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Articles 1 - 30 of 186
Full-Text Articles in Physical Sciences and Mathematics
Moments And Zero Density Estimates For Dirichlet $L$-Functions, Keiju Sono
Moments And Zero Density Estimates For Dirichlet $L$-Functions, Keiju Sono
Turkish Journal of Mathematics
In this paper, we estimate the density of zeros of primitive Dirichlet $L$-functions in the half-plane $\Re (s)>1/2$, under the assumption of a plausible conjecture on high moments of Dirichlet $L$-functions on the critical line. We conditionally improve the results of Huxley [9], Jutila [13], Heath-Brown [5, 6] and Bourgain [1].
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.
Optimization Of Mayer Functional In Problems With Discrete And Differential Inclusions And Viability Constraints, Gülseren Çi̇çek, Eli̇mhan N. Mahmudov
Optimization Of Mayer Functional In Problems With Discrete And Differential Inclusions And Viability Constraints, Gülseren Çi̇çek, Eli̇mhan N. Mahmudov
Turkish Journal of Mathematics
This paper derives the optimality conditions for a Mayer problem with discrete and differential inclusions with viable constraints. Applying necessary and sufficient conditions of problems with geometric constraints, we prove optimality conditions for second order discrete inclusions. Using locally adjoint mapping, we derive Euler-Lagrange form conditions and transversality conditions for the optimality of the discrete approximation problem. Passing to the limit, we establish sufficient conditions to the optimal problem with viable constraints. Conditions ensuring the existence of solutions to the viability problems for differential inclusions of second order have been studied in recent years. However, optimization problems of second-order differential …
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 …
On Fractional P-Laplacian Type Equations With General Nonlinearities, Adel Daouas, Mohamed Louchaich
On Fractional P-Laplacian Type Equations With General Nonlinearities, Adel Daouas, Mohamed Louchaich
Turkish Journal of Mathematics
In this paper, we study the existence and multiplicity of solutions for a class of quasi-linear elliptic problems driven by a nonlocal integro-differential operator with homogeneous Dirichlet boundary conditions. As a particular case, we study the following problem: \begin{equation*} \left\{ \begin{array}{l} (-\Delta)_p^s u= f(x,u) \quad \hfill \textrm{in} \ \Omega,\\ \quad u=0 \ \hfill \textrm{in} \ R^N \setminus \Omega, \end{array} \right.\\ \end{equation*} where $(-\Delta)_p^s$ is the fractional p-Laplacian operator, $\Omega$ is an open bounded subset of $R^N$ with Lipschitz boundary and $f:\Omega \times R \to R$ is a generic Carath\'eodory function satisfying either a $p-$sublinear or a $p-$superlinear growth condition.
Star Edge Coloring Of Graphs With Mad($G$)$, Kavita Pradeep
Star Edge Coloring Of Graphs With Mad($G$)$, Kavita Pradeep
Turkish Journal of Mathematics
A star edge coloring of a graph $G$ is a proper edge coloring such that there is no bicolored path or cycle of length four. The minimum number of colors needed for a graph $G$ to admit a star edge coloring is called the star chromatic index and it is denoted by $\chi_s^{'}(G)$. In this paper, we consider graphs of maximum degree $\Delta \geq 4$ and show that if the maximum average degree of a graph is less than $\frac{14}{5}$ then $\chi_s^{'}(G) \leq 2\Delta + 1$.
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.
Gauss-Bonnet Theorems And The Lorentzian Heisenberg Group, Tong Wu, Sining Wei, Yong Wang
Gauss-Bonnet Theorems And The Lorentzian Heisenberg Group, Tong Wu, Sining Wei, Yong Wang
Turkish Journal of Mathematics
In this paper, we compute sub-Riemannian limits of Gaussian curvature for a C$^{2}$-smooth surface in the Lorentzian Heisenberg group for the second Lorentzian metric and the third Lorentzian metric and signed geodesic curvature for C$^{2}$-smooth curves on surfaces. We get Gauss-Bonnet theorems in the Lorentzian Heisenberg group for the second Lorentzian metric and the third Lorentzian metric.
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.
On Ordered $\Gamma$-Hypersemigroups And Their Relation To Lattice Ordered Semigroups, Niovi Kehayopulu
On Ordered $\Gamma$-Hypersemigroups And Their Relation To Lattice Ordered Semigroups, Niovi Kehayopulu
Turkish Journal of Mathematics
The concept of $\Gamma$-hypersemigroup has been introduced in Turk J Math 2020; 44 (5): 1835-1851 in which it has in which it has been shown that various results on $\Gamma$-hypersemigroups can be obtained directly as corollaries of more general results from the theory of $le$-semigroups (i.e. lattice ordered semigroups having a greatest element) or $poe$-semigroups. As a continuation of the paper mentioned above, in the present paper, the concept of ordered $\Gamma$-hypersemigroups has been introduced, and their relation to lattice ordered semigroups is given. It has been shown that although the results on ordered $\Gamma$-hypersemigroups cannot be obtained as corollaries …
Existence Results For A Class Of Boundary Value Problems For Fractional Differential Equations, Abdülkadi̇r Doğan
Existence Results For A Class Of Boundary Value Problems For Fractional Differential Equations, Abdülkadi̇r Doğan
Turkish Journal of Mathematics
By application of some fixed point theorems, that is, the Banach fixed point theorem, Schaefer's and the Leray-Schauder fixed point theorem, we establish new existence results of solutions to boundary value problems of fractional differential equations. This paper is motivated by Agarwal et al. (Georgian Math. J. 16 (2009) No.3, 401-411).
Relative Conics And Their Brianchon Points, Magdalena Lampa-Baczynska, Daniel Wojcik
Relative Conics And Their Brianchon Points, Magdalena Lampa-Baczynska, Daniel Wojcik
Turkish Journal of Mathematics
The purpose of this paper is to study some additional relations between lines and points in the configuration of six lines tangent to the common conic. One of the most famous results concerning with this configuration is Brianchon theorem. It says that three diagonals of a hexagon circumscribing around conic are concurrent. They meet in the so called Brianchon point. In fact, by relabeling the vertices of hexagon, we obtain $60$ distinct Brianchon points. We prove, among others, that, in the set of all intersection points of six tangents to the same conic, there exist exactly $10$ sextuples of points …
On The Spectra Of Generalized Fibonomial And Jacobsthal-Binomial Graphs, Hati̇ce Topcu, Nurten Yücel
On The Spectra Of Generalized Fibonomial And Jacobsthal-Binomial Graphs, Hati̇ce Topcu, Nurten Yücel
Turkish Journal of Mathematics
In this work, we first give a more general form of the binomial, Fibonomial, and balance-binomial graphs that is called generalized Fibonomial graph. We also argue the spectra of generalized Fibonomial graph. Next, we introduce a new type of graph on Jacobsthal numbers that is called Jacobsthal-binomial graph and denoted by $JB_{n}$. We obtain the adjacency, Laplacian and signless Laplacian characteristic polynomials of $JB_{n}$, respectively. We lastly give inequalities for the adjacency, Laplacian and signless Laplacian energies of $JB_{n}$.
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.
Uniform Convergent Modified Weak Galerkin Method For Convection-Dominated Two-Point Boundary Value Problems, Şuayi̇p Toprakseven, Peng Zhu
Uniform Convergent Modified Weak Galerkin Method For Convection-Dominated Two-Point Boundary Value Problems, Şuayi̇p Toprakseven, Peng Zhu
Turkish Journal of Mathematics
We propose and analyze a modified weak Galerkin finite element method (MWG-FEM) for solving singularly perturbed problems of convection-dominated type. The proposed method is constructed over piecewise polynomials of degree $k\geq1$ on interior of each element and piecewise constant on the boundary of each element. The present method is parameter-free and has less degrees of freedom compared to the classical weak Galerkin finite element method. The method is shown uniformly convergent for small perturbation parameters. An uniform convergence rate of $\mathcal {O}((N^{-1}\ln N)^k)$ in the energy-like norm is established on the piecewise uniform Shishkin mesh, where $N$ is the number …
Higher Cohomologies For Presheaves Of Commutative Monoids, Pilar Carrasco, Antonio M. Cegarra
Higher Cohomologies For Presheaves Of Commutative Monoids, Pilar Carrasco, Antonio M. Cegarra
Turkish Journal of Mathematics
We present an extension of the classical Eilenberg-MacLane higher order cohomology theories of abelian groups to presheaves of commutative monoids (and of abelian groups, then) over an arbitrary small category. These high-level cohomologies enjoy many desirable properties and the paper aims to explore them. The results apply directly in several settings such as presheaves of commutative monoids on a topological space, simplicial commutative monoids, presheaves of simplicial commutative monoids on a topological space, commutative monoids or simplicial commutative monoids on which a fixed monoid or group acts, and so forth. As a main application, we state and prove a precise …
Closure Operators In Convergence Approach Spaces, Muhammad Qasim, Mehmet Baran, Hassan Abughalwa
Closure Operators In Convergence Approach Spaces, Muhammad Qasim, Mehmet Baran, Hassan Abughalwa
Turkish Journal of Mathematics
In this paper, we characterize closed and strongly closed subsets of convergence approach spaces and introduce two notions of closure in the category of convergence approach spaces which satisfy idempotent, productive and (weakly) hereditary properties. Furthermore, we explicitly characterize each of $T_{i}$ convergence approach spaces, $i=0,1,2$ with respect to these closure operators and show that each of these subcategories of $T_{i}$ convergence approach spaces, $i=0,1,2$ are epireflective as well as we investigate the relationship among these subcategories. Finally, we characterize connected convergence approach spaces.
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.
Modularly Equidistant Numerical Semigroups, José Carlos Rosales, Manuel Baptista Branco, Márcio Andre Traesel
Modularly Equidistant Numerical Semigroups, José Carlos Rosales, Manuel Baptista Branco, Márcio Andre Traesel
Turkish Journal of Mathematics
IfS is a numerical semigroup and s ∈ S , we denote by next$_{S}$(s) = min {x ∈ S s < x}. Leta be an integer greater than or equal to two. A numerical semigroup is equidistant modulo a if next$_{S}$((s) - s - 1 is a multiple of a for every s ∈ S . In this note, we give algorithms for computing the whole set of equidistant numerical semigroups modulo a with fixed multiplicity, genus, and Frobenius number. Moreover, we will study this kind of semigroups with maximal embedding dimension.
On A Coupled Caputo Conformable System Of Pantograph Problems, Sabri T. M. Thabet, Sina Etemad, Shahram Rezapour
On A Coupled Caputo Conformable System Of Pantograph Problems, Sabri T. M. Thabet, Sina Etemad, Shahram Rezapour
Turkish Journal of Mathematics
Our fundamental purpose in the present manuscript is to explore existence and uniqueness criteria for a new coupled Caputo conformable system of pantograph problems in which for the first time, the given boundary conditions are formulated in the Riemann-Liouville conformable framework. To reach the mentioned aims, we utilize different analytical techniques in which some fixed point results play a vital role. In the final part, a simulative example is designed to cover the applicability aspects of theoretical findings available in this research manuscript from a numerical point of view.
Order Compact And Unbounded Order Compact Operators, Nazi̇fe Erkurşun Özcan, Ni̇yazi̇ Anil Gezer, Şazi̇ye Ece Özdemi̇r, İrem Mesude Geyi̇kçi̇
Order Compact And Unbounded Order Compact Operators, Nazi̇fe Erkurşun Özcan, Ni̇yazi̇ Anil Gezer, Şazi̇ye Ece Özdemi̇r, İrem Mesude Geyi̇kçi̇
Turkish Journal of Mathematics
We investigate properties of order compact, unbounded order compact and relatively uniformly compact operators acting on vector lattices. An operator is said to be order compact if it maps an arbitrary order bounded net to a net with an order convergent subnet. Analogously, an operator is said to be unbounded order compact if it maps an arbitrary order bounded net to a net with uo-convergent subnet. After exposing the relationships between order compact, unbounded order compact, semicompact and GAM-compact operators; we study those operators mapping an arbitrary order bounded net to a net with a relatively uniformly convergent subnet. By …
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 …
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.
On Self-Orthogonality And Self-Duality Of Matrix-Product Codes Over Commutative Rings, Abdulaziz Deajim, Mohamed Bouye
On Self-Orthogonality And Self-Duality Of Matrix-Product Codes Over Commutative Rings, Abdulaziz Deajim, Mohamed Bouye
Turkish Journal of Mathematics
Self-orthogonal codes and self-dual codes, on the one hand, and matrix-product codes, on the other, form important and sought-after classes of linear codes. Combining the two constructions would be advantageous. Adding to this combination the relaxation of the underlying algebraic structures to be commutative rings instead of fields would be even more advantageous. The current article paves a path in this direction. The authors study the problem of self-orthogonality and self-duality of matrix-product codes over a commutative ring with identity. Some methods as well as special matrices are introduced for the construction of such codes. A characterization of such codes …
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 …
A Short Note On Generic Initial Ideals, Beki̇r Daniş
A Short Note On Generic Initial Ideals, Beki̇r Daniş
Turkish Journal of Mathematics
The definition of a generic initial ideal includes the assumption $x_1>x_2> \cdots >x_n$. A natural question is how generic initial ideals change when we permute the variables. In the article [1, §2], it is shown that the generic initial ideals are permuted in the same way when the variables in the monomial order are permuted. We give a different proof of this theorem. Along the way, we study the Zariski open sets which play an essential role in the definition of a generic initial ideal and also prove a result on how the Zariski open set changes after a …
Ranks Of Nilpotent Subsemigroups Of Order-Preserving And Decreasing Transformation Semigroups, Emrah Korkmaz, Hayrullah Ayik
Ranks Of Nilpotent Subsemigroups Of Order-Preserving And Decreasing Transformation Semigroups, Emrah Korkmaz, Hayrullah Ayik
Turkish Journal of Mathematics
Let $\mathcal{C}_{n}$ be the semigroup of all order-preserving and decreasing transformations on $X=\{1,\ldots ,n\}$ under its natural order, and let $N(\mathcal{C}_{n})$ be the subsemigroup of all nilpotent elements of $\mathcal{C}_{n}$. For $1\leq r \leq n-1$, let \begin{eqnarray*} N(\mathcal{C}_{n,r})&=&\{ \alpha\in N(\mathcal{C}_{n}) : \lvert im(\alpha)\rvert \leq r\} ,\\ N_{r}(\mathcal{C}_{n})&=&\{\alpha\in N\mathcal({C}_{n}):\alpha\mbox{ is an } m\mbox{-potent for any } 1\leq m\leq r\} . \end{eqnarray*} In this paper we find the cardinality and the rank of the subsemigroup $N(\mathcal{C}_{n,r})$ of $\mathcal{C}_{n}$. Moreover, we show that the set $N_{r}(\mathcal{C}_{n})$ is a subsemigroup of $N(\mathcal{C}_{n})$ and then, we find a lower bound for the rank of $N_{r}(\mathcal{C}_{n})$.
Ideal Triangulation And Disc Unfolding Of A Singular Flat Surface, İsmai̇l Sağlam
Ideal Triangulation And Disc Unfolding Of A Singular Flat Surface, İsmai̇l Sağlam
Turkish Journal of Mathematics
An ideal triangulation of a singular flat surface is a geodesic triangulation such that its vertex set is equal to the set of singular points of the surface. Using the fact that each pair of points in a surface has a finite number of geodesics having length $\leq L$ connecting them, where $L$ is any positive number, we prove that each singular flat surface has an ideal triangulation provided that the surface has singular points when it has no boundary components, or each of its boundary components has a singular point. Also, we prove that such a surface contains a …
On The Local And Global Stability Of An Sirs Epidemic Model With Logistic Growth And Information Intervention, İrem Çay
Turkish Journal of Mathematics
In this study, we investigate an susceptible-infected-recovered-susceptible (SIRS) epidemic model with logistic growth and information intervention. Firstly, the basic reproduction number $R_0$ is defined and the main results are given in terms of local stability. Then, sufficient conditions for the global stability of endemic equilibrium are obtained. Finally, some numerical simulations are given to validate our theoretical conclusions.