• Bulletin of the Korean Mathematical Society
• /
• v.47 no.6
• /
• pp.1131-1138
• /
• 2010

In the present paper, we evaluate an analytic formula as a solution of Susceptible Infective (SI) model problem for communicable disease in which the daily contact rate (C(N)) is supposed to be varied linearly with population size N(t) that is large so that it is considered as a continuous variable of time t. Again, we introduce some Lie group of operators to make an extension of above analytic formula of the determin-istic epidemics model problem. Finally, we discuss some of its particular cases.

• Journal of the Korean Mathematical Society
• /
• v.35 no.1
• /
• pp.149-164
• /
• 1998

We study the homology of the tripe loop space of the exceptional Lie group $F_4$ by exploiting the spectral sequences and the homology operators.

• Journal of the Korean Mathematical Society
• /
• v.60 no.1
• /
• pp.143-165
• /
• 2023

For each connected and simply connected three-dimensional non-unimodular Lie group, we classify the left invariant Lorentzian metrics up to automorphism, and study the extent to which curvature can be altered by a change of metric. Thereby we obtain the Ricci operator, the scalar curvature, and the sectional curvatures as functions of left invariant Lorentzian metrics on each of these groups. Our study is a continuation and extension of the previous studies done in [3] for Riemannian metrics and in [1] for Lorentzian metrics on unimodular Lie groups.

• East Asian mathematical journal
• /
• v.11 no.2
• /
• pp.249-258
• /
• 1995

• Journal of the Korean Mathematical Society
• /
• v.34 no.3
• /
• pp.633-651
• /
• 1997

For a non-degenerate symmetric bilinear form $\sigma$ on a finite dimensional vector space E, the Jordan algebra of $\sigma$-symmetric operators has a symmetric cone $\Omega_\sigma$ of positive definite operators with respect to $\sigma$. The cone $C_\sigma$ of elements (x,y) \in E \times E with \sigma(x,y) \geq 0$ gives the compression semigroup. In this work, we show that in the sutomorphism group of the tube domain over $\Omega_\sigma$, this semigroup has a UDL and Ol'shanskii decompositions and is exactly the compression semigroup of $\Omega_sigma$.

• Korean Journal of Human Ecology
• /
• v.18 no.4
• /
• pp.841-855
• /
• 2009

The main objective of this study is to examine the situations of group-homes for the elderly and clarify the problems of them. This study investigates the present conditions of welfare facilities and supply conditions. 4 group-homes were surveyed in Jeonju and Kwangju cities. Data was collected through various ways including the survey conducted by facility operators, the measurement of living space, and photo-takings. The major results of this study are as follows: 1) With the introduction of nursing care insurance in 2008, the increase of the demand and supply to group-home will be expected, due to less cost for recuperation. The care of elderly in homelike atmosphere is effective to the elderly suffering from dementia. Therefore, it is proper that the supply of group-homes for dementia will be needed. 2) Group-homes for the elderly are being supplied under the standards of welfare facilities in the present. Separate supply standards, however, are needed because they are not suitable for small scale group-homes. 3) To supply Group-homes for the elderly on a one-unit basis would cause various problems such as economical unreality, personnel distribution and so on. It is necessary to supply more than two units for more efficient management. 4) The management of group-homes for the elderly is financially unstable because the operating funds heavily depend on the users or people who are connected with the facilities through private networks. Therefore, additional support is needed to settle the financial problem. It would be helpful to build the public networking that provides information about the group-home for the elderly for the public. 5) In case of the increase in the supply of the group-home in a residential area, it could be helpful to promote the group-home to the public. 6) The operators state that the main problems of group homes for the elderly lie in financial difficulties and the shortage of professionals and volunteers. The financial, personnel, and material support for personnel and the supervision of management are required for the transparency and effectiveness of the facility management. In addition, the closer network and cooperation system with the community is required. 7) The present living environments for group-homes for the elderly leave much room for improvement, considering the physical condition of the elderly. The more careful selections in the color, shape, material, and equipment of the facilities should be made for the convenience of the elderly users.