• The Pure and Applied Mathematics
• /
• v.4 no.2
• /
• pp.137-144
• /
• 1997

In this paper we consider covering problems in spherical geometry. Let $cov_q{S_1}^n$ be the smallest radius of q equal metric balls that cover n-dimensional unit sphere ${S_1}^n$. We show that $cov_q{S_1}^n\;=\;\frac{\pi}{2}\;for\;2\leq\;q\leq\;n+1$ and $\pi-arccos(\frac{-1}{n+1})$ for q = n ＋ 2. The configuration of centers of balls realizing $cov_q{S_1}^n$ are established, simultaneously. Moreover, some properties of $cov_{q}$X for the compact metric space X, in general, are proved.

• Journal of the Korean Chemical Society
• /
• v.41 no.8
• /
• pp.427-436
• /
• 1997

A simple relation exists between electronegativities of cations and their oxidation states and ionic radii. An empirical law is proposed: X = 0.274 z-0.15 z r - 0.01 r+1+${\alpha}$, z being oxidation number, r ionic radius in $\AA$ and ${\alpha}$ a term related to the atomic number. this relation permits to calculate an electronegativity scale covering a large set of electronic and crystallographic situations. An application to the calculation of acid strengths of cations is presented.

• Journal of the Korea Society of Computer and Information
• /
• v.20 no.2
• /
• pp.21-28
• /
• 2015

In this paper, we propose a prototype-based classification learning by using the nearest-neighbor rule. The nearest-neighbor is applied to segment the class area of all the training data into spheres within which the data exist from the same class. Prototypes are the center of spheres and their radii are computed by the mid-point of the two distances to the farthest same class point and the nearest another class point. And we transform the prototype selection problem into a set covering problem in order to determine the smallest set of prototypes that include all the training data. The proposed prototype selection method is based on a greedy algorithm that is applicable to the training data per class. The complexity of the proposed method is not complicated and the possibility of its parallel implementation is high. The prototype-based classification learning takes up the set of prototypes and predicts the class of test data by the nearest neighbor rule. In experiments, the generalization performance of our prototype classifier is superior to those of the nearest neighbor, Bayes classifier, and another prototype classifier.