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Uncountably Many Nonoscillatory Bounded Solutions To Second-Order Nonlinear Neutral Dynamic Equations, Magdalena Nockowska Rosiak
Uncountably Many Nonoscillatory Bounded Solutions To Second-Order Nonlinear Neutral Dynamic Equations, Magdalena Nockowska Rosiak
Turkish Journal of Mathematics
This work is devoted to the study of the existence of uncountably many nonoscillatory bounded solutions to second-order nonlinear neutral dynamic equations by means of the Darbo fixed point theorem. We construct assumptions without sign conditions on the nonlinear part of the equation. Moreover, we prove the necessary condition for the existence of an asymptotically zero solution to the problem under consideration.
Companion Sequences Associated To The$R$-Fibonacci Sequence: Algebraic And Combinatorial Properties, Sadjia Abbad, Hacene Belbachir, Benali Benzaghou
Companion Sequences Associated To The$R$-Fibonacci Sequence: Algebraic And Combinatorial Properties, Sadjia Abbad, Hacene Belbachir, Benali Benzaghou
Turkish Journal of Mathematics
It is well known that the companion sequence of the Fibonacci sequence is Lucas's sequence. For the generalized Fibonacci sequences, the companion sequence is not unique. Several authors proposed different definitions, and they are in a certain sense all good. Our purpose is to introduce a family of companion sequences for some generalized Fibonacci sequence: the $r$-Fibonacci sequence. We evaluate the generating functions and give some applications, and we exhibit convolution relations that generalize some known identities such as Cassini's. Afterwards, we calculate the sums of their terms using matrix methods. Next, we propose a $q$-analogue and extend the definition …
Nonnegative Integer Solutions Of The Equation $F_{N}-F_{M}=5^{A}$, Fati̇h Erduvan, Refi̇k Keski̇n
Nonnegative Integer Solutions Of The Equation $F_{N}-F_{M}=5^{A}$, Fati̇h Erduvan, Refi̇k Keski̇n
Turkish Journal of Mathematics
In this study, we solve the Diophantine equation in the title in nonnegative integers $m,n,$ and $a$. The solutions are given by $F_{1}-F_{0}=F_{2}-F_{0}=F_{3}-F_{2}=F_{3}-F_{1}=F_{4}-F_{3}=5^{0}$ and $F_{5}-F_{0}=F_{6}-F_{4}=F_{7}-F_{6}=5.$ Then we give a conjecture that says that if $a\geq 2$ and $p>7$ is prime, then the equation $F_{n}-F_{m}=p^{a}$ has no solutions in nonnegative integers $m,n.$
On Wiener's Tauberian Theorems And Convolution For Oscillatory Integral Operators, Luis Pinheiro De Castro, Rita Correia Guerra, Nguyen Minh Tuan
On Wiener's Tauberian Theorems And Convolution For Oscillatory Integral Operators, Luis Pinheiro De Castro, Rita Correia Guerra, Nguyen Minh Tuan
Turkish Journal of Mathematics
The main aim of this work is to obtain Paley--Wiener and Wiener's Tauberian results associated with an oscillatory integral operator, which depends on cosine and sine kernels, as well as to introduce a consequent new convolution. Additionally, a new Young-type inequality for the obtained convolution is proven, and a new Wiener-type algebra is also associated with this convolution.
A New Solution Of Pair Matrix Equations With Arbitrary Triangular Fuzzy Numbers, Wan Suhana Wan Daud, Nazihah Ahmad, Ghassan Malkawi
A New Solution Of Pair Matrix Equations With Arbitrary Triangular Fuzzy Numbers, Wan Suhana Wan Daud, Nazihah Ahmad, Ghassan Malkawi
Turkish Journal of Mathematics
Pair matrix equations have numerous applications in control system engineering, such as for stability analysis of linear control systems and also for reduction of nonlinear control system models. There are some situations in which the classical pair matrix equations are not well equipped to deal with the uncertainty problem during the process of stability analysis and reduction in control system engineering. Thus, this study presents a new algorithm for solving fully fuzzy pair matrix equations where the parameters of the equations are arbitrary triangular fuzzy numbers. The fuzzy Kronecker product and fuzzy $Vec$-operator are employed to transform the fully fuzzy …
Multiplication Alteration By Two-Cocycles For Bialgebras With Weak Antipode, Jose Nicanor Alonso, José Manuel Fernandez Vilaboa, Ramon Gonzalez Rodriguez
Multiplication Alteration By Two-Cocycles For Bialgebras With Weak Antipode, Jose Nicanor Alonso, José Manuel Fernandez Vilaboa, Ramon Gonzalez Rodriguez
Turkish Journal of Mathematics
In this paper we introduce the theory of multiplication alteration by two-cocycles for bialgebras with weak antipode. Moreover, by the connection between two-cocycles and invertible skew pairings, we show that a special case of the double cross product of these bialgebras can be obtained as a deformation of a bialgebra with weak antipode.
A Fully Hadamard And Erdelyi-Kober-Type Integral Boundary Value Problem Of Acoupled System Of Implicit Differential Equations, Fatima Zohra Berrabah, Benaouda Hedia, Johnny Henderson
A Fully Hadamard And Erdelyi-Kober-Type Integral Boundary Value Problem Of Acoupled System Of Implicit Differential Equations, Fatima Zohra Berrabah, Benaouda Hedia, Johnny Henderson
Turkish Journal of Mathematics
In this article, we give sufficient conditions for the existence of solutions for a new coupled system of second-order implicit differential equations with Hadamard and Erdelyi-Kober fractional integral boundary conditions and nonlocal conditions at the boundaries in Banach space. The main result is based on a Mönch fixed point theorem combined with the measure of noncompactness of Kuratowski; an example is given to illustrate our approach.
On An Elliptic Boundary Value Problem With Critical Exponent, Khadijah Sharaf
On An Elliptic Boundary Value Problem With Critical Exponent, Khadijah Sharaf
Turkish Journal of Mathematics
We study a nonlinear critical second-order PDE with zero Dirichlet boundary condition. We prove existence and compactness results for the equation by using Bahri's method of critical points at infinity.
On The Cohen-Macaulayness Of Tangent Cones Of Monomial Curves In $\Mathbb{A}^{4}(K)$, Sefa Feza Arslan, Anargyros Katsampekis, Meli̇ssa Nalbandi̇yan
On The Cohen-Macaulayness Of Tangent Cones Of Monomial Curves In $\Mathbb{A}^{4}(K)$, Sefa Feza Arslan, Anargyros Katsampekis, Meli̇ssa Nalbandi̇yan
Turkish Journal of Mathematics
In this paper we give necessary and sufficient conditions for the Cohen-Macaulayness of the tangent cone of a monomial curve in 4-dimensional affine space. We particularly study the case where $C$ is a Gorenstein noncomplete intersection monomial curve and we generalize some results in the literature. Moreover, by using these results, we construct families supporting Rossi's conjecture, which is still open for monomial curves in 4-dimensional affine space.
Generalized Helices In Three-Dimensional Lie Groups, Alexander Yampolsky, Anastasiya Opariy
Generalized Helices In Three-Dimensional Lie Groups, Alexander Yampolsky, Anastasiya Opariy
Turkish Journal of Mathematics
We introduce three types of helices in three-dimensional Lie groups with left-invariant metric and give their geometrical description similar to that of Lancret. We generalize the results known for the case of three-dimensional Lie groups with bi-invariant metric.
On Expansions Of Prime And 2-Absorbing Hyperideals In Multiplicative Hyperrings, Gülşen Ulucak
On Expansions Of Prime And 2-Absorbing Hyperideals In Multiplicative Hyperrings, Gülşen Ulucak
Turkish Journal of Mathematics
In this paper, we study $ \delta $-primary and 2-absorbing $ \delta $-primary hyperideals which are the extended classes of prime and 2-absorbing hyperideals, respectively. Assume that $R$ is a commutative multiplicative hyperring with nonzero identity. We call $ I \in \mathcal{I*(R)}$ a $\delta $-primary hyperideal if $a,b\in R$ and $a\circ b\subseteq I$ imply either $a\in I$ or $b\in \delta (I)$ and also, $ I $ is called 2-absorbing $\delta $-primary hyperideal if $a,b,c\in R $ and $a\circ b\circ c \subseteq I$ imply $a\circ b\subseteq I$ or $b\circ c\subseteq \delta (I)$ or $a\circ c\subseteq \delta (I)$. Moreover, we give the …
Convolutionproperties For A Family Of Analytic Functions Involving $Q$-Analogue Ofruscheweyh Differential Operator, Khurshid Ahmad, Muhammad Arif, Jin Lin Liu
Convolutionproperties For A Family Of Analytic Functions Involving $Q$-Analogue Ofruscheweyh Differential Operator, Khurshid Ahmad, Muhammad Arif, Jin Lin Liu
Turkish Journal of Mathematics
The main object of the present paper is to investigate convolution properties for a new subfamily of analytic functions that are defined by $q$ -analogue of Ruscheweyh differential operator. Several consequences of the main results are also given.
The Frequency Function And Its Connections To The Lebesgue Points And The Hardy-Littlewood Maximal Function, Faruk Temur
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., Abdurrahman Muhammed Uludağ, Hakan Ayral
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, Gary Walls
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, Rahim Kargar, Lucyna Trojnar Spelina
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, Edoardo Ballico
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, Zahra Bahrami, Bijan Taeri
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, Ebru Yi̇ği̇t, Gonca Ayik, Hayrullah Ayik
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, Ayhan Aydin
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, Elvan Akin, Taher S. Hassan, Özkan Öztürk, İsmai̇l Uğur Ti̇ryaki̇
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, Oktay Veli̇ev
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, Pedro A. Garcia-Sanchez, Ignacio Ojeda
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, Ali Madanshekaf, Zeinab Kanjanzadeh
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, Niovi Kehayopulu
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, Hafiz Syed Husain, Mariam Sultana
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, Ahmad Mugbil Ahmad, Nasser Eddine Tatar
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, Ni̇hal Özgür
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, Martyn Russell Dixon, Leonid Andreevich Kurdachenko, Igor Yakov Subbotin
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.