Showing papers in "Communications of The Korean Mathematical Society in 2015"
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TL;DR: In this paper, mixed norm estimates for the spherical averaging operator were used to obtain some results concerning pinned distance sets, and they used the mixed norm estimate for the weighted average of the spherical average operator to obtain the results concerning the pinned distance set.
Abstract: We use mixed norm estimates for the spherical averaging operator to obtain some results concerning pinned distance sets.
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TL;DR: In this paper, the first and second maximum values of the atom-bond connectivity index among all n vertex cactusgraphs were obtained, and the aim of this paper was to obtain the first andsecond maximum values.
Abstract: . The atom-bond connectivity index of a graph G(ABC indexfor short) is defined as the summation of quantitiesq d(u)+d(v)−2d(u)d(v) overall edges of G. A cactus graph is a connected graph in which every blockis an edge or a cycle. The aim of this paper is to obtain the first andsecond maximum values of the ABC index among all n vertex cactusgraphs. 1. IntroductionSuppose G is a simple connected graph with vertex and edge sets V (G) andE(G), respectively. A block of G is a maximal connected subgraphof G withoutcut-vertex. A cactus is a connected graph in which every block is an edge or acycle [18, p. 160]. These are connected graphs in which each edge belongs toat most one cycle. An example of a cactus graph is depicted in Figure 1.Figure 1. Examples of cactus graphs.Cactus graphs have several applications in computer science and biologyand so it is a topic of interest among many researchers in different scientificdisciplines. In [1, 6], it is proved that some graph problems which are NP-hardfor general graphs can be solved in polynomial time for cacti. On the otherhand, in [15] a number of combinatorial optimization problems are presented
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TL;DR: Agarwal et al. as discussed by the authors gave a metric version of an iterationscheme of Agarwal et.al. [1] and approximate points of two families of nonexpansive mappings in hyperbolic spaces through this iter-ation scheme.
Abstract: . In this article, we first give metric version of an iterationscheme of Agarwal et al. [1] and approximate fixed points of two finitefamilies of nonexpansive mappings in hyperbolic spaces through this iter-ation scheme which is independent of but faster than Mann and Ishikawascheme. Also we consider case of three finite families of nonexpansivemappings. But, we need an extra condition to get convergence. Our con-vergence theorems generalize and refine many know results in the currentliterature. 1. IntroductionThroughout the article, Ndenotes the set of positive integers and I denotesthe set of first N natural numbers. Let (X,d) be a metric space and K bea nonempty subset of X. A selfmap T on K is said to be nonexpansive ifd(Tx,Ty) ≤ d(x,y). Denote by F (T) the set of fixed points of T and byF = ∩ Ni=1 (F (T i ) ∩F (S i )) the set of common fixed points of two finite familiesof mappings {T i : i ∈ I} and {S i : i ∈ I}.We know that Mann and Ishikawa iteration processes are defined for givenx
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TL;DR: In this paper, the interplay between the ring-theoretical properties of R((S,!)) and its zero-divisor graph was investigated, and the preservation of diameter and girth of the graph under skew generalized power series rings was examined.
Abstract: Let R be a ring, (S,�) a strictly ordered monoid and ! : S ! End(R) a monoid homomorphism. The skew generalized power se- ries ring R((S,!)) is a common generalization of (skew) polynomial rings, (skew) power series rings, (skew) Laurent polynomial rings, (skew) group rings, and Mal'cev-Neumann Laurent series rings. In this paper, we in- vestigate the interplay between the ring-theoretical properties of R((S,!)) and the graph-theoretical properties of its zero-divisor graph ( R((S,!))). Furthermore, we examine the preservation of diameter and girth of the zero-divisor graph under extension to skew generalized power series rings.
TL;DR: In this article, the uniqueness of entire functions concerning differential polynomials and deficient value was studied, and the results extend and improve Theorem 2 in Yi [13].
Abstract: In this paper, we study the uniqueness of entire functions concerning differential polynomials and deficient value. The results extend and improve Theorem 2 in Yi [13].
TL;DR: In this article, a generalized fractional integral version of Grüss type integral inequality was established by making use of the Gauss hypergeometric function fractional integrality operator.
Abstract: In this paper, we aim at establishing a generalized fractional integral version of Grüss type integral inequality by making use of the Gauss hypergeometric function fractional integral operator. Our main result, being of a very general character, is illustrated to specialize to yield numerous interesting fractional integral inequalities including some known results.
TL;DR: In this paper, a double generating relation of a product of a pair of Laguerre polynomials and a number of useful relations with elementary functions, Bessel functions, Hermite polynomorphisms, and single series expansions of pairs of pairs were derived by using a two-dimensional extension of a very general series transform.
Abstract: By utilizing a two-dimensional extension of a very general series transform given by Bailey, Exton [Indian J. pure appl. Math. 24 (6) (1993), 401-408] deduced a very general double generating relation of a product of a pair of Laguerre polynomials and obtained a number of useful relations with elementary functions, Bessel functions, Hermite polynomials and single series expansions of pairs of Laguerre polynomials. Unfortunately, some of the results given by Exon contain errors and thus this is the aim of this short note to provide the corrected form of these results. 2000 AMS Subject Classification: 33C20; 33C05; 33B20.
TL;DR: In this paper, it was shown that if a space has a set which is both maximal and minimal open, then either this set is the only nontrivial open set in the space or the space is disconnected.
Abstract: We obtain some conditions for disconnectedness of a topolog- ical space in terms of maximal and minimal open sets, and some similar results in terms of maximal and minimal closed sets along with interre- lations between them. In particular, we show that if a space has a set which is both maximal and minimal open, then either this set is the only nontrivial open set in the space or the space is disconnected. We also obtain a result concerning a minimal open set on a subspace.
TL;DR: In this article, the authors investigated the Hopf algebra conjugation of the mod 2 Steenrod algebra, A 2, in terms of Hopf algebras conjugated by the Steenrodsquares Sq n.
Abstract: . We investigate the Hopf algebra conjugation, χ, of the mod2 Steenrod algebra, A 2 , in terms of the Hopf algebra conjugation, χ ′ , ofthe mod 2 Leibniz–Hopf algebra. We also investigate the fixed points ofA 2 under χ and their relationship to the invariants under χ ′ . 1. IntroductionThe mod 2 Steenrod algebra A 2 is the free associative graded algebra gen-erated by the Steenrodsquares Sq n [18] of degree n, n ≥ 1, over F 2 subject tothe AdemrelationsSq a Sq b = ⌊ X a/2⌋s=0 b−1−sa−2sSq a+b−s Sq s for 0 < a < 2b.Conventionally, Sq 0 = 1, the multiplicative identity. Topologically, A 2 is thealgebra of stable cohomology operations for ordinary cohomology H ∗ over F 2 .A monomial in A 2 can be written in the form Sq j 1 Sq j 2 ···Sq j r , which weshall denote by Sq j 1 ,j 2 ,...,j r . Admissible monomials form a vector space ba-sis “admissible basis” for A 2 . Milnor [16] determined the graded connectedHopf algebra structure of A 2 by a cocomutative coproduct given by ∆(Sq
TL;DR: In this paper, it was shown that there are no 1-light-like submanifolds of an indefinitetrans-Sasakian manifold M¯ admitting non-metric connections.
Abstract: . We study two types of 1-lightlike submanifolds, so-calledlightlike hypersurface and half lightlikesubmanifold, of an indefinite trans-Sasakian manifold M¯ admitting non-metric θ-connection. We prove thatthere exist no such two types of 1-lightlike submanifolds of an indefinitetrans-Sasakian manifold M¯ admitting non-metric θ-connections. 1. IntroductionA linear connection ∇¯ on a semi-Riemannian manifold (M,¯ ¯g) is called anon-metric θ-connection if, for any vector fields X, Y and Z on M¯, it satisfies(1.1) (∇¯ X g¯)(Y,Z) = −θ(Y )¯g(X,Z)−θ(Z)¯g(X,Y ),where θ is a 1-form, associated with a non-vanishing smooth vector field ζ byθ(X) = ¯g(X,ζ).Two special cases are important for both the mathematical study and theapplications to physics: (1) A non-metric θ-connection ∇¯ on M¯ is called asemi-symmetric non-metric connection if its torsion tensor T¯ satisfiesT¯(X,Y ) = θ(Y )X −θ(X)Y.The notion of semi-symmetric non-metric connections on a Riemannian man-ifold was introduced by Ageshe and Chafle [1] and later studied by many au-thors. The lightlike version of Riemannian manifolds with semi-symmetricnon-metric connections has been studied by some authors [18, 20, 21, 23, 27].(2) A non-metric θ-connection ∇¯ on M¯ is called a quarter-symmetric non-metric connection if its torsion tensor T¯ satisfiesT¯(X,Y) = θ(Y )φX −θ(X)φY,
TL;DR: In this paper, the convergence theorems of modified Ishikawa iteration methods with respect to a pair of the single valued asymptotically nonexpansive mapping t and the multi-valued non-ansive map T were established.
Abstract: We establish the convergence theorems of the modified Ishikawa iteration methods with respect to a pair of the single valued asymptotically nonexpansive mapping t and the multi-valued nonexpansive mapping T . This results we obtain are analogs of Banach space results of Sokhuma [7], Sokhuma and Keawkhao [6]. Mathematics Subject Classification: 54H25, 54E40
TL;DR: In this paper, the authors reviewed recent mathematical progresses made on the study of the initial-value problem for nonlinear Dirac equations in one-dimensional dimension and showed the global existence of solutions to somenonlinear DirAC equations and proposed a model problem.
Abstract: . This paper reviews recent mathematical progresses made onthe study of the initial-value problem for nonlinear Dirac equations in onespace dimension. We also prove the global existence of solutions to somenonlinear Dirac equations and propose a model problem (3.6). 1. IntroductionWe are interested in the following initial value problem for the one dimen-sional nonlinear Dirac equationsi(∂ t U 1 +∂ x U 1 ) +mU 2 = ∂ U¯ 1 W(U 1 , U 2 ),i(∂ t U 2 −∂ x U 2 ) +mU 1 = ∂ U¯ 2 W(U 1 , U 2 ),U j (x, 0) = u j (x),(1.1)where U j : R 1+1 → C for j = 1, 2 and m(≥ 0) is a mass. U¯ is a complexconjugate of U. The potential W satisfies the following properties:1. Symmetry: W(U 1 , U 2 ) = W(U 2 , U 1 ).2. Gauge invariance: W(e iθ U 1 , e iθ U 2 ) = W(U 1 , U 2 ) for any θ ∈ R.3. Polynomial in (U 1 , U 2 ) and (U¯ 1 , U¯ 2 ).It is known [11] that fourth order homogeneous polynomial satisfying theabove properties takes the formW = a 1 |U 1 | 2 |U 2 | 2 +a 2 (U¯ 1 U 2 +U¯ 2 U 1 ) 2 +a 3 (|U 1 | 4
TL;DR: In this article, all Weierstrass points on the hyperelliptic modular curves are shown to be non-exceptional, i.e., induced by matrices in the matrix space.
Abstract: In this paper, we find all Weierstrass points on the hyperelliptic modular curves $X_{0}(N)$ whose hyperelliptic involutions are non-exceptional, i.e., induced by matrices in $\mathrm{GL}_{2}(\mathbf{R})$.
TL;DR: Non-classical logic has become a formal and useful tool in dealing with fuzzy and uncertain informations in algebraic structures as well as other mathematical tools available which deal with uncertainty.
Abstract: . Strong uni-soft filters and divisible uni-soft filters in resid-uated lattices are introduced, and several properties are investigated.Characterizations of a strong and divisible uni-soft filter are discussed.Conditions for a uni-soft filter to be divisible are established. Relationsbetween a divisible uni-soft filter and a strong uni-soft filter are consid-ered. 1. IntroductionUncertainty is an attribute of information. There are three major theoriesdealing with uncertainty viz. theory of probability, theory of fuzzy sets andinterval mathematics. But these theories have their own difficulties. Thereare other mathematical tools available which deal with uncertainty, such asintuitionistic fuzzy sets, vague sets, and rough sets but these theories also havedifficulties as mentioned by Maji et al. [8]. As a new mathematical tool fordealing with uncertainties, Molodtsov [9] introduced the concept of soft sets.Since then several authors studied (fuzzy) algebraic structures based on soft settheory in several algebraic structures. Non-classical logic has become a formaland useful tool in dealing with fuzzy and uncertain informations. Variouslogical algebras have been proposed as the semantical systems of non-classicallogic systems. Residuated lattices are important algebraic structures whichare basic of BL-algebras, MV-algebras, MTL-algebras, Godel algebras, R
TL;DR: In this paper, the image of the embedding is determined, and the index of the image is also computed for a cyclic group of prime power order, and it is shown that the necessary and sufficient condition for β ∈ Φ(Z[G]) as congruence relations among the charactervalues of β.
Abstract: . Let G be a cyclic group of prime power order. There is anatural embedding of Z[G] into a product of rings of integers of cyclotomicfields. In this paper the image of the embedding is determined, and wealso compute the index of the image. 1. IntroductionFor a finite abelian group Glet Z[G] be the integral group ring of G, andlet I G be the augmentation ideal. For each complex character χof Glet Q(χ)be the cyclotomic field generated by the values of χand Z[χ] be its ring ofintegers.ConsiderΦ : Z[G] −→Y χ∈Gb Z[χ]Φ(α) = (...,χ(α),...),where the domain of χis extended to Z[G] by linearity. The map Φ is aninjective ring homomorphism. The goal of this paper is to determine Φ(Z[G])when Gis cyclic of prime power order.For an elementβ= (...,β χ ,...) ∈Y χ∈Gb Z[χ],let us refer to its components β χ as the character values of β. We find that,when Gis cyclic of prime power order, we can express the necessary and suf-ficient condition for β∈ Φ(Z[G]) as congruence relations among the charactervalues of β. As a byproduct, we also compute the index of Φ(Z[G]) inQZ[χ].There are refined type of conjectures on the values of L-functions (cf. [1],[2], [4], [5]) which predict (among others) that certain elements ofQ
TL;DR: In this article, the authors introduce the -Lauricella functions and the confluent forms and of n variables, and systematically investigate their various integral representations of each of these functions including their generating functions.
Abstract: Motivated mainly by certain interesting extensions of the -hypergeometric function defined by Virchenko et al. [11] and some -Appell's function introduced by Al-Shammery and Kalla [1], we introduce here the -Lauricella functions , and and the confluent forms and of n variables. We then systematically investigate their various integral representations of each of these -Lauricella functions including their generating functions. Various (known or new) special cases and consequences of the results presented here are also considered.
TL;DR: In this paper, the authors used the Legendre self-similar measure on the selfsimilar set to derive the cylindrical lower or upper local dimension set for the self-Similar measure.
Abstract: . The natural projection of a parameter lower (upper) distri-bution set for a self-similar measure on a self-similar set satisfying theopen set condition is the cylindrical lower or upper local dimension setfor the Legendre self-similarmeasure which is derived from the self-similarmeasure and the self-similar set. 1. IntroductionRecently, we [1] investigated the relation between spectral classes of a self-similar Cantor set in a set theoretical sense. More recently, using the parameterdistribution, we find the parallel results for the self-similar set (attractor of theIFS consisting of n(≥ 2) similitudes satisfying the OSC (open set condition))instead of the self-similar Cantor set (attractor of the IFS consisting of 2 simil-itudes satisfying the SSC (strong separation condition)), which leads to a gen-eralization of [1]. In this paper, we define the Legendre self-similar measureson the self-similar set which is derived from the self-similar measure and theself-similar set. Using the Legendre self-similar measures on the self-similar set,we give full relationship between the natural projection of a parameter lower(upper) distribution set for a self-similar measure on a self-similar set and thecylindrical lower or upper local dimension set for the Legendre self-similar mea-sures.2. PreliminariesLet N and R be the set of positive integers and the set of real numbersrespectively. An attractor K in the d-dimensional Euclidean space R
TL;DR: In this article, the optimality conditions for optimal control problem of Belousov-Zhabotinskii reaction model were obtained by showing the differentiability of the solution with respect to the control.
Abstract: This paper is concerned with the optimality conditions for optimal control problem of Belousov-Zhabotinskii reaction model. That is, we obtain the optimality conditions by showing the differentiability of the solution with respect to the control. We also show the uniqueness of the optimal control.