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Articles 241 - 270 of 2595
Full-Text Articles in Mathematics
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.
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.
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 …
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.
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 …
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 …
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.
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.
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.
Numerical Solutions Of Differential Equations Having Cubic Nonlinearity Using Boole Collocation Method, Kübra Erdem Bi̇çer, Hale Gül Dağ
Numerical Solutions Of Differential Equations Having Cubic Nonlinearity Using Boole Collocation Method, Kübra Erdem Bi̇çer, Hale Gül Dağ
Turkish Journal of Mathematics
The aim of the study is to develop a numerical method for the solution of cubic nonlinear differential equations in which the numerical solution is based on Boole polynomials. That solution is in the form of the truncated series and gives approximate solution for nonlinear equations of cubic type. In this method, firstly, the matrix form of the serial solution is set and the nonlinear differential equation is converted into a matrix equation system. By adding the effect of both the conditions of the problem and the collocation points to this system of equations, we obtain the new system of …
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 …
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 …
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.
Unipotence In Positive Characteristic For Groups Of Finite Morley Rank, Jules Gael Tindzogho Ntsiri
Unipotence In Positive Characteristic For Groups Of Finite Morley Rank, Jules Gael Tindzogho Ntsiri
Turkish Journal of Mathematics
In this article we define a new form of unipotence in groups of finite Morley rank which extends Burdges unipotence to any characteristic. In particular, we show that every connected solvable group of finite Morley rank $G$ has a definable connected subgroup $H$ whose derived subgroup $H'$ is a good unipotent subgroup of finite Morley rank.
Effect Of Fractional Analysis On Some Special Curves, Aykut Has, Beyhan Yilmaz
Effect Of Fractional Analysis On Some Special Curves, Aykut Has, Beyhan Yilmaz
Turkish Journal of Mathematics
In this study, the effect of fractional derivatives, whose application area is increasing day by day, on curves is investigated. As it is known, there are not many studies on a geometric interpretation of fractional calculus. When examining the effect of fractional analysis on a curve, the Caputo fractional analysis that fits the algebraic structure of differential geometry is used. This is because the Caputo fractional derivative of the constant function is zero. This is an important advantage and allows a variety of fractional physical problems to be based on a geometric basis. This effect is examined with the help …
Boundary Value Problem For A Loaded Fractional Diffusion Equation, Arsen V. Pskhu, Murat I. Ramazanov, Minzilya Kosmakova
Boundary Value Problem For A Loaded Fractional Diffusion Equation, Arsen V. Pskhu, Murat I. Ramazanov, Minzilya Kosmakova
Turkish Journal of Mathematics
In this paper we consider a boundary value problem for a loaded fractional diffusion equation. The loaded term has the form of the Riemann-Liouville fractional derivative or integral. The BVP is considered in the open right upper quadrant. The problem is reduced to an integral equation that, in some cases, belongs to the pseudo-Volterra type, and its solvability depends on the order of differentiation in the loaded term and the behavior of the support line of the load in a neighborhood of the origin. All these cases are considered. In particular, we establish sufficient conditions for the unique solvability of …
Characterizations Of The Commutators Involving Idempotents In Certain Subrings Of $M_{2}(\Mathbb{Z})$, Tufan Özdi̇n, Günseli̇ Gümüşel
Characterizations Of The Commutators Involving Idempotents In Certain Subrings Of $M_{2}(\Mathbb{Z})$, Tufan Özdi̇n, Günseli̇ Gümüşel
Turkish Journal of Mathematics
In this paper, we characterize the idempotency, cleanness, and unit-regularity of the commutator $[E_1, E_2]=E_1E_2-E_2E_1$ involving idempotents $E_1,E_2$ in certain subrings of $M_{2}(\mathbb{Z})$.
On The Frobenius Norm Of Commutator Of Cauchy-Toeplitz Matrix And Exchange Matrix, Süleyman Solak, Mustafa Bahşi̇
On The Frobenius Norm Of Commutator Of Cauchy-Toeplitz Matrix And Exchange Matrix, Süleyman Solak, Mustafa Bahşi̇
Turkish Journal of Mathematics
Matrix commutator and anticommutator play an important role in mathematics, mathematical physic, and quantum physic. The commutator and anticommutator of two $n\times n$ complex matrices $A$ and $B$ are defined by $\left[ A,B% \right] =AB-BA$ and $\left( A,B\right) =AB+BA$, respectively. Cauchy-Toeplitz matrix and exchange matrix are two of the special matrices and they have excellent properties. In this study, we mainly focus on Frobenius norm of the commutator of Cauchy-Toeplitz matrix and exchange matrix. Moreover, we give upper and lower bounds for the Frobenius norm of the commutator of Cauchy-Toeplitz matrix and exchange matrix.
What Can Lattices Do For Hypersemigroups?, Niovi Kehayopulu
What Can Lattices Do For Hypersemigroups?, Niovi Kehayopulu
Turkish Journal of Mathematics
This is from Birkhoff, the "father of lattice theory" in Trends in Lattice Theory. Van Nostrand 1970: "Lattices can do things for you, no matter what kind of mathematician you are!". The aim of this paper is to show that the $le$-semigroups (lattice ordered semigroups possessing a greatest element) play the main role in studying the ordered hypersemigroups. From many results on lattice ordered semigroups corresponding results on ordered semigroups can be obtained. The converse is also possible but the beauty and simplicity of "order" makes it easier to investigate the lattice ordered semigroup at first. After getting the results …
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 $L^{p,q}_\alpha(\Omega).$
Between Graphical Zonotope And Graph-Associahedron, Marko Pesovic, Tanja Stojadinovic
Between Graphical Zonotope And Graph-Associahedron, Marko Pesovic, Tanja Stojadinovic
Turkish Journal of Mathematics
This manuscript introduces a finite collection of generalized permutohedra associated to a simple graph. The first polytope of this collection is the graphical zonotope of the graph, and the last is the graph-associahedron associated to it. We describe the weighted integer points enumerators for polytopes in this collection as Hopf algebra morphisms of combinatorial Hopf algebras of decorated graphs. In the last section, we study some properties related to $\mathcal{H}$-polytopes.
Some Estimates On The Exponential Stability Of Solutions Of Nonlinear Neutral Type Systems With Periodic Coefficients, Yener Altun
Some Estimates On The Exponential Stability Of Solutions Of Nonlinear Neutral Type Systems With Periodic Coefficients, Yener Altun
Turkish Journal of Mathematics
In this present study, we pay attention to a class of nonlinear neutral type systems (NNSs) with periodic coefficients and construct some assumptions guaranteeing the exponential stability (ES) of the trivial solutions of the system considered. To get specific conditions guaranteeing the ES, we use a modified Lyapunov functional. In conclusion, we get some estimates for the exponential decay of the solutions at infinity with the constructed sufficient conditions. We give two examples to demonstrate the applicability of the results obtained with the constructed assumptions.
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.