Showing papers in "Kyungpook Mathematical Journal in 2020"
TL;DR: Fractional calculus has gained considerable popularity and importance during the past over four decades, due mainly to its demonstrated applications in numerous seemingly diverse and widespread fields of mathematical, physical, engineering and statistical sciences as mentioned in this paper.
Abstract: The subject of fractional calculus (that is, the calculus of integrals and derivatives of any arbitrary real or complex order) has gained considerable popularity and importance during the past over four decades, due mainly to its demonstrated applications in numerous seemingly diverse and widespread fields of mathematical, physical, engineering and statistical sciences. Various operators of fractional-order derivatives as well as fractional-order integrals do indeed provide several potentially useful tools for solving differential and integral equations, and various other problems involving special functions of mathematical physics as well as their extensions and generalizations in one and more variables. The main object of this survey-cum-expository article is to present a brief elementary and introductory overview of the theory of the integral and derivative operators of fractional calculus and their applications especially in developing solutions of certain interesting families of ordinary and partial fractional “differintegral” equations. This general talk will be presented as simply as possible keeping the likelihood of non-specialist audience in mind. Received February 1, 2019; revised October 7, 2019; accepted October 29, 2019. 2020 Mathematics Subject Classification: primary 26A33, 33B15, 33C05, 33C20, 33E12, 34A25, 44A10, secondary 33C65, 34A05, 34A08.
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TL;DR: In this paper, the authors studied the energy-momentum tensor T of a space-time having a divergence free $W$-curvature tensor is of Codazzi type.
Abstract: This paper aims to study the $W$-curvature tensor on relativistic space-times. The energy-momentum tensor T of a space-time is semi-symmetric given that the $W$-curvature tensor is semi-symmetric whereas energy-momentum tensor T of a space-time having a divergence free $W$-curvature tensor is of Codazzi type. A space-time having a traceless $W$-curvature tensor is Einstein. A $W$-curvature flat space-time is Einstein. Perfect fluid space-times which admits $W$-curvature tensor are considered.
6 citations
2 citations
TL;DR: In this article, the Miao-Tam critical point equation (CPE) on 3-dimensional cosymplectic manifolds was studied, and it was shown that the manifold is of constant sectional curvature −α, provided Dλ 6 = (ξλ)ξ.
Abstract: The object of the present paper is to study the critical point equation (CPE) on 3-dimensional α-cosymplectic manifolds. We prove that if a 3-dimensional connected αcosymplectic manifold satisfies the Miao-Tam critical point equation, then the manifold is of constant sectional curvature −α, provided Dλ 6= (ξλ)ξ. We also give several interesting corollaries of the main result.
2 citations
TL;DR: In this article, it was shown that there are no PR-semi-slant warped product submanifolds with proper slant coefficients in para-Kähler manifolds.
Abstract: In this paper, we prove that there are no non-trivial PR-semi-slant warped product submanifolds with proper slant coefficients in para-Kähler manifolds M . We also present a numerical example that illustrates the existence of a PR-warped product submanifold in M .
2 citations
TL;DR: In this article, a class of biharmonic maps from and between doubly product manifolds is characterized in terms of theie warping function, where all of the factors are Euclidean spaces.
Abstract: In this paper, we characterize a class of biharmonic maps from and between doubly product manifolds in terms of theie warping function. Examples are constructed when all of the factors are Euclidean spaces.
2 citations
TL;DR: In this paper, the authors define a module M to be generalized FI-extending if for any fully invariant submodule N of M, there exists a direct summand D of M such that N ≤ D and that D/N is singular.
Abstract: A module M is called FI-extending if every fully invariant submodule of M is essential in a direct summand of M . In this work, we define a module M to be generalized FI-extending (GFI-extending) if for any fully invariant submodule N of M , there exists a direct summand D of M such that N ≤ D and that D/N is singular. The classes of FI-extending modules and singular modules are properly contained in the class of GFIextending modules. We first develop basic properties of this newly defined class of modules in the general module setting. Then, the GFI-extending property is shown to carry over to matrix rings. Finally, we show that the class of GFI-extending modules is closed under direct sums but not under direct summands. However, it is proved that direct summands are GFI-extending under certain restrictions.
1 citations
TL;DR: In this article, the maximal ideal space of the Lipschitz algebras of infinitely differentiable functions is derived. But the maximal optimal space of these extensions is not known.
Abstract: In this paper, we first introduce new classes of Lipschitz algebras of infinitely differentiable functions which are extensions of the standard Lipschitz algebras of infinitely differentiable functions. Then we determine the maximal ideal space of these extended algebras. Finally, we show that if X and K are uniformly regular subsets in the complex plane, then R(X,K) is natural.
1 citations
TL;DR: In this paper, Khandaker and Raffoul considered a Volterra discrete system with nonlinear perturbation and showed that the stability of the system can be improved by using a discrete version of the difference equation.
Abstract: Difference equations are the discrete analogues of differential equations and they usually describe certain phenomena over the course of time. Difference equations have many applications in a wide variety of disciplines, such as economics, mathematical biology, social sciences and physics. We refer to [1, 2, 4, 6] for the basic theory and some applications of difference equations. Volterra difference equations are extensively used to model phenomena in engineering, economics, and in the natural and social sciences; their stability has been studied by many authors. In [5], Khandaker and Raffoul considered a Volterra discrete system with nonlinear perturbation
1 citations
TL;DR: In this article, the authors consider the problem of finding a ring D such that A ⊆ D ⊂ B and the extension B ⊈ B is inert and show that the number of such rings may be any non-negative integer or infinite.
Abstract: Let (A,M) ⊂ (B,N) be commutative quasi-local rings. We consider the property that there exists a ring D such that A ⊆ D ⊂ B and the extension D ⊂ B is inert. Examples show that the number of such D may be any non-negative integer or infinite. The existence of such D does not imply M ⊆ N . Suppose henceforth that M ⊆ N . If the field extension A/M ⊆ B/N is algebraic, the existence of such D does not imply that B is integral over A (except when B has Krull dimension 0). If A/M ⊆ B/N is a minimal field extension, there exists a unique such D, necessarily given by D = A+N (but it need not be the case that N = MB). The converse fails, even if M = N and B/M is a finite
TL;DR: In this article, the authors proved that the ring of 2×2 matrices over an arbitrary field is quasi-reversible, which is an answer to the question given by Da Woon Jung et al. in [Bull. Korean Math. Soc., 56(4) (2019) 993-1006].
Abstract: A ring R is quasi-reversible if 0 6= ab ∈ I(R) for a, b ∈ R implies ba ∈ I(R), where I(R) is the set of all idempotents in R. In this short paper, we prove that the ring of 2×2 matrices over an arbitrary field is quasi-reversible, which is an answer to the question given by Da Woon Jung et al. in [Bull. Korean Math. Soc., 56(4) (2019) 993-1006].
TL;DR: In this article, the authors studied the properties of several generalizations of prime subsemimodules and showed that a φ-prime submodule is weakly prime.
Abstract: Let R be a commutative semiring with identity and M be a unitary Rsemimodule. Let φ : S(M) → S(M) ∪ {∅} be a function, where S(M) is the set of all subsemimodules of M . A proper subsemimodule N of M is called φ-prime subsemimodule, if r ∈ R and x ∈M with rx ∈ N \\φ(N) implies that r ∈ (N :R M) or x ∈ N . So if we take φ(N) = ∅ (resp., φ(N) = {0}), a φ-prime subsemimodule is prime (resp., weakly prime). In this article we study the properties of several generalizations of prime subsemimodules.
TL;DR: In this article, a light-like hypersurface M of an indefinite nearly trans-Sasakian manifold M is studied with an (l,m)-type connection such that the structure vector field ζ of M is tangent to M.
Abstract: We study a lightlike hypersurface M of an indefinite nearly trans-Sasakian manifold M̄ with an (l,m)-type connection such that the structure vector field ζ of M̄ is tangent to M . In particular, we focus on such lightlike hypersurfaces M for which the structure tensor field F is either recurrent or Lie recurrent, or such that M itself is totally umbilical or screen totally umbilical.
TL;DR: In this article, it was shown that the Brück conjecture holds in a special case when the hyper order of the function f is 1/2, which is not an integer.
Abstract: The Brück conjecture is still open for an entire function f with hyper order of no less than 1/2, which is not an integer. In this paper, it is proved that the hyper order of solutions of a linear complex differential equation that is related to the Brück Conjecture is infinite. The results show that the conjecture holds in a special case when the hyper order of f is 1/2.
TL;DR: In this article, the diameter of a chemical graph in terms of its inverse degree is given, and an ordering of connected chemical graphs with respect to the inverse degree has also been obtained, where the cyclomatic number is defined as γ = m − n + k, where m, n and k are the number of edges, vertices and components of G, respectively.
Abstract: Let G be a chemical graph with vertex set {v1, v1, . . . , vn} and degree sequence d(G) = (degG(v1), degG(v2), . . . , degG(vn)). The inverse degree, R(G) of G is defined as R(G) = ∑n i=1 1 degG(vi) . The cyclomatic number of G is defined as γ = m − n + k, where m, n and k are the number of edges, vertices and components of G, respectively. In this paper, some upper bounds on the diameter of a chemical graph in terms of its inverse degree are given. We also obtain an ordering of connected chemical graphs with respect to the inverse degree.
TL;DR: The class of rings which satisfy the property of inserting regular elements at zero products, and rings with such property are called regular-IFP, were studied in this article, where conditions under which the regularIFPness pass to polynomial rings, and equivalent conditions to the regular-IFPness.
Abstract: This article concerns the class of rings which satisfy the property of inserting regular elements at zero products, and rings with such property are called regular-IFP. We study the structure of regular-IFP rings in relation to various ring properties that play roles in noncommutative ring theory. We investigate conditions under which the regularIFPness pass to polynomial rings, and equivalent conditions to the regular-IFPness.
TL;DR: In this paper, the geometry of contact CR submanifolds and radical transversal light-like submansifolds of Sasaki-like almost contact manifolds with Bmetric was introduced.
Abstract: In this paper, we introduce the geometry of contact CR submanifolds and radical transversal lightlike submanifolds of Sasaki-like almost contact manifolds with Bmetric. We obtain some new results that establish a relationship between these two submanifolds.