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Full-Text Articles in Mathematics
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 …
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.
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.
A New Implicit-Explicit Local Differential Method For Boundary Value Problems, Hüseyi̇n Tunç, Murat Sari
A New Implicit-Explicit Local Differential Method For Boundary Value Problems, Hüseyi̇n Tunç, Murat Sari
Turkish Journal of Mathematics
In this study, an effective numerical method based on Taylor expansions is presented for boundary value problems. This method is arbitrary directional and called as implicit-explicit local differential transform method (IELDTM). With the completion of this study, a reliable numerical method is derived by optimizing the required degrees of freedom. It is shown that the order refinement procedure of the IELDTM does not affect the degrees of freedom. A priori error analysis of the current method is constructed and order conditions are presented in a detailed analysis. The theoretical order expectations are verified for nonlinear BVPs. Stability of the IELDTM …
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.
Estimations On Some Hybrid Exponential Sums Related To Kloosterman Sums, Yingjie Cheng, Xiwang Cao, Liqin Qian, Jinlong Wan
Estimations On Some Hybrid Exponential Sums Related To Kloosterman Sums, Yingjie Cheng, Xiwang Cao, Liqin Qian, Jinlong Wan
Turkish Journal of Mathematics
In this paper, we revisit the bounds of the mixed exponential sums introduced by Lv and Zhang (2020). Moreover, we give some estimations for some new hybrid exponential sums related to Kloosterman sums over finite fields of odd characteristic by using the properties of Jacobi sums and Gaussian sums.
On Some Generalizations Of The Beta Function In Several Variables, Mustapha Raissouli, Salma El-Soubhy
On Some Generalizations Of The Beta Function In Several Variables, Mustapha Raissouli, Salma El-Soubhy
Turkish Journal of Mathematics
Intensive studies aiming to extend the gamma and beta functions and to establish some properties for these extensions have been recently carried out. In this paper, we first introduce a generalized gamma function in n variables. Afterwards, two generalized beta functions in several variables are introduced and their properties are discussed. Among others, we investigate recurrence relationships, Mellin transform properties, and partial differential equations involving these generalized functions. At the end, some results about partial derivatives of these extended functions are presented as well.
On Elements Whose Moore-Penrose Inverse Is Idempotent In A ${\Ast}$-Ring, Haiyang Zhu, Jianlong Chen, Yukun Zhou
On Elements Whose Moore-Penrose Inverse Is Idempotent In A ${\Ast}$-Ring, Haiyang Zhu, Jianlong Chen, Yukun Zhou
Turkish Journal of Mathematics
In this paper, we investigate the elements whose Moore-Penrose inverse is idempotent in a ${\ast}$-ring. Let $R$ be a ${\ast}$-ring and $a\in R^\dagger$. Firstly, we give a concise characterization for the idempotency of $a^\dagger$ as follows: $a\in R^\dagger$ and $a^\dagger$ is idempotent if and only if $a\in R^{\#}$ and $a^2=aa^*a$, which connects Moore-Penrose invertibility and group invertibility. Secondly, we generalize the results of Baksalary and Trenkler from complex matrices to ${\ast}$-rings. More equivalent conditions which ensure the idempotency of $a^\dagger$ are given. Particularly, we provide the characterizations for both $a$ and $a^\dagger$ being idempotent. Finally, the equivalent conditions under which …
The Lebesgue Constants On Projective Spaces, Alexander Kushpel
The Lebesgue Constants On Projective Spaces, Alexander Kushpel
Turkish Journal of Mathematics
We give the solution of a classical problem of Approximation Theory on sharp asymptotic of the Lebesgue constants or norms of the Fourier-Laplace projections on the real projective spaces $\mathrm{P}^{d}(\mathbb{R})$. In particular, these results extend sharp asymptotic found by Fejer [2] in the case of $\mathbb{S}^{1}$ in 1910 and by Gronwall [4] in 1914 in the case of $\mathbb{S}^{2}$. The case of spheres, $\mathbb{S}^{d}$, complex and quaternionic projective spaces, $\mathrm{P}^{d}(\mathbb{C})$, $% \mathrm{P}^{d}(\mathbb{H})$ and the Cayley elliptic plane $\mathrm{P}^{16}(% \mathrm{Cay})$ was considered by Kushpel [8].
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 $(\rho_k)_{k\in\mathbb N}$.
Existence Of Nonnegative Solutions For Discrete Robin Boundary Value Problems With Sign-Changing Weight, Yan Zhu
Turkish Journal of Mathematics
In this paper,~we are concerned with the following discrete problem first $$\left\{ \begin{array}{ll} -\Delta^{2}u(t-1)=\lambda p(t)f(u(t)), &t\in[1,N-1]_{\mathbb{Z}},\\ \Delta u(0)=u(N)=0,\\ \end{array} \right. $$ where $N>2$~is an integer,~$\lambda>0$~is a parameter,~$p:[1,N-1]_{\mathbb{Z}}\rightarrow\mathbb{R}$~is a sign-changing function,~$f:[0,+\infty)\rightarrow[0,+\infty)$~is a continuous and nondecreasing function.~$\Delta u(t)=u(t+1)-u(t)$,~$\Delta^{2}u(t)=\Delta(\Delta u(t))$.~By using the iterative method and Schauder's fixed point theorem,~we will show the existence of nonnegative solutions to the above problem. Furthermore, we obtain the existence of nonnegative solutions for discrete Robin systems with indefinite weights.
New Oscillation Criteria For Differential Equations With Sublinear And Superlinear Neutral Terms, Ali Muhib, Elmetwally M. Elabbasy, Osama Moaaz
New Oscillation Criteria For Differential Equations With Sublinear And Superlinear Neutral Terms, Ali Muhib, Elmetwally M. Elabbasy, Osama Moaaz
Turkish Journal of Mathematics
The aim of this article is to establish some new oscillation criteria for the differential equation of even-order of the form \begin{equation*} (r\left( l\right) (y^{\left( n-1\right) }\left( l\right) )^{\alpha })^{\prime }+f(l,x(\tau (l)))=0, \end{equation*} where $y\left( l\right) =x\left( l\right) +p\left( l\right) x^{\beta }\left( \sigma _{1}\left( l\right) \right) +h\left( l\right) x^{\delta }\left( \sigma _{2}\left( l\right) \right) $. By using Riccati transformations, we present new conditions for oscillation of the studied equation. Furthermore, two illustrative examples showing applicability of the new results are included.
Volume Properties And Some Characterizations Of Ellipsoids In ${\Bbb E}^{N+1}$, Dong-Soo Kim, Incheon Kim, Young Ho Kim
Volume Properties And Some Characterizations Of Ellipsoids In ${\Bbb E}^{N+1}$, Dong-Soo Kim, Incheon Kim, Young Ho Kim
Turkish Journal of Mathematics
Suppose that $M$ is a strictly convex and closed hypersurface in ${\Bbb E}^{n+1}$ with the origin $o$ in its interior. We consider the homogeneous function $g$ of positive degree $d$ satisfying $M=g^{-1}(1)$. Then, for a positive number $h$ the level hypersurface $g^{-1}(h)$ of $g$ is a homothetic hypersurface of $M$ with respect to the origin $o$. In this paper, for tangent hyperplanes $\Phi_h$ to $g^{-1}(h)$ ($0
On Ordered $\Gamma$-Hypersemigroups, Minimal Bi-Ideals, And Minimal Left Ideals, Niovi Kehayopulu
On Ordered $\Gamma$-Hypersemigroups, Minimal Bi-Ideals, And Minimal Left Ideals, Niovi Kehayopulu
Turkish Journal of Mathematics
The definition of ordered $\Gamma$-hypersemigroups and the definitions of regular and intra-regular ordered $\Gamma$-hypersemigroups in the existing bibliography should be corrected. Care should be given to the definitions of bi-$\Gamma$-hyperideals and quasi-$\Gamma$-hyperideals as well. The main results are a characterization of minimal bi-ideals of an ordered $\Gamma$-hypersemigroup $S$ in terms of $\cal B$-simple bi-ideals of $S$ and a characterization of minimal left (resp. right) ideals of an ordered $\Gamma$-hypersemigroup $S$ in terms of left (resp. right) simple subsemigroups of $S$.
Almost Quasi Clean Rings, Tufan Özdi̇n
Almost Quasi Clean Rings, Tufan Özdi̇n
Turkish Journal of Mathematics
The element $q$ of a ring $R$ is called quasi-idempotent element if $q^2=uq$ for some central unit $u$ of $R$, or equivalently $q=ue$, where $u$ is a central unit and $e$ is an idempotent of $R$. In this paper, we define that the ring $R$ is almost quasi-clean if each element of $R$ is the sum of a regular element and a quasi-idempotent element. Several properties of almost-quasi clean rings are investigated. We prove that every quasi-continuous and nonsingular ring is almost quasi-clean. Finally, it is determined that the conditions under which the idealization of an $R$-module $M$ is almost …
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.
On The Spectral And Scattering Properties Of Eigenparameter Dependent Discrete Impulsive Sturm-Liouville Equations, Yelda Aygar Küçükevci̇li̇oğlu, Elgi̇z Bayram, Güher Gülçehre Özbey
On The Spectral And Scattering Properties Of Eigenparameter Dependent Discrete Impulsive Sturm-Liouville Equations, Yelda Aygar Küçükevci̇li̇oğlu, Elgi̇z Bayram, Güher Gülçehre Özbey
Turkish Journal of Mathematics
This work develops scattering and spectral analysis of a discrete impulsive Sturm-Liouville equation with spectral parameter in boundary condition. Giving the Jost solution and scattering solutions of this problem, we find scattering function of the problem. Discussing the properties of scattering function, scattering solutions, and asymptotic behavior of the Jost solution, we find the Green function, resolvent operator, continuous and point spectrum of the problem. Finally, we give an example in which the main results are made explicit.
Operators Between Different Weighted Frechet And (Lb)-Spaces Of Analytic Functions, Ersi̇n Kizgut
Operators Between Different Weighted Frechet And (Lb)-Spaces Of Analytic Functions, Ersi̇n Kizgut
Turkish Journal of Mathematics
We study some classical operators defined on the weighted Bergman Frechet space $A^p_{\alpha+}$ (resp. weighted Bergman (LB)-space $A^p_{\alpha-}$) arising as the projective limit (resp. inductive limit) of the standard weighted Bergman spaces into the growth Frechet space $H^\infty_{\alpha+}$ (resp. growth (LB)-space $H^\infty_{\alpha-}$), which is the projective limit (resp. inductive limit) of the growth Banach spaces. We show that, for an analytic self map $\varphi$ of the unit disc $\mathbb{D}$, the continuities of the weighted composition operator $W_{g,\varphi}$, the Volterra integral operator $T_g$, and the pointwise multiplication operator $M_g$ defined via the identical symbol function are characterized by the same condition …
Preservers Of The Local Spectral Radius Zero Of Jordan Product Of Operators, Mhamed Elhodaibi, Somaya Saber
Preservers Of The Local Spectral Radius Zero Of Jordan Product Of Operators, Mhamed Elhodaibi, Somaya Saber
Turkish Journal of Mathematics
Let $\mathscr{B}(X)$ be the algebra of all bounded linear operators on an infinite-dimensional complex Banach space $X$, and denote by $r_{T}(x)$ the local spectral radius of any operator $T \in \mathscr{B}(X)$ at any vector $x \in X$. In this paper, we characterize surjective maps $\phi$ on $ \mathscr{B}(X)$ satisfying $ r_{\phi(T)\phi(A) + \phi(A)\phi(T)}(x)=0$ if and only if $ r_{TA+AT}(x)=0 $
Solving Fractional Differential Equations Using Collocation Method Based On Hybrid Of Block-Pulse Functions And Taylor Polynomials, Yao Lu, Yinggan Tang
Solving Fractional Differential Equations Using Collocation Method Based On Hybrid Of Block-Pulse Functions And Taylor Polynomials, Yao Lu, Yinggan Tang
Turkish Journal of Mathematics
In this paper, a novel approach is proposed to solve fractional differential equations (FDEs) based on hybrid functions. The hybrid functions consist of block-pulse functions and Taylor polynomials. The exact formula for the Riemann--Liouville fractional integral of the hybrid functions is derived via Laplace transform. The FDE under consideration is converted into an algebraic equation with undetermined coefficients by using this formula. A set of linear or nonlinear equations are obtained through collocating the algebraic equation at Newton-Cotes nodes. The numerical solution of the FDE is achieved by solving the linear or nonlinear equations. Error analysis is performed on the …
Soft $\Beta$-Rough Sets And Their Application To Determine Covid-19, Mostafa K. El Bably, Abd El Fattah A. El Atik
Soft $\Beta$-Rough Sets And Their Application To Determine Covid-19, Mostafa K. El Bably, Abd El Fattah A. El Atik
Turkish Journal of Mathematics
Soft rough set theory has been presented as a basic mathematical model for decision-making for many real-life data. However, soft rough sets are based on a possible fusion of rough sets and soft sets which were proposed by Feng et al. [20]. The main contribution of the present article is to introduce a modification and a generalization for Feng's approximations, namely, soft $\beta$-rough approximations, and some of their properties will be studied. A comparison between the suggested approximations and the previous one [20] will be discussed. Some examples are prepared to display the validness of these proposals. Finally, we put …
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).
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.
Yau-Type Ternary Hom-Lie Bialgebras, Elkadri Abdaoui, Sami Mabrouk, Abdenacer Makhlouf, Sonia Massoud
Yau-Type Ternary Hom-Lie Bialgebras, Elkadri Abdaoui, Sami Mabrouk, Abdenacer Makhlouf, Sonia Massoud
Turkish Journal of Mathematics
The purpose of this paper is to introduce and study $3$-Hom-Lie bialgebras, which are a ternary version of Hom-Lie bialgebras introduced by Yau (2015). We provide their properties, some key constructions and their 3-dimensional classification. Moreover we discuss their representation theory and their generalized derivations and coderivations. Furthermore, a more generalized notion called generalized $3$-Hom-Lie bialgebra is also considered.
The $2$-Rank Of The Class Group Of Some Real Cyclic Quartic Number Fields Ii, Abdelmalek Azizi, Mohammed Tamimi, Abdelkader Zekhnini
The $2$-Rank Of The Class Group Of Some Real Cyclic Quartic Number Fields Ii, Abdelmalek Azizi, Mohammed Tamimi, Abdelkader Zekhnini
Turkish Journal of Mathematics
In this paper, we determine the $2$-rank of the class group of certain classes of real cyclic quartic number fields. Precisely, we consider the case in which the quadratic subfield is $\mathbb{Q}(\sqrt{\ell})$ with $\ell=2$ or a prime congruent to $1\,\pmod8$.
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 …
A Class Of Operators Related To $M$-Symmetric Operators, Fei Zuo, Salah Mecheri
A Class Of Operators Related To $M$-Symmetric Operators, Fei Zuo, Salah Mecheri
Turkish Journal of Mathematics
$m$-symmetric operator plays a crucial role in the development of operator theory and has been widely studied due to unexpected intimate connections with differential equations, particularly conjugate point theory and disconjugacy. For positive integers $m$ and $k$, an operator $T$ is said to be a $k$-quasi-$m$-symmetric operator if $T^{*k}(\sum\limits_{j=0}^{m}(-1)^{j}(^{m}_{j})T^{*m-j}T^{j})T^{k}=0$, which is a generalization of $m$-symmetric operator. In this paper, some basic structural properties of $k$-quasi-$m$-symmetric operators are established with the help of operator matrix representation. In particular, we also show that every $k$-quasi-$3$-symmetric operator has a scalar extension. Finally, we prove that generalized Weyl's theorem holds for $k$-quasi-$3$-symmetric operators.
On 2-Algebras: Crossed R-Modules And Categorical R-Algebras, Zekeri̇ya Arvasi̇, Eli̇f Ilgaz Çağlayan
On 2-Algebras: Crossed R-Modules And Categorical R-Algebras, Zekeri̇ya Arvasi̇, Eli̇f Ilgaz Çağlayan
Turkish Journal of Mathematics
In this work, we describe the category of categorical $R$-algebras and show that a categorical $R$-algebra is a category object in $\mathcal{C=}A\lg _{R}$. By using this property of categorical $R$-algebras, we can give an equivalency between the category of categorical $R$-algebras and the category of crossed $R$-modules and also the category of simplicial $R$-algebras.
Multipliers And $\Mathcal{I}$-Core For Sequences, Mustafa Gülfirat, Ni̇lay Şahi̇n Bayram
Multipliers And $\Mathcal{I}$-Core For Sequences, Mustafa Gülfirat, Ni̇lay Şahi̇n Bayram
Turkish Journal of Mathematics
In this paper we mainly deal with $\mathcal{I}_{c}^{\left( q\right) }-$% convergence. In particular we study bounded multipliers of bounded $\mathcal{% I}_{c}^{\left( q\right) }-$convergent sequences. We also give some $\mathcal{% I}-$core results and characterize the inclusion $K-core\left \{ Ax\right \} \subseteq \mathcal{I}-core\left \{ x\right \} $ for bounded sequences $% x=\left( x_{n}\right) $.