On The Affine-Periodic Solutions Of Discrete Dynamical Systems,
2018
TÜBİTAK
On The Affine-Periodic Solutions Of Discrete Dynamical Systems, Hali̇s Can Koyuncuoğlu, Murat Adivar
Turkish Journal of Mathematics
Affine periodicity is a generalization of the notion of conventional periodicity and it is a symmetry property for classes of functions. This study is concerned with the existence of $(Q,T)$-affine periodic solutions of discrete dynamical systems. Sufficient conditions for the main results are proposed due to discrete exponential dichotomy and fixed point theory. Obtained results are also implemented for some economical and biological models. In particular cases, our results cover some existing results in the literature for periodic, antiperiodic, or quasiperiodic solutions of difference equations.
Generating Sets Of Certain Finite Subsemigroups Of Monotone Partial Bijections,
2018
TÜBİTAK
Generating Sets Of Certain Finite Subsemigroups Of Monotone Partial Bijections, Leyla Bugay, Hayrullah Ayik
Turkish Journal of Mathematics
Let $I_{n}$ be the symmetric inverse semigroup, and let $PODI_{n}$ and $POI_{n}$ be its subsemigroups of monotone partial bijections and of isotone partial bijections on $X_{n}=\{1,\ldots ,n\}$ under its natural order, respectively. In this paper we characterize the structure of (minimal) generating sets of the subsemigroups $PODI_{n,r}=\{ \alpha \in PODI_{n}: \im(\alpha) \leq r\}$, $POI_{n,r}=\{ \alpha \in POI_{n}: \im(\alpha) \leq r\}$, and $E_{n,r}=\{ \id_{A}\in I_{n}:A\subseteq X_n\mbox{ and } A \leq r\}$ where $id_{A}$ is the identity map on $A\subseteq X_n$ for $0\leq r\leq n-1$.
On A Class Of Kazdan--Warner Equations,
2018
TÜBİTAK
On A Class Of Kazdan--Warner Equations, Yu Fang, Mengjie Zhang
Turkish Journal of Mathematics
Let $(\small{\Si},g)$ be a compact Riemannian surface without boundary and $W^{1,2}(\Si)$ be the usual Sobolev space. For any real number $p>1$ and $\alpha\in\mathbb{R}$, we define a functional $$ J_{\alpha,8\pi}(u)=\frac{1}{2}\le( \int_\Si \nabla_g u ^2dv_g-\alpha (\int_\Si u ^pdv_g)^{2/p}\ri)-8\pi\log\int_\Si he^u dv_g $$ on a function space $\mathcal{H}=\le\{u\in W^{1,2}(\Si):\int_{\Si}u dv_{g}=0\ri\}$, where $h$ is a positive smooth function on $\Si$. Denote $$\lambda_{1,p}(\Si)=\inf_{u\in \mathcal{H},\,\int_\Si u ^p dv_g=1}\int_{\Si} \nabla_{g}u ^{2}\mathrm{d}v_{g}. $$ If $\alpha
On The Summability Methods Of Logarithmic Type And The Berezin Symbol,
2018
TÜBİTAK
On The Summability Methods Of Logarithmic Type And The Berezin Symbol, Ulaş Yamanci
Turkish Journal of Mathematics
We prove by means of the Berezin symbols some theorems for the $\left( L\right) $-summability method for sequences and series. Also, we prove a new Tauberian type theorem for $\left( L\right) $-summability.
Green's Relations And Regularity On Some Subsemigroups Of Transformations That Preserve Equivalences,
2018
TÜBİTAK
Green's Relations And Regularity On Some Subsemigroups Of Transformations That Preserve Equivalences, Nares Sawatraksa, Chaiwat Namnak
Turkish Journal of Mathematics
Let $T(X)$ be the full transformation semigroup on a set $X$. For two equivalence relations $E$ and $F$ on $X$ with $F \subseteq E$, let $T(X, E, F) = \{ \alpha \in T(X) : \forall x, y \in X, (x, y)\in E \Rightarrow (x\alpha, y\alpha) \in F \}. $
Global Attractors For The Semilinear Beam Equationwith Localized Viscosity,
2018
TÜBİTAK
Global Attractors For The Semilinear Beam Equationwith Localized Viscosity, Sema Yayla
Turkish Journal of Mathematics
In this paper, we deal with the semilinear beam equation with localized viscosity. Under mild conditions on the viscous coefficient, we establish the well-posedness and boundedness of the weak solutions. Then we prove that the semigroup generated by this problem has a smooth global attractor in $H^{3}\left( 0,1\right) \times H_{0}^{1}\left( 0,1\right) $.
3-Class Groups Of Cubic Cyclic Function Fields,
2018
TÜBİTAK
3-Class Groups Of Cubic Cyclic Function Fields, Zhengjun Zhao
Turkish Journal of Mathematics
Let $F$ be a global function field over the finite constant field $\mathbb{F}_q$ with $3\mid q-1$, and let $K/F$ be a cubic cyclic function fields extension with Galois group $G=$Gal$(K/F)=$. Denote by $\mathcal{C}(K)$ and $\mathcal{C}(K)_3$ the ideal class group of $K$ and its Sylow 3-subgroup, respectively. Let $\mathcal{C}(K)_3^G=\{[\fa]\in \mathcal{C}(K)_3 \ \sigma[\fa]=[\fa]\}$ and $\mathcal{C}(K)_3^{1-\sigma}=\{[\fa](\sigma[\fa])^{-1} \ [\fa]\in \mathcal{C}(K)_3\}$. In this paper, we present a method for computing the 3-rank of the quotient group $\mathcal{C}(K)_3^G\mathcal{C}(K)_3^{1-\sigma}/\mathcal{C}(K)_3^{1-\sigma}$. Specifically, when $K$ is a cubic Kummer extension of $\mathbb{F}_q(T)$, we determine explicitly the key factors $t$, $x_1,\cdots, x_t$, and $[\mathfrak{A}_1],\cdots, [\mathfrak{A}_t]$ in the process of computing the …
Higher Order Generalized Geometric Polynomials,
2018
TÜBİTAK
Higher Order Generalized Geometric Polynomials, Levent Kargin, Bayram Çeki̇m
Turkish Journal of Mathematics
According to the generalized Mellin derivative, we introduce a new family of polynomials called higher order generalized geometric polynomials and obtain some arithmetical properties of them. Then we investigate the relationship of these polynomials with degenerate Bernoulli, degenerate Euler, and Bernoulli polynomials. Finally, we evaluate several series and integrals in closed forms.
Legendrian Torus Knots In Lens Spaces,
2018
TÜBİTAK
Legendrian Torus Knots In Lens Spaces, Si̇nem Onaran
Turkish Journal of Mathematics
In this study, we first classify all topological torus knots lying on the Heegaard torus in lens spaces, and then we study Legendrian representatives of these knots. We classify oriented positive Legendrian torus knots in the universally tight contact structures on the lens spaces up to contactomorphism.
Variational Problem Involving Operator Curl Associated With $P$-Curl System,
2018
TÜBİTAK
Variational Problem Involving Operator Curl Associated With $P$-Curl System, Junichi Aramaki
Turkish Journal of Mathematics
We shall study the problem of minimizing a functional involving curl of vector fields in a three-dimensional, bounded multiconnected domain with the prescribed tangent component of a given vector field on the boundary. It will be seen that the minimizers are weak solutions of the $p$-curl type system. We shall prove the existence and the estimate of minimizers of a more general functional that contains the $L^p$ norm of the curl of vector fields. We shall also give the continuity with respect to the given data.
Lower And Upper Solutions Method For A Problem Of An Elastic Beam Whose One End Is Simply Supported And The Other End Is Sliding Clamped, Man Xu, Ruyun Ma, Jin Wen
Turkish Journal of Mathematics
In this paper we develop the lower and upper solutions method for the fourth-order boundary value problem of the form $$ \left\{ \aligned &y^{(4)}(x)+(k_{1}+k_{2})y''(x)+k_{1}k_{2}y(x)=f(x,y(x)), \ \ x\in (0,1),\\ &y(0)=y'(1)=y''(0)=y'''(1)=0,\\ \endaligned \right. $$ which models a statically elastic beam with one of its ends simply supported and the other end clamped by sliding clamps, where $k_{1}
Graphs Of $Bci/Bck$-Algebras,
2018
TÜBİTAK
Graphs Of $Bci/Bck$-Algebras, Atena Tahmasbpour Meikola
Turkish Journal of Mathematics
The aim of this paper is to study special graphs of $BCI/BCK$-algebras. In this paper, we introduce one kind of graph of $BCI$-algebras based on branches of $X$ and two kinds of graphs of $BCK$-algebras based on ideal $I$. Then we study some of the essential properties of graph theory on the basis of those structures. In particular, we study the planar, outerplanar, toroidal, $K$-connected, chordal, $K$-partite, and Eulerian properties of graph theory.
On Some Multivariate Lcm And Gcd Sums,
2018
TÜBİTAK
On Some Multivariate Lcm And Gcd Sums, Khola Algali
Turkish Journal of Mathematics
In this paper we obtain an asymptotic formula with a power saving error term for the summation function of a family of generalized least common multiple and greatest common divisor functions of several integer variables.
Diagonal Lift In The Semi-Cotangent Bundle And Its Applications,
2018
TÜBİTAK
Diagonal Lift In The Semi-Cotangent Bundle And Its Applications, Furkan Yildirim
Turkish Journal of Mathematics
The present paper is devoted to some results concerning the diagonal lift of tensor fields of type (1,1) from manifold M to its semi-cotangent bundle t*M. In this context, cross-sections in the semi-cotangent (pull-back) bundle t*M of cotangent bundle T*M by using projection (submersion) of the tangent bundle TM can be also defined.
Fréchet-Hilbert Spaces And The Property Scbs,
2018
TÜBİTAK
Fréchet-Hilbert Spaces And The Property Scbs, Eli̇f Uyanik, Murat Hayretti̇n Yurdakul
Turkish Journal of Mathematics
In this note, we obtain that all separable Fréchet-Hilbert spaces have the property of smallness up to a complemented Banach subspace (SCBS). Djakov, Terzioğlu, Yurdakul, and Zahariuta proved that a bounded perturbation of an automorphism on Fréchet spaces with the SCBS property is stable up to a complemented Banach subspace. Considering Fréchet-Hilbert spaces we show that the bounded perturbation of an automorphism on a separable Fréchet-Hilbert space still takes place up to a complemented Hilbert subspace. Moreover, the strong dual of a real Fréchet-Hilbert space has the SCBS property.
Jakimovski-Leviatan Operators Of Durrmeyer Type Involving Appell Polynomials,
2018
TÜBİTAK
Jakimovski-Leviatan Operators Of Durrmeyer Type Involving Appell Polynomials, Pooja Gupta, Purshottam Narain Agrawal
Turkish Journal of Mathematics
The purpose of the present paper is to establish the rate of convergence for a Lipschitz-type space and obtain the degree of approximation in terms of Lipschitz-type maximal function for the Durrmeyer type modification of Jakimovski-Leviatan operators based on Appell polynomials. We also study the rate of approximation of these operators in a weighted space of polynomial growth and for functions having a derivative of bounded variation.
A New Class Of Generalized Polynomials,
2018
TÜBİTAK
A New Class Of Generalized Polynomials, Nabiullah Khan, Talha Usman, Junesang Choi
Turkish Journal of Mathematics
Motivated by their importance and potential for applications in a variety of research fields, recently, various polynomials and their extensions have been introduced and investigated. In this sequel, we modify the known generating functions of polynomials, due to both Milne-Thomson and Dere and Simsek, to introduce a new class of generalized polynomials and present some of their involved properties. As obvious special cases of the newly introduced polynomials, we also introduce so-called power sum-Laguerre--Hermite polynomials and generalized Laguerre and Euler polynomials and we present some of their involved identities and formulas. The results presented here, being very general, are pointed …
The Classification Of Rings With Its Genus Of Class Of Graphs,
2018
TÜBİTAK
The Classification Of Rings With Its Genus Of Class Of Graphs, Thangaraj Asir, Karuppiah Mano
Turkish Journal of Mathematics
Let $R$ be a commutative ring, $I$ be a proper ideal of $R$, and $S(I)=\{a\in R : ra\in I \text{ for some } r\in R\sm I\}$ be the set of all elements of $R$ that are not prime to $I$. The total graph of $R$ with respect to $I$, denoted by $T(\Gamma_I(R))$, is the simple graph with all elements of $R$ as vertices, and for distinct $x,y\in R$, the vertices $x$ and $y$ are adjacent if and only if $x+y\in S(I)$. In this paper, we determine all isomorphic classes of commutative Artinian rings whose ideal-based total graph has genus at …
Convergence Analysis And Numerical Solution Of The Benjamin-Bona-Mahony Equation By Lie-Trotter Splitting,
2018
TÜBİTAK
Convergence Analysis And Numerical Solution Of The Benjamin-Bona-Mahony Equation By Lie-Trotter Splitting, Fatma Zürnaci, Nurcan Gücüyenen Kaymak, Muaz Seydaoğlu, Gamze Tanoğlu
Turkish Journal of Mathematics
In this paper, an operator splitting method is used to analyze nonlinear Benjamin-Bona-Mahony-type equations. We split the equation into an unbounded linear part and a bounded nonlinear part and then Lie-Trotter splitting is applied to the equation. The local error bounds are obtained by using the approach based on the differential theory of operators in a Banach space and the quadrature error estimates via Lie commutator bounds. The global error estimate is obtained via Lady Windermere's fan argument. Finally, to confirm the expected convergence order, numerical examples are studied.
On Reflexivity Of The Bochner Space $L^{P}(\Mu, E)$ For Arbitrary $\Mu$,
2018
TÜBİTAK
On Reflexivity Of The Bochner Space $L^{P}(\Mu, E)$ For Arbitrary $\Mu$, Bahaetti̇n Cengi̇z, Banu Güntürk
Turkish Journal of Mathematics
Let $(\Omega ,\mathcal{A},\mu )$ be a finite positive measure space, $E$ a Banach space, and $1
