Three species of Bosmina BAIRD are found in Japan. Bosmina fatalis BURCKHARDT, B. longirostris (O.F. MULLER) and B. longispina LEYDIG. B. fatalis is a valid species lying between B. longirostris and B. longispina in the broad meanings, and seems to be nearer the former species than latter. The present paper is considered the geographical distribution of B. fatalis BURCKHARDT in Japan in comparison with that in continental Eastern Asia.

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In this report, we explain the way of guidance of the diffusion equation which describes diffusion phenomena. We also show the approach method from the finite difference approximation in order to understand it if possible. Next, a simple diffusion program and a program of the convective diffusion equation are shown according to the Fortran Language. Finally, it close to the analysis of actual phenomenon by showing a example of the three-dimensional convective diffusion equation.

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We have been advancing a project for a few years from a viewpoint of elucidation of water pollution mechanism in Ise bay. Though we described detailed numerical models for the three dimensional numerical simulator in the previous paper, we remained a problem about a computational method to determine vertical turbulent viscosity and diffusivity. We gave constant values for those parameters as a first approximation and applied the classical equation of Munk and Anderson to take into account an effect of density gradient. Consequently, we neglected the change of those parameters due to velocity shear. In this paper we newly applied Mellor and Yamada level 2 model to computation of those parameters, by which model the log-law distribution of velocity in boudary layers can be reproduced fairy well. We carried out the simulation for 150 tides (about 78 days) by setting parameters in the early summer, using this model. The features of obtained flow structure are summarized as follows ; (1) The strong stratification of water temperature and salinity field are seen from the bay head to the bay center in the vertical section, which vanish or are weakened at north of the bay mouth. (2) The water from Kiso rivers flows from the bay head to the mouth in the upper layer by entraining underlying water, while the oceanic sea water from the bay mouth goes in the middle layer (not the lower layer) to the bay head (i.e., Esturine Circulation). At the sunken basin of the bay center (the lower layer), the stagnation of flow is observed. (3) The flow from Kiso rivers makes clockwise circulations at the bay head and the bay center in the upper layer, which quite resemble the observation data. The streamlines of the circulations are almost parallel to the contour lines of the water surface level (i.e. quasi-geostrophic flow). The flow from the bay mouth constitutes anti-clockwise circulations at the bay head and the bay center in the middle layer, contrary to the upper layer. (4) The relatively strong vertical residual currents is computed in the vicinity of the bay mouth, which is estimated to play an important role for transportation of matter and energy of the bay. Fujiwara et. al (1999) also found similar flow structures as (1) to (3) in the observation data and carried out theoretical considerations. They described the mechanism of generation of such flow structures and concluded those should be universal in small gulf where the bay head is wide compared with the Rossby internal deformation radius (gulf type ROFI).

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Realizability conditions for a non-linear k-ε model, which includes the strain parameter S and the rotation parameter Ω, are examined in 2-D flow fields. Restrictions for Cμ under three types of basic flow patterns, namely, a simple shear flow, a flow around a saddle point and a flow around a focal point are derived in a S-Ω plane.

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Our concern is to consider the characteristic of infinite series and their development that appeared in the treatise Tetsujutsu Sankei (1722) and Enri Kohaijutsu (n.d.) by Takebe Katahiro (1664-1739). Enrico Giusti hypothesizes in his recent book, Ipotesi sulla natura degli oggetti matematici (1999), that mathematical objects did not originate from the real objects in the world, but from the method of proving problems. We discuss Takebe's study on infinite series from this point of view and conclude that Giusti's hypothesis does not applicable to Takebe's case.

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This study examines the effect of the social capital on the education of the regional economy over the period from 1976-96. As a result of this analysis, the following facts can be summarized. The investment of the education decreases after 1994 in the regional economy. Then, the regional differences has remarkably appeared, when the per capital of the education in 1975 and 1996 were compared. The social capital and the social capital for the education contributes to increase in the production in the case when divided Japan into 11 regions and in the case when divided by 47 prefectures. And, the regional characteristic factors have the relation which is positive to the income. Therefore, there is a considerably high possibility which the social capital utilizes for the modification of income difference. In addition, the marginal productivity of the social capital by the specific region shows a considerably high value. Therefore, it is necessary to efficiently invest the public investment in the region of which the marginal productivity of social capital is high.

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