Polyhedral Optimization Of Second-Order Discrete And Differential Inclusions With Delay,
2021
TÜBİTAK
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,
2021
TÜBİTAK
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.
Generalized Littlewood-Paley Functions On Product Spaces,
2021
TÜBİTAK
Generalized Littlewood-Paley Functions On Product Spaces, Hussain Alqassem, Leslie Cheng, Yibiao Pan
Turkish Journal of Mathematics
We are interested in investigating the $L^{p}$ boundedness of the product of generalized Littlewood-Paley functions $S_{\Phi }^{(\lambda )}(f)$ arising from kernels satisfying only size and cancellation conditions. We obtain $L^{p}$ estimates of $S_{\Phi }^{(\lambda )}(f)$ for a sharp range of $p$ and under optimal conditions on $\Phi $. Using these estimates and an extrapolation argument, we obtain some new and improved results on generalized Littlewood-Paley functions on product spaces. As a consequence of our main results, we get two results, one of which answers a question posed by D. Fan and H. Wu and the other one answers a question …
Self-Adjoint Extensions For A Class Of Singular Operators,
2021
TÜBİTAK
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.
On $Q$- And $H$-Deformations Of 3d-Superspaces,
2021
TÜBİTAK
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 ${\mathbb A}_{p,q}^{1 2}$.
Traces And Inverse Nodal Problems For A Class Of Delay Sturm-Liouville Operators,
2021
TÜBİTAK
Traces And Inverse Nodal Problems For A Class Of Delay Sturm-Liouville Operators, Erdoğan Şen
Turkish Journal of Mathematics
In this study, we investigate the regularized sums of eigenvalues, oscillation of eigenfunctions and solutions of inverse nodal problems of discontinuous Sturm-Liouville operators with a delayed argument and with a finite number of transmission conditions. With this aim, we obtain asymptotic formulas for eigenvalues, eigenfunctions and nodal points of the problem. Moreover, some numerical examples are given to illustrate the results. The problem differs from the other discontinuous Sturm-Liouville problems with retarded argument in that it contains a spectral parameter in boundary conditions. If we take the delayed argument $\Delta\equiv0$, the coefficients $\alpha _{i}^{+}=\beta _{i}^{+}=0$ ($i=1,2$) in boundary conditions and …
On $F$-Kenmotsu $3$-Manifolds With Respect To The Schouten-Van Kampen Connection,
2021
TÜBİTAK
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.
Peiffer Pairings In Multisimplicial Groups And Crossed $N$-Cubes And Applications For Bisimplicial Groups,
2021
TÜBİTAK
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.
Crossed Product Of Infinite Groups And Complete Rewriting Systems,
2021
TÜBİTAK
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.
On The Number Of Non-$G$-Equivalent Minimal Abelian Codes,
2021
TÜBİTAK
On The Number Of Non-$G$-Equivalent Minimal Abelian Codes, Fatma Altunbulak Aksu, İpek Tuvay
Turkish Journal of Mathematics
Let $G$ be a finite abelian group. Ferraz, Guerreiro, and Polcino Milies (2014) proved that the number of $G$-equivalence classes of minimal abelian codes is equal to the number of $G$-isomorphism classes of subgroups for which corresponding quotients are cyclic. In this article, we prove that the notion of $G$-isomorphism is equivalent to the notion of isomorphism on the set of all subgroups $H$ of $G$ with the property that $G/H$ is cyclic. As an application, we calculate the number of non-$G$-equivalent minimal abelian codes for some specific family of abelian groups. We also prove that the number of non-$G$-equivalent …
On Some Topological Properties In The Class Of Alexandroff Spaces,
2021
TÜBİTAK
On Some Topological Properties In The Class Of Alexandroff Spaces, Sami Lazaar, Houssem Sabri, Randa Tahri
Turkish Journal of Mathematics
In the class of Alexandroff spaces we study the properties of being a submaximal, door, Whyburn and weakly Whyburn space. We provide characterizations in order theoretical terms. Connections with posets, counting formulas and numerical results in the class of finite spaces are also given.
Ulam-Hyers Stability Results For A Novel Nonlinear Nabla Caputo Fractional Variable-Order Difference System,
2021
TÜBİTAK
Ulam-Hyers Stability Results For A Novel Nonlinear Nabla Caputo Fractional Variable-Order Difference System, Danfeng Luo, Thabet Abdeljawad, Zhiguo Luo
Turkish Journal of Mathematics
This paper is concerned with a kind of nonlinear Nabla Caputo fractional difference system with variable-order and fixed initial valuable. By applying Krasnoselskii's fixed point theorem, we give some sufficient conditions to guarantee the existence results for the considered fractional discrete equations. In addition, we further consider the Ulam-Hyers stability by means of generalized Gronwall inequality. At last, two typical examples are delineated to demonstrate the effectiveness of our theoretical results.
An Improved Oscillation Criteria For First Order Dynamic Equations,
2021
TÜBİTAK
An Improved Oscillation Criteria For First Order Dynamic Equations, Özkan Öcalan
Turkish Journal of Mathematics
In this work, we consider the first-order dynamic equations \begin{equation*} x^{\Delta }(t)+p(t)x\left( \tau (t)\right) =0,\text{ }t\in \lbrack t_{0},\infty )_{\mathbb{T}} \end{equation*} where $p\in C_{rd}\left( [t_{0},\infty )_{\mathbb{T}},\mathbb{R}^{+}\right) , $ $\tau \in C_{rd}\left( [t_{0},\infty )_{\mathbb{T}},\mathbb{T}\right) $ and $\tau (t)\leq t,\ \lim_{t\rightarrow \infty }\tau (t)=\infty $. When the delay term $\tau (t)$ is not necessarily monotone, we present a new sufficient condition for the oscillation of first-order delay dynamic equations on time scales.
On A Coupled Caputo Conformable System Of Pantograph Problems,
2021
TÜBİTAK
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.
Numerical Investigation Of Viscous Effects On The Nonlinear Burgers Equation,
2021
TÜBİTAK
Numerical Investigation Of Viscous Effects On The Nonlinear Burgers Equation, Muhammad Imran Khan, Abdul Rauf, Abdullah Shah
Turkish Journal of Mathematics
This research article presents the numerical solution of the viscous Burgers equation. The diagonally implicit fractional step $\theta$ (DIFST) scheme is used for the time discretization and the space derivative is discretized by the conforming finite element method with quadrilateral mesh. The viscosity effect on the shock wave is calculated with an estimation of the $L_2$ error. For comparison of different time discretization schemes, three test problems are computed. The stability and accuracy of the schemes are given by estimating the $L_2$ error norm. Numerical simulation for one- and two-dimensional problems are given and illustrated graphically. The effect of the …
Infinitesimal Bending Of Dna Helices,
2021
TÜBİTAK
Infinitesimal Bending Of Dna Helices, Miroslav Maksimovic, Ljubica Velimirovic, Marija Najdanovic
Turkish Journal of Mathematics
The mathematics of DNA molecules is often studied as a double helix model. This paper focuses on the modelling of infinitesimal bending of DNA helices. The paper checks the flexibility of DNA molecule, i.e. the flexibility of double helix in infinitesimal bending theory. Actually, first, we find infinitesimal bending field of an arbitrary curve on the helicoid, that leaves bent curves on the helicoid, and show that helix bending on the helicoid is not possible. Finally, we deal with the infinitesimal bending of helicoid, using PDEs. Visualization of infinitesimal bending was done in Mathematica.
A Study Of Impulsive Discrete Dirac System With Hyperbolic Eigenparameter,
2021
TÜBİTAK
A Study Of Impulsive Discrete Dirac System With Hyperbolic Eigenparameter, Turhan Köprübaşi
Turkish Journal of Mathematics
Let $L$ denote the discrete Dirac operator generated in $\ell _{2}\left( %TCIMACRO{\U{2115} }% %BeginExpansion \mathbb{N} %EndExpansion ,% %TCIMACRO{\U{2102} }% %BeginExpansion \mathbb{C} %EndExpansion ^{2}\right) $ by the difference operators of first order% \begin{equation*} \left\{ \begin{array}{cc} {\bigtriangleup y_{n}^{\left( 2\right) }+p_{n}y_{n}^{\left( 1\right) }=\lambda y_{n}^{(1)}} & \\ {\bigtriangleup y_{n-1}^{\left( 1\right) }+q_{n}y_{n}^{\left( 2\right) }=\lambda y_{n}^{(2)}}, \end{array} \text{ }n\in \mathbb{N} \setminus \left\{ k-1,k,k+1\right\} \right. \end{equation*} with boundary and impulsive conditions% \begin{equation*} \begin{array}{c} y_{0}^{(1)}=0\text{ }, \\ \\ \left( \begin{array}{c} y_{k+1}^{(1)} \\ y_{k+2}^{(2)}% \end{array}% \right) =\theta \left( \begin{array}{c} y_{k-1}^{(2)} \\ y_{k-2}^{(1)}% \end{array}% \right) ;\text{ }\theta =\left( \begin{array}{cc} \theta _{1} & \theta _{2} \\ \theta _{3} & \theta _{4}% …
A Generalization Of Parabolic Potentials Associated To Laplace-Bessel Differential Operator And Its Behavior In The Weighted Lebesque Spaces, Çağla Seki̇n
Turkish Journal of Mathematics
In this work we introduce some generalizations of the singular parabolic Riesz and parabolic Bessel potentials. Namely, $\Delta _{\nu }$ being the Laplace-Bessel singular differential operator, we define the families of operators \begin{equation*} H_{\beta ,\nu }^{\alpha }=\left( \frac{\partial }{\partial t}+(-\Delta _{\nu })^{\beta /2}\right) ^{-\alpha /\beta }\text{ and }\mathcal{H}_{\beta ,\nu }^{\alpha }=\left( I+\frac{\partial }{\partial t}+(-\Delta _{\nu })^{\beta /2}\right) ^{-\alpha /\beta }\text{ , (}\alpha ,\beta >0\text{),} \end{equation*} and investigate their properties in the special weighted $L_{p,\nu }$-spaces.
Cyclic And Constacyclic Codes Over The Ring $\Mathbb{Z}_{4}[U]/\Langle U^3-U^2\Rangle$ And Their Gray Image,
2021
TÜBİTAK
Cyclic And Constacyclic Codes Over The Ring $\Mathbb{Z}_{4}[U]/\Langle U^3-U^2\Rangle$ And Their Gray Image, Mehmet Özen, Fatma Zehra Uzekmek, Eli̇f Segah Öztaş
Turkish Journal of Mathematics
In this article, the structure of generator polynomial of the cyclic codes with odd length is formed over the ring $\mathbb{Z}_{4}+u\mathbb{Z}_{4}+u^{2}\mathbb{Z}_{4}$ where $u^3=u^2$. With the isomorphism we have defined, the generator polynomial of constacyclic codes with odd length over this ring is created from the generator of the cyclic codes. Additionally, necessary and sufficient conditions for a linear code in this ring to be a self dual code and a LCD code are mentioned. Furthermore, for all units over this ring, $\mathbb{Z}_{4}$-images of $\lambda$-constacyclic codes and also $\mathbb{Z}_{4}$-images of cyclic codes are examined by using related ones from defined three …
Hilbert Series Of Tangent Cones For Gorenstein Monomial Curves In $\Mathbb{A}^{4}(K)$,
2021
TÜBİTAK
Hilbert Series Of Tangent Cones For Gorenstein Monomial Curves In $\Mathbb{A}^{4}(K)$, Anargyros Katsabekis
Turkish Journal of Mathematics
In this paper, we study the Hilbert series of the tangent cone of Gorenstein monomial curves in the 4-dimensional affine space. We give an explicit formula for the reduced Hilbert series of the tangent cone of a noncomplete intersection Gorenstein monomial curve whose tangent cone is Cohen-Macaulay.
