Showing papers in "Communications of The Korean Mathematical Society in 2008"
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TL;DR: In this article, the concept of soft sets was applied to the theory of subtraction algebras, and the notion of soft WS-algebra, soft subalgebra and soft deductive systems were derived.
Abstract: Molodtsov [8] introduced the concept of soft set as a new mathematical tool for dealing with uncertainties that is free from the difficulties that have troubled the usual theoretical approaches. In this paper we apply the notion of soft sets by Molodtsov to the theory of subtraction algebras. The notion of soft WS-algebras, soft subalgebras and soft deductive systems are introduced, and their basic properties are derived.
53 citations
TL;DR: In this article, the authors studied some properties of a quasi-Einstein manifold, and a non-trivial concrete example of such a manifold is also given, where the properties of the manifold are investigated.
Abstract: The object of the present paper is to study some properties of a quasi Einstein manifold. A non-trivial concrete example of a quasi Einstein manifold is also given.
36 citations
TL;DR: In this article, the authors give some new definitions of compatible mappings in intuitionistic fuzzy metric spaces and prove a common fixed point theorem for four mappings under the condition of compatibility mappings of type (I) and type (II) in complete intuitionistic metric spaces.
Abstract: In this paper, we give some new definitions of compatible mappings in intuitionistic fuzzy metric spaces and we prove a common fixed point theorem for four mappings under the condition of compatible mappings of type (I) and of type (II) in complete intuitionistic fuzzy metric spaces.
34 citations
TL;DR: The results extend and generalize some fixed point theorems on complete fuzzy metric spaces by using a new technique.
Abstract: In this paper, we give some fixed point theorems on fuzzy metric spaces with an implicit relation. Our results extend and generalize some fixed point theorems on complete fuzzy metric spaces by using a new technique.
32 citations
TL;DR: In this paper, a new Monte Carlo method is presented to compute the prices of barrier options on stocks and the key idea of the new method is to use an exit probability and uniformly distributed random numbers in order to efficiently estimate the first hitting time of barriers.
Abstract: A new Monte Carlo method is presented to compute the prices of barrier options on stocks The key idea of the new method is to use an exit probability and uniformly distributed random numbers in order to efficiently estimate the first hitting time of barriers It is numerically shown that the first hitting time error of the new Monte Carlo method decreases much faster than that of standard Monte Carlo methods
24 citations
TL;DR: In this paper, the notion of two-sided Γ-α-derivation of a near-ring was introduced and some generalizations of (1, 2) were given.
Abstract: We introduce the notion of two-sided Γ-α-derivation of a Γ- near-ring and give some generalizations of (1, 2).
9 citations
TL;DR: In this article, the existence of LP-Sasakian manifold with Ricci tensor tensors is studied with several non-trivial examples, including generalized Ricci recurrent LP-sakian manifolds with various examples.
Abstract: The object of the present paper is to provide the existence of LP-Sasakian manifolds with ·-recurrent, ·-parallel, `-recurrent, `- parallel Ricci tensor with several non-trivial examples Also generalized Ricci recurrent LP-Sasakian manifolds are studied with the existence of various examples
9 citations
TL;DR: In this paper, it was shown that every positive solution of the third order rational difference equation converges to the positive equilibrium point, where, where, and where, respectively,.
Abstract: In this paper we prove that every positive solution of the third order rational difference equation converges to the positive equilibrium point , where ,
9 citations
TL;DR: In this article, the Noether inequality is shown to hold in the case of a curve, and the existence of a counter example for this inequality is established in the special case of the linear system.
Abstract: For a nef and big divisor D on a smooth projective surface S, the inequality h 0 (S;OS(D)) • D 2 + 2 is well known. For a nef and big canonical divisor KS, there is a better inequality h 0 (S;OS(KS)) • 1 2 KS 2 + 2 which is called the Noether inequality. We investigate an inequality h 0 (S;OS(D)) • 1 D 2 + 2 like Cliord theorem in the case of a curve. We show that this inequality holds except some cases. We show the existence of a counter example for this inequality. We prove also the base-locus freeness of the linear system in the exceptional cases.
8 citations
TL;DR: In this paper, the authors investigate approximately higher ternary derivations in Banach ternaries via the Cauchy functional equation via a Cauche functional equation, and show that higher derivations of Banach algebras can be obtained via the same approach.
Abstract: We investigate approximately higher ternary derivations in Banach ternary algebras via the Cauchy functional equation .
8 citations
TL;DR: In this paper, the notion of weakly prime left ideals in near-subtraction semigroups was introduced and the corresponding conditions for a left ideal to be weakly PM were obtained.
Abstract: In this paper we introduce the notion of weakly prime left ideals in near-subtraction semigroups. Equivalent conditions for a left ideal to be weakly prime are obtained. We have also shown that if (M, L) is a weak m∗-system and if P is a left ideal which is maximal with respect to containing L and not meeting M, then P is weakly prime.
TL;DR: In this article, the relation between the vector variable biadditive functional equation and the multi-variable quadratic functional equation was investigated and the general solution of the above two functional equations was found.
Abstract: We investigate the relation between the vector variable biadditive functional equation f ( n ∑ i=1 xi, n ∑ i=1 yj ) = n ∑ i=1 n ∑ j=1 f(xi, yj) and the multi-variable quadratic functional equation g ( n ∑ i=1 xi ) + ∑ 1≤i
TL;DR: In this article, the authors generalize the Catalan number to the (n, k)-th Catalan number and find a combinatorial description that the number of partitions of n(k-1)+2 polygon by (k+1)-gon where all vertices of all (k + 1)-gons lie on the vertices in the polygon.
Abstract: In this paper, we generalize the Catalan number to the (n, k)-th Catalan numbers and find a combinatorial description that the (n, k)-th Catalan numbers is equal to the number of partitions of n(k-1)+2 polygon by (k+1)-gon where all vertices of all (k+1)-gons lie on the vertices of n(k-1)+2 polygon.
TL;DR: In this paper, it was shown that any complete immersed super stable minimalsubmanifold with ° at normal bundle has only one end and therefore is not a hyperplane.
Abstract: . Let M n be a complete immersed super stable minimal sub-manifold in R n + p with °at normal bundle. We prove that if M has flnitetotal L 2 norm of its second fundamental form, then M is an a–ne n -plane. We also prove that any complete immersed super stable minimalsubmanifold with °at normal bundle has only one end. 1. IntroductionLet M be an n -dimensional complete minimal submanifold in R n + p . When n = 2 and p = 1, do Carmo and Peng [3], Fischer-Colbrie and Schoen [5]independently showed that the only complete stable minimal surface is a plane.Recall that a minimal submanifold is stable if the second variation of its volumeis always nonnegative for any normal variation with compact support. Forhigher dimensional minimal hypersurfaces, do Carmo and Peng [4] generalizedthe result mentioned as above. We will denote by A the second fundamentalform of M .Theorem ([4]). Let M n be a complete stable minimal hypersurface in R n +1 satisfying R M jAj 2 dv < 1. Then M must be a hyperplane.
TL;DR: Li and Zhang as discussed by the authors proved the complete moment convergence of moving average processes under dependence assumptions under some suitable conditions, and extended this result to the -mixing case, which is the case we consider in this paper.
Abstract: Let {} be a doubly infinite sequence of identically distributed and -mixing random variables with zero means and finite variances and {} an absolutely summable sequence of real numbers. In this paper, we prove the complete moment convergence of {; } under some suitable conditions. We extend Theorem 1.1 of Li and Zhang [Y. X. Li and L. X. Zhang, Complete moment convergence of moving average processes under dependence assumptions, Statist. Probab. Lett. 70 (2004), 191.197.] to the -mixing case.
TL;DR: The notion of order systems in subtraction algebras was introduced by Jun et al. as discussed by the authors, and conditions for an ideal to be irreducible are provided.
Abstract: Conditions for an ideal to be irreducible are provided. The notion of an order system in a subtraction algebra is introduced, and related properties are investigated. Relations between ideals and order systems are given. The concept of a fixed map in a subtraction algebra is discussed, and related properties are investigated. semigroup of invertible functions. B. Zelinka (15) discussed a problem proposed by B. M. Schein concerning the struc- ture of multiplication in a subtraction semigroup. He solved the problem for subtraction algebras of a special type, called the atomic subtraction algebras. Y. B. Jun et al. (10) introduced the notion of ideals in subtraction algebras and discussed characterization of ideals. In (6), Y. B. Jun and H. S. Kim es- tablished the ideal generated by a set, and discussed related results. Y. B. Jun and K. H. Kim (11) introduced the notion of prime and irreducible ideals of a subtraction algebra, and gave a characterization of a prime ideal. They also provided a condition for an ideal to be a prime/irreducible ideal. In this paper, we give conditions for an ideal to be irreducible. We introduce the notion of an order system in a subtraction algebra, and investigate related properties. We provide relations between ideals and order systems. We deal with the concept of a fixed map in a subtraction algebra, and investigate related properties. 2. Preliminaries By a subtraction algebra we mean an algebra (X;i) with a single binary operation "i" that satisfies the following identities: for any x;y;z 2 X,
TL;DR: In this article, the authors derived the nonlinear equation for European option pricing containing liquidity risk which can be defined as the inverse of the partial derivative of the underlying asset price with respect to the amount of assets traded in the efficient market.
Abstract: . In this paper, we derive the nonlinear equation for Europeanoption pricing containing liquidity risk which can be defined as the inverseof the partial derivative of the underlying asset price with respect to theamount of assets traded in the efficient market. Numerical solutions areobtained by using finite element method and compared with option pricesof KOSPI200 Stock Index. These prices computed with liquidity risk areconsidered more realistic than the prices of Black-Scholes model withoutliquidity risk. 1. IntroductionClassical option pricing theory was suggested by Black and Scholes [4] andextended by Merton [7]. They assume that markets are frictionless and com-petitive. These option pricing models are not applicable in the presence ofliquidity risk occurred in we trade underlying assets in illiquid markets.Liquidity risk is the risk that arises from the difficulty of selling an asset.An investment may sometimes need to be sold quickly. Unfortunately, aninsufficient secondary market may prevent the liquidation or limit the fundsthat can be generated from the asset. Some assets are highly liquid and havelow liquidity risk (such as stock), while other assets are highly illiquid and havehigh liquidity risk (such as a house).Recently, some investigators have tried to advance option pricing modelscontaining liquidity risk. Amihud and Mendelson [2, 3] suggested that liquidityrisk measured by bid-ask spread affects underlying asset prices, less liquid assetsgive higher expected returns. Karakovsky [5, 6] proposed a portfolio for bondsand stocks, and the option pricing equation using the idea of the liquiditynumber which has a positive sign whenever the underlying asset price goesdown or up. Acharya and Pedersen [1] solve explicitly a simple equilibriummodel with liquidity risk which a underlying asset’s required return depends
TL;DR: In this paper, the authors introduce and study lacunary statistical convergence for double sequences of fuzzy numbers and also present some inclusion theorems for fuzzy numbers with and without a fixed number of entries.
Abstract: In this paper we introduce and study lacunary statistical convergence for double sequences of fuzzy numbers and we shall also present some inclusion theorems.
TL;DR: In this paper, the Hyers-Ulam stability of trigonometric functional equations has been proved for trigonometrical functional equations with respect to trigonometry and functional functions.
Abstract: In this article we prove the Hyers–Ulam stability of trigonometric functional equations.
TL;DR: The strong generalized neighborhood systems which are generalizations of neighborhood systems are introduced and every (ˆ;ˆ 0 )-continuous function is shown to be a generalized neighborhood space.
Abstract: We introduce and study the concepts of strong generalized neighborhood systems, SGNS and sg-open sets We also introduce and investigate the concept of (ˆ;ˆ 0 )-continuity and sg-continuity on SGNS's A Csazar introduced the notions of generalized neighborhood sys- tems and generalized topological spaces He also introduced the notions of continuous functions and associated interior and closure operators on gener- alized neighborhood systems and generalized topological spaces In particu- lar, he investigated characterizations for the generalized continuous function(= (ˆ;ˆ 0 )-continuous function) by using a closure operator defined on generalized neighborhood systems In this paper we introduce the strong generalized neighborhood systems which are generalizations of neighborhood systems The strong generalized neighborhood system induces a strong generalized neighborhood space (briefly SGNS) which it implies a generalized neighborhood space And the SGNS induces a structure(= the collection of all sg-open sets on an SGNS) which is a generalization of topology We introduce the new concepts of interior and closure on an SGNS and investigate some properties In particular, we introduce the concept of sg-open sets on a given SGNS and investigate some properties We introduce the concepts of sg-continuity and (ˆ;ˆ 0 )-continuity and we characterize some properties by the new interior and closure operators defined on an SGNS Finally we show that every (ˆ;ˆ 0 )-continuous function is
TL;DR: In this paper, a method for constructing a class of grade 3, grade 3 perfect ideals which are not Gorenstein is described, and it is shown that they are algebraically linked to an even type grade 3 almost complete intersection.
Abstract: Buchsbaum and Eisenbud showed that every Gorenstein ideal of grade 3 is generated by the submaximal order pfaffians of an alternat- ing matrix. In this paper, we describe a method for constructing a class of type 3, grade 3, perfect ideals which are not Gorenstein. We also prove that they are algebraically linked to an even type grade 3 almost complete intersection.
TL;DR: In this paper, the stability of a Cauchy-Jensen functional equation was proved in the sense of Th. M. Rassias, and the stability was shown for a functional equation with constant number of variables.
Abstract: In this paper, we prove the stability of a Cauchy-Jensen functional equation =f(x, z)+f(x, w)+f(y, z)+f(y, w) in the sense of Th. M. Rassias.
TL;DR: In this article, the authors introduce the concepts of the ordered n-prime ideals and the ordered N-semiprime ideals in ordered -semigroups and characterize the relationship between these ideals and ideal extensions in ordered semigroups.
Abstract: The motivation mainly comes from the conditions of the (ordered) ideals to be prime or semiprime that are of importance and interest in (ordered) semigroups and in (ordered) -semigroups In 1981, Sen [8] has introduced the concept of the -semigroups We can see that any semigroup can be considered as a -semigroup The concept of ordered ideal extensions in ordered -semigroups was introduced in 2007 by Siripitukdet and Iampan [12] Our purpose in this paper is to introduce the concepts of the ordered n-prime ideals and the ordered n-semiprime ideals in ordered -semigroups and to characterize the relationship between the ordered n-prime ideals and the ordered ideal extensions in ordered -semigroups
TL;DR: In this article, the global existence and blow-up properties of a non-Newton polytropic filtration system with homogeneous Dirichlet boundary condition were analyzed.
Abstract: This paper deals the global existence and blow-up properties of the following non-Newton polytropic filtration system, ut − △m,pu = u α1 Z Ω v β1 (x, t)dx, vt − △n,qv = v α2 Z Ω u β2 (x, t)dx, with homogeneous Dirichlet boundary condition. Under appropriate hy- potheses, we prove that the solution either exists globally or blows up in finite time depends on the initial data and the relations of the parameters in the system.
TL;DR: In this paper, the authors investigated the relationship between the first Betti number and stable minimal surfaces and studied the analytic properties of stable minimal surface in M for n = 3, where n is the number of vertices in the manifold.
Abstract: It is well known that critical points of the total scalar curvature functional S on the space of all smooth Riemannian structures of volume 1 on a compact manifold M are exactly the Einstein metrics. When the domain of S is restricted to the space of constant scalar curvature metrics, there has been a conjecture that a critical point is isometric to a standard sphere. In this paper we investigate the relationship between the first Betti number and stable minimal surfaces, and study the analytic properties of stable minimal surfaces in M for n = 3.
TL;DR: In this paper, the authors derived the asymptotic expansions of solutions of the heat equation with hyperfunctions initial data and showed that these expansions can be obtained from a single hyperfunction.
Abstract: We will derive the asymptotic expansions of solutions of the heat equation with hyperfunctions initial data.
TL;DR: In this paper, it is shown that it is natural for BCC-algebras to have many clopen sets and thus to be highly connected via the ideal theory of BCCalgebas.
Abstract: In this paper, we show how to associate certain topologies with special ideals of BCC-algebras on these BCC-algebras. We show that it is natural for BCC-algebras to be topological BCC-algebras with respect to theses topologies. Furthermore, we show how certain standard properties may arise. In addition we demonstrate that it is natural for these topologies to have many clopen sets and thus to be highly connected via the ideal theory of BCC-algebras.
TL;DR: In this paper, the concept of semi-preconvex sets on preconvexity spaces was introduced, and the concepts of the sc-concvex function and -concave function were introduced.
Abstract: In this paper, we introduce the concept of the semi-preconvex set on preconvexity spaces. We study some properties for the semi-preconvex set. Also we introduce the concepts of the sc-convex function and -convex function. Finally, we characterize sc-convex functions, -convex functions and semi-preconvex sets by using the co-convexity hull and the convexity hull.
TL;DR: In this paper, the authors investigate some prop- erties of Feynman's operational calculi which include a variety of blends of discrete and continuous measures in the time dependent setting.
Abstract: Feynman's operational calculus for noncommuting operators was studied via measures on the time interval. We investigate some prop- erties of Feynman's operational calculi which include a variety of blends of discrete and continuous measures in the time dependent setting.