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Vol.7 No.2
Abstract
Any Hausdoroff space on a set which has at least two points a regular closed Boolean algebra different from the indiscrete regular closed Boolean algebra as indiscrete space. The Sierpinski space and the space with finite complement topology on any infinite set etc. do the same. However, there is <TEX>$T_{0}$</TEX> space which does the same with Hausdorpff space as above. The regular closed Boolean algebra in a topological space is isomorphic to that algebra in the space with its open extension topology.
Abstract
In this paper, we introduce the classes H(p,q,k),K(p;k) of operators determined by the Heinz-Kato-Furuta inequality and Holer-McCarthy inequality. We characterize relationship between p-quasihyponormal, <TEX>$\kappa$</TEX>-quasihyponormal and <TEX>$\kappa$</TEX>-p-quasihyponormal operators. And it is proved that every operator in K(p;1) for some <TEX>$0<p{\leq}1$</TEX> is paranormal.
Abstract
In this paper, we try to approach chasos with numerical method. After investigating nonlinear dynamcis (chaos) theory, we introduce Lyapunov exponent as chaos\`s index. To look into the existence of chaos in 2-dimensional difference equation we computes Lypunov exponent and examine the various behaviors of solutions by difurcation map.
Abstract
In this paper, we study controllability of nonlinear delay parabolic equa-tions with nonlocal initial condition under boundary input.
Abstract
The purpose of this paper is to prove the fundamental existence and uniqueness theorems of null curves in semi-Riemannian manifolds M of index 2.
Abstract
We show that a compact subset M of X is asymptotically stable if and only if a strict Lyapunov function of M exists.
Abstract
In this paper, we define the uniformly sequence for the vector valued McShand-Stieltjes integrable functions and prove the dominated convergence theorem for the McShand-Stieltjes integrable functions.