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Articles 1 - 30 of 186
Full-Text Articles in Physical Sciences and Mathematics
Notes On Product Semisymmetric Connection In A Locally Decomposable Riemannian Space, Miroslav Maksimovic, Mica Stankovic
Notes On Product Semisymmetric Connection In A Locally Decomposable Riemannian Space, Miroslav Maksimovic, Mica Stankovic
Turkish Journal of Mathematics
The purpose of this paper is to investigate the product semisymmetric connection in a locally decomposable Riemannian space. The curvature tensors of this connection were considered. Some properties of almost product structure, some properties of torsion tensor of product semisymmetric connection and some relations between curvature tensors and almost product structure are given. Also, the paper checks a special case of such connection when its generator is a gradient vector.
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.
On $Q$- And $H$-Deformations Of 3d-Superspaces, Sali̇h Çeli̇k
On $Q$- And $H$-Deformations Of 3d-Superspaces, Sali̇h Çeli̇k
Turkish Journal of Mathematics
In this paper, we introduce nonstandard deformations of (1+2)- and (2+1)-superspaces via a contraction using standard deformations of them. This deformed superspaces are denoted by ${\mathbb A}_h^{1 2}$ and ${\mathbb A}_{h'}^{2 1}$, respectively. We find a two-parameter $R$-matrix satisfying quantum Yang--Baxter equation and thus obtain a { new} two-parameter nonstandard deformation of the supergroup ${\rm GL}(1 2)$. Finally, we get a new superalgebra derived from the Hopf superalgebra of functions on the quantum superspace ${\mathbb A}_{p,q}^{1 2}$.
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.
Maps On $\Mathcal{S}(\Mathcal{H})$ Preserving The Difference Of Noninvertible Algebraic Operators, Zynab Izadi, Rahmat Soltani
Maps On $\Mathcal{S}(\Mathcal{H})$ Preserving The Difference Of Noninvertible Algebraic Operators, Zynab Izadi, Rahmat Soltani
Turkish Journal of Mathematics
The aim of this paper is to present the general structure of nonlinear surjective maps on $\mathcal S(\mathcal H)$ preserving the operator pairs in which their difference is a noninvertible algebraic operator. $\mathcal S(\mathcal H)$ represents the real Jordan algebra of bounded self-adjoint operators acting on an infinite dimensional Hilbert space $\mathcal{ H}$.
Close-To-Convexity Of A Class Of Harmonic Mappings Defined By A Third-Order Differential Inequality, Eli̇f Yaşar, Si̇bel Yalçin Tokgöz
Close-To-Convexity Of A Class Of Harmonic Mappings Defined By A Third-Order Differential Inequality, Eli̇f Yaşar, Si̇bel Yalçin Tokgöz
Turkish Journal of Mathematics
In this paper, we consider a class of normalized harmonic functions in the unit disk satisfying a third-order differential inequality and we investigate several properties of this class such as close-to-convexity, coefficient bounds, growth estimates, sufficient coefficient condition, and convolution. Moreover, as an application, we construct harmonic polynomials involving Gaussian hypergeometric function which belong to the considered class. We also provide examples illustrating graphically with the help of Maple.
Portfolio Optimization With Two Quasiconvex Risk Measures, Çağin Ararat
Portfolio Optimization With Two Quasiconvex Risk Measures, Çağin Ararat
Turkish Journal of Mathematics
We study a static portfolio optimization problem with two risk measures: a principle risk measure in the objective function and a secondary risk measure whose value is controlled in the constraints. This problem is of interest when it is necessary to consider the risk preferences of two parties, such as a portfolio manager and a regulator, at the same time. A special case of this problem where the risk measures are assumed to be coherent (positively homogeneous) is studied recently in a joint work of the author. The present paper extends the analysis to a more general setting by assuming …
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.
On Rings Whose Jacobson Radical Coincides With Upper Nilradical, Guanglin Ma, Yao Wang, Yanli Ren
On Rings Whose Jacobson Radical Coincides With Upper Nilradical, Guanglin Ma, Yao Wang, Yanli Ren
Turkish Journal of Mathematics
We call a ring~R is JN if whose Jacobson radical coincides with upper nilradical, and R is right SR if each element r∈ R can be written as r=s+r where s is an element from the right socle and r is a regular element of~R. SR rings is a class of special subrings of JN rings, which is the extension of soclean rings. We give their some characterizations and examples, and investigate the relationship between JN rings, SR rings and related rings, respectively.
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.
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 General Double Series Identity And Its Application In Hypergeometric Reduction Formulas, Mohammad Idris Qureshi, Shakir Hussain Malik
A General Double Series Identity And Its Application In Hypergeometric Reduction Formulas, Mohammad Idris Qureshi, Shakir Hussain Malik
Turkish Journal of Mathematics
In this paper, we obtain a general double-series identity involving the bounded sequence of arbitrary complex numbers. As application of our double-series identity, we establish some reduction formulas for Srivastava--Daoust double hypergeometric function and Gaussian generalized hypergeometric function $_4F_3$. As special cases of our reduction formula for $_4F_3$ lead to some corollaries involving Clausen hypergeometric functions ${_{3}F_{2}}$. Making suitable adjustment of parameters in reduction formulas for $_4F_3$ and ${_{3}F_{2}}$, we obtain some results in terms of elementary functions and some special functions like Lerch generalized zeta function and incomplete beta function.
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 …
On The Analytical Development Of Incomplete Riemann-Liouville Fractional Calculus, Arran Fernandez, Ceren Ustaoğlu, Mehmet Ali̇ Özarslan
On The Analytical Development Of Incomplete Riemann-Liouville Fractional Calculus, Arran Fernandez, Ceren Ustaoğlu, Mehmet Ali̇ Özarslan
Turkish Journal of Mathematics
The theoretical development of fractional calculus includes the formulation of different definitions, the extension of properties from standard calculus, and the application of fractional operators to special functions. In two recent papers, incomplete versions of classical fractional operators were formulated in connection with special functions. Here, we develop the theory of incomplete fractional calculus more deeply, investigating further properties of these operators and answering some fundamental questions about how they work. By considering appropriate function spaces, we discover that incomplete fractional calculus may be used to analyse a wider class of functions than classical fractional calculus can consider. By using …
Integer-Valued Polynomials Satisfying The Lucas Property, Rattiya Meesa, Vichian Laohakosol, Tuangrat Chaichana
Integer-Valued Polynomials Satisfying The Lucas Property, Rattiya Meesa, Vichian Laohakosol, Tuangrat Chaichana
Turkish Journal of Mathematics
The classical theorem of Lucas states that the binomial polynomials, which form a basis for integer-valued polynomials, satisfy a congruence relation related to their integer parameters. We consider here three problems connected with this result in the setting of discrete valued structures. The first problem asks for the shapes of Lagrange-type interpolation polynomials which constitute a basis for integer-valued polynomials and satisfy the Lucas property; the result so obtained extends a 2001 result of Boulanger and Chabert. For the second problem, we show that the Carlitz polynomials, which form a basis for integer-valued polynomials in a function field, satisfy the …
Theory And Numerical Approaches Of High Order Fractional Sturm-Liouville Problems, Tahereh Houlari, Mohammad Dehghan, Jafar Biazar, Alireza Nouri
Theory And Numerical Approaches Of High Order Fractional Sturm-Liouville Problems, Tahereh Houlari, Mohammad Dehghan, Jafar Biazar, Alireza Nouri
Turkish Journal of Mathematics
In this paper, fractional Sturm--Liouville problems of high-order are studied. A simple and efficient approach is presented to determine more eigenvalues and eigenfunctions than other approaches. Existence and uniqueness of solutions of a fractional high-order differential equation with initial conditions is addressed as well as the convergence of the proposed approach. This class of eigenvalue problems is important in finding solutions to linear fractional partial differential equations (LFPDE). This method is illustrated by three examples to signify the efficiency and reliability of the proposed numerical approach.
On Sense Of Yamakawa Family Of Meromorphic Bi-Univalent And Bi-Subordinate Functions, Fethi̇ye Müge Sakar
On Sense Of Yamakawa Family Of Meromorphic Bi-Univalent And Bi-Subordinate Functions, Fethi̇ye Müge Sakar
Turkish Journal of Mathematics
This study offers three different univalent function families of bi-meromorphic and bi-subordinate functions defined on $\Delta=\{z:z\in\mathbb{C}, 1
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.
Count Of Genus Zero $J$-Holomorphic Curves In Dimensions Four And Six, Ahmet Beyaz
Count Of Genus Zero $J$-Holomorphic Curves In Dimensions Four And Six, Ahmet Beyaz
Turkish Journal of Mathematics
The abstract should provide clear information about the research and the results obtained, and should not exceed 200 words. The abstract should not contain citations. An application of Gromov--Witten invariants is that they distinguish the deformation types of symplectic structures on a smooth manifold. In this manuscript, it is proven that the use of Gromov--Witten invariants in the class of embedded $J$-holomorphic spheres is restricted. This restriction is in the sense that they cannot distinguish the deformation types of symplectic structures on $X_1\times S^2$ and $X_2\times S^2$ for two minimal, simply connected, symplectic $4$-manifolds $X_1$ and $X_2$ with $b_2^+(X_1)>1$ …
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 $D_{z}^{\lambda }f\left( z\right) .$
On $(K,N)$ Power Quasi-Normal Operators, Salah Mecheri, Aissa Nasli Bakir
On $(K,N)$ Power Quasi-Normal Operators, Salah Mecheri, Aissa Nasli Bakir
Turkish Journal of Mathematics
The aim of this paper is to present certain basic properties of some classes of nonnormal operators defined on a complex separable Hilbert space. Both of the normality of their integer powers and their relations with isometries are established. The ascent of such operators as well as other important related results are also established. The decomposition of such operators, their restrictions on invariant subspaces, and some spectral properties are also presented.
A Fourth Order One Step Method For Numerical Solution Of Good Boussinesq Equation, Emre Kirli, Dursun Irk
A Fourth Order One Step Method For Numerical Solution Of Good Boussinesq Equation, Emre Kirli, Dursun Irk
Turkish Journal of Mathematics
In this paper, we investigate the numerical solution of "good" Boussinesq equation by using the quartic B-spline Galerkin method for space discretization and the fourth order one-step method for time discretization.The proposed numerical scheme is analyzed for truncation error. Four test problems are studied. The accuracy and efficiency are measured by computing error norm $L_{\infty }$ and the order of convergence for the proposed method. The results of numerical experiments confirm that the proposed method has a higher accuracy.
Some New Representations Of Hikami's Second-Order Mock Theta Function $\Mathfrak{D}_5(Q)$, Qiuxia Hu
Some New Representations Of Hikami's Second-Order Mock Theta Function $\Mathfrak{D}_5(Q)$, Qiuxia Hu
Turkish Journal of Mathematics
In this paper, a second-order mock theta function $\mathfrak{D}_5(q)$ given by Hikami [11] is studied. By using basic hypergeometric transformation formulae, we attain some new representations of Hikami's mock theta function $\mathfrak{D}_5(q)$. Meanwhile, dual nature of bilateral series associated to mock theta function $\mathfrak{D}_5(q)$ is also discussed.
Secondary Constructions Of (Non)-Weakly Regular Plateaued Functions Over Finite Fields, Si̇hem Mesnager, Ferruh Özbudak, Ahmet Sinak
Secondary Constructions Of (Non)-Weakly Regular Plateaued Functions Over Finite Fields, Si̇hem Mesnager, Ferruh Özbudak, Ahmet Sinak
Turkish Journal of Mathematics
Plateaued (vectorial) functions over finite fields have diverse applications in symmetric cryptography, coding theory, and sequence theory. Constructing these functions is an attractive research topic in the literature. We can distinguish two kinds of constructions of plateaued functions: secondary constructions and primary constructions. The first method uses already known functions to obtain new functions while the latter do not need to use previously constructed functions to obtain new functions. In this work, the first secondary constructions of (non)weakly regular plateaued (vectorial) functions are presented over the finite fields of odd characteristics. We also introduce some recursive constructions of (non)weakly regular …