The Frequency Function And Its Connections To The Lebesgue Points And The Hardy-Littlewood Maximal Function,
2019
TÜBİTAK
The Frequency Function And Its Connections To The Lebesgue Points And The Hardy-Littlewood Maximal Function, Faruk Temur
Turkish Journal of Mathematics
The aim of this work is to extend the recent work of the author on the discrete frequency function to the more delicate continuous frequency function $\mathcal{T}$, and further to investigate its relations to the Hardy-Littlewood maximal function $\mathcal{M}$, and to the Lebesgue points. We surmount the intricate issue of measurability of $\mathcal{T}f$ by approaching it with a sequence of carefully constructed auxiliary functions for which measurability is easier to prove. After this, we give analogues of the recent results on the discrete frequency function. We then connect the points of discontinuity of $\mathcal{M}f$ for $f$ simple to the zeros …
An Involution Of Reals, Discontinuous On Rationals, And Whose Derivative Vanishes A.E.,
2019
TÜBİTAK
An Involution Of Reals, Discontinuous On Rationals, And Whose Derivative Vanishes A.E., Abdurrahman Muhammed Uludağ, Hakan Ayral
Turkish Journal of Mathematics
We study the involution of the real line, induced by Dyer's outer automorphism of PGL(2,Z). It is continuous at irrationals with jump discontinuities at rationals. We prove that its derivative exists almost everywhere and vanishes almost everywhere.
Some Sufficient Conditions For A Group To Be Abelian,
2019
TÜBİTAK
Some Sufficient Conditions For A Group To Be Abelian, Gary Walls
Turkish Journal of Mathematics
A group is said to satisfy a word $w$ in the symbols $\{x, x^{-1}, y, y^{-1} \}$ provided that if the 'x' and 'y' are replaced by arbitrary elements of the group then the equation $w=1$ is satisfied. This paper studies certain equations in words, as above, which together with other conditions imply that groups which satisfy these equations and conditions must be abelian.
Some Applications Of Differential Subordination For Certain Starlike Functions,
2019
TÜBİTAK
Some Applications Of Differential Subordination For Certain Starlike Functions, Rahim Kargar, Lucyna Trojnar Spelina
Turkish Journal of Mathematics
Let $\mathcal{S}^*(q_c)$ denote the class of functions $f$ analytic in the open unit disc $\Delta$, normalized by the condition $f(0)=0=f'(0)-1$ and satisfying the following inequality $\left \left(\frac{zf'(z)}{f(z)}\right)^2-1\right < c \quad (z\in\Delta, 0
The Matrix-Valued Numerical Range Over Finite Fields,
2019
TÜBİTAK
The Matrix-Valued Numerical Range Over Finite Fields, Edoardo Ballico
Turkish Journal of Mathematics
In this paper we define and study the matrix-valued $k\times k$ numerical range of $n\times n$ matrices using the Hermitian product and the product with $n\times k$ unitary matrices $U$ (on the right with $U$, on the left with its adjoint $U^\dagger = U^{-1}$). For all $i, j=1,\dots ,k$ we study the possible $(i,j)$-entries of these $k\times k$ matrices. Our results are for the case in which the base field is finite, but the same definition works over $\mathbb {C}$. Instead of the degree $2$ extension $\mathbb {R}\hookrightarrow \mathbb {C}$ we use the degree $2$ extension $\mathbb {F} _q\hookrightarrow \mathbb …
Further Results On The Join Graph Of A Finite Group,
2019
TÜBİTAK
Further Results On The Join Graph Of A Finite Group, Zahra Bahrami, Bijan Taeri
Turkish Journal of Mathematics
Let $G$ be a finite group which is not cyclic of prime power order. The join graph $\Delta(G)$ is an undirected simple whose vertices are the proper subgroups of $G$, which are not contained in the Frattini subgroup $\Phi(G)$ of $G$ and two vertices $H$ and $K$ are joined by an edge if and only if $G=\langle H,K\rangle$. We classify finite groups whose join graphs have domination number $\leq 2$ and independence number $\leq 3$. We show that $\Delta(G)\cong \Delta(A_4)$ if and only if $G\cong A_4$. We also show that if the independence number of $\Delta(G)$ is less than $15$, …
Relative Ranks Of Some Partial Transformation Semigroups,
2019
TÜBİTAK
Relative Ranks Of Some Partial Transformation Semigroups, Ebru Yi̇ği̇t, Gonca Ayik, Hayrullah Ayik
Turkish Journal of Mathematics
Let $P_{n}$, $T_{n}$, $I_{n}$, and $S_{n}$ be the partial transformation semigroup, the (full) transformation semigroup, the symmetric inverse semigroup, and the symmetric group on $X_{n}=\{1,\ldots ,n \}$, respectively. For $1\leq r\leq n-1$, let $PK_{n,r}$ be the subsemigroup consisting $\alpha\in P_{n}$ such that $ \im\alpha \leq r$ and let $SPK_{n,r}=PK_{n,r}\setminus T_{n}$. In this paper, we first examine the subsemigroup $I_{n,r}=I_{n}\cup PK_{n,r}$ and we find the necessary and sufficient conditions for any nonempty subset of $PK_{n,r}$ to be a (minimal) relative generating set of the subsemigroup $I_{n,r}$ modulo $I_{n}$. Then we examine the subsemigroups $PI_{n,r}= SI_{n}\cup PK_{n,r}$ and $SI_{n,r}=SI_{n}\cup SPK_{n,r}$ for $1\leq …
A Convergent Two-Level Linear Scheme For The Generalizedrosenau-Kdv-Rlw Equation,
2019
TÜBİTAK
A Convergent Two-Level Linear Scheme For The Generalizedrosenau-Kdv-Rlw Equation, Ayhan Aydin
Turkish Journal of Mathematics
A new convergent two-level finite difference scheme is proposed for the numerical solution of initial value problem of the generalized Rosenau--KdV--RLW equation. The new scheme is second-order, linear, conservative, and unconditionally stable. It contains one free parameter. The impact of the parameter to error of the numerical solution is studied. The prior estimate of the finite difference solution is obtained. The existence, uniqueness, and convergence of the scheme are proved by the discrete energy method. Accuracy and reliability of the scheme are tested by simulating the solitary wave graph of the equation. Wave generation subject to initial Gaussian condition has …
On Nonoscillatory Solutions Of Three Dimensional Time-Scale Systems,
2019
TÜBİTAK
On Nonoscillatory Solutions Of Three Dimensional Time-Scale Systems, Elvan Akin, Taher S. Hassan, Özkan Öztürk, İsmai̇l Uğur Ti̇ryaki̇
Turkish Journal of Mathematics
In this article, we classify nonoscillatory solutions of a system of three-dimensional time scale systems. We use the method of considering the sign of components of such solutions. Examples are given to highlight some of our results. Moreover, the existence of such solutions is obtained by Knaster's fixed point theorem.
On A Class Of Nonself-Adjoint Multidimensional Periodic Schrödinger Operators,
2019
TÜBİTAK
On A Class Of Nonself-Adjoint Multidimensional Periodic Schrödinger Operators, Oktay Veli̇ev
Turkish Journal of Mathematics
We investigate the Schrödinger operator $L(q)$ in $L_{2}\left( \mathbb{R}^{d}\right) \ (d\geq1)$ with the complex-valued potential $q$ that is periodic with respect to a lattice $\Omega.$ Besides, it is assumed that the Fourier coefficients $q_{\gamma}$ of $q$ with respect to the orthogonal system $\{e^{i\left\langle \gamma x\right\rangle }:\gamma\in\Gamma\}$ vanish if $\gamma$ belongs to a half-space, where $\Gamma$ is the lattice dual to $\Omega.$ We prove that the Bloch eigenvalues are $\mid\gamma+t\mid^{2}$ for $\gamma\in\Gamma,$ where $t$ is a quasimomentum and find explicit formulas for \ the Bloch functions. Moreover, we investigate the multiplicity of the Bloch eigenvalue and consider necessary and sufficient conditions …
Almost Symmetric Numerical Semigroups With High Type,
2019
TÜBİTAK
Almost Symmetric Numerical Semigroups With High Type, Pedro A. Garcia-Sanchez, Ignacio Ojeda
Turkish Journal of Mathematics
We establish a one-to-one correspondence between numerical semigroups of genus $g$ and almost symmetric numerical semigroups with Frobenius number $F$ and type $F-2g$, provided that $F$ is greater than or equal to $4g-1$.
Po-Groups And Hypergroups In A Topos,
2019
TÜBİTAK
Po-Groups And Hypergroups In A Topos, Ali Madanshekaf, Zeinab Kanjanzadeh
Turkish Journal of Mathematics
This paper deals with two constructions in topos theory: po-groups and hypergroups. After a deep analysis of these, we restrict our attention to find a hypergroup associated to a po-group $G$ in a topos $\mathcal{E}$. The method that we use here is based on the Mitchell--B$\acute{{\rm e}}$nabou language. Then, we show that on the negative and positive cones of a po-group $G$ in $\mathcal{E},$ the left and right translations are hyperhomomorphisms in $\mathcal{E}.$ Our aim is to find two faithful and left exact functors from the category of po-groups in $\mathcal{E}$ to the (smallest in some sense) finitely complete category …
Lattice Ordered Semigroups And Hypersemigroups,
2019
TÜBİTAK
Lattice Ordered Semigroups And Hypersemigroups, Niovi Kehayopulu
Turkish Journal of Mathematics
This paper shows that many results on hypersemigroups do not need any proof as can be obtained from lattice ordered semigroups.
Principal Parts Of A Vector Bundle On Projective Line And The Fractional Derivative,
2019
TÜBİTAK
Principal Parts Of A Vector Bundle On Projective Line And The Fractional Derivative, Hafiz Syed Husain, Mariam Sultana
Turkish Journal of Mathematics
This work is an exposition on computational aspects of principal parts of a vector bundle on projective line over the field of characteristic zero. Principal parts help determine the possibility of algebraically formalizing infinitesimal-neighborhoods of subschemes inside some ambient scheme. The purpose of this study is to look for the possibility of formalizing the algebraic geometric interpretation of fractional derivative. For the latter, this study follows theapproachproposedbyVasilyTarasov. The difference is that Tarasov proposeda geometric interpretation using finite order jet bundles from differential geometry. Present study proposes finite-order principal parts of the structure-sheaf of real projective line as its formal algebraic …
Nonexistence Of Global Solutions For A Fractional System Of Strongly Coupled Integro-Differential Equations,
2019
TÜBİTAK
Nonexistence Of Global Solutions For A Fractional System Of Strongly Coupled Integro-Differential Equations, Ahmad Mugbil Ahmad, Nasser Eddine Tatar
Turkish Journal of Mathematics
In this paper, we study the nonexistence of nontrivial global solutions for a system of two strongly coupled fractional differential equations. Each equation involves two fractional derivatives and a nonlinear source term. The fractional derivatives are of Caputo type of subfirst orders. The nonlinear sources are nonlocal in time. They have the form of a convolution of a polynomial of the state with a (possibly singular) kernel. The system under consideration is a generalization of many interesting special systems of equations whose solutions do not exist globally in time. We establish some criteria under which no nontrivial global solutions exist. …
Fixed-Disc Results Via Simulation Functions,
2019
TÜBİTAK
Fixed-Disc Results Via Simulation Functions, Ni̇hal Özgür
Turkish Journal of Mathematics
In this paper, our aim is to obtain new fixed-disc results on metric spaces. To do this, we present a new approach using the set of simulation functions and some known fixed-point techniques. We do not need to have some strong conditions such as completeness or compactness of the metric space or continuity of the self-mapping in our results. Taking only one geometric condition, we ensure the existence of a fixed disc of a new type contractive mapping.
On Composition Factors In Modules Over Some Group Rings,
2019
TÜBİTAK
On Composition Factors In Modules Over Some Group Rings, Martyn Russell Dixon, Leonid Andreevich Kurdachenko, Igor Yakov Subbotin
Turkish Journal of Mathematics
The aim of this paper is to prove the following result: Let G be an FC-hypercentral group and let A have a finite FG-composition series. Then A contains two FG-submodules B,C such that A = B ⊕ C, where each FG-composition factor of B has finite F -dimension and each FG-composition factor of C has infinite F -dimension. Thishasconsequencesfor FG-modules whose proper submodules all have finite F -dimensionandforthose FG-modules whose proper quotients all have finite F -dimension.
Zeros Of The Extended Selberg Class Zeta-Functions And Of Their Derivatives,
2019
TÜBİTAK
Zeros Of The Extended Selberg Class Zeta-Functions And Of Their Derivatives, Ramunas Garunkstis
Turkish Journal of Mathematics
Levinson and Montgomery proved that the Riemann zeta-function ζ(s) and its derivative have approximately the same number of nonreal zeros left of the critical line. Spira showed that ζ'(1/2+it) = 0 implies that ζ(1/2+it) = 0. Here we obtain that in small areas located to the left of the critical line and near it the functions ζ(s) and ζ'(s) have the same number of zeros. We prove our result for more general zeta-functions from the extended Selberg class S. We also consider zero trajectories of a certain family of zeta-functions from S.
A Variational Study On A Natural Hamiltonian For Curves,
2019
TÜBİTAK
A Variational Study On A Natural Hamiltonian For Curves, Gözde Özkan Tükel
Turkish Journal of Mathematics
A variational study of finding critical points of the total squared torsion functional for curves in Euclidean 3-spaces is presented. Critical points of this functional also known as one of the natural Hamiltonians of curves are characterized by two Euler-Lagrange equations in terms of curvature and torsion of a curve. To solve these balance equations, the curvature of the critical curve is expressed by its torsion so that equations are completely solved by quadratures. Then two Killing fields along the critical curve are found for integrating the structural equations of the critical curve and this curve is expressed by quadratures …
Extensions And Topological Conditions Of Nj Rings,
2019
TÜBİTAK
Extensions And Topological Conditions Of Nj Rings, Meimei Jiang, Yao Wang, Yanli Ren
Turkish Journal of Mathematics
A ring $R$ is said to be NJ if $J(R)=N(R)$. This paper mainly studies the relationship between NJ rings and related rings, and investigates the Dorroh extension, the Nagata extension, the Jordan extension, and some other extensions of NJ rings. At the same time, we also prove that if $R$ is a weakly 2-primal $\alpha$-compatible ring with an isomorphism $\alpha$ of $R$, then $R[x;\alpha]$ is NJ; if $R$ is a weakly 2-primal $\delta$-compatible ring with a derivation $\delta$ of $R$, then $R[x;\delta]$ is NJ. Moreover, we consider some topological conditions for NJ rings and show for a NJ ring $R$ …
