Showing papers in "Journal of The Korean Mathematical Society in 2002"
TL;DR: In this paper, a translation theorem in an analogue of Wiener space (C(0;t);!') and formulas for the con-ditional!'-integral given by the condition X(x) = (x(t0,t1);¢¢¢ ; x(tn)) were established.
Abstract: In this note, we establish a translation theorem in an analogue of Wiener space (C(0;t);!') and find formulas for the con- ditional !'-integral given by the condition X(x) = (x(t0);x(t1);¢¢¢ ; x(tn)) which is the generalization of Chang and Chang's results in 1984. Moreover, we prove a translation theorem for the conditional !'-integral.
44 citations
TL;DR: In this paper, the method of quasilinearization is applied to two families of three-point boundary value problems for second order ordinary differential equations: linear boundary conditions and nonlinear boundary conditions are addressed independently.
Abstract: The method of quasilinearization generates a monotone iteration scheme whose iterates converge quadratically to a unique solution of the problem at hand. In this paper, we apply the method to two families of three-point boundary value problems for second order ordinary differential equations: Linear boundary conditions and nonlinear boundary conditions are addressed independently. For linear boundary conditions, an appropriate Green\`s function is constructed. Fer nonlinear boundary conditions, we show that these nonlinearities can be addressed similarly to the nonlinearities in the differential equation.
38 citations
TL;DR: In this article, a fixed point analysis of self-maps is presented, which relies on a factorization idea and the notion of an essential map is introduced for a wide class of maps.
Abstract: New fixed Point results for the (equation omitted) selfmaps ale given. The analysis relies on a factorization idea. The notion of an essential map is also introduced for a wide class of maps. Finally, from a new fixed point theorem of ours, we deduce some equilibrium theorems.
29 citations
TL;DR: In this article, a generalized Ricci-recurrent trans-Sasakian manifold is studied and it is shown that the manifold is always recurrent with cyclic Ricci tensor and non-zero A(n) everywhere.
Abstract: Generalized Ricci-recurrent trans-Sasakian manifolds are studied. Among others, it is proved that a generalized Ricci- recurrent cosymplectic manifold is always recurrent. Generalized Ricci-recurrent trans-Sasakian manifolds of dimension ‚ 5 are lo- cally classified. It is also proved that if M is one of Sasakian, fi-Sasakian, Kenmotsu or fl-Kenmotsu manifolds, which is gener- alized Ricci-recurrent with cyclic Ricci tensor and non-zero A(») everywhere; then M is an Einstein manifold.
25 citations
TL;DR: By considering the n-particle system of stochastic fragmentation processes, the general conditions of the rates which guarantee the occurrence of the shattering transition are found.
Abstract: We investigate the fragmentation process developed by Kolmogorov and Filippov, which has been studied extensively by many physicists (independently for some time). One of the most interesting phenomena is the shattering (or disintegration of mass) transition which is considered a counterpart of the well known gelation phenomenon in the coagulation process. Though no masses are subtracted from the system during the break-up process, the total mass decreases in finite time. The occurrence of shattering transition is explained as due to the decomposition of the mass into an infinite number of particles of zero mass. It is known only that shattering phenomena occur for some special types of break-up rates. In this paper, by considering the n-particle system of stochastic fragmentation processes, we find general conditions of the rates which guarantee the occurrence of the shattering transition.
16 citations
TL;DR: In this paper, the Bergman kernel function and its derivatives are estimated in a neighborhood of a point of finite type in a smoothly bounded pseudoconvex domain, assuming that the Levi form of the point is comparable to the point of type b.
Abstract: Let be a smoothly bounded pseudoconvex domain in and let b a point of finite type. We also assume that the Levi form of b is comparable in a neighborhood of . Then we get precise estimates of the Bergman kernel function, (z, w), and its derivatives in a neighborhood of . .
14 citations
TL;DR: In this paper, the concepts of chain U-complex, U-homology, chain (U, U')-map, chain U, U'-homotopy and -functor were introduced.
Abstract: Our aim in this paper is to introduce a generalization of some notions in homological algebra We define the concepts of chain U-complex, U-homology, chain (U, U')-map, chain (U, U')-homotopy and -functor We also obtain some interesting results We use these results to find a generalization of Lambek Lemma, Snake Lemma, Connecting Homomorphism and Exact Triangle
14 citations
TL;DR: In this paper, the existence of solu- tions for the hyperbolic equations with Bessel operators in another special case has been shown and the uniqueness of solutions has been established.
Abstract: In the article (2), the conjugate Darboux-Protter prob- lem Dn is formulated for the two dimensional wave equation in the class of unbounded functions and the uniqueness of solutions has been established. In this paper, we shall show the existence of solu- tions for the hyperbolic equations with Bessel operators in another special case.
11 citations
TL;DR: In this paper, the existence and necessary conditions for the optimal constant parameters based on the fundamental optimal control theory and the transposition method studied in Lions and Magenes (5) were established.
Abstract: We study the problems of identification for the damped sine-Gordon equations with constant parameters. That is, we estab- lish the existence and necessary conditions for the optimal constant parameters based on the fundamental optimal control theory and the transposition method studied in Lions and Magenes (5).
10 citations
9 citations
TL;DR: In this paper, the existence of mild solutions for semilinear dierential equations in a Banach space was proved by using the semigroup theory and the Schaefer fixed point theorem.
Abstract: In this paper we prove the existence of mild solutions for semilinear dierential equations in a Banach space. The results are obtained by using the semigroup theory and the Schaefer fixed point theorem. An example is provided to illustrate the theory.
TL;DR: In this paper, a complete system of finite order for the infinitesimal deformations of a CR manifold with non-degenerate Levi forms is constructed. And the space of infiniteimal deformation of f forms a finite dimensional Lie algebra, where f : M! N is a CR mapping.
Abstract: Let M and N be CR manifolds with nondegenerate Levi forms of hypersurface type of dimension 2m + 1 and 2n + 1, respectively, where 1 • mn. Let f : M ! N be a CR mapping. Under a generic assumption we construct a complete system of finite order for the infinitesimal deformations of f. In particular, we prove the space of infinitesimal deformations of f forms a finite dimensional Lie algebra.
TL;DR: In this article, the uniqueness of the positive solution for the general elliptic system was studied, which is the general model for the steady state of a com- petitive interacting system and the techniques used in this paper are upper-lower solutions, maximum principles and spectrum estimates.
Abstract: In this paper, we concentrate on the uniqueness of the positive solution for the general elliptic system 8 : ¢u + u(g1(u) i g2(v)) = 0 ¢v + v(h1(u) i h2(v)) = 0 in R + £ ›; uj@› = vj@› = 0: This system is the general model for the steady state of a com- petitive interacting system. The techniques used in this paper are upper-lower solutions, maximum principles and spectrum estimates. The arguments also rely on some detailed properties for the solution of logistic equations.
TL;DR: In this paper, the Holder-McCarthy inequality for a positive and an arbitrary operator is extended for the first time and the powers of each inequality are given and the improved Reid's inequality by Halmos is generalized.
Abstract: We extend the Holder-McCarthy inequality for a positive and an arbitrary operator, respectively. The powers of each inequality are given and the improved Reid's inequality by Halmos is generalized. We also give the bound of the Holder-McCarthy inequality by recursion.
TL;DR: In this paper, the authors extend the construction of Dirichlet forms and Markovian semigroups on standard forms of von Neumann algebra given in [13] to the case of unbounded operators satiated with the von NEAs.
Abstract: We extend the construction of Dirichlet forms and Markovian semigroups on standard forms of von Neumann algebra given in [13] to the case of unbounded operators satiated with the von Neumann algebra. We then apply our result to give Dirichlet forms associated to the momentum and position operators on quantum mechanical systems.
TL;DR: A new notion of Hausdorffness, which can not be defined in crisp theory of filters, is defined on IVF filters and their properties are studied.
Abstract: The notion of Interval Valued Fuzzy Sets (IVF sets) was introduced by T. K. Mondal. In this paper a notion of IVF filter is introduced and studied. A new notion of Hausdorffness, which can not be defined in crisp theory of filters, is defined on IVF filters and their properties are studied.
TL;DR: In this article, the Frobenius theorem was applied to a PDE system associated with complete prolongation and a unique solution for any ini-tial condition that belongs to this set if and only if the complete system satisfies compatibility conditions on the initial data set.
Abstract: We study the compatibility conditions and the exis- tence of solutions for overdetermined PDE systems that admit com- plete prolongation. For a complete system of order k there exists a submanifold of the (k i1)st jet space of unknown functions that is the largest possible set on which the initial conditions of (k i 1)st order may take values. There exists a unique solution for any ini- tial condition that belongs to this set if and only if the complete system satisfies the compatibility conditions on the initial data set. We prove by applying the Frobenius theorem to a Pfaan dier- ential system associated with the complete prolongation.
TL;DR: Using the p-adic q-integral due to T. Kim (4) as discussed by the authors, a number B ⁄ (q) and a polynomial B Ω(x;q) which are p-advised q-analogue of the ordinary Bernoulli number and Bernoullis polyno-mial, respectively, are investigated.
Abstract: Using the p-adic q-integral due to T. Kim (4), we de- fine a number B ⁄ (q) and a polynomial B ⁄ (x;q) which are p-adic q-analogue of the ordinary Bernoulli number and Bernoulli polyno- mial, respectively. We investigate some properties of these. Also, we give slightly dierent construction of Tsumura's p-adic function 'p(u;s;´) (14) using the p-adic q-integral in (4).
TL;DR: Using the well known Hermite-Hadamard integral inequality for convex functions, some inequalities for the finite Hilbert transform of functions whose first derivatives are convex are established.
Abstract: Using the well known Hermite-Hadamard integral inequality for convex functions, some inequalities for the finite Hilbert transform of functions whose first derivatives are convex are established. Some numerical experiments are performed as well.
TL;DR: In this article, the open unit ball with center 0 in the complex space is represented by a holomorphic function f : B longrightarrow C which satisfies sup z B $(1-parallel z \parallel^2)^q\parallel
abla f(z)\parallel (0 : ｜f(z)-f()｜(z, ) for some constant C).
Abstract: Let B be the open unit ball with center 0 in the complex space . For each q>0, consists of holomorphic functions f : B longrightarrow C which satisfy sup z B $(1-\parallel z \parallel^2)^q\parallel
abla f(z)\parallel (0 : ｜f(z)-f()｜(z, ) for some constant C.ℊ攀Ѐ㘱〻ጀ䵥摩捩湥湤敡汴栀
TL;DR: In this paper, it was shown that polygonal products of central subgroup separable groups, amalgamating trivial intersecting central subgroups, are double coset separable relative to certain central groups of their vertex groups.
Abstract: Let G = E, where A is a finitely generated abelian subgroup. We prove a criterion for G to be {A}-double coset separable. Applying this result, we show that polygonal products of central subgroup separable groups, amalgamating trivial intersecting central subgroups, are double coset separable relative to certain central subgroups of their vertex groups. Finally we show that such polygonal products are conjugacy separable. It follows that polygonal products of polycyclic-by-finite groups, amalgamating trivial intersecting central subgroups, are conjugacy separable.
TL;DR: In this paper, the warped product L F of a line L and a Kaehler manifold F is a typical example of a Kenmotsu manifold and the submanifolds of L F which are tangent to the structure vector field and satisfy certain conditions concerning with Ricci curvature and mean curvature are determined.
Abstract: The warped product L F of a line L and a Kaehler manifold F is a typical example of Kenmotsu manifold. In this paper we determine submanifolds of L F which are tangent to the structure vector field and satisfy certain conditions concerning with Ricci curvature and mean curvature.ure.
TL;DR: In this article, a nonzero-sum group pursuit game with bounded velocities is considered and the main point of the work is to construct and compare cooperative and non-cooperative solutions and make a conclusion about cooperation possibility in dierential pursuit games.
Abstract: In this paper we study a time-optimal model of pursuit in which the players move on a plane with bounded velocities. This game is supposed to be a nonzero-sum group pursuit game. The main point of the work is to construct and compare cooperative and non-cooperative solutions in the game and make a conclusion about cooperation possibility in dierential pursuit games. We consider all possible cooperations of the players in the game. For that purpose for every game i(x0;y0;z0) we construct the corresponding game in characteristic function form iv(x0;y0;z0). We show that in this game there exists the nonempty core for any initial positions of the players. The core can take four various forms depending on initial positions of the players. We study how the core changes when the game is proceeding. For the original agreement (an imputation from the original core) to remain in force at each current instant t it is necessary for the core to be time-consistent. Nonemptiness of the core in any current subgame constructing along a cooperative trajectory and its time-consistency are shown. Finally, we discuss advantages and disadvantages of choosing this or that imputation from the core.
TL;DR: A generalization of Liouville's theorem on integration in finite terms, by enlarging the class of fields to an extension called Ei-Gamma extension is established in this paper.
Abstract: A generalization of Liouville's theorem on integration in finite terms, by enlarging the class of fields to an extension called Ei-Gamma extension is established. This extension includes the EL-elementary extension of Singer, Saunders and Caviness and con- tains the Gamma function.
TL;DR: In this article, the boundedness of commutators related to linear operators on weak Herz spaces is studied, where the authors show that the commutator is bounded by a linear operator on Herz spaces.
Abstract: In this paper, the boundedness of some commutators related to linear operators on weak Herz spaces are obtained.
TL;DR: For a smooth projective irreducible algebraic curve C of odd gonality, the maximal possible dimension of the variety of special linear systems (C) is d－3r by a result of M. Coppens et al..
Abstract: For a smooth projective irreducible algebraic curve C of odd gonality, the maximal possible dimension of the variety of special linear systems (C) is d－3r by a result of M. Coppens et at. [4]. This bound also holds if C does not admit an involution. Furthermore it is known that if dim d-3r-1 for a curve C of odd gonality, then C is of very special type of curves by a recent progress made by G. Martens [11] and Kato-Keem [9]. The purpose of this paper is to pursue similar results for curves of even gonality which does not admit an involution.
TL;DR: In this article, the multiplicity of ordered positive radial solutions for a semilinear elliptic problem defined on an exterior domain was shown to be multiplicity multiplicative in the presence of two known solutions.
Abstract: We prove the multiplicity of ordered positive radial solutions for a semilinear elliptic problem defined on an exterior domain. The key argument is to prove the existence of the third solution in presence of two known solutions. For this, we obtain some partial results related to three solutions theorem for certain singular boundary value problems. Proof are mainly based on the upper and lower solutions method and degree theory.
TL;DR: In this article, the notion of K-G-convex space was introduced, and fixed point theorems, section properties and minimax inequalities were obtained for maps defined on some locally G-Convex subsets of a generalized convex space.
Abstract: In (11) Kim obtained fixed point theorems for maps defined on some "locally G-convex" subsets of a generalized convex space. Theorem 2 in Kim's article determines us to introduce, in this paper, the notion of K-G-convex space. In this framework we obtain fixed point theorems, section properties and minimax inequalities.
TL;DR: In this paper, a new representation of the generalized Fisher flocks is presented and it is shown that there is a unique flock for each full field K of odd or zero characteristic that has a full field quadratic extension.
Abstract: This article discusses a new representation of the generalized Fisher flocks and shows that there is a unique flock for each full field K of odd or zero characteristic that has a full field quadratic extension. It is also shown that partial flock extensions of 'critical linear subflocks'are completely determined.
TL;DR: In this article, a stable functor (B, ) is introduced and it is shown that it admits an abelian group structure when dim B∥G = 1, where B is a reductive algebraic group and G is a G-module.
Abstract: Let G be a reductive algebraic group and let B, F be G-modules. We denote by (B, F) the set of isomorphism classes in algebraic G-vector bundles over B with F as the fiber over the origin of B. Schwarz (or Karft-Schwarz) shows that (B, F) admits an abelian group structure when dim B∥G = 1. In this paper, we introduce a stable functor (B, ) and prove that it is an abelian group for any G-module B. We also show that this stable functor will have nice properties.