• Journal of the Korean Mathematical Society
• /
• v.29 no.1
• /
• pp.15-42
• /
• 1992

• Kyungpook Mathematical Journal
• /
• v.10 no.1
• /
• pp.65-68
• /
• 1970

• Journal of the Korean Society of Manufacturing Technology Engineers
• /
• v.9 no.2
• /
• pp.45-51
• /
• 2000

This study proposes that analysis and evaluation method of time series ultrasonic signal using the chaotic feature extrac-tion for degradation extent. Features extracted from time series data using the chaotic time series signal analyze quantitatively material degradation extent. For this purpose analysis objective in this study if fractal dimension lyapunov exponent and strange attractor on hyperspace. The lyapunov exponent is a measure of the rate at which nearby trajectories in phase space diverge. Chaotic trajectories have at least one positive lyapunov exponent. The fractal dimension appears as a metric space such as the phase space trajectory of a dynamical syste, In experiment fractal(correlation) dimensions and lyapunov experiments showed values of mean 3.837-4.211 and 0.054-0.078 in case of degradation material The proposed chaotic feature extraction in this study can enhances ultrasonic pattern recognition results from degrada-tion signals.

• The Pure and Applied Mathematics
• /
• v.20 no.1
• /
• pp.71-78
• /
• 2013

Let X be a space and $2^X$(C(X);K(X);$C_K$(X)) denote the hyperspace of nonempty closed subsets(connected closed subsets, compact subsets, subcontinua) of X with the Vietoris topology. We investigate the relationships between the space X and its hyperspaces concerning the properties of connectedness im kleinen. We obtained the following : Let X be a locally compact Hausdorff space. Let $x{\in}X$. Then the following statements are equivalent: (1) X is connected im kleinen at $x$. (2) $2^X$ is arcwise connected im kleinen at {$x$}. (3) K(X) is arcwise connected im kleinen at {$x$}. (4) $C_K$(X) is arcwise connected im kleinen at {$x$}. (5) C(X) is arcwise connected im kleinen at {$x$}.

• The Transactions of the Korea Information Processing Society
• /
• v.4 no.12
• /
• pp.3023-3032
• /
• 1997

This study examined individual differences in navigating in hyperspace learning environment where a minimum structure is provided. Using a hypercard stack called "Pearl Harbor", Field Dependent people used guidance more often than those in Field Indepedent; FI achieved scored higher at the end of the study; and FI people had some type of pattern showing from them audit trail when FD people did not show any trail of patterns. Also people with higher visual thinking scores achieved higher scores in hyperspace environment.

• Journal of the Korean Mathematical Society
• /
• v.34 no.2
• /
• pp.303-303
• /
• 1997

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 2002.12a
• /
• pp.59-62
• /
• 2002

We investigate some relations between the separation axioms in fuzzy topological spaces and one in fuzzy hyperspaces.

• The Pure and Applied Mathematics
• /
• v.22 no.2
• /
• pp.139-144
• /
• 2015

Abstract. In this paper, we investigate the relationships between the space X and the hyperspace C(X) concerning admissibility and connectedness im kleinen. The following results are obtained: Let X be a Hausdorff continuum, and let A ∈ C(X). (1) If for each open set U containing A there is a continuum K and a neighborhood V of a point of A such that V ⊂ IntK ⊂ K ⊂ U, then C(X) is connected im kleinen. at A. (2) If IntA ≠ ø, then for each open set U containing A there is a continuum K and a neighborhood V of a point of A such that V ⊂ IntK ⊂ K ⊂ U. (3) If X is connected im kleinen. at A, then A is admissible. (4) If A is admissible, then for any open subset U of C(X) containing A, there is an open subset V of X such that A ⊂ V ⊂ ∪U. (5) If for any open subset U of C(X) containing A, there is a subcontinuum K of X such that A ∈ IntK ⊂ K ⊂ U and there is an open subset V of X such that A ⊂ V ⊂ ∪ IntK, then A is admissible.

• Bulletin of the Korean Mathematical Society
• /
• v.31 no.1
• /
• pp.105-113
• /
• 1994

In the course of study of dendroids, Czuba [3] introduced a notion of $R^{i}$ -continua which is a generalization of R-arc [1]. He showed a new class of non-contractible dendroids, namely of dendroids which contain an $R^{i}$ -continuum. Subsecequently Charatonik [2] attempted to extend the notion into hyperspace C(X) of metric continuum X. In so doing, there were some oversights in extending some of the results relating $R^{i}$ -continua of dendroids for metric continua. In fact, Proposition 1 in [2] is false (see example C below) and his proof of Theorem 6 in [2] is not correct (Take Example 4 in [4] with K = [e,e'] as an $R^{1}$-continuum of X and work it out. Then one seens that K not .mem. K as he claimed otherwise.). The aims of this paper are to introduce a notion of w-regular convergence which is weaker than 0-regular convergence and to prove that the w-regular convergence of a sequence {Xn}$^{\infty}$$_{n=1}$ to $X_{0}$ of subcontinua of a metric continuum X is a necessary and sufficient for the sequence {C( $X_{n}$)}$^{\infty}$$_{n=1}$ to converge to C( $X_{0}$ ), and also to prove that if a metric continuum X contains an $R^{i}$ -continuum with w-regular convergence, then the hyperspace C(X) of X contains $R^{i}$ -continuum.inuum.uum.

• Journal of the Chungcheong Mathematical Society
• /
• v.16 no.1
• /
• pp.1-6
• /
• 2003

By considering a hyperspace CL(X) of a Hausdorffspace X with the Vietoris topology [6] also called the finite topology and treating X as a subspace of CL(X) with the natural embedding, it is obtained that homotopic maps f, g : $X{\rightarrow}Y$ are lifted to homotopic maps on the respective hyperspaces.