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On The Growth Of Meromorphic Solutions Of Some Higher Order Linear Differential Equations, Farid Mesbout, Tahar Zerzaihi
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, Kerem Uğurlu
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, Başak Karpuz
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, Selma Altinok Bhupal, Mohan Lal Bhupal
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, Zohra Sabrina Delhoum, Sonia Radjef, Fatima Boudaoud
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, Bi̇lender Paşaoğlu Allahverdi̇ev, Hüseyi̇n Tuna
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
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, Anurag Jayswal, Tadeusz Antczak, Shalini Jha
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, Sofiya Ostrovska, Mehmet Turan
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, Maurizio Imbesi, Monica La Barbiera
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, Bülent Altunkaya, Levent Kula
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.
Co-Maximal Signed Graphs Of Commutative Rings, Deepa Sinha, Anita Kumari Rao
Co-Maximal Signed Graphs Of Commutative Rings, Deepa Sinha, Anita Kumari Rao
Turkish Journal of Mathematics
Let $ \Gamma(R)$ be a graph with element of $R$ (finite commutative ring with unity) as vertices, where two vertices $a$ and $b$ are adjacent if and only if $Ra+Rb = R$. In this paper, we characterize the rings for which a co-maximal meet signed graph $ \Gamma_{\Sigma}(R)$, a co-maximal join signed graph $ \Gamma_{\Sigma}^{\vee}(R)$, a co-maximal ring sum signed graph $ \Gamma_{\Sigma}^{\oplus}(R)$, their negation signed graphs $ \eta(\Gamma_{\Sigma}(R))$, $ \eta(\Gamma_{\Sigma}^{\vee}(R))$, $ \eta(\Gamma_{\Sigma}^{\oplus}(R))$ respectively and their line signed graphs are balanced, clusterable, and sign-compatible.
Some Series Involving The Euler Zeta Function, Min-Soo Kim
Some Series Involving The Euler Zeta Function, Min-Soo Kim
Turkish Journal of Mathematics
In this paper, using the Boole summation formula, we obtain a new integral representation of $n$-th quasi-periodic Euler functions $\overline{E}_n(x)$ for $n=1,2,\ldots.$ We also prove several series involving Euler zeta functions $\zeta_{E}(s),$ which are analogues of the corresponding results by Apostol on some series involving the Riemann zeta function $\zeta(s).$
Just Non-Artinian Modules Over Some Group Rings, Leonid A. Kurdachenko, Marco Trombetti
Just Non-Artinian Modules Over Some Group Rings, Leonid A. Kurdachenko, Marco Trombetti
Turkish Journal of Mathematics
Let $D$ be a Dedekind domain and $G$ be a periodic Abelian-by-finite group. In this paper we study $DG$-modules in which every factor-module, apart from the trivial one, is $DG$-Artinian. In particular we prove that such modules cannot be $D$-periodic and that $G$ must be subject to some restrictions. Finally, we give a detailed description of such modules when $G$ is periodic Abelian and the spectrum of $D$ is infinite.
Quasi-Proper Efficiency: A Quantitative Enhanced Efficiency, Latif Pourkarimi, Masoud Karimi
Quasi-Proper Efficiency: A Quantitative Enhanced Efficiency, Latif Pourkarimi, Masoud Karimi
Turkish Journal of Mathematics
This paper deals with an extension of proper efficiency that considers bounded and unbounded trade-offs between objective functions. While trade-offs between objective functions are unbounded, the rate of growth for these trade-offs is computed by applying a metric. A new concept, namely quasi-proper efficiency is introduced that shows that rate of growth of trade-off between objective functions. Two appropriate characterizations for this concept are developed: the first one is based on a scalar function utilizing the Chebyshev norm and the second one is in terms of the concept of stability.
A Study On (Strong) Order-Congruences In Ordered Semihypergroups, Jian Tang, Yanfeng Luo, Xiangyun Xie
A Study On (Strong) Order-Congruences In Ordered Semihypergroups, Jian Tang, Yanfeng Luo, Xiangyun Xie
Turkish Journal of Mathematics
In this paper, we introduce the concepts of order-congruences and strong order-congruences on an ordered semihypergroup $S,$ and obtain the relationship between strong order-congruences and pseudoorders on $S.$ Furthermore, we characterize the (strong) order-congruences by the $\rho$-chains, where $\rho$ is a (strong) congruence on $S.$ Moreover, we give a method of constructing order-congruences, and prove that every hyperideal $I$ of an ordered semihypergroup $S$ is congruence class of one order-congruence on $S$ if and only if $I$ is convex. Finally, we define and study the strong order-congruence generated by a strong congruence. As an application of the results of this …
More On Sequential Order Of Compact Scattered Spaces, Alan Dow, Seçi̇l Tokgöz
More On Sequential Order Of Compact Scattered Spaces, Alan Dow, Seçi̇l Tokgöz
Turkish Journal of Mathematics
The proper forcing axiom is shown to imply that a compact scattered sequential space with scattering height at most $\omega_1$ must have sequential order at most $\omega$.
On The Solutions Of A Fractional Boundary Value Problem, Eki̇n Uğurlu, Dumitru Baleanu, Kenan Taş
On The Solutions Of A Fractional Boundary Value Problem, Eki̇n Uğurlu, Dumitru Baleanu, Kenan Taş
Turkish Journal of Mathematics
This paper is devoted to showing the existence and uniqueness of solution of a regular second-order nonlinear fractional differential equation subject to the ordinary boundary conditions. The Banach fixed point theorem is used to prove the results.
On Hypersurfaces With Parallel Möbius Form Andconstant Para-Blaschke Eigenvalues, Shujie Zhai, Xiuli Guo, Zejun Hu
On Hypersurfaces With Parallel Möbius Form Andconstant Para-Blaschke Eigenvalues, Shujie Zhai, Xiuli Guo, Zejun Hu
Turkish Journal of Mathematics
In this paper, we classify umbilic-free hypersurfaces of the unit sphere that have constant para-Blaschke eigenvalues and possess parallel Möbius form. To achieve the classification, we first of all show that, under the condition of having constant para-Blaschke eigenvalues, an umbilic-free hypersurface of the unit sphere is of parallel Möbius form if and only if its Möbius form vanishes identically.
Analysis Of Mixed-Order Caputo Fractional System With Nonlocal Integral Boundary Condition, Tuğba Akman Yildiz, Neda Khodabakhshi, Dumitru Baleanu
Analysis Of Mixed-Order Caputo Fractional System With Nonlocal Integral Boundary Condition, Tuğba Akman Yildiz, Neda Khodabakhshi, Dumitru Baleanu
Turkish Journal of Mathematics
This paper deals with a mixed-order Caputo fractional system with nonlocal integral boundary conditions. This study can be considered as an extension of previous studies, since the orders of the equations lie on different intervals. We discuss the existence and uniqueness of the solution using fixed point methods. We enrich the study with an example.
Gröbner-Shirshov Basis For The Singular Part Of The Brauer Semigroup, Firat Ateş, Ahmet Si̇nan Çevi̇k, Eylem Güzel Karpuz
Gröbner-Shirshov Basis For The Singular Part Of The Brauer Semigroup, Firat Ateş, Ahmet Si̇nan Çevi̇k, Eylem Güzel Karpuz
Turkish Journal of Mathematics
In this paper, we obtain a Gröbner-Shirshov (noncommutative Gröbner) basis for the singular part of the Brauer semigroup. It gives an algorithm for getting normal forms and hence an algorithm for solving the word problem in these semigroups.
On The Local Superconvergence Of The Fully Discretized Multiprojection Method For Weakly Singular Volterra Integral Equations Of The Second Kind, Hossein Beyrami, Taher Lotfi
On The Local Superconvergence Of The Fully Discretized Multiprojection Method For Weakly Singular Volterra Integral Equations Of The Second Kind, Hossein Beyrami, Taher Lotfi
Turkish Journal of Mathematics
In this paper, we extend the well-known multiprojection method for solving the second kind of weakly singular Volterra integral equations. We apply this method based on the collocation projection and develop a fully discretized version using appropriate quadrature rules. This method has a superconvergence property that the classic collocation method lacks. Although the new approach results in a significant increase in computational cost, when performing the related matrix-matrix products in parallel the computational time can be reduced. We provide a rigorous mathematical discussion about error analysis of this method. Finally, we present some numerical examples to confirm our theoretical results.
Conformable Fractional Sturm-Liouville Equation And Some Existenceresults On Time Scales, Tüba Gülşen, Emrah Yilmaz, Hi̇kmet Kemaloğlu
Conformable Fractional Sturm-Liouville Equation And Some Existenceresults On Time Scales, Tüba Gülşen, Emrah Yilmaz, Hi̇kmet Kemaloğlu
Turkish Journal of Mathematics
In this study, we analyze a conformable fractional (CF) Sturm-Liouville (SL) equation with boundary conditions on an arbitrary time scale $\mathbb{T}$. Then we extend the basic spectral properties of the classical SL equation to the CF case. Finally, some sufficient conditions are established to guarantee the existence of a solution for this CF-SL problem on $\mathbb{T}$ by using certain fixed point theorems. For explaining these existence theorems, we give an example with appropriate choices.
On Strongly Autinertial Groups, Cansu Beti̇n Onur
On Strongly Autinertial Groups, Cansu Beti̇n Onur
Turkish Journal of Mathematics
A subgroup $ X $ of $ G $ is said to be inert under automorphisms (autinert) if $ X : X^\alpha \cap X $ is finite for all $ \alpha \in Aut(G)$ and it is called strongly autinert if $ :X $ is finite for all $ \alpha \in Aut(G).$ A group is called strongly autinertial if all subgroups are strongly autinert. In this article, the strongly autinertial groups are studied. We characterize such groups for a finitely generated case. Namely, we prove that a finitely generated group $ G $ is strongly autinertial if and only if one …
Differential Subordination And Radius Estimates For Starlike Functions Associated With The Booth Lemniscate, Nak Eun Cho, Sushil Kumar, Virendra Kumar, V. Ravichandran
Differential Subordination And Radius Estimates For Starlike Functions Associated With The Booth Lemniscate, Nak Eun Cho, Sushil Kumar, Virendra Kumar, V. Ravichandran
Turkish Journal of Mathematics
We obtain several inclusions between the class of functions with positive real part and the class of starlike univalent functions associated with the Booth lemniscate. These results are proved by applying the well-known theory of differential subordination developed by Miller and Mocanu and these inclusions give sufficient conditions for normalized analytic functions to belong to some subclasses of Ma-Minda starlike functions. In addition, by proving an associated technical lemma, we compute various radii constants such as the radius of starlikeness, radius of convexity, radius of starlikeness associated with the lemniscate of Bernoulli, and other radius estimates for functions in the …
Modules Whose $P$-Submodules Are Direct Summands, Yeli̇z Kara
Modules Whose $P$-Submodules Are Direct Summands, Yeli̇z Kara
Turkish Journal of Mathematics
In this article we deal with modules with the property that all $p$-submodules are direct summands. In contrast to $CLS$-modules, it is shown that the former property is closed under finite direct sums, but it is not inherited by direct summands. Hence we focus on when the direct summands of aforementioned modules enjoy the property. Moreover, we characterize the forenamed class of modules in terms of lifting homomorphisms.
Integral Laminations On Nonorientable Surfaces, S. Öykü Yurttaş, Mehmetci̇k Pamuk
Integral Laminations On Nonorientable Surfaces, S. Öykü Yurttaş, Mehmetci̇k Pamuk
Turkish Journal of Mathematics
We describe triangle coordinates for integral laminations on a nonorientable surface $N_{k,n}$ of genus $k$ with $n$ punctures and one boundary component, and we give an explicit bijection from the set of integral laminations on $N_{k,n}$ to $(\mathbb{Z}^{2(n+k-2)}\times \mathbb{Z}^k)\setminus \left\{0\right\}$.
Nonstandard Hulls Of Lattice-Normed Ordered Vector Spaces, Abdullah Aydin, Svetlana Gorokhova, Hasan Gül
Nonstandard Hulls Of Lattice-Normed Ordered Vector Spaces, Abdullah Aydin, Svetlana Gorokhova, Hasan Gül
Turkish Journal of Mathematics
Nonstandard hulls of a vector lattice were introduced and studied in many papers. Recently, these notions were extended to ordered vector spaces. In the present paper, following the construction of associated Banach--Kantorovich space due to Emelyanov, we describe and investigate the nonstandard hull of a lattice-normed space, which is the foregoing generalization of Luxemburg's nonstandard hull of a normed space.
The Brezis-Lieb Lemma In Convergence Vector Lattices, Mohammad Marabeh
The Brezis-Lieb Lemma In Convergence Vector Lattices, Mohammad Marabeh
Turkish Journal of Mathematics
Recently measure-free versions of the Brezis-Lieb lemma were proved for unbounded order convergence in vector lattices. In this article, we extend these versions to convergence vector lattices.
Multiplier And Approximation Theorems In Smirnov Classes Withvariable Exponent, Daniyal Israfilzade, Ahmet Testici
Multiplier And Approximation Theorems In Smirnov Classes Withvariable Exponent, Daniyal Israfilzade, Ahmet Testici
Turkish Journal of Mathematics
Let $G\subset \mathbb{C}$ be a bounded Jordan domain with a rectifiable Dini-smooth boundary $\Gamma $ and let $G^{-}:=ext~ \Gamma $. In terms of the higher order modulus of smoothness the direct and inverse problems of approximation theory in the variable exponent Smirnov classes $E^{p(\cdot )}(G)$ and $E^{p(\cdot )}(G^{-})$ \ are investigated. Moreover, the Marcinkiewicz and Littlewood-Paley type theorems are proved. As a corollary some results on the constructive characterization problems in the generalized Lipschitz classes are presented.