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2021

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Articles 1201 - 1230 of 1313

Full-Text Articles in Mathematics

Finite Topological Type Of Complete Finsler Gradient Shrinking Ricci Solitons, Mohamad Yar Ahmadi, Sina Hedayatian Jan 2021

Finite Topological Type Of Complete Finsler Gradient Shrinking Ricci Solitons, Mohamad Yar Ahmadi, Sina Hedayatian

Turkish Journal of Mathematics

In the present work it is shown that on a Finslerian space, a forward complete gradient shrinking Ricci soliton has finite topological type, provided either the Ricci scalar is bounded above or the Ricci scalar is bounded from below and injectivity radius is bounded away from zero.

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A Semi-Symmetric Metric Connection On Almost Contact B-Metric Manifolds, Şenay Bulut Jan 2021

A Semi-Symmetric Metric Connection On Almost Contact B-Metric Manifolds, Şenay Bulut

Turkish Journal of Mathematics

The object of the present paper is to study a semisymmetric metric connection on an almost contact $B-$metric manifold. We deduce a relation between the Levi-Civita connection and the semisymmetric metric connection on the considered manifold. We determined the class of the torsion tensor corresponding to the semisymmetric connection. We study Ricci-like solitons on almost contact $B-$metric manifolds with the semisymmetric connection. Finally, we give some examples to considered manifolds with the semisymmetric connection.

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On The Paper "Regular Equivalence Relations On Ordered $*$-Semihypergroups", Niovi Kehayopulu Jan 2021

On The Paper "Regular Equivalence Relations On Ordered $*$-Semihypergroups", Niovi Kehayopulu

Turkish Journal of Mathematics

If $(S,\circ,\le)$ is an ordered hypersemigroup, an equivalence relation $\rho$ on $S$ is called congruence if $(a,b)\in\rho$ implies $(a\circ x, b\circ x)\in\rho$ and $(x\circ a, x\circ b)\in\rho$ for every $x\in S$; in the sense that for every $u\in a\circ x$ there exists $v\in b\circ x$ such that $(u,v)\in\rho$ and for every $u\in x\circ a$ there exists $v\in x\circ b$ such that $(u,v)\in\rho$. It has been proved in Turk J Math 2021(5) [On the paper "A study on (strong) order-congruences in ordered semihypergroups"] that if $S$ is an ordered hypersemigroup, then there exists a congruence $\rho$ on $S$ such that $S/\rho$ …

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Non-Singular Cubic Surfaces Over $\Mathbb{F}_{2^K}$, Fatma Karaoğlu Jan 2021

Non-Singular Cubic Surfaces Over $\Mathbb{F}_{2^K}$, Fatma Karaoğlu

Turkish Journal of Mathematics

We perform an opportunistic search for cubic surfaces over small fields of characteristic two. The starting point of our work is a list of surfaces complied by Dickson over the field with two elements. We consider the nonsingular ones arising in Dickson' s work for the fields of larger orders of characteristic two. We investigate the properties such as the number of lines, singularities and automorphism groups. The problem of determining the possible numbers of lines of a nonsingular cubic surface over the fields of $\mathbb{C}, \mathbb{R}, \mathbb{Q}, \mathbb{F}_q$ where q odd, $\mathbb{F}_2$ was considered by Cayley and Salmon, Schlafli, …

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Decompositions Of Semigroups, Rida E. Zenab Jan 2021

Decompositions Of Semigroups, Rida E. Zenab

Turkish Journal of Mathematics

In this article we discuss the factorisations of semigroups and monoids in the context of direct, semidirect and Zappa-Szep products addressing the question of uniqueness. An equivalence between external and internal Zappa-Szep product of groups and monoids is known, but no such correspondence exists for semigroups in general. We prove the equivalence between external and internal Zappa-Szep product of semigroups subject to certain conditions in this article. We end with some illustrative examples of the Zappa-Szep product of the bisimple inverse monoids.

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Linear Stability Of Periodic Standing Waves Of The Kgz System, Sevdzhan Ahmedov Hakkaev, Fati̇h Hunutlu Jan 2021

Linear Stability Of Periodic Standing Waves Of The Kgz System, Sevdzhan Ahmedov Hakkaev, Fati̇h Hunutlu

Turkish Journal of Mathematics

In this work we consider the periodic standing wave solutions for a Klein-Gordon-Zakharov system. We find the conditions on the parameters, for which the periodic waves of dnoidal type are linear stable/unstable.

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Higher Cohomologies For Presheaves Of Commutative Monoids, Pilar Carrasco, Antonio M. Cegarra Jan 2021

Higher Cohomologies For Presheaves Of Commutative Monoids, Pilar Carrasco, Antonio M. Cegarra

Turkish Journal of Mathematics

We present an extension of the classical Eilenberg-MacLane higher order cohomology theories of abelian groups to presheaves of commutative monoids (and of abelian groups, then) over an arbitrary small category. These high-level cohomologies enjoy many desirable properties and the paper aims to explore them. The results apply directly in several settings such as presheaves of commutative monoids on a topological space, simplicial commutative monoids, presheaves of simplicial commutative monoids on a topological space, commutative monoids or simplicial commutative monoids on which a fixed monoid or group acts, and so forth. As a main application, we state and prove a precise …

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On The Betti Numbers Of The Tangent Cones For Gorenstein Monomial Curves, Pinar Mete Jan 2021

On The Betti Numbers Of The Tangent Cones For Gorenstein Monomial Curves, Pinar Mete

Turkish Journal of Mathematics

The aim of the article is to study the Betti numbers of the tangent cone of Gorenstein monomial curves in affine 4-space. If $C_S$ is a noncomplete intersection Gorenstein monomial curve whose tangent cone is Cohen--Macaulay, we show that the possible Betti sequences are (1,5,5,1), (1,5,6,2) and (1,6,8,3).

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On Lyapunov-Type Inequalities For $(N+1)$St Order Nonlinear Differential Equations With The Anti-Periodic Boundary Conditions, Mustafa Fahri̇ Aktaş Jan 2021

On Lyapunov-Type Inequalities For $(N+1)$St Order Nonlinear Differential Equations With The Anti-Periodic Boundary Conditions, Mustafa Fahri̇ Aktaş

Turkish Journal of Mathematics

In this paper, we establish new Lyapunov-type inequalities for $\left(n+1\right)$st order nonlinear differential equation including $p$-relativistic operator and $q$-prescribed curvature operator under the antiperiodic boundary conditions.

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An Exponential Equation Involving $K$-Fibonacci Numbers, Alioune Gueye, Salah Eddine Rihane, Alain Togbe Jan 2021

An Exponential Equation Involving $K$-Fibonacci Numbers, Alioune Gueye, Salah Eddine Rihane, Alain Togbe

Turkish Journal of Mathematics

For $k\geq 2$, consider the $k$-Fibonacci sequence $(F_n^{(k)})_{n\geq 2-k}$ having initial conditions $0, \ldots, 0, 1$ ($k$ terms) and each term afterwards is the sum of the preceding $k$ terms. Some well-known sequences are special cases of this generalization. The Fibonacci sequence is a special case of $(F_n^{(k)})_{n\geq 2-k}$ with $k=2$ and Tribonacci sequence is $(F_n^{(k)})_{n\geq 2-k}$ with $k=3$. In this paper, we use Baker's method to show that 4, 16, 64, 208, 976, and 1936 are all $k$-Fibonacci numbers of the form $(3^a\pm 1)(3^b\pm 1)$, where $a$ and $b$ are nonnegative integers.

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Hermitian-Toeplitz Determinants For Functions With Bounded Turning, Virendra Kumar, Nak Eun Cho Jan 2021

Hermitian-Toeplitz Determinants For Functions With Bounded Turning, Virendra Kumar, Nak Eun Cho

Turkish Journal of Mathematics

There is a rich literature on estimation of second and third Hankel determinants for normalised analytic functions in geometric function theory. It is also, therefore, natural to explore the concept of the Hermitian-Toeplitz determinants for such functions. In this paper, the sharp lower and upper estimations for third-order Hermitian-Toeplitz determinant for functions with bounded turning of order $\alpha$, are obtained. \keywords{Analytic functions, functions with bounded turning of order $\alpha$, Hermitian-Toeplitz determinant

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On The Extension Of Hermite-Hadamard Type Inequalities For Co-Ordinated Convex Mappings, Mehmet Zeki̇ Sarikaya, Di̇lşatnur Kiliçer Jan 2021

On The Extension Of Hermite-Hadamard Type Inequalities For Co-Ordinated Convex Mappings, Mehmet Zeki̇ Sarikaya, Di̇lşatnur Kiliçer

Turkish Journal of Mathematics

In this paper, we obtain an important inequalities for coordinated convex functions and as a result of these inequalities we give the extension of Hermite-Hadamard type inequalities for Riemann-Liouville fractional integral and logarithmic integral. The inequalities obtained in this study provide generalizations of some result given in earlier works.

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Cameron-Storvick Theorem Associated With Gaussian Paths On Function Space, Jae Gil Choi Jan 2021

Cameron-Storvick Theorem Associated With Gaussian Paths On Function Space, Jae Gil Choi

Turkish Journal of Mathematics

The purpose of this paper is to provide a more general Cameron-Storvick theorem for the generalized analytic Feynman integral associated with Gaussian process $\mathcal Z_k$ on a very general Wiener space $C_{a,b}[0,T]$. The general Wiener space $C_{a,b}[0,T]$ can be considered as the set of all continuous sample paths of the generalized Brownian motion process determined by continuous functions $a(t)$ and $b(t)$ on $[0,T]$. As an interesting application, we apply this theorem to evaluate the generalized analytic Feynman integral of certain monomials in terms of Paley-Wiener-Zygmund stochastic integrals.

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A General Double Series Identity And Its Application In Hypergeometric Reduction Formulas, Mohammad Idris Qureshi, Shakir Hussain Malik Jan 2021

A General Double Series Identity And Its Application In Hypergeometric Reduction Formulas, Mohammad Idris Qureshi, Shakir Hussain Malik

Turkish Journal of Mathematics

In this paper, we obtain a general double-series identity involving the bounded sequence of arbitrary complex numbers. As application of our double-series identity, we establish some reduction formulas for Srivastava--Daoust double hypergeometric function and Gaussian generalized hypergeometric function $_4F_3$. As special cases of our reduction formula for $_4F_3$ lead to some corollaries involving Clausen hypergeometric functions ${_{3}F_{2}}$. Making suitable adjustment of parameters in reduction formulas for $_4F_3$ and ${_{3}F_{2}}$, we obtain some results in terms of elementary functions and some special functions like Lerch generalized zeta function and incomplete beta function.

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A Classification Of 1-Well-Covered Graphs, Zaki̇r Deni̇z Jan 2021

A Classification Of 1-Well-Covered Graphs, Zaki̇r Deni̇z

Turkish Journal of Mathematics

A graph is well-covered if all its maximal independent sets have the same size. If a graph is well-covered and remains well-covered upon removal of any vertex, then it is called 1-well-covered graph. It is well-known that $[\frac{n}{2}]+1\leq \alpha(G) + \mu(G) \leq n$ for any graph $G$ with $n$ vertices where $\alpha(G)$ and $\mu(G)$ are the independence and matching numbers of $G$, respectively. A graph $G$ satisfying $\alpha(G) + \mu(G) = n$ is known as König-Egervary graph, and such graphs are characterized by Levit and Mandrescu [14] under the assumption that $G$ is 1-well-covered. In this paper, we investigate connected …

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Recent Developments In $\Delta$-Casorati Curvature Invariants, Bang-Yen Chen Jan 2021

Recent Developments In $\Delta$-Casorati Curvature Invariants, Bang-Yen Chen

Turkish Journal of Mathematics

The theory of $\delta$-invariants, initiated by the author in the early 1990s, is a challenging topic in modern differential geometry, having a lot of applications. In the spirit of $\delta$-invariants, Decu et al. (2007) initiated the study of $\delta$-Casorati curvatures. Since then there are many interesting results on $\delta$-Casorati curvatures obtained by many authors. In this article we provide a comprehensive survey on recent developments in $\delta$-Casorati curvatures done during the last decade.

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Star Edge Coloring Of Graphs With Mad($G$)$, Kavita Pradeep Jan 2021

Star Edge Coloring Of Graphs With Mad($G$)$, Kavita Pradeep

Turkish Journal of Mathematics

A star edge coloring of a graph $G$ is a proper edge coloring such that there is no bicolored path or cycle of length four. The minimum number of colors needed for a graph $G$ to admit a star edge coloring is called the star chromatic index and it is denoted by $\chi_s^{'}(G)$. In this paper, we consider graphs of maximum degree $\Delta \geq 4$ and show that if the maximum average degree of a graph is less than $\frac{14}{5}$ then $\chi_s^{'}(G) \leq 2\Delta + 1$.

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On Neutrosophic Soft Continuous Mappings, Taha Yasi̇n Öztürk, Eli̇f Karataş, Adem Yolcu Jan 2021

On Neutrosophic Soft Continuous Mappings, Taha Yasi̇n Öztürk, Eli̇f Karataş, Adem Yolcu

Turkish Journal of Mathematics

In this paper, the concept of neutrosophic soft continuous mapping, neutrosophic soft open mapping, neutrosophic soft closed mapping and neutrosophic soft homeomorphism have been introduced along with the investigation of their several characteristics, and verified by proper examples.

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Existence Of A Positive Solution For A Singular Fractional Boundary Value Problem With Fractional Boundary Conditions Using Convolution And Lower Order Problems, Jeffrey W. Lyons, Jeffrey T. Neugebauer Jan 2021

Existence Of A Positive Solution For A Singular Fractional Boundary Value Problem With Fractional Boundary Conditions Using Convolution And Lower Order Problems, Jeffrey W. Lyons, Jeffrey T. Neugebauer

Turkish Journal of Mathematics

Existence of a positive solution is shown for two singular two-point fractional boundary value problems with fractional boundary conditions using fixed point theory, lower order problems, and convolution of Green's functions. A nontrivial example is included.

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Closure Operators In Convergence Approach Spaces, Muhammad Qasim, Mehmet Baran, Hassan Abughalwa Jan 2021

Closure Operators In Convergence Approach Spaces, Muhammad Qasim, Mehmet Baran, Hassan Abughalwa

Turkish Journal of Mathematics

In this paper, we characterize closed and strongly closed subsets of convergence approach spaces and introduce two notions of closure in the category of convergence approach spaces which satisfy idempotent, productive and (weakly) hereditary properties. Furthermore, we explicitly characterize each of $T_{i}$ convergence approach spaces, $i=0,1,2$ with respect to these closure operators and show that each of these subcategories of $T_{i}$ convergence approach spaces, $i=0,1,2$ are epireflective as well as we investigate the relationship among these subcategories. Finally, we characterize connected convergence approach spaces.

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Quasi-Cesaro Matrix And Associated Sequence Spaces, Hadi Roopaei, Taja Yaying Jan 2021

Quasi-Cesaro Matrix And Associated Sequence Spaces, Hadi Roopaei, Taja Yaying

Turkish Journal of Mathematics

In the present study, we construct a new matrix which we call quasi-Cesaro matrix and is a generalization of the ordinary Cesaro matrix, and introduce $BK$-spaces $C^q_k$ and $C^q_{\infty}$ as the domain of the quasi-Cesaro matrix $C^q$ in the spaces $\ell_k$ and $\ell_{\infty},$ respectively. Furthermore, we exhibit some topological properties and inclusion relations related to these newly defined spaces. We determine the basis of the space $C^q_k$ and obtain Köthe duals of the spaces $C^q_k$ and $C^q_{\infty}.$ Based on the newly defined matrix, we present a factorization for the Hilbert matrix and generalize Hardy's inequality, as an application. Moreover we …

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Widths And Entropy Of Sets Of Smooth Functions On Compact Homogeneous Manifolds, Alexander Kushpel, Kenan Taş, Jeremy Levesley Jan 2021

Widths And Entropy Of Sets Of Smooth Functions On Compact Homogeneous Manifolds, Alexander Kushpel, Kenan Taş, Jeremy Levesley

Turkish Journal of Mathematics

We develop a general method to calculate entropy and $n$-widths of sets of smooth functions on an arbitrary compact homogeneous Riemannian manifold $% \mathbb{M}^{d}$. Our method is essentially based on a detailed study of geometric characteristics of norms induced by subspaces of harmonics on $% \mathbb{M}^{d}$. This approach has been developed in the cycle of works [1, 2, 10-19]. The method's possibilities are not confined to the statements proved but can be applied in studying more general problems. As an application, we establish sharp orders of entropy and $n$-widths of Sobolev's classes $W_{p}^{\gamma }\left( \mathbb{M}^{d}\right) $ and their generalisations in …

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A Gompertz Distribution For Time Scales, Tom Cuchta, Robert Jon Niichel, Sabrina Streipert Jan 2021

A Gompertz Distribution For Time Scales, Tom Cuchta, Robert Jon Niichel, Sabrina Streipert

Turkish Journal of Mathematics

We investigate a family of probability distributions, with three parameters associated with the dynamic Gompertz function. We prove its existence for various parameter sets and discuss the existence of its time scale moments. Afterwards, we investigate the special case of discrete time scales, where it is shown that the discrete Gompertz distribution is a $q$-geometric distribution of the second kind. Further, we find their $q$-binomial moments, we bound their expected value, and we show how a classical Gompertz distribution is obtained from them.

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Number Fields And Divisible Groups Via Model Theor, Şermi̇n Çam Çeli̇k, Haydar Göral Jan 2021

Number Fields And Divisible Groups Via Model Theor, Şermi̇n Çam Çeli̇k, Haydar Göral

Turkish Journal of Mathematics

In this note, we first show that solutions of certain equations classify the number fields lying in imaginary quadratic number fields. Then, we study divisible groups with a predicate. We show that these structures are not simple and have the independence property under some natural assumptions.

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Rotating Periodic Integrable Solutions For Second-Order Differential Systems With Nonresonance Condition, Yi Cheng, Ke Jin, Ravi Agarwal Jan 2021

Rotating Periodic Integrable Solutions For Second-Order Differential Systems With Nonresonance Condition, Yi Cheng, Ke Jin, Ravi Agarwal

Turkish Journal of Mathematics

In this paper, by using Parseval's formula and Schauder's fixed point theorem, we prove the existence and uniqueness of rotating periodic integrable solution of the second-order system $x''+f(t,x)=0$ with $x(t+T)=Qx(t)$ and $\int_{(k-1)T}^{kT}x(s)ds=0$, $k\in Z^+$ for any orthogonal matrix $Q$ when the nonlinearity $f$ satisfies nonresonance condition.

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Polyhedral Optimization Of Second-Order Discrete And Differential Inclusions With Delay, Sevi̇lay Demi̇r Sağlam, Eli̇mhan N. Mahmudov Jan 2021

Polyhedral Optimization Of Second-Order Discrete And Differential Inclusions With Delay, Sevi̇lay Demi̇r Sağlam, Eli̇mhan N. Mahmudov

Turkish Journal of Mathematics

he present paper studies the optimal control theory of second-order polyhedral delay discrete and delay differential inclusions with state constraints. We formulate the conditions of optimality for the problems with the second-order polyhedral delay discrete $(PD_d)$ and the delay differential $(PC_d)$ in terms of the Euler-Lagrange inclusions and the distinctive ''transversality'' conditions. Moreover, some linear control problem with second-order delay differential inclusions is given to illustrate the effectiveness and usefulness of the main theoretic results.

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A New Gauss--Newton-Like Method For Nonlinear Equations, Haijun Wang, Qi Wang Jan 2021

A New Gauss--Newton-Like Method For Nonlinear Equations, Haijun Wang, Qi Wang

Turkish Journal of Mathematics

In this paper, a new Gauss-Newton-like method that is based on a rational approximation model with linear numerator is proposed for solving nonlinear equations. The new method revises the $J_k^\mathrm{T}J_k$ matrix by a rank-one matrix at each iteration. Furthermore, we design a new iterative algorithm for nonlinear equations and prove that it is locally q-quadratically convergent. The numerical results show that the new proposed method has better performance than the classical Gauss-Newton method.

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Modularly Equidistant Numerical Semigroups, José Carlos Rosales, Manuel Baptista Branco, Márcio Andre Traesel Jan 2021

Modularly Equidistant Numerical Semigroups, José Carlos Rosales, Manuel Baptista Branco, Márcio Andre Traesel

Turkish Journal of Mathematics

IfS is a numerical semigroup and s ∈ S , we denote by next$_{S}$(s) = min {x ∈ S s < x}. Leta be an integer greater than or equal to two. A numerical semigroup is equidistant modulo a if next$_{S}$((s) - s - 1 is a multiple of a for every s ∈ S . In this note, we give algorithms for computing the whole set of equidistant numerical semigroups modulo a with fixed multiplicity, genus, and Frobenius number. Moreover, we will study this kind of semigroups with maximal embedding dimension.

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Self-Adjoint Extensions For A Class Of Singular Operators, Rauf Ami̇rov, Hidayat Mehmetoğlu Huseynov, Sevi̇m Durak Jan 2021

Self-Adjoint Extensions For A Class Of Singular Operators, Rauf Ami̇rov, Hidayat Mehmetoğlu Huseynov, Sevi̇m Durak

Turkish Journal of Mathematics

In this study, we consider the domains of the minimal and maximal operators generated of singular differential-expression-type Sturm-Liouville and obtain all self-adjoint extensions of the operator in terms of boundary conditions.

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Traces And Inverse Nodal Problems For A Class Of Delay Sturm-Liouville Operators, Erdoğan Şen Jan 2021

Traces And Inverse Nodal Problems For A Class Of Delay Sturm-Liouville Operators, Erdoğan Şen

Turkish Journal of Mathematics

In this study, we investigate the regularized sums of eigenvalues, oscillation of eigenfunctions and solutions of inverse nodal problems of discontinuous Sturm-Liouville operators with a delayed argument and with a finite number of transmission conditions. With this aim, we obtain asymptotic formulas for eigenvalues, eigenfunctions and nodal points of the problem. Moreover, some numerical examples are given to illustrate the results. The problem differs from the other discontinuous Sturm-Liouville problems with retarded argument in that it contains a spectral parameter in boundary conditions. If we take the delayed argument $\Delta\equiv0$, the coefficients $\alpha _{i}^{+}=\beta _{i}^{+}=0$ ($i=1,2$) in boundary conditions and …

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