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Articles 151 - 180 of 2494
Full-Text Articles in Physical Sciences and Mathematics
On The Geometry Of Nearly Trans-Sasakian Manifolds, Aligadzhi R. Rustanov, Tatiana L. Melekhina, Svetlana V. Kharitonova
On The Geometry Of Nearly Trans-Sasakian Manifolds, Aligadzhi R. Rustanov, Tatiana L. Melekhina, Svetlana V. Kharitonova
Turkish Journal of Mathematics
The geometry of nearly trans-Sasakian manifolds is researched in this paper. The complete group of structural equations and the components of the Lee vector on the space of the associated $G$-structure are obtained for such manifolds. Conditions are found under which a nearly trans-Sasakian structure is a trans-Sasakian, a cosymplectic, a closely cosymplectic, a Sasakian structure or a Kenmotsu structure. The conditions are obtained when the nearly trans-Sasakian structure is a special generalized Kenmotsu structure of the second kind. A complete classification of nearly trans-Sasakian manifolds is obtained, i.e. it is proved that a nearly trans-Sasakian manifold is either a …
A Generalization Of The Notion Of Helix, Pascual Lucas, Jose Antonio Ortega-Yagues
A Generalization Of The Notion Of Helix, Pascual Lucas, Jose Antonio Ortega-Yagues
Turkish Journal of Mathematics
In this paper we generalize the notion of helix in the three-dimensional Euclidean space, which we define as that curve $\alpha$ for which there is an $F$-constant vector field $W$ along $\alpha$ that forms a constant angle with a fixed direction $V$ (called an axis of the helix). We find the natural equation and the geometric integration of helices $\alpha$ where the $F$-constant vector field $W$ is orthogonal to its axis.
Polynomials Taking Integer Values On Primes In A Function Field, Tuangrat Chaichana, Vichian Laohakosol, Rattiya Meesa, Boonrod Yuttanan
Polynomials Taking Integer Values On Primes In A Function Field, Tuangrat Chaichana, Vichian Laohakosol, Rattiya Meesa, Boonrod Yuttanan
Turkish Journal of Mathematics
Let $\mathbb{F}_q[x]$ be the ring of polynomials over a finite field $\mathbb{F}_q$ and $\mathbb{F}_q(x)$ its quotient field. Let $\mathbb{P}$ be the set of primes in $\mathbb{F}_q[x]$, and let $\mathcal{I}$ be the set of all polynomials $f$ over $\mathbb{F}_q(x)$ for which $f(\mathbb{P})\subseteq\mathbb{F}_q[x]$. The existence of a basis for $\mathcal{I}$ is established using the notion of characteristic ideal; this shows that $\mathcal{I}$ is a free $\mathbb{F}_q[x]$-module. Through localization, explicit shapes of certain bases for the localization of $\mathcal{I}$ are derived, and a well-known procedure is described as to how to obtain explicit forms of some bases of $\mathcal{I}$.
Twisted Dirac Operators And The Kastler-Kalau-Walze Type Theorem For Five Dimensional Manifolds With Boundary, Tong Wu, Sining Wei, Yong Wang
Twisted Dirac Operators And The Kastler-Kalau-Walze Type Theorem For Five Dimensional Manifolds With Boundary, Tong Wu, Sining Wei, Yong Wang
Turkish Journal of Mathematics
In this paper, we prove the Kastler-Kalau-Walze type theorems for twisted Dirac operators on 5-dimensional manifolds with boundary.
On The Relation Between Oscillation Of Solutions Of Differential Equations And Corresponding Equations On Time Scales, Olexandr Stanzhytskyi, Roza Uteshova, Victoriia Tsan, Zoia Khaletska
On The Relation Between Oscillation Of Solutions Of Differential Equations And Corresponding Equations On Time Scales, Olexandr Stanzhytskyi, Roza Uteshova, Victoriia Tsan, Zoia Khaletska
Turkish Journal of Mathematics
This paper studies oscillatory properties of solutions of a dynamic equation on the set of time scales $\mathbf{T}_\lambda$ provided that the graininess function $\mu_\lambda$ approaches zero as $\lambda\to 0$. We derived the conditions under which oscillation of solutions of differential equations implies that of solutions of the corresponding equations defined on time scales with the same initial data, and vice versa.
Qualitative Study Of A Second Order Difference Equation, Messaoud Berkal, Juan Francisco Navarro
Qualitative Study Of A Second Order Difference Equation, Messaoud Berkal, Juan Francisco Navarro
Turkish Journal of Mathematics
In this paper, we study a second order rational difference equation. We analyze the stability of the unique positive equilibrium of the equation and prove the existence of a Neimark-Sacker bifurcation, validating our theoretical analysis via a numerical exploration of the system.
On Max-Min Solutions Of Fuzzy Games With Nonlinear Memberships Functions, Adem Cengi̇z Çevi̇kel
On Max-Min Solutions Of Fuzzy Games With Nonlinear Memberships Functions, Adem Cengi̇z Çevi̇kel
Turkish Journal of Mathematics
In this paper, we deal with two-person zero-sum games with fuzzy goals. We investigated the cases where the membership functions of the players are nonlinear. We examined how the solutions should be if the membership functions of players were exponential functions. In case players' membership functions are exponential, we developed a new method for the maximin solution according to a degree of attainment of the fuzzy goals. An application was made to show the effectiveness of the method.
On Conditions Of Regular Solvability For Two Classes Of Third-Order Operator-Differential Equations In A Fourth-Order Sobolev-Type Space, Araz R. Aliev, Nazila L. Muradova
On Conditions Of Regular Solvability For Two Classes Of Third-Order Operator-Differential Equations In A Fourth-Order Sobolev-Type Space, Araz R. Aliev, Nazila L. Muradova
Turkish Journal of Mathematics
In this paper, we study two classes of operator-differential equations of the third order with a multiple characteristic, considered on the whole axis. We introduce the concept of a smooth regular solution of order 1 and obtain sufficient conditions for the "smoothly" regular solvability of these equations.
Geodesics And Natural Complex Magnetic Trajectories On Tangent Bundles, Mohamed Tahar Kadaoui Abbassi, Noura Amri
Geodesics And Natural Complex Magnetic Trajectories On Tangent Bundles, Mohamed Tahar Kadaoui Abbassi, Noura Amri
Turkish Journal of Mathematics
In this paper, we investigate geodesics of the tangent bundle $TM$ of a Riemannian manifold $(M,g)$ endowed with an arbitrary pseudo-Riemannian $g$-natural metric of Kaluza-Klein type. Then considering a class of naturally defined almost complex structures on $TM$, constructed by V. Oproiu, we construct a class of magnetic fields and we characterize the corresponding magnetic curves on $TM$, when $(M,g)$ is a space form.
Curves And Stick Figures Not Contained In A Hypersurface Of A Given Degree, Edoardo Ballico
Curves And Stick Figures Not Contained In A Hypersurface Of A Given Degree, Edoardo Ballico
Turkish Journal of Mathematics
A stick figure $X\subset \mathbb{P}^r$ is a nodal curve whose irreducible components are lines. For fixed integers $r\ge 3$, $s\ge 2$ and $d$ we study the maximal arithmetic genus of a connected stick figure (or any reduced and connected curve) $X\subset \mathbb{P}^r$ such that $\deg (X)=d$ and $h^0(\mathcal{I}_X(s-1))=0$. We consider Halphen's problem of obtaining all arithmetic genera below the maximal one.
Novel Fano Type Lower Bounds On The Minimum Error Probability Of List $M$-Ary Hypothesis Testing, Berkan Dülek
Novel Fano Type Lower Bounds On The Minimum Error Probability Of List $M$-Ary Hypothesis Testing, Berkan Dülek
Turkish Journal of Mathematics
he problem of list $M$-ary hypothesis testing with fixed list size $L< M$ is considered. Based on some random observation, the test outputs a list of $L$ candidates out of $M$ possible hypotheses. The probability of list error is defined as the probability of the event that the list output by the test does not contain the true hypothesis that has generated the observation. An identity is derived that relates the minimum average probability of error of the optimal list hypothesis test to the minimum average probability of error of an optimal maximum a posteriori probability decision rule. The latter decides among an alternative set of hypotheses corresponding to all possible $L$-component mixtures of the distributions that characterize the observation under the original $M$ candidate hypotheses. As an application, the proposed identity is employed to obtain novel Fano type lower bounds on the minimum error probability of list $M$-ary hypothesis testing.
On The Hilbert Series Of The Tangent Cones For Some 4-Generated Pseudosymmetric Monomial Curves, Ni̇l Şahi̇n
On The Hilbert Series Of The Tangent Cones For Some 4-Generated Pseudosymmetric Monomial Curves, Ni̇l Şahi̇n
Turkish Journal of Mathematics
In this article, we study Hilbert series of non-Cohen-Maculay tangent cones for some 4-generated pseudosymmetric monomial curves. We show that the Hilbert function is nondecreasing by explicitly computing it. We also compute standard bases of these toric ideals.
Scattering Solutions And Scattering Function Of A Klein-Gordon S-Wave Equation With Jump Conditions, Hali̇t Taş, Yelda Aygar Küçükevci̇li̇oğlu, Elgi̇z Bayram
Scattering Solutions And Scattering Function Of A Klein-Gordon S-Wave Equation With Jump Conditions, Hali̇t Taş, Yelda Aygar Küçükevci̇li̇oğlu, Elgi̇z Bayram
Turkish Journal of Mathematics
In this work, we are interested in a boundary value problem (BVP) generated by a Klein -Gordon equation (KG) with Jump conditions and a boundary condition. First, we introduce scattering solutions and Jost solution of the problem. Then, we give the scattering function and we prove some properties of it. Lastly, we conclude the paper by a special example.
Metrical Almost Periodicity, Metrical Approximations Of Functions And Applications, Belkacem Chaouchi, Marko Kostic, Daniel Velinov
Metrical Almost Periodicity, Metrical Approximations Of Functions And Applications, Belkacem Chaouchi, Marko Kostic, Daniel Velinov
Turkish Journal of Mathematics
In this paper, we analyze Levitan and Bebutov metrical approximations of functions $F :\Lambda \times X \rightarrow Y$ by trigonometric polynomials and $\rho$-periodic type functions, where $\emptyset \neq \Lambda \subseteq {\mathbb R}^{n}$, $X$ and $Y$ are complex Banach spaces, and $\rho$ is a general binary relation on $Y$. We also analyze various classes of multidimensional Levitan almost periodic functions in general metric and multidimensional Bebutov uniformly recurrent functions in general metric. We provide several applications of our theoretical results to the abstract Volterra integro-differential equations and the partial differential equations.
Clairaut Riemannian Maps, Kiran Meena, Akhilesh Yadav
Clairaut Riemannian Maps, Kiran Meena, Akhilesh Yadav
Turkish Journal of Mathematics
In this paper, first we define Clairaut Riemannian map between Riemannian manifolds by using a geodesic curve on the base space and find necessary and sufficient conditions for a Riemannian map to be Clairaut with a nontrivial example. We also obtain necessary and sufficient condition for a Clairaut Riemannian map to be harmonic. Thereafter, we study Clairaut Riemannian map from Riemannian manifold to Ricci soliton with a nontrivial example. We obtain scalar curvatures of $rangeF_\ast$ and $(rangeF_\ast)^\bot$ by using Ricci soliton. Further, we obtain necessary conditions for the leaves of $rangeF_\ast$ to be almost Ricci soliton and Einstein. We also …
Closure Operators, Irreducibility, Urysohn's Lemma, And Tietze Extension Theorem For Proximity Spaces, Samed Özkan, Muammer Kula, Sümeyye Kula, Tesni̇m Meryem Baran
Closure Operators, Irreducibility, Urysohn's Lemma, And Tietze Extension Theorem For Proximity Spaces, Samed Özkan, Muammer Kula, Sümeyye Kula, Tesni̇m Meryem Baran
Turkish Journal of Mathematics
In this paper, we introduce two notions of closure in the category of proximity spaces which satisfy (weak) hereditariness, productivity, and idempotency, and we characterize each of $T_{i}, i=0,1,2$, proximity spaces by using these closure operators and show how these subcategories are related. Furthermore, we characterize the irreducible proximity spaces and investigate the relationship among each of irreducible, connected and $T_{i}, i=1,2$, proximity spaces. Finally, we present Tietze extension theorem and Urysohn's lemma for proximity spaces.
The Set Of Arf Numerical Semigroups With Given Frobenius Number, María Ángeles Moreno-Frías, Jose Carlos Rosales
The Set Of Arf Numerical Semigroups With Given Frobenius Number, María Ángeles Moreno-Frías, Jose Carlos Rosales
Turkish Journal of Mathematics
A covariety is a nonempty family $C$ of numerical semigroups that satisfies a certain conditions. In this work we will show that if $F$ is a positive integer, then the set of Arf numerical semigroup with Frobenius number $F$, denoted by $(F)$, is a covatiety. The previous results will be used to give an algorithm which calculates the set $(F).$ Also we will see that if $X\subseteq S\backslash \Delta(F)$ for some $S\in (F),$ then there is the smallest element of $(F)$ containing $X.$
Numerical Radius, Berezin Number, And Berezin Norm Inequalities For Sums Of Operators, Najla Altwaijry, Kais Feki, Nicusor Minculete
Numerical Radius, Berezin Number, And Berezin Norm Inequalities For Sums Of Operators, Najla Altwaijry, Kais Feki, Nicusor Minculete
Turkish Journal of Mathematics
The purpose of this article is to explore various inequalities pertaining to the numerical radius of operators in a Hilbert space. Additionally, we present several bounds for the Berezin number and Berezin norm of operators that act on a reproducing kernel Hilbert space. Finally, we establish a necessary and sufficient condition for the triangle inequality related to the Berezin number to hold.
Generalization Of Statistical Limit-Cluster Points And The Concepts Of Statistical Limit Inferior-Superior On Time Scales By Using Regular Integral Transformations, Ceylan Yalçin
Turkish Journal of Mathematics
With the aid of regular integral operators, we will be able to generalize statistical limit-cluster points and statistical limit inferior-superior ideas on time scales in this work. These two topics, which have previously been researched separately from one another sometimes only in the discrete case and other times in the continuous case, will be studied at in a single study. We will investigate the relations of these concepts with each other and come to a number of new conclusions. On some well-known time scales, we shall analyze these ideas using examples.
A Note On $Ss$-Supplement Submodules, Emi̇ne Önal Kir
A Note On $Ss$-Supplement Submodules, Emi̇ne Önal Kir
Turkish Journal of Mathematics
In this paper, we describe $ss$-supplement submodules in terms of a special class of endomorphisms. Let $R$ be a ring with semisimple radical and $P$ be a projective $R-$module. We show that there is a bijection between ss-supplement submodules of $P$ and ss-supplement submodules of $End_{R}(P)$. Moreover, we define radical-s-projective modules as a generalization of projective modules. We prove that every $ss$-supplement submodule of a projective $R-$module is radical-s-projective over the ring $R$ with semisimple radical. We show that over $SSI$-ring $R$, every radical-s-projective $R-$module is projective. We provide that over a ring $R$ with semisimple radical, every $ss$-supplement submodule …
Bi-Periodic Incomplete Horadam Numbers, Eli̇f Tan, Mehmet Dağli, Amine Belkhir
Bi-Periodic Incomplete Horadam Numbers, Eli̇f Tan, Mehmet Dağli, Amine Belkhir
Turkish Journal of Mathematics
In this paper, we introduce bi-periodic~incomplete~Horadam numbers as a natural generalization of incomplete Horadam numbers. We study their basic properties and provide recurrence relations. In particular, we derive the generating function of these numbers.
On Solvability Of Homogeneous Riemann Boundary Value Problems In Hardy-Orlicz Classes, Yusuf Zeren, Fi̇dan A. Ali̇zadeh, Feyza Eli̇f Dal
On Solvability Of Homogeneous Riemann Boundary Value Problems In Hardy-Orlicz Classes, Yusuf Zeren, Fi̇dan A. Ali̇zadeh, Feyza Eli̇f Dal
Turkish Journal of Mathematics
This work deals with the Orlicz space and the Hardy-Orlicz classes generated by this space, which consist of analytic functions inside and outside the unit disk. The homogeneous Riemann boundary value problems with piecewise continuous coefficients are considered in these classes. New characteristic of Orlicz space is defined which depends on whether the power function belongs to this space or not. Relationship between this characteristic and Boyd indices of Orlicz space is established. The concept of canonical solution of homogeneous problem is defined, which depends on the argument of the coefficient. In terms of the above characteristic, a condition on …
Contiguity Distance Between Simplicial Maps, Ayşe Borat, Mehmetci̇k Pamuk, Tane Vergi̇li̇
Contiguity Distance Between Simplicial Maps, Ayşe Borat, Mehmetci̇k Pamuk, Tane Vergi̇li̇
Turkish Journal of Mathematics
For simplicial complexes and simplicial maps, the notion of being in the same contiguity class is defined as the discrete version of homotopy. In this paper, we study the contiguity distance, $SD$, between two simplicial maps adapted from the homotopic distance. In particular, we show that simplicial versions of $LS$-category and topological complexity are particular cases of this more general notion. Moreover, we present the behaviour of $SD$ under the barycentric subdivision, and its relation with strong collapsibility of a simplicial complex.
Boundedness Of Bergman Projections Acting On Weighted Mixed Norm Spaces, Ivana Savkovic
Boundedness Of Bergman Projections Acting On Weighted Mixed Norm Spaces, Ivana Savkovic
Turkish Journal of Mathematics
We prove that Bergman projections on weighted mixed norm spaces on smoothly bounded domains in $\mathbb{R}^n$ are bounded for a certain range of parameters of such spaces and assuming certain conditions on weights. The proof relies on estimates of integral means of $M_p(P_\gamma f, r)$ in terms of integral means of $f$. This result complements earlier result on boundedness of $P_\gamma$ on a closely related space $L^{p,q}_\alpha(\Omega).$
A Calculus For Intuitionistic Fuzzy Values, Enes Yavuz
A Calculus For Intuitionistic Fuzzy Values, Enes Yavuz
Turkish Journal of Mathematics
We introduce $^\oplus$calculus and $^\otimes$calculus for intuitionistic fuzzy values and prove some basic theorems by using multiplicative calculus which has useful tools to represent the concepts of introduced calculi. Besides, we construct some isomorphic mappings to interpret the relationships between $^\oplus$calculus and $^\otimes$calculus. This paper reveals also new calculi for fuzzy sets in particular.
Lyapunov-Type Inequalities For $(\Mathtt{N},\Mathtt{P})$-Type Nonlinear Fractional Boundary Value Problems, Paul W. Eloe, Muralee Bala Krushna Boddu
Lyapunov-Type Inequalities For $(\Mathtt{N},\Mathtt{P})$-Type Nonlinear Fractional Boundary Value Problems, Paul W. Eloe, Muralee Bala Krushna Boddu
Turkish Journal of Mathematics
This paper establishes Lyapunov-type inequalities for a family of two-point $(\mathtt{n},\mathtt{p})$-type boundary value problems for Riemann-Liouville fractional differential equations. To demonstrate how the findings can be applied, we provide a few examples, one of which is a fractional differential equation with delay.
Generating Functions For Reciprocal Catalan-Type Sums: Approach To Linear Differentiation Equation And ($P$-Adic) Integral Equations, Damla Gün, Yilmaz Şi̇mşek
Generating Functions For Reciprocal Catalan-Type Sums: Approach To Linear Differentiation Equation And ($P$-Adic) Integral Equations, Damla Gün, Yilmaz Şi̇mşek
Turkish Journal of Mathematics
This article is inspired by the reciprocal Catalan sums associated with problem 11765, proposed by David Beckwith and Sag Harbor. For this reason, partial derivative equations, the first-order linear differentiation equation and integral representations for series and generating functions for reciprocal Catalan-type sums containing the Catalan-type numbers are constructed. Some special values of these series and generating functions, which are given solutions of problem 11765, are found. Partial derivative equations of the generating function for the Catalan-type numbers are given. By using these equations, recurrence relations and derivative formulas involving these numbers are found. Finally, applying the $p$-adic Volkenborn integral …
On Generalized Darboux Frame Of A Spacelike Curve Lying On A Lightlike Surface In Minkowski Space $\Mathbb{E}^{3}_{1}$, Jelena Djordjevic, Emilija Nesovic, Ufuk Öztürk
On Generalized Darboux Frame Of A Spacelike Curve Lying On A Lightlike Surface In Minkowski Space $\Mathbb{E}^{3}_{1}$, Jelena Djordjevic, Emilija Nesovic, Ufuk Öztürk
Turkish Journal of Mathematics
In this paper we introduce generalized Darboux frame of a spacelike curve $\alpha$ lying on a lightlike surface in Minkowski space $\mathbb{E}_{1}^{3}$. We prove that $\alpha$ has two such frames and obtain generalized Darboux frame's equations. We find the relations between the curvature functions $k_g$, $k_n$, $\tau_g$ of $\alpha$ with respect to its Darboux frame and the curvature functions $\tilde{k}_{g}$, $\tilde{k}_{n}$, $\tilde{\tau}_{g}$ with respect to generalized Darboux frames. We show that such frames exist along a spacelike straight line lying on a ruled surface which is not entirely lightlike, but contains some lightlike points. We define lightlike ruled surfaces on …
Novel Results On Trapezoid-Type Inequalities For Conformable Fractional Integrals, Fati̇h Hezenci̇, Hüseyi̇n Budak
Novel Results On Trapezoid-Type Inequalities For Conformable Fractional Integrals, Fati̇h Hezenci̇, Hüseyi̇n Budak
Turkish Journal of Mathematics
This paper establishes an identity for the case of differentiable $s-$convex functions with respect to the conformable fractional integrals. By using this identity, sundry trapezoid-type inequalities are proven by $s-$convex functions with the help of the conformable fractional integrals. Several important inequalities are acquired with taking advantage of the convexity, the Hölder inequality, and the power mean inequality. Moreover, an example using graph is given in order to show that our main results are correct. By using the special choices of the obtained results, we present several new results connected with trapezoid-type inequalities.
Numerical Solution For Benjamin-Bona-Mahony-Burgers Equation With Strang Time-Splitting Technique, Meli̇ke Karta
Numerical Solution For Benjamin-Bona-Mahony-Burgers Equation With Strang Time-Splitting Technique, Meli̇ke Karta
Turkish Journal of Mathematics
In the present manuscript, the Benjamin-Bona-Mahony-Burgers (BBMB) equation will be handled numerically by Strang time-splitting technique. While applying this technique, collocation method based on quintic B-spline basis functions is applied. In line with our purpose, after splitting the BBM-Burgers equation given with appropriate initial boundary conditions into two subequations containing the derivative in terms of time, the quintic B-spline based collocation finite element method (FEM) for spatial discretization and the suitable finite difference approaches for time discretization is applied to each subequation and hereby two different systems of algebraic equations are obtained. Four test problems are utilized to test the …