Showing papers in "Turkish Journal of Mathematics in 2019"

On S-prime submodules

Abstract: In this study, we introduce the concepts of S -prime submodules and S -torsion-free modules, which are generalizations of prime submodules and torsion-free modules. Suppose S ⊆ R is a multiplicatively closed subset of a commutative ring R , and let M be a unital R -module. A submodule P of M with (P :R M) ∩ S = ∅ is called an S -prime submodule if there is an s ∈ S such that am ∈ P implies sa ∈ (P :R M) or sm ∈ P. Also, an R -module M is called S -torsion-free if ann(M) ∩ S = ∅ and there exists s ∈ S such that am = 0 implies sa = 0 or sm = 0 for each a ∈ R and m ∈ M. In addition to giving many properties of S -prime submodules, we characterize certain prime submodules in terms of S -prime submodules. Furthermore, using these concepts, we characterize some classical modules such as simple modules, S -Noetherian modules, and torsion-free modules.

Separation axioms on neutrosophic soft topological spaces

Abstract: A neutrosophic set, proposed by Smarandache, considers a truth membership function, an indeterminacy membership function, and a falsity membership function. Neutrosophic soft sets combined by Maji have been utilized successfully to model uncertainty in several areas of application such as control, reasoning, pattern recognition, and computer vision. In the present paper, some basic notions of neutrosophic soft sets have been redefined and the neutrosophic soft point concept has been introduced. Later we give the neutrosophic soft T i " role="presentation"> T i T i T_{i} -space and the relationships between them are discussed in detail.

Study on the q-analogue of a certain family of linear operators

Abstract: Inthispaper, weintroducetheq-analogueofacertainfamilyoflinearoperatorsingeometricfunctiontheory. Our main purpose is to define some subclasses of analytic functions by means of the q-analogue of linear operators and investigate various inclusion relationships with integral preserving properties.

Ricci-Yamabe maps for Riemannian flows and their volume variation and volume entropy

Abstract: The aim of this short note is to produce new examples of geometrical flows associated to a given Riemannian flow $g(t)$. The considered flow in covariant symmetric $2$-tensor fields will be called Ricci-Yamabe map since it involves a scalar combination of Ricci tensor and scalar curvature of $g(t)$. Due to the signs of considered scalars the Ricci-Yamabe flow can be also a Riemannian or semi-Riemannian or singular Riemannian flow. We study the associated function of volume variation as well as the volume entropy. Finally, since the two-dimensional case was the most handled situation we express the Ricci flow equation in all four orthogonal separable coordinate systems of the plane.

Fixed-disc results via simulation functions

Abstract: 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.

Solvability of a system of nonlinear difference equations of higher order

Abstract: In this paper, we show that the following higher-order system of nonlinear difference equations, $ x_{n}=\frac{x_{n-k}y_{n-k-l}}{y_{n-l}\left( a_{n}+b_{n}x_{n-k}y_{n-k-l}\right)}, \ y_{n}=\frac{y_{n-k}x_{n-k-l}}{x_{n-l}\left( \alpha_{n}+\beta_{n}y_{n-k}x_{n-k-l}\right)}, \ n\in \mathbb{N}_{0}, $ where $k,l\in \mathbb{N}$, $\left(a_{n} \right)_{n\in \mathbb{N}_{0}}, \left(b_{n} \right)_{n\in \mathbb{N}_{0}}, \left(\alpha_{n} \right)_{n\in \mathbb{N}_{0}}, \left(\beta_{n} \right)_{n\in \mathbb{N}_{0}}$ and the initial values $x_{-i}, \ y_{-i}$, $i=\overline {1,k+l}$, are real numbers, can be solved and some results in the literature can be extended further. Also, by using these obtained formulas, we investigate the asymptotic behavior of well-defined solutions of the above difference equations system for the case $k=2, l=k$.

An approach to negative hypergeometric distribution by generating function for special numbers and polynomials

Abstract: The aim of this paper is to not only provide a definition of a new family of special numbers and polynomials of higher-order with their generating functions, but also to investigate their fundamental properties in the spirit of probabilistic distributions. By applying generating functions methods, we derive miscellaneous novel identities and formulas involving the Chu–Vandermonde-type convolution formulas, combinatorial sums, Bernstein basis functions, and the other well-known special numbers and polynomials. Moreover, we provide a computational algorithm which returns special values of these numbers and polynomials. In addition, we show that our new identities and formulas are connected with the interpolation functions of the Apostol-type numbers and polynomials. Finally, we present some theoretical and applied details on probabilistic distributions arising from the aforementioned Chu–Vandermonde-type convolution formulas.

Star-likeness associated with the exponential function

Abstract: Given a domain $\Omega$ in the complex plane $\mathbb{C}$ and a univalent function $q$ defined in an open unit disk $\mathbb{D}$ with nice boundary behaviour, Miller and Mocanu studied the class of admissible functions $\Psi(\Omega,q)$ so that the differential subordination $\psi(p(z),zp'(z),z^2p''(z);z)\prec h(z)$ implies $p(z)\prec q(z)$, where $p$ is an analytic function in $\mathbb{D}$ with $p(0)=1$, $\psi:\mathbb{C}^3\times \mathbb{D}\to\mathbb{C}$ and $\Omega=h(\mathbb{D})$. This paper investigates the properties of this class for $q(z)=e^z$. As application, several sufficient conditions for normalized analytic functions $f$ to be in the subclass of star-like functions associated with the exponential function are obtained.

Basicity of a system of exponents with a piecewise linear phase in Morrey-typespaces

Abstract: In this paper a perturbed system of exponents with a piecewise linear phase depending on two real parameters is considered. The sufficient conditions for these parameters are found, under which the considered system of exponents is complete, minimal, or it forms a basis for a Morrey-type space.

Some operator inequalities associated with Kantorovich and Hölder–McCarthy inequalities and their applications

Abstract: We prove analogs of certain operator inequalities, including Hölder–McCarthy inequality, Kantorovich inequality, and Heinz–Kato inequality, for positive operators on the Hilbert space in terms of the Berezin symbols and the Berezin number of operators on the reproducing kernel Hilbert space.

Enveloping algebras of color hom-Lie algebras

Abstract: In this paper, the universal enveloping algebra of color hom-Lie algebras is studied. A construction of the free involutive hom-associative color algebra on a hom-module is described and applied to ...

Quartic trigonometric B-spline algorithm for numerical solution of the regularized long wave equation

Abstract: In this paper, an application of the quartic trigonometric B-spline finite element method is used to solve the regularized long wave equation numerically. This approach involves a Galerkin method based on the quartic trigonometric B-spline function in space discretization together with second and fourth order schemes in time discretization. The accuracy of the proposed methods are demonstrated by test problems and numerical results are compared with the exact solution and some previous results.

Properties in $L_p$ of root functions for a nonlocal problem with involution

Abstract: The spectral problem − u ″ ( x ) + α u ″ ( − x ) = λ u ( x ) " role="presentation"> − u ″ ( x ) + α u ″ ( − x ) = λ u ( x ) − u ″ ( x ) + α u ″ ( − x ) = λ u ( x ) -u''(x)+\alpha u''(-x)=\lambda u(x) , − 1 " role="presentation"> − 1 − 1 -1 %lt; x " role="presentation"> x x x 1 1 1 , with nonlocal boundary conditions u ( − 1 ) = β u ( 1 ) " role="presentation"> u ( − 1 ) = β u ( 1 ) u ( − 1 ) = β u ( 1 ) u(-1)=\beta u(1) , u ′ ( − 1 ) = u ′ ( 1 ) " role="presentation"> u ′ ( − 1 ) = u ′ ( 1 ) u ′ ( − 1 ) = u ′ ( 1 ) u'(-1)=u'(1) , is studied in the spaces L p ( − 1 , 1 ) " role="presentation"> L p ( − 1 , 1 ) L p ( − 1 , 1 ) L_p(-1,1) for any α ∈ ( − 1 , 1 ) " role="presentation"> α ∈ ( − 1 , 1 ) α ∈ ( − 1 , 1 ) \alpha\in (-1,1) and β ≠ ± 1 " role="presentation"> β ≠ ± 1 β ≠ ± 1 \beta e\pm 1 . It is proved that if r = ( 1 − α ) / ( 1 + α ) " role="presentation"> r = ( 1 − α ) / ( 1 + α ) ‾ ‾ ‾ ‾ ‾ ‾ ‾ ‾ ‾ ‾ ‾ ‾ ‾ ‾ √ r = ( 1 − α ) / ( 1 + α ) r=\sqrt{(1-\alpha)/(1+\alpha)} is irrational then the system of its eigenfunctions is complete and minimal in L p ( − 1 , 1 ) " role="presentation"> L p ( − 1 , 1 ) L p ( − 1 , 1 ) L_p(-1,1) for any p > 1 " role="presentation"> p > 1 p > 1 p>1 , but does not form a basis. In the case of a rational value of r " role="presentation"> r r r , the way of supplying this system with associated functions is specified to make all the root functions a basis in L p ( − 1 , 1 ) " role="presentation"> L p ( − 1 , 1 ) L p ( − 1 , 1 ) L_p(-1,1) .

Unpredictable solutions of linear differential and discrete equations

Abstract: The existence and uniqueness of unpredictable solutions in the dynamics of nonhomogeneous linear systems of differential and discrete equations are investigated. The hyperbolic cases are under discussion. The presence of unpredictable solutions confirms the existence of Poincaré chaos. Simulations illustrating the chaos are provided.

On the solvability of the main boundary value problems for a nonlocal Poisson equation

Abstract: Solvability of the main boundary value problems for the nonlocal Poisson equation is studied. Existence and uniqueness theorems for the considered problems are obtained. The necessary and sufficient solvability conditions for all problems are given and integral representations for the solutions are constructed.

Converse theorems in Lyapunov's second method and applications for fractional order systems

Abstract: We establish a characterization of the Lyapunov and Mittag-Leffler stability through (fractional) Lyapunov functions, by proving converse theorems for Caputo fractional order systems. A hierarchy for the Mittag-Leffler order convergence is also proved which shows, in particular, that fractional differential equation with derivation order lesser than one cannot be exponentially stable. The converse results are then applied to show that if an integer order system is (exponentially) stable, then its corresponding fractional system, obtained from changing its differentiation order, is (Mittag-Leffler) stable. Hence, available integer order control techniques can be disposed to control nonlinear fractional systems. Finally, we provide examples showing how our results improve recent advances published in the specialized literature.

A generalization of -regular rings

Abstract: We introduce the class of so-called regularly nil clean rings and systematically study their fundamental characteristic properties accomplished with relationships among certain classical sorts of rings such as exchange rings, Utumi rings etc. These rings of ours naturally generalize the long-known classes of π -regular and strongly π -regular rings. We show that the regular nil cleanness possesses a symmetrization which extends the corresponding one for strong π -regularity that was visualized by Dischinger [10]. Likewise, our achieved results substantially improve on establishments presented in two recent papers by Danchev and Šter [8] and Danchev [6].

Fibonacci and Lucas numbers as products of two repdigits

Abstract: In this study, it is shown that the largest Fibonacci number that is the product of two repdigits is F10 = 55 = 5 · 11 = 55 · 1 and the largest Lucas number that is the product of two repdigits is L6 = 18 = 2 · 9 = 3 · 6.

Stability analysis for a class of nabla (q; h)-fractional difference equations

Abstract: This paper investigates stability of the nabla (q, h) -fractional difference equations. Asymptotic stability of the special nabla (q, h) -fractional difference equations are discussed. Stability theorems for discrete fractional Lyapunov direct method are proved. Furthermore, we give some new lemmas (including important comparison theorems) related to the nabla (q, h) -fractional difference operators that allow proving the stability of the nabla (q, h) -fractional difference equations, by means of the discrete fractional Lyapunov direct method, using Lyapunov functions. Some examples are given to illustrate these results.

(P, Q)-Lucas polynomial coefficient inequalities of the bi-univalent function class

Abstract: Recently, Lucas polynomials and other special polynomials gained importance in the field of geometric function theory. In this study, by connecting these polynomials, subordination, and the Al-Oboudi differential operator, we introduce a new class of bi-univalent functions and obtain coefficient estimates and Fekete–Szegö inequalities for this new class.

On the exponential Diophantine equation $P_n^x+P_{n+1}^x=P_m$

Abstract: In this paper, we find all the solutions of the title Diophantine equation in nonnegative integer variables $(m, n, x)$, where $P_k$ is the $k$th term of the Pell sequence.

Coefficient estimates for a new subclasses of λ-pseudo biunivalent functions with respect to symmetrical points associated with the Horadam Polynomials

Abstract: In the present article, we introduce two new subclasses of λ-pseudo biunivalent functions with respect to symmetrical points in the open unit disk U defined by means of the Horadam polynomials. For functions belonging to these subclasses, estimates on the Taylor -Maclaurin coefficients ja2j and ja3j are obtained. Fekete-Szego inequalities of functions belonging to these subclasses are also founded. Furthermore, we point out several new special cases of our results.

An integral-boundary value problem for a partial differential equation of second order

Abstract: An integral-boundary value problem for a hyperbolic partial differential equation in two independent variables is considered. By introducing additional functional parameters, we investigate the solvability of the problem and develop an algorithm for finding its approximate solutions. The problem is reduced to an equivalent one, consisting of the Goursat problem for a hyperbolic equation with parameters and boundary value problems with an integral condition for ODEs with respect to the parameters entered. We propose an algorithm to find an approximate solution to the original problem, which is based on the algorithm for finding a solution to the equivalent problem. The convergence of the algorithms is proved. A coefficient criterion for the unique solvability of the integral-boundary value problem is established.

Some results related to the Berezin number inequalities

Abstract: In this paper, we prove reverse inequalities for the so-called Berezin number of some operators. Also, by using the classical Jensen and Young inequalities, we obtain upper bounds for Berezin number of AXB and AαXB1−α for the case when 0 ≤ α ≤ 1 .

Approximation by generalized Bernstein-Stancu operators

Abstract: In this paper, we investigate approximation properties of the Stancu type generalization of the α -Bernstein operator. We obtain a recurrence relation for moments and the rate of convergence by means of moduli of continuity. Also, we present Voronovskaya and Grüss–Voronovskaya type asymptotic results for these operators. Finally, the study contains numerical considerations regarding the constructed operators based on Maple algorithms.

A certain subclass of bi-univalent analytic functions introduced by means of the q-analogue of Noor integral operator and Horadam polynomials

Abstract: In the present study, by using the Horadam Polnomials and q−analogue of Noor integral oprerator, we target to construct an interesting connection between the geometric function theory and that of special functions. Also, by defining a new class of bi-univalent analytic functions, we investigate coefficient estimates and famous Fekete-Szegö inequality for functions belonging to this interesting class.

$C$-Paracompactness and $C_2$-paracompactness

Abstract: A topological space X " role="presentation"> X X X is called C " role="presentation"> C C C - paracompact if there exist a paracompact space Y " role="presentation"> Y Y Y and a bijective function f : X ⟶ Y " role="presentation"> f : X ⟶ Y f : X ⟶ Y f:X\longrightarrow Y such that the restriction f | A : A ⟶ f ( A ) " role="presentation"> f | A : A ⟶ f ( A ) f | A : A ⟶ f ( A ) f|_{A}:A\longrightarrow f(A) is a homeomorphism for each compact subspace A ⊆ X " role="presentation"> A ⊆ X A ⊆ X A\subseteq X . A topological space X " role="presentation"> X X X is called C 2 " role="presentation"> C 2 C 2 C_2 - paracompact if there exist a Hausdorff paracompact space Y " role="presentation"> Y Y Y and a bijective function f : X ⟶ Y " role="presentation"> f : X ⟶ Y f : X ⟶ Y f:X\longrightarrow Y such that the restriction f | A : A ⟶ f ( A ) " role="presentation"> f | A : A ⟶ f ( A ) f | A : A ⟶ f ( A ) f|_{A}:A\longrightarrow f(A) is a homeomorphism for each compact subspace A ⊆ X " role="presentation"> A ⊆ X A ⊆ X A\subseteq X . We investigate these two properties and produce some examples to illustrate the relationship between them and C " role="presentation"> C C C -normality, minimal Hausdorff, and other properties.

Convolution properties for a family of analytic functions involving $q$-analogue of Ruscheweyh differential operator

Abstract: 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.