On Ordered $\Gamma$-Hypersemigroups, Minimal Bi-Ideals, And Minimal Left Ideals,
2021
TÜBİTAK
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,
2021
TÜBİTAK
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,
2021
TÜBİTAK
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,
2021
TÜBİTAK
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,
2021
TÜBİTAK
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,
2021
TÜBİTAK
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
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,
2021
TÜBİTAK
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,
2021
TÜBİTAK
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,
2021
TÜBİTAK
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,
2021
TÜBİTAK
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,
2021
TÜBİTAK
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,
2021
TÜBİTAK
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,
2021
TÜBİTAK
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,
2021
TÜBİTAK
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,
2021
TÜBİTAK
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,
2021
TÜBİTAK
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) $.
Banach Algebra Structure On Strongly Simple Extensions,
2021
TÜBİTAK
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.
Solvability, Stability, Smoothness And Compactness Of The Set Of Solutions For A Nonlinear Functional Integral Equation,
2021
TÜBİTAK
Solvability, Stability, Smoothness And Compactness Of The Set Of Solutions For A Nonlinear Functional Integral Equation, Nguyen Dat Thuc, Le Thi Phuong Ngoc, Nguyen Thanh Long
Turkish Journal of Mathematics
This paper is devoted to the study of the following nonlinear functional integral equation \begin{equation} f(x)=\sum\limits_{i=1}^{q}\alpha _{i}(x)f(\tau_{i}(x))+\int_{0}^{\sigma_{1}(x)}\Psi \left( x,t,f(\sigma _{2}(t)),\int_{0}^{\sigma_{3}(t)}f(s)ds\right) dt+g(x),\text{ }\forall x\in \lbrack 0,1], \tag{E} \label{E} \end{equation} where $\tau _{i},$ $\sigma _{1},$ $\sigma _{2},$ $\sigma _{3}:[0,1]\rightarrow \lbrack 0,1];$ $\alpha _{i},$ $g:[0,1]\rightarrow \mathbb{R};$ $\Psi :[0,1]\times \lbrack 0,1]\times \mathbb{R}^{2}\rightarrow \mathbb{R}$ are the given continuous functions and $f:[0,1]\,\rightarrow \mathbb{R}$ is an unknown function. First, two sufficient conditions for the existence and some properties of solutions of Eq. (E) are proved. By using Banach's fixed point theorem, we have the first sufficient condition yielding existence, uniqueness and stability of the solution. By applying …
Ranked List Fusion And Re-Ranking With Pre-Trained Transformers For Arqmath Lab,
2021
Old Dominion University
Ranked List Fusion And Re-Ranking With Pre-Trained Transformers For Arqmath Lab, Shaurya Rohatgi, Jian Wu, C. Lee Giles
Computer Science Faculty Publications
This paper elaborates on our submission to the ARQMath track at CLEF 2021. For our submission this year we use a collection of methods to retrieve and re-rank the answers in Math Stack Exchange in addition to our two-stage model which was comparable to the best model last year in terms of NDCG’. We also provide a detailed analysis of what the transformers are learning and why is it hard to train a math language model using transformers. This year’s submission to Task-1 includes summarizing long question-answer pairs to augment and index documents, using byte-pair encoding to tokenize formula and …
