha,\beta)$ of p-valently Bazilevi\'c functions defined by higher order derivatives, and we defined and studied some properties of the images of the functions of these classes by the integral operators $\mathrm{I}_{n,p}$ and $\mathrm{J}_{n,p}$ for multivalent functions, defined by using higher order derivatives.
T$_{4}$, Urysohn's Lemma, And Tietze Extension Theorem For Constant Filter Convergence Spaces, Tesni̇m Meryem Baran, Ayhan Erci̇yes
T$_{4}$, Urysohn's Lemma, And Tietze Extension Theorem For Constant Filter Convergence Spaces, Tesni̇m Meryem Baran, Ayhan Erci̇yes
Turkish Journal of Mathematics
In this paper, we characterize various local forms of T$_{4}$ constant filter convergence spaces and investigate the relationships among them as well as showing that the full subcategories of the category of constant filter convergence spaces consisting of local T$_{4}$ constant filter convergence spaces that are hereditary. Furthermore, we examine the relationship between local T$_{4}$ and general T$_{4}$ constant filter convergence spaces. Finally, we present Urysohn's lemma and Tietze extension theorem for constant filter convergence spaces.
Korovkin Type Approximation Via Triangular $A-$Statistical Convergence On An Infinite Interval, Seli̇n Çinar, Sevda Yildiz, Kami̇l Demi̇rci̇
Korovkin Type Approximation Via Triangular $A-$Statistical Convergence On An Infinite Interval, Seli̇n Çinar, Sevda Yildiz, Kami̇l Demi̇rci̇
Turkish Journal of Mathematics
In the present paper, using the triangular $A-$statistical convergence for double sequences, which is an interesting convergence method, we prove a Korovkin-type approximation theorem for positive linear operators on the space of all real-valued continuous functions on $\left[ 0,\infty \right)\times \left[ 0,\infty \right) $ with the property that have a finite limit at the infinity. Moreover, we present the rate of convergence via modulus of continuity. Finally, we give some further developments.
Repdigits As Sums Of Two Generalized Lucas Numbers, Sai Gopal Rayaguru, Jhon Jairo Bravo
Repdigits As Sums Of Two Generalized Lucas Numbers, Sai Gopal Rayaguru, Jhon Jairo Bravo
Turkish Journal of Mathematics
A generalization of the well-known Lucas sequence is the $k$-Lucas sequence with some fixed integer $k \geq 2$. The first $k$ terms of this sequence are $0,\ldots,0,2,1$, and each term afterwards is the sum of the preceding $k$ terms. In this paper, we determine all repdigits, which are expressible as sums of two $k$-Lucas numbers. This work generalizes a prior result of Şiar and Keskin who dealt with the above problem for the particular case of Lucas numbers and a result of Bravo and Luca who searched for repdigits that are $k$-Lucas numbers.
Banach Algebra Structure On Strongly Simple Extensions, Sara El Kinani
Banach Algebra Structure On Strongly Simple Extensions, Sara El Kinani
Turkish Journal of Mathematics
We consider strongly simple extensions of unitary commutative Banach algebras. We study these Banach algebra structure without assuming the continuity of the canonical injection. The link of the integrality with these extensions is studied. Several algebraic results are also obtained.
Liftings And Covering Morphisms Of Crossed Modules In Group-Groupoids, Serap Demi̇r Karakaş, Osman Mucuk
Liftings And Covering Morphisms Of Crossed Modules In Group-Groupoids, Serap Demi̇r Karakaş, Osman Mucuk
Turkish Journal of Mathematics
In this work we introduce lifting and covering of a crossed module in the category of group-groupoids; and then we prove the categorical equivalence of horizontal actions of a double group-groupoid and lifting crossed modules of corresponding crossed module in group-groupoids. These allow us to produce more examples of double group-groupoids.
Decompositions Of Complete Symmetric Directed Graphs Into The Oriented Heptagons, Uğur Odabaşi
Decompositions Of Complete Symmetric Directed Graphs Into The Oriented Heptagons, Uğur Odabaşi
Turkish Journal of Mathematics
The complete symmetric directed graph of order $v$, denoted by $K_{v}$, is the directed graph on $v$~vertices that contains both arcs $(x,y)$ and $(y,x)$ for each pair of distinct vertices $x$ and~$y$. For a given directed graph $D$, the set of all $v$ for which $K_{v}$ admits a $D$-decomposition is called the spectrum of~$D$-decomposition. There are 10 nonisomorphic orientations of a $7$-cycle (heptagon). In this paper, we completely settled the spectrum problem for each of the oriented heptagons.
Some Applications Of Fractional Calculus For Analytic Functions, Nesli̇han Uyanik, Shi̇geyoshi̇ Owa
Some Applications Of Fractional Calculus For Analytic Functions, Nesli̇han Uyanik, Shi̇geyoshi̇ Owa
Turkish Journal of Mathematics
For analytic functions $f\left( z\right) $ in the class $A_{n},$ fractional calculus (fractional integrals and fractional derivatives) $D_{z}^{\lambda }f\left( z\right) $ of order $\lambda $ are introduced. Applying $% D_{z}^{\lambda }f\left( z\right) $ for $f\left( z\right) \in A_{n},$ we introduce the interesting subclass $A_{n}\left( \alpha _{m},\beta ,\rho ,\lambda \right) $ of $A_{n}.$ The object of this paper is to discuss some properties of $f\left( z\right) $ concerning $D_{z}^{\lambda }f\left( z\right) .$