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- Oscillation (23)
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Articles 1171 - 1200 of 2494
Full-Text Articles in Physical Sciences and Mathematics
On Biquaternion Algebras With Orthogonal Involution, Amir Hossein Nokhodkar
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.
Existence Of Positive Periodic Solution Of Second-Order Neutral Differential Equations, Tuncay Candan
Existence Of Positive Periodic Solution Of Second-Order Neutral Differential Equations, Tuncay Candan
Turkish Journal of Mathematics
In this work, we consider two types of second-order neutral differential equations and we obtain sufficient conditions for the existence of positive $\om$-periodic solutions for these equations. We employ Krasnoselskii's fixed point theorem for the sum of a completely continuous and a contraction mapping. An example is included to illustrate our results.
Continuous Dependence Of Solutions To The Strongly Damped Nonlinear Klein-Gordon Equation, Şevket Gür, Mesude Eli̇f Uysal
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.
Legendrian Torus Knots In Lens Spaces, Si̇nem Onaran
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, Junichi Aramaki
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.
Nearly Kahler And Nearly Kenmotsu Manifolds, Nikrooz Heidari, Niloufar Hoseein Pour Kashani, Behzad Najafi
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, Takao Komatsu, Laszlo Szalay
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
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 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.
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 …
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.
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.
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.
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.
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 …
Graphs Of $Bci/Bck$-Algebras, Atena Tahmasbpour Meikola
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 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.
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 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 …
The Classification Of Rings With Its Genus Of Class Of Graphs, Thangaraj Asir, Karuppiah Mano
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 …
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.
Gadjieva's Conjecture, $K$-Functionals, And Someapplications In Weighted Lebesgue Spaces, Ramazan Akgün
Gadjieva's Conjecture, $K$-Functionals, And Someapplications In Weighted Lebesgue Spaces, Ramazan Akgün
Turkish Journal of Mathematics
We prove that Gadjieva's conjecture holds true as stated in her PhD thesis. The positive solution of this conjecture allows us to obtain improved versions of the Jackson--Stechkin type inequalities obtained in her thesis and some others. As an application, an equivalence of the modulus of smoothness with the realization functional is established. We obtain a characterization class for the modulus of smoothness.
Remarks On The Zero Toeplitz Product Problem In The Bergman And Hardy Spaces, Mübari̇z Tapdigoğlu Garayev, Mehmet Gürdal
Remarks On The Zero Toeplitz Product Problem In The Bergman And Hardy Spaces, Mübari̇z Tapdigoğlu Garayev, Mehmet Gürdal
Turkish Journal of Mathematics
In this article, we are interested in the zero Toeplitz product problem: for two symbols $f,g\in L^{\infty}\left( \mathbb{D},dA\right) ,$\ if the product $T_{f}T_{g}$\ is identically zero on $L_{a}^{2}\left( \mathbb{D}\right), $\ then can we claim $T_{f}$\ or $T_{g}$\ is identically zero? We give a particular solution of this problem. A new proof of one particular case of the zero Toeplitz product problem in the Hardy space $H^{2}\left( \mathbb{D}% \right) $ is also given.
On Small Covers Over A Product Of Simplices, Murat Altunbulak, Asli Güçlükan İlhan
On Small Covers Over A Product Of Simplices, Murat Altunbulak, Asli Güçlükan İlhan
Turkish Journal of Mathematics
In this paper, we give a formula for the number of $\mathbb{Z}_2^n$-equivariant homeomorphism classes of small covers over a product of simplices. We also give an upper bound for the number of small covers over a product of simplices up to homeomorphism.
On Reflexivity Of The Bochner Space $L^{P}(\Mu, E)$ For Arbitrary $\Mu$, Bahaetti̇n Cengi̇z, Banu Güntürk
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
Neumann Boundary Value Problems In Fan-Shaped Domains, Mohamed Akel, Mona Aldawsari
Neumann Boundary Value Problems In Fan-Shaped Domains, Mohamed Akel, Mona Aldawsari
Turkish Journal of Mathematics
n this article we give the solvability conditions and the integral representations of the solutions of the Neumann boundary value problem for the Cauchy-Riemann operator and the Beltrami operator with constant coefficient in a disc sector with angle $\vartheta=\frac{\pi}{n},\,n\in\mathbb N$. Moreover, the Neumann problem for second-order operators with the Bitsadze/Laplace operator as the main part is studied. Classical results of complex analysis are used to obtain the expressions of the solvability conditions and the integral representations for the solutions explicitly.
On The Type And Generators Of Monomial Curves, Nguyen Thi Dung
On The Type And Generators Of Monomial Curves, Nguyen Thi Dung
Turkish Journal of Mathematics
Let $n_1, n_2,\ldots, n_d$ be positive integers and $H $ be the numerical semigroup generated by $n_1,n_2, \ldots, n_d$. Let $A:=k[H]:=k[t^{n_1}, t^{n_2},\ldots, t^{n_d}]\cong k[x_1,x_2,\ldots,x_d]/I$ be the numerical semigroup ring of $H $ over $k.$ In this paper we give a condition $(*)$ that implies that the minimal number of generators of the defining ideal $I$ is bounded explicitly by its type. As a consequence for semigroups with $d=4$ satisfying the condition $(*)$ we have $\mu ({\rm in}(I))\leq 2(t(H))+1$.
Corrigendum And Addendum To "Modules Whose $P$-Submodules Are Direct Summands", Yeli̇z Kara
Corrigendum And Addendum To "Modules Whose $P$-Submodules Are Direct Summands", Yeli̇z Kara
Turkish Journal of Mathematics
This paper is written to correct the proof of Lemma 2.1$(i)$ in \cite{K} and to add some decomposition results for the class of $PD$-modules defined in \cite{K}.