지진예측을 위한 확률론적퍼지모형을 제안하였다. 제안원 모형은 지진발생에 대하여 부작위성 (randomness) 과 퍼 지니스( fuzziness )를 같이 사용하여， 기존의 확률론에 근거한 지진예측방볍을 개선할 수 있도록 하였다. 이 연구의 설과는 (a) 주어진 초과확률에 대한 지반가속도 또는 주어진 지반가속도에 대한 초과확률의 멤벼쉽함수와 (b) 멤써 쉽함수릎 대표할 수 있는 특성값 (characteristic value) 이다. 확률론적퍼지모형을 띠 놔 Utah 주의 Wasatch Front Range 의 자료에 적용하여 서로 다른 연간초파확률， 최대지반가속도에 대하여 지진도른 작성하였다

본고에서는 Sandhu 둥에 의해 개발된 다변수경계치문제의 변분모델화 방법올 이용하여 범함수의 독립변 수로써 변위와 웅력 을 동시에 포함하는 이방성탄성문제의 혼합형변분원리 (Mixed Variational P띠lciple) 를 유도한다. 탄성방정 식올 內tJ空間에서 self -adjoint 한 미분연산자매트릭스 방정식으로 표시한 후 다변수 경계치 문 제의 변분이론을 적 용하므 로써 일반적 범함수가 구해지며 ， 이때에 지배방정식의 미분연산자와 경계조 건 식의 연산자의 일 관성 (Consistency)올 유지하므로써 경계조건도 체계적으로 벙함수내에 포함시킬 수 있다. 이 일반적 범함수에서 미분연산자의 self - adjointness 성질을 이용하여 웅력함수의 도함수를 제거 하고 탄성방정식중 특정식이 항상， 정확히 만족된다고 가정하므로써 원하는 혼합형변분원리의 범함수를 유도할 수 있다. 여기에서 유도된 변분원리는 최 근 Reissner에 의해 개발된 변분원리와 유사한 물리적 의미를 가지나 유도방법이 다를 뿐 아니라 일반적 이방성탄성체에 적용할 때 보다 면리한 형태로 된다. 이 혼합형변분원리 는 다양하게 응용될 수 있으나， 복합재료적충판과 같은 이질성， 이방성 명판이론， 또는 웰이론의 유도에 유용 하게 사용 할 수 있다

The evolution of the Galaxy is examined by the halo-disk model, using the time-dependent bimodal IMF and contraints such as cumulative metallicity distribution, differential metallicity distribution and PDMF of main sequence stars. The time scale of the Galactic halo formation is about 3Gyr during which the most of halo stars and metal abundance are formed and ∼ 95 of the initial halo mass falls to the disk. The G-dwarf problem could be explained by the time-dependent bimodal IMF which is suppressed for low mass stars at the early phase (t < 1Gyr) of the disk evolution. However, the importance of this problem is much weakened by the Pagel's differential metallicity distribution which leads to less initial metal enrichment and many long-lived metal-poor stars with Z < 1 / 3 Z ⊙ The observational distribution of abundance ratios of C, N, O elements with respect to [Fe/H] could be reproduced by the halo-disk model, including the contribution of iron product by SNIs of intermediate mass stars. The initial enrichment of elements in the disk could be explained by the halo-disk model, resulting in the slight decrease and then the increase in the slopes of the [N/Fe]- and [C/Fe]-distributions with increasing [Fe/H] in the range of [Fe/H] < -1.

We construct a simple photometric evolution model of galaxies based on the evolutionary population synthesis. In our models an exponentially decreasing SFR with a power law IMF is used to compute the UBV colors of galaxies from ellipticals to late type spirals. It is shown that the integrated colors of galaxies with different Hubble type can be explained by one parameter, SFR.

Two perforated plates(a square plate and a rectangular plate having an as야ct ratlO 1.57(L,=11, L,= 7)) are taken as analysis examples. Each of these plates is given some changes in the boundary ∞nditions. The size of cutouts as well as their locations are also changed in order to examine the variation of two eigenvalues corresponding to the fundamental mode. The relationship between two eigenvalues is estab!ished by changing the magnitude of edge thrust

We present (U-B) and (U-V) radial color distributions of 103 galaxies based on the UBV multiaperture photometry compiled by Longo, de Vaucouleurs, and Corwin (1983). About half of the galaxies show radial negative color gradients (i. e., bluer at the outer parts of the galaxies). E and SO galaxies have similar color gradients. and there appears to be no correlation between the size of color gradients in these galaxies and their luminosity, but the luminous spiral galaxies tend to have steeper color gradients. The metallicity gradients of elliptical galaxies derived from the (U-V) color gradients agree with those from the magnesium gradients within the errors.

The initial mass functions (IMF) of 15 selected open clusters are investigated by making use of C-M diagrams and theoretical evolutionary tracks. Among 15 clusters 13 have peaks in their IMFs and it is thought to be not due to incomplete photometry but to intrinsic property. The mass where IMF peaks is about 2 M ⊙ and it is similar to that of the second peak in the IMF of nearby field stars. The mean slope of the IMF in the high mass part is 1.9 ± 0.6 with some variations among clusters. But there seems to be no correlation between the slope and physical parameters such as ages, diameters, and metal abundances.

The ages of field stars given in the catalogue of Cayrel de Strobel et al. (1985) are derived by the five different methods with combination of theoretical isochrones. By using these ages and metal abundances homogenized by Lee and Choe (1988), the age-metallicity relations are obtained. For disk stars of [Fe/H] > -0.9, the present age-metallicity relations are nearly consistent with those given by Twarog (1980) and Carlberg et al. (1985).

We have examined how sensitively the extinction value determined by the method of star-count depends on such factors as the plate limit, the size of counting reseau, the non-linearity in the number distribution of stars with magnitude, and the angular resolution demanded by the given problem. We let the Poisson distribution portray the statistical nature of the countings, and chose the region containing the globule Barnard 361 as an example field. Uncertainties due to various combinations of the factors are presented in graphic forms: (1) Dynamic range in the extinction measurements is evaluated as a function of reseau size for varying plate limits. (2) Statistical errors involved in the star-count are analized in terms of the signal-to-noise ratio, the plate limit and the reseau size. (3) Systematic error due to the non-linearity in the number distribution are thoroughly analized. (4) Finally, a methodology is presented for correcting the systematic error in the observed radial density gradient. These graphs are meant to be used in selecting proper size of the reseau and in estimating errors inherent to the star-count analysis.

We have investigated hydrodynamical behaviors of spicules by solving numerically the hydrodynamic equations subject to proper boundary conditions using the method of characteristics. We examined the behaviors of MHD slow mode waves propagating through rigid magnetic flux tubes which were excited by the pressure perturbations at the lower boundary. It is found that the spicules are identified as the manifestation of the movement of the transition region being pushed upward by collisions with the shock waves. One of the most important findings is the presence of the rebound shocks and their roles. We interpreted the rebound shocks in terms of the observed recurrent spicules.

To examine relations between stellar activity and rotation we estimated parameters of stellar activity such as R′ H K , R′ M g I I , R′ C I I , R′ C I V and R′ X − r a y from the published data which measure the activity levels of stellar chromospheres, transition regions and coronae. In the present study we considered only the main sequence stars in an attempt to minimize the influence of other stellar parameters such as radius, age and stellar convection on stellar activity since they are also known to affect the magnetic field generation. In the present analysis we selected only those stars that satisfy the following conditions: (1) flux measurements are available together with Ca II fluxes and (2) rotation periods are determined by Ca II observations. We derived relations between the ¯Rossby number Ro and stellar activity R′ H K , R′ M g I I , R′ C I I , R′ C I V and R′ X − r a y and assessed the relations by plotting R′ H K , R′ M g I I and R′ X − r a y against rotation period P rot for comparison with observations. From the comparison it is found that as far as the rotation-activity relation is concerned, (1) normalized surface flux R′ H K is better than the surface flux F′ H K , in the sense that R′ H K differentiates the color dependence better and (2) R′ H K defined by Rutten (1984) describes the observations notably better than R′ H K of Noyes et al. (1984).

Using the detailed two-dimensional surface photometry of 39 galaxies, the observed profiles are decomposed into spheroid, disk and bar components simultaneously. From the analyses of decomposition parameters, the correlations among the three components are investigated to find the global property of barred galaxies. And the lens and ring components, and spiral arm patterns are also examined with Hubble type and decomposition parameters.