Showing papers in "Journal of The Korean Mathematical Society in 1995"

$zeta$-null geodesic gradient vector fields on a lorentzian para-sasakian manifold

Abstract: A Lorentzian para-Sasakian manifold M$(\varphi, \zeta, \eta, g)$ (abr. LPS-manifold) has been defined and studied in [9] and [10]. On the other hand, para-Sasakian (abr. PS)-manifolds are special semi-cosympletic manifolds (in the sense of [2]), that is, they are endowed with an almost cosympletic 2-form $\Omega$ such that $d^{2\eta}\Omega = \psi(d^\omega$ denotes the cohomological operator [6]), where the 3-form $\psi$ is the associated Lefebvre form of $\Omega$ ([8]). If $\eta$ is exact, $\psi$ is a $d^{2\eta}$-exact form, the manifold M is called an exact Ps-manifold. Clearly, any LPS-manifold is endowed with a semi-cosymplectic structure (abr. SC-structure).

Curvature homogeneity for four-dimensional manifolds

Abstract: Let (M,g) be an n-dimensional, connected Riemannian manifold with Levi Civita connection $ abla$ and Riemannian curvature tensor R defined by $$ R_XY = [ abla_X, abla_Y] - abla_{[X,Y]} $$ for all smooth vector fields X, Y. $ ablaR, \cdots, abla^kR, \cdots$ denote the successive covariant derivatives and we assume $ abla^0R = R$.

Coincidences of composites of u.s.c. maps on h-spaces and applications

Abstract: Applications of the classical Knaster - Kuratowski - Mazurkiewicz (si- mply, KKM) theorem and the fixed point theory of multifunctions defined on convex subsets of topological vector spaces have been greatly improved by adopting the concept of convex spaces due to Lassonde [LIJ. In this direction, the first author [P5J found that certain coinci­ dence theorems on a large class of composites of upper semicontinuous multifunctions imply many fundamental results in the KKM theory. On the other hand, the concept of convex spaces was extended by Horvath [HI-5J to spaces having certain families of contractible subsets or H -spaces. In this direction, a number of authors extended important results on convex spaces to those on H -spaces. See Bardaro and Cep­ pitelli [BCI-3J, Ding et al. [Di, DKTI-2, DTrJ, Park [PI-3]' Tarafdar [T], and H. Kim [KJ. In the present paper, we extend the main coincidence theorem in [P5J to H-spaces and apply it to obtain a far-reaching generalization of the KKM theorem, fixed point or coincidence theorems for H -spaces, and other results. We also obtain open-valued versions of a KKM theorem and a coincidence theorem for H-spaces. Many of the main results in the above-mentioned papers are extended and unified. Especially, the main theorems of [DiJ are improved and corrected.

Numerical solution for nonlinear klein-gordon equation by bollocation method with respect to spectral method

Abstract: We show that the numerical solution of two dimmensional Klein- Gordon equation by collocation method with error 1 .N 1/ hN . n 1/= N 2 !.

Estimates of invariant metrics on some pseudoconvex domains in $C^N$

Abstract: In this paper we will estimate from above and below the values of the Bergman, Caratheodory and Kobayashi metrics for a vector X at z, where z is any point near a given point $z_0$ in the boundary of pseudoconvex domains in $C^n$.

A relative nielsen number in coincidence theory

Abstract: Nielsen coincidence theory is concerned with the estimation of a lower bound for the number of coincidences of two maps $f,g: X \longrightarrow Y$. For this purpose the so-called Nielsen number N(f,g) is introduced, which is a lower bound for the number of coincidences ([1]). The relative Nielsen number N(f : X,A) in the fixed point theory is introduced in [3], which is a lower bound for the number of fixed points for all maps in the relative homotopy class of f:(X,A) $\longrightarrow$ (X,A), and its estimation is given in [5].

The doubly stochastic matrices of a multivariate majorization

Abstract: Throughout this paper, let $M_{mn}(R)$ be the set of all $m \times n$ real matrices, and let $R^n$ the set of all real row vectors with n components.

Complete convergence for weighted sums of arrays of random elements

Abstract: Let $(B, \left\ \right\)$ be a real separable Banach space. Let $(\Omega, F, P)$ denote a probability space. A random elements in B is a function from $\Omega$ into B which is $F$-measurable with respect to the Borel $\sigma$-field $B$(B) in B.

Column ranks and their preservers of general boolean matrices

Abstract: There is much literature on the study of matrices over a finite Boolean algebra. But many results in Boolean matrix theory are stated only for binary Boolean matrices. This is due in part to a semiring isomorphism between the matrices over the Boolean algebra of subsets of a k element set and the k tuples of binary Boolean matrices. This isomorphism allows many questions concerning matrices over an arbitrary finite Boolean algebra to be answered using the binary Boolean case. However there are interesting results about the general (i.e. nonbinary) Boolean matrices that have not been mentioned and they differ somwhat from the binary case.

Planar harmonic mappings and curvature estimates

Abstract: Let $\Sigma$ be the class of all complex-valued, harmonic, orientation-preserving, univalent mappings defined on $\Delta = {z : z > 1}$ that map $\infty$ to $\infty$.

A singular nonlinear boundary value problem in the nonlinear circular membrane under normal pressure

Abstract: The nonlinear boundary value problem $$ y" = f(x, y, y') = -\frac{x}{3}y' - \frac{y^2}{g(x)}, 0 0 $$ $$ or (S) : y'(1) + (1 - \upsilon)y(1) = 0, 1 - \upsilon > 0, $$ $$g \in C[0, 1], k \leq g(x) \leq K on [0, 1] for some k, K > 0 $$ arises in the nonlinear circular membrane under normal pressure [2, 3]., 3].

On the gauss map of hypersurfaces in the space form

Abstract: Let $M^n$ be a hypersurface in the Euclidean space $R^{n+1}$ with position vector field x and unit normal vector field G.

Cauchy problem for the euler equations of a nonhomogeneous ideal incompressible fluid ii

Abstract: Let us consider the Cauchy problem $$ {\rho_t + \upsilon \cdot abla\rho = 0 {\rho[\upsilon_t + (\upsilon \cdot abla)\upsilon] + abla p + \rho f {div \upsilon = 0 (1.1) {\rho_t = 0 = \rho_0(x) {\upsilon_t = 0 = \upsilon_0(x) $$ in $Q_T = R^3 \times [0,T]$, where $f(x,t), \rho_0(x) and \upsilon_0(x)$ are given, while the density $\rho(x,t)$, the velocity vector $\upsilon(x,t) = (\upsilon^1(x,t),\upsilon^2(x,t),\upsilon^3(x,t))$ and the pressure p(x,t) are unknowns. The equations $(1.1)_1 - (1.1)_3$ describe the motion of a nonhomogeneous ideal incompressible fluid.

Continuity of directional entropy for a class of $Z^2$-actions

Abstract: J.Milnor[Mi2] has introduced the notion of directional entropy in his study of Cellular Automata. Cellular Automaton map can be considered as a continuous map from a space $K^Z^n$ to itself which commute with the translation of the lattice $Z^n$. Since the space $K^Z^n$ is compact, map S is uniformly continuous. Hence S is a block map(a finite code)[He]. (S is said to have a finite memory.) In the case of n = 1, we have a shift map, T on $K^Z$, and a block map S and they together generate a $Z^2$ action.

A study on the geometry of 2-dimensional re-manifold $X_2$

Abstract: Manifolds with recurrent connections have been studied by many authors, such as Chung, Datta, E.M.Patterson, M.Prvanovitch, Singal, and TAkano, etc (refer to [2] and [3]). Examples of such manifolds are those of recurrent curvature, Ricci-recurrent manifolds, and birecurrent manifolds.

On the structure of discrete spectrum of the non-selfadjoint system of differential equations in the first order

Abstract: This paper is concerned with the problem given below $$ (1.1) i\frac{dx}{du_1(x,\lambda)} + q1(x)u_2(x,\lambda) = \lambdau_1(x,\lambda) 0 \leq x

A characterization of crossed products without cohomology

Abstract: Let N be a $II_1$ factor and G be a finite group acting outerly on N. Then the crossed product algebra $M = N \rtimes G$ is also a $II_1$ factor and $N' \cap M = CI$, i.e. N is irreducible in M. Moreover, N is regular in M, in other words, M is generated by the normalizer $N_M (N)$.

The well posedness of a parabolic double free boundary problem

Abstract: We consider the reaction-diffusion system of two-component model in one-dimensional space described by $$ (1) u_s = d_1 u_{xx} + f(u, \upsilon) \upsilon_t = d_2\upsilon_{xx} + \gammag(u, \upsilon) $$ where $d_1$ and $d_2$ are the diffusion rates of u and $\upsilon$, and $\gamma$ is the ration of reaction rates. It is interesting the case of that there are differences in the diffusion and reaction rates of u and $\upsilon$.

Pseudo-umbilical surfaces in a pseudo-riemannian sphere or a pseudo-hyperbolic space

Abstract: The notion of finite type submanifold was introduced by B.-Y. Chen [1]. A lot of works were done in this field of study by many authors. B.-Y. Chen also extended this notion to pseudo-Riemannian submanifold of pseudo-Euclidean space ([2]).

A hopf bifurcation on a parabolic free boundary problem with pushchino dynamics

Abstract: A hopf bifurcation of a free boundary (or an internal layer) occurs in solidification, chemical reactions and combustion. It is a well-known fact that a free boundary usually appear as sharp transitions with narrow width between two materials ([2]).

The state space of a canonical linear system

Abstract: A fundamental problem is to construct linear systems with given transfer functions. This problem has a well known solution for unitary linear systems whose state spaces and coefficient spaces are Hilbert spaces. The solution is due independently to B. Sz.-Nagy and C. Foias [15] and to L. de Branges and J. Ball and N. Cohen [4]. Such a linear system is essentially uniquely determined by its transfer function. The de Branges-Rovnyak construction makes use of the theory of square summable power series with coefficients in a Hilbert space. The construction also applies when the coefficient space is a Krein space [7].

On convergence of finite difference schemes fr generalized solutions of sobolev equations

Abstract: Let $\Omega$ be a rectangular domain in $R^2$ with boundary $\partial\Omega$, and T be a positive real number such that $0

An extension of the hong-park version of the chow-robbins theorem on sums of nonintegrable random variables

Abstract: A famous result of Chow and Robbins [8] asserts that if ${X_n, n \geq 1}$ are independent and identically distributed (i.i.d.) random variables with $EX_1 = \infty$, then for each sequence of constants ${M_n, n \geq 1}$ either $$ (1) lim inf_{n\to\infty} \frac{M_n}{\sum_{j=1}^{n}X_j} = 0 almost certainly (a.c.) $$ or $$ (2) lim sup_{n\to\infty}\frac{M_n}{\sum_{j=1}^{n}X_j} = \infty a.c. $$ and thus $P{lim_{n\to\infty} \sum_{j=1}^{n}X_j/M_n = 1} = 0$. Note that both (1) and (2) may indeed prevail.

Characterizations of some real hypersurfaces in a complex space form in terms of lie derivative

Abstract: A complex $n(\geq 2)$-dimensional Kaehlerian manifold of constant holomorphic sectional curvature c is called a complex space form, which is denoted by $M_n(c)$. A complete and simply connected complex space form is a complex projective space $P_nC$, a complex Euclidean space $C^n$ or a complex hyperbolic space $H_nC$, according as c > 0, c = 0 or c

The invariance principle for $\rho$-mixing random fields

Abstract: Ibragimov(1975) showed the central limit theorem and the invariance principle for $\rho$-mixing random variables satisfying $\sigma^2(n) = nh(n) \longrightarrow \infty$ and $E\zeta_0^{2+\delta} 0$ where $\sigma^2(n)$ denotes the variance of the partial sum $S_n$ and h(n) is a slowly varying function.

An empirical clt for stationary martingale differences

Abstract: Let S be a set and B be a $\sigma$-field on S. We consider $(\Omega = S^Z, T = B^z, P)$ as the basic probability space. We denote by T the left shift on $\Omega$. We assume that P is invariant under T, i.e., $PT^{-1} = P$, and that T is ergodic. We denote by $X = \cdots, X_-1, X_0, X_1, \cdots$ the coordinate maps on $\Omega$. From our assumptions it follows that ${X_i}_{i \in Z}$ is a stationary and ergodic process.

Totally real submanifolds with parallel mean curvature vector in a complex space form

Abstract: Let $M_n$(c) be an n-dimensional complete and simply connected Kahlerian manifold of constant holomorphic sectional curvature c, which is called a complex space form. Then according to c > 0, c = 0 or c

Generalized fractions, galois theory and injective envelopes of simple modules over polynomial rings

Abstract: In [9], we gave a very explicit description of the injective envelope of an arbitray simple module over a polynomial ring $K[X_1, \ldots, X_n]$ over a field K in indeterminates $X_1, \ldots, X_n$. This paper presents another approach to give a description.

Convergence of nonlinear algorithms

Abstract: 1. Accretive operators and nonlinear semigroups Our purpose in this paper is to prove a new version of the nonlinear Chernoff th eorem and to discuss the equivalence between resolvent consistency and converge nce for nonlinear algorithms acting on different Banach spaces. Such results are useful in the numerical treatment of partial d ifferential equations via difference schemes. Let X be a Banach space with normjj .I f Ais a subset of X X and x 2 X ,w e letAx Df y 2Ax :[ x ; y ] 2 A g. The domain of A is D.A/Df x2 X :Ax6D ;g and the range is R.A/D[fAx : x2 D.A/g: The inverse of A is defined by A 1 yDf x2 X : y2Axg. Let! be non-negative and let A X X. The operator AC!I is said

Unified jackknife estimation for parameter changes in an exponential distribution

Abstract: Many authors have utilized an exponential distribution because of its wide applicability in reliability engineering and statistical inferences (see Bain & Engelhart(1987) and Saunders & Mann(1985)). Here we are considering the parametric estimation in an exponential distribution when its scale and location parametes are linear functions of a known exposure level t, which often occurs in the engineering and physical phenomena.