Showing papers in "Kyungpook Mathematical Journal in 2015"
TL;DR: In this article, a 7-term 3-D novel jerk chaotic system with two quadratic nonlinearities has been proposed, and an adaptive backstepping controller is designed to achieve complete chaos synchronization.
Abstract: In this research work, a seven-term 3-D novel jerk chaotic system with two quadratic nonlinearities has been proposed. The basic qualitative properties of the novel jerk chaotic system have been described in detail. Next, an adaptive backstepping controller is designed to stabilize the novel jerk chaotic system with two unknown parameters. Moreover, an adaptive backstepping controller is designed to achieve complete chaos synchronization of the identical novel jerk chaotic systems with two unknown parameters. MATLAB simulations have been shown in detail to illustrate all the main results developed for the 3-D novel jerk chaotic system.
77 citations
TL;DR: In this article, it was shown that if S is an anti-archimedean subset of D, then D is a t-locally S-Noetherian domain if and only if the polynomial ring D(X)Nv is a T-Nagata ring of S-noetherian domains.
Abstract: Let D be an integral domain, t be the so-called t-operation on D; and S be a (not necessarily saturated) multiplicative subset of D. In this paper, we study the Nagata ring of S-Noetherian domains and locally S-Noetherian domains. We also inves- tigate the t-Nagata ring of t-locally S-Noetherian domains. In fact, we show that if S is an anti-archimedean subset of D, then D is an S-Noetherian domain (respectively, locally S-Noetherian domain) if and only if the Nagata ring D(X)N is an S-Noetherian domain (respectively, locally S-Noetherian domain). We also prove that if S is an anti-archimedean subset of D, then D is a t-locally S-Noetherian domain if and only if the polynomial ring D(X) is a t-locally S-Noetherian domain, if and only if the t-Nagata ring D(X)Nv is a t-locally S-Noetherian domain.
26 citations
TL;DR: In this article, the generalized Apostol type Hermite-based polynomials of high order were studied and some implicit summation formulae and general symmetry identities were derived by using different analytical means and applying generating functions.
Abstract: . In this paper, we study some properties of the generalized Apostol type Hermite-based polynomials. which extend some known results. We also deduce some properties of the generalized Apostol-Bernoulli polynomials, the generalized Apostol-Euler polynomials and the generalized Apostol-Genocchi polynomials of high order. Numerous properties of these polynomials and some relationships between F (α) n (x; λ; μ, ν, c) and HF (α) n (x, y; λ; μ, ν, c) are established. Some implicit summation formulae and general symmetry identities are derived by using different analytical means and applying generating functions.
22 citations
TL;DR: In this paper, the Fekete-Szego inequalities for analytic univalent functions of complex order associated with quasi-subordination were obtained for certain subclasses of analytic functions.
Abstract: In this paper, we obtain Fekete-Szego inequalities for certain subclasses of analytic univalent functions of complex order associated with quasi-subordination.
19 citations
TL;DR: In this article, the concept of graded quasi-prime submodules is introduced and a topology related to graded quasi prime submodules of graded modules is introduced, where the properties of these submodules are investigated.
Abstract: Let G be a group with identity e. Let R be a G-graded commutative ring and M a graded R-module. In this paper, we introduce the concept of graded quasi-prime submodules and give some basic results about graded quasi-prime submodules of graded modules. Special attention has been paid, when graded modules are graded multiplication, to find extra properties of these submodules. Furthermore, a topology related to graded quasi-prime submodules is introduced.
15 citations
TL;DR: In this paper, the authors introduced the concept of the forbidden den number, which is the minimum number of forbidden moves necessary to unknot a given classical or virtual knot via a sequence of extended Reidemeister moves and the so-called forbidden moves.
Abstract: Every classical or virtual knot is equivalent to the unknot via a sequence of extended Reidemeister moves and the so-called forbidden moves. The minimum number of forbidden moves necessary to unknot a given knot is an invariant we call the forbid- den number. We relate the forbidden number to several known invariants, and calculate bounds for some classes of virtual knots.
11 citations
TL;DR: In this paper, the almost convergent sequence space was introduced by using the Fibonacci difference matrix, and it was shown that the spaces and are linearly isomorphic, and the -dual of the space and some matrix classses on this space were characterized.
Abstract: In the present paper, by using the Fibonacci difference matrix, we introduce the almost convergent sequence space . Also, we show that the spaces and are linearly isomorphic. Further, we determine the -dual of the space and characterize some matrix classses on this space. Finally, Fibonacci core of a complex-valued sequence has been introduced, and we prove some inclusion theorems related to this new type of core.
9 citations
TL;DR: In this paper, the gyrovector spaces do not satisfy the distributivity with scalarmultiplication, and the gyrogroup is a most natural extension of a group into the nonassociative algebra.
Abstract: . As a vector space provides a fundamental tool for the study of Euclideangeometry, a gyrovector space provides an algebraic tool for the study of hyperbolic ge-ometry. In general, the gyrovector spaces do not satisfy the distributivity with scalarmultiplication. In this article, we see under what condition the distributivity with scalarmultiplication is satis ed. 1. IntroductionIn order to provide an algebraic tool to study Einstein’s relativistic velocitysum, A. A. Ungar [2] has introduced a notion of gyrogroup and has developed to-gether the study of analytic hyperbolic geometry. The gyrogroup is a most naturalextension of a group into the nonassociative algebra. The associativity (and thecommutativity) of group operations is salvaged in a suitably modified form, calleda gyroassociativity (and a gyrocommutativity). In Section 2 we introduce a notionof (gyrocommutative) gyrogroup with its examples.Later on it is known that gyrocommutative gyrogroups are equivalent to Bruckloops (see [1]). To elaborate a precise language, we prefix a
9 citations
TL;DR: In this paper, the authors established some fractional integral formulas involving the extended generalized Gauss hypergeometric function by using certain general pair of integral operators involving Gauss HOGs.
Abstract: Several interesting and useful extensions of some familiar special functions such as Beta and Gauss hypergeometric functions and their properties have, recently, been investigated by many authors. Motivated mainly by those earlier works, we establish some fractional integral formulas involving the extended generalized Gauss hypergeometric function by using certain general pair of fractional integral operators involving Gauss hypergeometric function , Some interesting special cases of our main results are also considered.
7 citations
TL;DR: In this article, integral type boundary value problems of second order singular differential equations with quasi-Laplacian on whole lines are studied and sufficient conditions to guarantee the existence and non-existence of positive solutions are established.
Abstract: This paper is concerned with integral type boundary value problems of second order singular differential equations with quasi-Laplacian on whole lines. Sufficient conditions to guarantee the existence and non-existence of positive solutions are established. The emphasis is put on the non-linear term involved with the nonnegative singular function and the singular nonlinearity term f in differential equations. Two examples are given to illustrate the main results.
6 citations
TL;DR: In this article, a new multivalued mapping in R-trees, called k-strictly pseudononspreading, was introduced and studied, and strong convergence theorems of the proposed iteration to a common fixed point of two k-strategically nonsmooth pseudononons-preading mappings were established.
Abstract: In this paper, we introduce and study a new multivalued mapping in Rtrees, called k-strictly pseudononspreading. We also introduce a new two-step iterative process for two k-strictly pseudononspreading multivalued mappings in R-trees. Strong convergence theorems of the proposed iteration to a common fixed point of two k-strictly pseudononspreading multivalued mappings in R-trees are established. Our results improve and extend the corresponding results existing in the literature.
TL;DR: In this paper, the equivalence of generalized Weyl's theorem with generalized Browder's theorem, property (gw) with property (gb) and property (w), with property(b) has been established.
Abstract: If T is an unbounded hyponormal operator on an infinite dimensional complex Hilbert space H with , then it is shown that T satisfies Weyl's theorem, generalized Weyl's theorem, Browder's theorem and generalized Browder's theorem. The equivalence of generalized Weyl's theorem with generalized Browder's theorem, property (gw) with property (gb) and property (w) with property (b) have also been established. It is also shown that a-Browder's theorem holds for T as well as its adjoint .
TL;DR: For functions f(z) = z + a2z 2 + a3z 3 + ¢¢¢ with ja2j = 2b, b ‚ 0, sharp radii of starlikeness of order fi (0 • fi 0) were obtained in this paper.
Abstract: For functions f(z) = z + a2z 2 + a3z 3 + ¢¢¢ with ja2j = 2b, b ‚ 0, sharp radii of starlikeness of order fi (0 • fi 0). Radii constants in other instances are also obtained.
TL;DR: In this article, the authors extend the definition of harmonic and biharmonic maps via the variation of energy and bienergy between two Riemannian manifolds, and present some new properties for the generalized stress energy tensor and the divergence of generalized stress bienergy.
Abstract: In this note, we extend the definition of harmonic and biharmonic maps via the variation of energy and bienergy between two Riemannian manifolds. In particular we present some new properties for the generalized stress energy tensor and the divergence of the generalized stress bienergy.
TL;DR: In this article, the notion of quasi-valuation maps based on a subalgebra and an ideal in BCK/BCI-algebras is introduced, and several properties are investigated.
Abstract: The notion of quasi-valuation maps based on a subalgebra and an ideal in BCK/BCI-algebras is introduced, and then several properties are investigated. Relations between a quasi-valuation map based on a subalgebra and a quasi-valuation map based on an ideal is established. In a BCI-algebra, a condition for a quasi-valuation map based on an ideal to be a quasi-valuation map based on a subalgebra is provided, and conditions for a real-valued function on a BCK/BCI-algebra to be a quasi-valuation map based on an ideal are discussed. Using the notion of a quasi-valuation map based on an ideal, (pseudo) metric spaces are constructed, and we show that the binary operation * in BCK-algebras is uniformly continuous.
TL;DR: In this article, the functional equations of Dirichlet and Hurwitz L-functions associated with Bernoulli numbers and polynomials attached to Dirichlets character are investigated.
Abstract: In this paper, we investigate the functional equations of the multiple Dirichlet and Hurwitz L-functions associated with Bernoulli numbers and polynomials attached to Dirichlet character.
TL;DR: In this paper, the Ricci tensor and 1-form of a weakly Ricci-symmetric manifold is analyzed and shown to be an -Einstein manifold.
Abstract: We analyze the -manifolds endowed with some symmetric properties, focusing on Ricci tensor and the 1-form . We study some properties of special Weakly Ricci-Symmetric -manifolds and also shown that Weakly -Ricci Symmetric -manifold is an -Einstein manifold.
TL;DR: In this paper, the authors constructed a state model for the two-variable Kauman polynomial using planar trivalent graphs, and used this model to obtain a Polynomial invariant for a certain type of trivalents embedded in.
Abstract: We construct a state model for the two-variable Kauman polynomial using planar trivalent graphs. We also use this model to obtain a polynomial invariant for a certain type of trivalent graphs embedded in .
TL;DR: In this article, the authors consider Witt-type formula for the extension of Changchee and Daehee numbers and polynomials and derive some identities and properties of those numbers which are related to a special polynomial.
Abstract: We consider Witt-type formula for the extension of Changchee and Daehee numbers and polynomials. We derive some identities and properties of those numbers and polynomials which are related to special polynomials.
TL;DR: In this article, it was shown that every f -biharmonic map from a complete Rieman-nian manifold into a Riemannian manifold with non-positive sectional curvature, satisfying some condition, is f -harmonic.
Abstract: In this paper, we prove that every f -biharmonic map from a complete Rieman- nian manifold into a Riemannian manifold with non-positive sectional curvature,satisfying some condition, is f -harmonic. Also we present some properties for the f -biharmonicity of submanifolds of S n , and we give the classification of f -biharmonic curves in 3-dimensional sphere.
TL;DR: In this article, a flxed point method is presented to prove generalized Hyers{ Ulam stability of the systems of quadratic-cubic functional equations with constant coef-flcients in modular spaces.
Abstract: In this paper, we present a flxed point method to prove generalized Hyers{ Ulam stability of the systems of quadratic-cubic functional equations with constant coef- flcients in modular spaces.
TL;DR: In this article, the authors prove that among strictly locally convex plane curves, those properties characterize parabolas and show that the center of gravity lies on the axis of the parabola.
Abstract: Archimedes determined the center of gravity of a parabolic section as follows. For a parabolic section between a parabola and any chord AB on the parabola, let us denote by P the point on the parabola where the tangent is parallel to AB and by V the point where the line through P parallel to the axis of the parabola meets the chord AB. Then the center G of gravity of the section lies on PV called the axis of the parabolic section with PG = 3 PV . In this paper, we study strictly locally convex plane curves satisfying the above center of gravity properties. As a result, we prove that among strictly locally convex plane curves, those properties characterize parabolas.
TL;DR: In this paper, differential subordinations and superordinations results are obtained for meromorphic functions in the punctured unit disk which are associated with an inte-gral operator.
Abstract: Difierential subordinations and superordinations results are obtained for cer- tain meromorphic functions in the punctured unit disk which are associated with an inte- gral operator. These results are obtained by investigating appropriate classes of a dmissible functions. Sandwich-type results are also obtained.
TL;DR: In this paper, the authors obtained a zero-free region for polynomials in terms of j and j and also obtained the bound for number of zeros that can lie in a prescribed region.
Abstract: Let P(z) = n ∑ j=0 a jz j be a polynomial of degree n and Re aj = j; Im aj = j: In this paper, we have obtained a zero- free region for polynomials in terms of j and j and also obtain the bound for number of zeros that can lie in a prescribed region.
TL;DR: In this paper, the standard identity in 4 variables for R satises s4, which is defined as follows: if either char(R) > n or char (R) = 0, then R satis s4.
Abstract: Let R be a prime ring with center Z, I a nonzero ideal of R, and a non- trivial automorphism of R such that {(x ◦ y) − (x ◦ y)} n ∈ Z for all x;y ∈ I. If either char(R) > n or char (R) = 0, then R satises s4, the standard identity in 4 variables.
TL;DR: In this paper, a characteristic lattice point invariant for 3-manifolds was constructed by using an embedding of the prime links into the set of lattice points.
Abstract: A complete invariant defined for (closed connected orientable) 3-manifolds is an invariant defined for the 3-manifolds such that any two 3-manifolds with the same invariant are homeomorphic. Further, if the 3-manifold itself can be reconstructed from the data of the complete invariant, then it is called a characteristic invariant defined for the 3-manifolds. In a previous work, a characteristic lattice point invariant defined for the 3-manifolds was constructed by using an embedding of the prime links into the set of lattice points. In this paper, a characteristic rational invariant defined for the 3-manifolds called the characteristic genus defined for the 3-manifolds is constructed by using an embedding of a set of lattice points called the PDelta set into the set of rational numbers. The characteristic genus defined for the 3-manifolds is also compared with the Heegaard genus, the bridge genus and the braid genus defined for the 3-manifolds. By using this characteristic rational invariant defined for the 3-manifolds, a smooth real function with the definition interval (-1, 1) called the characteristic genus function is constructed as a characteristic invariant defined for the 3-manifolds.
TL;DR: In this article, the braid indices of the Kanenobu knots have been studied and sharp upper and lower bounds of the khanobu indices have been obtained. But it is not easy to determine the kanobu index of a link.
Abstract: We study the braid indices of the Kanenobu knots. It is known that the Kanenobu knots have the same HOMFLYPT polynomial and the same Khovanov-Rozansky homology. The MFW inequality is known for giving a lower bound of the braid index of a link by applying the HOMFLYPT polynomial. Therefore, it is not easy to determine the braid indices of the Kanenobu knots. In our previous paper, we gave upper bounds and sharper lower bounds of the braid indices of the Kanenobu knots by applying the 2-cable version of the zeroth coefficient HOMFLYPT polynomial. In this paper, we give sharper upper bounds of the braid indices of the Kanenobu knots.
TL;DR: In this article, the generalized non-linear differential polynomials, used in this paper, share a nonzero polynomial, which is a generalization of the specific type of differential poynomials as used in [14] and [15].
Abstract: In this paper we shall stress on the generalization of the specific type of differential polynomials as used in [14] and [15]. Actually we use the notion of weighted sharing to study different relationship of meromorphic functions when the generalized non-linear differential polynomials, used in the paper share a nonzero polynomial. Two examples are provided to show that certain conditions used in the paper are the best possible when the differential polynomial takes the special form. 2010 Mathematics Subject Classification: 30D35.