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".
Iterative Roots Of Some Functions,
2018
TÜBİTAK
Iterative Roots Of Some Functions, Sukrawan Mavecha, Vichian Laohakosol, Boonrod Yuttanan
Turkish Journal of Mathematics
The iterative equation $f^{q}(x)=g(x)$, $x\in X$ for a given function $g$ and a positive integer $q$ is solved in the following two main cases: (i) $X=\mathbb{Z}$, $g(x)=ax+b$, ($a,b\in\mathbb{Z}$; $a\neq0,1$); (ii) $X=\mathbb{N}\cup\left\{ 0\right\} $, $g$ is increasing with no fixed point.
Weyl- And Horn-Type Inequalities For Cyclically Compact Operators,
2018
TÜBİTAK
Weyl- And Horn-Type Inequalities For Cyclically Compact Operators, Uğur Gönüllü
Turkish Journal of Mathematics
A variant of Weyl- and Horn-type inequalities for cyclically compact operators on Kaplansky-Hilbert modules is given.
Three Binomial Sums Weighted By Falling And Rising Factorials,
2018
TÜBİTAK
Three Binomial Sums Weighted By Falling And Rising Factorials, Emrah Kiliç
Turkish Journal of Mathematics
In this paper, we will investigate and evaluate, in closed forms, three binomial sums weighted by falling and rising factorials. We first use the relationships between the rising, falling factorials and the binomial coefficients. Then we rewrite the claimed identities in terms of generalized hypergeometric functions to prove the claimed results.
On A New Identity For The H-Function With Applications To The Summation Of Hypergeometric Series,
2018
TÜBİTAK
On A New Identity For The H-Function With Applications To The Summation Of Hypergeometric Series, Arjun Kumar Rathie, Luan Carlos De Sena Monteiro Ozelim, Pushpa Narayan Rathie
Turkish Journal of Mathematics
Using generalized hypergeometric functions to perform symbolic manipulations of equations is of great importance to pure and applied scientists. There are in the literature a great number of identities for the Meijer-G function. On the other hand, when more complex expressions arise, that function is not capable of representing them. The H-function is an alternative to overcome this issue, as it is a generalization of the Meijer-G function. In the present paper, a new identity for the H-function is derived. In short, this result enables one to split a particular H-function into the sum of two other H-functions. The new …
Continuous Dependence Of Solutions To The Strongly Damped Nonlinear Klein-Gordon Equation,
2018
TÜBİTAK
Continuous Dependence Of Solutions To The Strongly Damped Nonlinear Klein-Gordon Equation, Şevket Gür, Mesude Eli̇f Uysal
Turkish Journal of Mathematics
This article is devoted to the study of the initial-boundary value problem for the strongly damped nonlinear Klein-Gordon equation. It is proved that the solution depends continuously on changes in the damping terms, diffusion, mass, and nonlinearity effect term in the $H^1$ norm.
Nearly Kahler And Nearly Kenmotsu Manifolds,
2018
TÜBİTAK
Nearly Kahler And Nearly Kenmotsu Manifolds, Nikrooz Heidari, Niloufar Hoseein Pour Kashani, Behzad Najafi
Turkish Journal of Mathematics
We study the class of strict nearly Kenmotsu manifolds and prove that there is no Einstein manifold or locally symmetric or locally $\phi$-symmetric in this class of manifolds. We describe strict nearly Kenmotsu manifolds in low dimensions. Finally, we obtain a relation between the curvature of nearly Kenmotsu manifolds and nearly Kahler manifolds.
A New Formula For Hyper-Fibonacci Numbers, And The Number Of Occurrences,
2018
TÜBİTAK
A New Formula For Hyper-Fibonacci Numbers, And The Number Of Occurrences, Takao Komatsu, Laszlo Szalay
Turkish Journal of Mathematics
In this paper, we develop a new formula for hyper-Fibonacci numbers $F_n^{[k]}$, wherein the coefficients (related to Stirling numbers of the first kind) of the polynomial ingredient $p_k(n)$ are determined. As an application we investigate the number of occurrences of positive integers among $F_n^{[k]}$ and determine all the solutions in nonnegative integers $x$ and $y$ to the Diophantine equation $F_x^{[k]}=F_y^{[\ell]}$, where $0\le k
Reflexivity Of Vector-Valued Köthe-Orlicz Sequence Spaces,
2018
TÜBİTAK
Reflexivity Of Vector-Valued Köthe-Orlicz Sequence Spaces, Mohamed Ahmed Ould Sidaty
Turkish Journal of Mathematics
Let $E$ be a Banach space, $\lambda$ a perfect sequence space, and $M$ an Orlicz function. Denote by $\lambda \left(E, M\right)_{r}$ the space of all weakly $(M, \lambda)$-summable sequences from $E$ that are the limit of their finite sections. In this paper, we describe the continuous linear functionals on $\lambda \left(E, M\right)_{r}$ in terms of strongly $(N, \lambda^{\ast})$-summable sequences in the dual $E^{*}$ of $E$, and then we give a characterization of the reflexivity of $\lambda \left(E, M\right)$ in terms of that of $\lambda$ and of $E$ and the AK-property.
On The Growth Of Meromorphic Solutions Of Some Higher Order Linear Differential Equations,
2018
TÜBİTAK
On The Growth Of Meromorphic Solutions Of Some Higher Order Linear Differential Equations, Farid Mesbout, Tahar Zerzaihi
Turkish Journal of Mathematics
Let $k,m,n $ be integers such that $k\geq 1$, $n\geq 2$ and $1\leq m\leq n$. In this article we study the order $\rho(f)$ and the hyperorder $\rho_2(f)$ of nonzero meromorphic solutions $f$ of the differential equation $$\sum_{j=1,j\ne m}^{n}A_j(z)f^{(j)}(z)+A_m(z)e^{p_m(z)}f^{(m)}(z)+\left(A_0(z)e^{p(z)}+B_0(z)e^{q(z)}\right)f(z)=0,$$ where $B_0(z)$, $A_0(z), \cdots, A_n(z)$ are meromorphic functions such that $A_0A_mA_nB_0\not\equiv 0$, $\max\{\rho(B_0), \rho(A_0), \cdots,\rho(A_n)\}
Dynamic Optimal Contract Under Parameter Uncertainty With Risk-Averse Agent And Principal,
2018
TÜBİTAK
Dynamic Optimal Contract Under Parameter Uncertainty With Risk-Averse Agent And Principal, Kerem Uğurlu
Turkish Journal of Mathematics
We consider a continuous-time principal--agent model on a finite time horizon, where we look for the existence of an optimal contract that both parties agreed on. Contrary to the mainstream, where the principal is modeled as risk-neutral, we assume that both the principal and the agent have exponential utility and are risk-averse with same risk awareness level. Moreover, the agent's quality is unknown and is modeled as a filtering term in the problem, which is revealed as time passes. The principal cannot observe the agent's real action, but can only recommend action levels to the agent. Hence, we have a …
On The Existence And Uniqueness Of Solutions To Dynamic Equations,
2018
TÜBİTAK
On The Existence And Uniqueness Of Solutions To Dynamic Equations, Başak Karpuz
Turkish Journal of Mathematics
In this paper, we prove the well-known Cauchy-Peano theorem for existence of solutions to dynamic equations on time scales. Some simple examples are given to show that there may exist more than a single solution for dynamic initial value problems. Under some certain conditions, it is also shown that there exists only one solution.
On The Monodromy Of Milnor Open Books,
2018
TÜBİTAK
On The Monodromy Of Milnor Open Books, Selma Altinok Bhupal, Mohan Lal Bhupal
Turkish Journal of Mathematics
We present some techniques that can be used to factorize the monodromy of certain Milnor open books. We also describe a class of Milnor open books for which we can explicitly express the monodromy as a product of Dehn twists.
Generation Of Efficient And $\Epsilon$-Efficient Solutionsin Multiple Objective Linear Programming,
2018
TÜBİTAK
Generation Of Efficient And $\Epsilon$-Efficient Solutionsin Multiple Objective Linear Programming, Zohra Sabrina Delhoum, Sonia Radjef, Fatima Boudaoud
Turkish Journal of Mathematics
We develop an algorithm to solve a multiple objective linear programming problem with bounded variables. It is based on the scalarization theorem of optimal solutions of multiobjective linear programs and the single objective adaptive method. We suggest a process for the search for the first efficient solution without having to calculate a feasible solution, and we elaborate a method to generate efficient solutions, weakly efficient solutions, and $\epsilon$-efficient solutions. Supporting theoretical results are established and the method is demonstrated on a numerical example.
An Expansion Theorem For $Q$-Sturm-Liouville Operators On The Wholeline,
2018
TÜBİTAK
An Expansion Theorem For $Q$-Sturm-Liouville Operators On The Wholeline, Bi̇lender Paşaoğlu Allahverdi̇ev, Hüseyi̇n Tuna
Turkish Journal of Mathematics
In this work, we establish a Parseval equality and an expansion formula in eigenfunctions for a singular $q-$Sturm-Liouville operator on the whole line.
The United Stable Solution Set Of Interval Continuous-Time Algebraic Riccati Equation And Verified Numerical Computation Of Its Outer Estimation, Tayyebe Haqiri, Mahmoud Mohseni Moghadam, Azim Rivaz
Turkish Journal of Mathematics
This paper introduces the interval continuous-time algebraic Riccati equation $\mathbf{A}^* X + X\mathbf{A} + \mathbf{Q} -X \mathbf{G} X=0$, where $\mathbf{A}, \mathbf{G}$, and $\mathbf{Q}$ are known $n \times n$ complex interval matrices, $\mathbf{G}$ and $\mathbf{Q}$ are Hermitian, and $X$ is an unknown matrix of the same size, and develops two approaches for enclosing the united stable solution set of this interval equation. We first discuss the united stable solution set and then derive a nonlinear programming method in order to find an enclosure for the united stable solution set. We also advance an efficient technique for enclosing the united stable solution …
Modified Objective Function Approach For Multitime Variational Problems,
2018
TÜBİTAK
Modified Objective Function Approach For Multitime Variational Problems, Anurag Jayswal, Tadeusz Antczak, Shalini Jha
Turkish Journal of Mathematics
The present paper is devoted to studying the modified objective function approach used for solving the considered multitime variational problem. In this method, a new multitime variational problem is constructed by modifying the objective function in the original considered multitime variational problem. Further, the equivalence between an optimal solution to the original multitime variational problem and its associated modified problem is established under both hypotheses of invexity and generalized invexity defined for a multitime functional. Thereafter, using the modified objective function method, we derive the saddle-point results for the considered multitime variational problem. Moreover, we provide some examples to illustrate …
Fedja's Proof Of Deepti's Inequality,
2018
TÜBİTAK
Fedja's Proof Of Deepti's Inequality, Sofiya Ostrovska, Mehmet Turan
Turkish Journal of Mathematics
The paper aims to present, in a systematic way, an elegant proof of Deepti's inequality. Both the inequality and various ideas concerning the issue were discussed on the Mathoverflow website by a number of users, but none have appeared in the literature thus far. In this work, suggestions pertaining to users 'Deepti' and 'fedja' are traced, whence the title. The results or the paper are new, and the proof is divided into a series of statements, many of which are of interest in themselves.
Vertex Covers In Graphs With Loops,
2018
TÜBİTAK
Vertex Covers In Graphs With Loops, Maurizio Imbesi, Monica La Barbiera
Turkish Journal of Mathematics
We investigate ideals of vertex covers for the edge ideals associated to considerable classes of connected graphs with loops and exhibit algebraic information about them, such as the existence of linear quotients, the computation of invariant values, and the Cohen-Macaulay property. These algebraic procedures are good instruments for evaluating situations of minimal node coverings in networks.
On Spacelike Rectifying Slant Helices In Minkowski 3-Space,
2018
TÜBİTAK
On Spacelike Rectifying Slant Helices In Minkowski 3-Space, Bülent Altunkaya, Levent Kula
Turkish Journal of Mathematics
In this paper, we study the position vector of a spacelike rectifying slant helix with non-lightlike principal normal vector field in $E_1^3$. First we find the general equations of the curvature and the torsion of spacelike rectifying slant helices. After that, we construct second-order linear differential equations. By their solutions, we determine families of spacelike rectifying slant helices that lie on cones.
