$\Mathbb{Q}$-Korselt Numbers,
2018
TÜBİTAK
$\Mathbb{Q}$-Korselt Numbers, Nejib Ghanmi
Turkish Journal of Mathematics
Let $\alpha=\dfrac{\alpha_{1}}{\alpha_{2}}\in \mathbb{Q}\setminus \{0\}$; a positive integer $N$ is said to be an \emph{$\alpha$-Korselt number} (\emph{$K_{\alpha}$-number}, for short) if $N\neq \alpha$ and $\alpha_{2}p-\alpha_{1}$ divides $\alpha_{2}N-\alpha_{1}$ for every prime divisor $p$ of $N$. In this paper we prove that for each squarefree composite number $N$ there exist finitely many rational numbers $\alpha$ such that $N$ is a $K_{\alpha}$-number and if $\alpha\leq1$ then $N$ has at least three prime factors. Moreover, we prove that for each $\alpha\in \mathbb{Q}\setminus \{0\}$ there exist only finitely many squarefree composite numbers $N$ with two prime factors such that $N$ is a $K_{\alpha}$-number.
Jackson And\ Stechkin Type Inequalities Of Trigonometricapproximation In $A_{W,\Vartheta }^{P,Q(\Cdot )}$,
2018
TÜBİTAK
Jackson And\ Stechkin Type Inequalities Of Trigonometricapproximation In $A_{W,\Vartheta }^{P,Q(\Cdot )}$, Ahmet Hamdi̇ Avşar, Hüseyi̇n Koç
Turkish Journal of Mathematics
In this paper, we study Jackson and Stechkin type theorems of trigonometric polynomial approximation in the space $A_{w,\vartheta }^{p,q(\cdot )}$ by considering a modulus of smoothness defined by virtue of the Steklov operator.
On Spanning Sets And Generators Of Near-Vector Spaces,
2018
TÜBİTAK
On Spanning Sets And Generators Of Near-Vector Spaces, Karin-Therese Howell, Sogo Pierre Sanon
Turkish Journal of Mathematics
In this paper we study the quasi-kernel of certain constructions of near-vector spaces and the span of a vector. We characterize those vectors whose span is one-dimensional and those that generate the whole space.
Symmetry Of Numerical Range And Semigroup Generation Of Infinite Dimensional Hamiltonian Operators,
2018
TÜBİTAK
Symmetry Of Numerical Range And Semigroup Generation Of Infinite Dimensional Hamiltonian Operators, Junjie Huang, Jie Liu, Alatancang Chen
Turkish Journal of Mathematics
This paper deals with the infinite dimensional Hamiltonian operator with unbounded entries. Using the core of its entries, we obtain the conditions under which the numerical range of such an operator is symmetric with respect to the imaginary axis. Based on the symmetry above, a necessary and sufficient condition for generating $C_0$ semigroups is further given.
Analysis Of Periodic And Asymptotically Periodic Solutions In Nonlinear Coupled Volterra Integro-Differential Systems,
2018
TÜBİTAK
Analysis Of Periodic And Asymptotically Periodic Solutions In Nonlinear Coupled Volterra Integro-Differential Systems, Youssef Raffoul
Turkish Journal of Mathematics
In this note, we investigate the existence of periodic and asymptotically periodic solutions of a system of coupled nonlinear Volterra integro-differential equations with infinite delay. We will make use of Schauder fixed point theorem to prove our maps have fixed points.
On The Isospectrality Of The Scalar Energy-Dependent Schrödingerproblems,
2018
TÜBİTAK
On The Isospectrality Of The Scalar Energy-Dependent Schrödingerproblems, Tüba Gülşen, Etibar Sadi Panakhov
Turkish Journal of Mathematics
In this study, we discuss the inverse spectral problem for the energy-dependent Schrödinger equation on a finite interval. We construct an isospectrality problem and obtain some relations between constants in boundary conditions of the problems that constitute isospectrality. Above all, we obtain degeneracy of $ K(x,t)-K_{0}{ (x,t)}$ and $L(x,t)-L_{0} (x,t)$ by using a different approach. Some of the main results of our study coincide with results reported by Jodeit and Levitan. However, the method to obtain degeneracy is completely different. Furthermore, we consider all above results for the nonisospectral case.
On The Density And Transitivity Of Sets Of Operators,
2018
TÜBİTAK
On The Density And Transitivity Of Sets Of Operators, Mohammad Ansari, Bahram Khani Robati, Karim Hedayatian
Turkish Journal of Mathematics
By the well-known result of Yood, every strictly transitive algebra of operators on a Banach space is WOT-dense. This motivated us to investigate the relationships between SOT and WOT largeness of sets of operators and the transitivity behavior of them. We show that, to obtain Yood's result, strict transitivity may not be replaced by the weaker condition of hypertransitivity. We prove that, for a wide class of topological vector spaces, every SOT-dense set of operators is hypertransitive. The general form of SOT-dense sets that are not strictly transitive is presented. We also describe the form of WOT-dense sets that are …
On Oscillation Of Integro-Differential Equations,
2018
TÜBİTAK
On Oscillation Of Integro-Differential Equations, Said R. Grace, Ağacik Zafer
Turkish Journal of Mathematics
We study the oscillatory behavior of solutions for integro-differential equations of the form $$x'(t) = e(t) -\int_0^t (t-s)^{\alpha-1}k(t, s)f(s, x(s))\, {\rm ds},\quad t\geq 0,$$ where $0
Bounds For Radii Of Starlikeness And Convexity Of Some Special Functions,
2018
TÜBİTAK
Bounds For Radii Of Starlikeness And Convexity Of Some Special Functions, İbrahi̇m Aktaş, Arpad Baricz, Hali̇t Orhan
Turkish Journal of Mathematics
In this paper we consider some normalized Bessel, Struve, and Lommel functions of the first kind and, by using the Euler--Rayleigh inequalities for the first positive zeros of a combination of special functions, we obtain tight lower and upper bounds for the radii of starlikeness of these functions. By considering two different normalizations of Bessel and Struve functions we give some inequalities for the radii of convexity of the same functions. On the other hand, we show that the radii of univalence of some normalized Struve and Lommel functions are exactly the radii of starlikeness of the same functions. In …
Variational Multiscale Method For The Optimal Control Problems Of Convectio--Diffusion-Reaction Equations,
2018
TÜBİTAK
Variational Multiscale Method For The Optimal Control Problems Of Convectio--Diffusion-Reaction Equations, Ayteki̇n Bayram Çibik, Fi̇kri̇ye Nuray Yilmaz
Turkish Journal of Mathematics
In this paper, we analyze a projection-based variational multiscale (VMS) method for the optimal control problems governed by the convection-diffusion-reaction equations. We derive the first-order optimality conditions by the \emph{optimize-then-discretize} method. After expressing the discrete optimal control problem, we obtain the stability properties of state and adjoint variables. We also prove that the error in each variable is optimal. Through numerical examples, we show the efficiency of the stabilization for the solutions of the control, state, and adjoint variables.
A Taylor Operation Method For Solutions Of Generalized Pantograph Type Delay Differential Equations,
2018
TÜBİTAK
A Taylor Operation Method For Solutions Of Generalized Pantograph Type Delay Differential Equations, Şuayi̇p Yüzbaşi, Nurbol Ismailov
Turkish Journal of Mathematics
In this paper, a new operational matrix method based on the Taylor polynomials is presented to solve generalized pantograph type delay differential equations. The method is based on operational matrices of integration and product for Taylor polynomials. These matrices are obtained by using the best approximation of function by the Taylor polynomials. The advantage of the method is that the method does not require collocation points. By using the proposed method, the generalized pantograph equation problem is reduced to a system of linear algebraic equations. The solving of this system gives the coefficients of our solution. Numerical examples are given …
Descent-Inversion Statistics In Riffle Shuffles,
2018
TÜBİTAK
Descent-Inversion Statistics In Riffle Shuffles, Ümi̇t Işlak
Turkish Journal of Mathematics
The purpose of this paper is to answer a question of Fulman on the asymptotic normality of the number of inversions in riffle shuffles. We will also study asymptotics for the number of descents and the length of the longest alternating subsequences in the same shuffling scheme.
The Cauchy-Kowalevski Theorem Applied For Counting Connections With A Prescribed Ricci Tensor,
2018
TÜBİTAK
The Cauchy-Kowalevski Theorem Applied For Counting Connections With A Prescribed Ricci Tensor, Barbara Opozda, Wlodzimierz M. Mikulski
Turkish Journal of Mathematics
How many linear connections are there with a prescribed Ricci tensor? The question is answered in the analytic case by using the Cauchy-Kowalevski theorem
Boundary Sentinels For The Resolution Of A Geometrical Problem,
2018
TÜBİTAK
Boundary Sentinels For The Resolution Of A Geometrical Problem, Saida Sandel, Abdelhamid Ayadi
Turkish Journal of Mathematics
The aim of this paper is to estimate the shape of an unknown part of the boundary of a geometrical domain. The identification technique used to estimate this part is the observation of the solution of a diffusion problem on the known part of this boundary. This technique is based on the sentinels theory.
A Result On The Maximal Length Of Consecutive 0 Digits In $\Beta$-Expansions,
2018
TÜBİTAK
A Result On The Maximal Length Of Consecutive 0 Digits In $\Beta$-Expansions, Xiang Gao, Hui Hu, Zhihui Li
Turkish Journal of Mathematics
Let $\beta>1$ be a real number. For any $x\in[0,1]$, let $r_{n}(x,\beta)$ be the maximal length of consecutive zero digits in the first $n$ digits of the $\beta$-expansion of $x$. In this note, it is proved that for any $0
Harmonic Quadrangle In Isotropic Plane,
2018
TÜBİTAK
Harmonic Quadrangle In Isotropic Plane, Ema Jurkin, Marija Simic Horvath, Vladimir Volenec, Jelena Beban-Brkic
Turkish Journal of Mathematics
The concept of the harmonic quadrangle and the associated Brocard points are introduced and investigated in the isotropic plane by employing suitable analytic methods.
An Application Of $Q$-Sumudu Transform For Fractional $Q$-Kinetic Equation,
2018
TÜBİTAK
An Application Of $Q$-Sumudu Transform For Fractional $Q$-Kinetic Equation, Sunil Dutt Purohit, Faruk Uçar
Turkish Journal of Mathematics
The aim of this paper is to give an alternative solution for the $q$-kinetic equation involving the Riemann--Liouville fractional $q$-integral operator. The solution is obtained in terms of the $q$-Mittag--Leffler functions using inverse $q$-Sumudu transform. As applications, some corollaries are presented to illustrate the main results.
The Local And Semilocal Convergence Analysis Of New Newton-Like Iteration Methods,
2018
TÜBİTAK
The Local And Semilocal Convergence Analysis Of New Newton-Like Iteration Methods, Vatan Karakaya, Kadri̇ Doğan, Yunus Atalan, Nour El Houda Bouzara
Turkish Journal of Mathematics
The aim of this paper is to find new iterative Newton-like schemes inspired by the modified Newton iterative algorithm and prove that these iterations are faster than the existing ones in the literature. We further investigate their behavior and finally illustrate the results by numerical examples.
On Biquaternion Algebras With Orthogonal Involution,
2018
TÜBİTAK
On Biquaternion Algebras With Orthogonal Involution, Amir Hossein Nokhodkar
Turkish Journal of Mathematics
We investigate the Pfaffians of decomposable biquaternion algebras with involution of orthogonal type. In characteristic two, a classification of these algebras in terms of their Pfaffians and some other related invariants is studied. Also, in arbitrary characteristic, a criterion is obtained for an orthogonal involution on a biquaternion algebra to be metabolic.
Connection Between Bi$^{S}$Nomial Coefficients And Their Analogs And Symmetric Functions,
2018
TÜBİTAK
Connection Between Bi$^{S}$Nomial Coefficients And Their Analogs And Symmetric Functions, Abdelghafour Bazeniar, Moussa Ahmia, Hacene Belbachir
Turkish Journal of Mathematics
In this paper, on one hand, we propose a new type of symmetric function to interpret the bi$^{s}$nomial coefficients and their analogs. On other hand, according to this function, we give an interpretation of these coefficients by lattice paths and tiling. Some identities of these coefficients are also established. This work is an extension of the results of Belbachir and Benmezai's ''A $\mathit{q}$-analogue for bi$^{\mathit{s}}$nomial coefficients and generalized Fibonacci sequences".
