The results of my investigation on the centers of population, for the period of 1920 to 1954, of each prefecture in Kyushu and of Kyushu as a whole, are shown in List 1, Diagram 1 and 2. The shift of the centers of population can be classified into the following four types.
The first type is seen in a prefecture which has in some part of it a rapidly developing industrial district. The center of population in such a prefecture had had a tendency to move to the industrial district before the war, but began to move in the opposite direAion in the period of post-war, confusion, and then since about 1947, it has shown again the same tendency as in the pre-war days. Miyazaki, Fukuoka, and Kyushu as a whole are the examples of this type.
The second type is seen in prefectures having several attracting centres, whose interrelatoin make the shift of population center exceedingly complicated. Kumamnoto and -Nagasaki are the examples of this type.
The third type is seen in those prefectures where the capital cities and the centers of population are virtually the same so that the shift of center has been very slight indeed. Examples are to be found in Oita, Saga, and Kagoshima exclusive of Amami-Oshim a.
The fourth and the last type is that of a prefecture in which, with a remarkable decrease of population in a certain district, the center of population moves in the opposite direction in almost a straight line. Kagoshima prefecture, inclusive of Amami-Oshima whose Poulation is rapidly decreasing, is a good example of this type.

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The features in population of a great city involve two phases, i. e., daytime population and nighttime population. Consequently, two kinds of centers or balanced points of population in space must be recognized corresponding to each of them. Up to this time, the center of population used to be signified as that of night-time population without any doubt, and the center of daytime population had long been put aside. However, the latter stands for the center of actual status of population in daytime, which accordingly might be called a center of citizens' activities. When they should not be coinciding at the same site in a metropolis, variuos questions must inevitably happen not only in traffic problems but also in every phase of urban adminstration.
It is not always easy, however, to find out the balanced point of daytime population in space. From the view-point taking the daytime population as a moving population, the writer believes that one can point out the balanced point in connection with the locational arrangement of terminal traffic volumes of suburbanrailways in the central area of metropolis.
Applying the theory of center of night-time population, we draw X- axis and Y- axis of our (own) accord at first. In this case, the balanced point is given with the following formula, letting Pi (Xi, Yi) stand as traffic volume at the i-th terminal station and N as the numbers of termini.
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Fig. 1 shows the centers of daytime population in Osaka both pre- and postwar, applying abovementioned method, while Fig. 3 that of night-time population and its shifting. Therefore, the distance between them is 1.5km in 1955. In comparison with this, the center of daytime population in Tokyo Central Station and that of night-time population with Shinjuku Station (Fig. 2). The distance between them is 6 KM. or about 4 times as long as the case in Osaka. Such a separation gives an additional burden on every citizen's trip on everyday life.
Through this fact we can recognize that the traffic difficulties with which Tokyo has been confronted are much severer than those of Osaka. Consequently, it would be more desirable than anything else in the city planning to give better administration on the metropolis so as to make those two kinds of centers of population as close as possible.

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　医療計画では医療資源を活用する外来を担う医療機関の明確化が進められていることから，高度医療機器の構想区域内での配置の妥当性についてオープンデータと

を活用して分析を行った．病床機能報告や医療機能情報提供制度に載せられている医療機関ごとの高度医療機器の設置台数や検査実施数などを利用して構想区域内での高度医療機器の分布状況を重心分析により把握し，受療率と人口分布による受療との距離並びに方位の比較分析を行った．高度医療機器の分布重心，機器1台当たりの検査数重心等のさまざまな重心指標と受療の比較では重心位置の一致は見られず，現在の設置状況・検査状況では地域住民の分布に即していないことがわかった．これに加えて高度医療機器の検査数，設置場所等を変化させるシミュレーションを行うことで，その地域に最適な配置が得られることもわかり，これを活用して，地域全体での設置・更新を進めていくべきだと考える．

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It is an important problem for the availability of an academic library whether a library is accessible for its clientele or not. But as a library collection grows larger and larger, it becomes more and more difficult to find the appropriate place for the library to build new large building. This paper tries to decide the center of a campus arithmetically, and examines the way of measuring the degree of nearness between the center and the library. The center of the gravity of population, which is computed in the census, is applied as one of the way to decide the center of a campus. The point which minimize the traffic of university members is also considered. To indicate the degree of nearness from the center, centrality index and centrality deviation value are devised. These ideas are applied to actual universities and co-value lines are drawn on campus maps.

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　人口減少社会の到来や地球温暖化への懸念などさまざまな要因を背景として，「コンパクトシティ」への関心が高まっている。このコンセプトが，地域を集約型の効率的な構造に変えることで地域の持続可能性を改善しようという政策として，現在すでに具現化している。 　この「地域構造が効率的かどうか」に関する指標には多くの指標が考えられるが，本稿では日常の交通行動の多くを占める通勤行動に注目する。即ち，居住地と勤務地の地理分布を分析し，通勤移動にかかる時間や消費エネルギーと密接に関係する「距離」について分析することで地域の構造を把握し，今後の地域への展望を得ることを目的とする。 　本稿では2 つの分析を行った結果を紹介する。第1 は，北部九州地域の市区町村単位での国勢調査による通勤データを分析した結果である。ここでは，福岡市および北九州市で働く就業者がどの市区町村に居住しているのか，という地理的分布と，その推移について考察する。第2 に，北九州市内の町丁字単位での国勢調査データを分析し，地域ごとの昼間人口と夜間人口の比率とその動向を分析する。さらに，町丁字別の主な通勤交通手段とその変化を調べ，通勤からみた地域構造を明らかにする。これらの分析から，北部九州地域の地域構造が効率的になっているのかどうかを明らかにする。

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This paper considers k -centrum criterion location model in a planar space. This criterion to be minimized is the sum of the k largest traveling costs. So that it generalizes the mini-sum criterion, which minimizes the sum of the all traveling costs, and the mini-max criterion, which minimizes the largest traveling costs, so it contains explicitly the tradeoff between both criteria. We characterize the optimal solution and the contour lines associated with the model. Then we exhibit its geometrical solution procedure based on higher-order Voronoi diagrams, taking account of the convexity of its objective function. Finally, we apply this location model to two prefectures in the north part of Kanto Region, in which the migration is serious.

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Quasi-zenith satellite system attracts the attention recently, at least one satellite of which is in high elevation angle. Large capacity communication system and GPS augmentation system using quasi-zenith satellite system are proposed. GPS augmentation satellites in high elevation can improve integrity capability and navigation accuracy of GPS. In the first half of paper, I show the constellation design of quasi-zenith satellite system to optimize for Japan. In the last half, I show the GPS augmentation effect by designed quasi-zenith satellite system.

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This paper presents a new measure of the central point of population using two-dimensional normal distribution theory. When a previously presented measure, for example, the center of population (equation (1)) is calculated for one city, its value does not necessarily indicate a singular point for that city. This is because previous measures depend on how an observer delimits the city area. The center of concentric contour circles of population density, however, should indicate the singular point for the city, if its population forms a normal distribution. The position of this center can be estimated from the two-dimensional normal distribution type of model (equation (3)), since a pair of variables (x_c, y_c) in the model are identified as the coordinates of the center. Thus, this paper defines a new measure as a pair of the least square estimates (x_c, y_c) and calls this measure the singular point of urban population. The estimates x_c and y_c are part of (d_c, a, x_c, y_c) which minimizes the error sum of squares S in equation (5). The variable d_i in (5) is an observed value of the population density at place (x_i, y_i).
Although (x_c, y_c) in (3) is equivalent to the mean value in a two-dimensional normal distribution, Figure 1 shows that (x_c, y_c) in (5) is different from the mean value in the sample distribution. Accordingly, the singular point of urban population is not a concept included in “ordinary” statistics, but a concept peculiar to spatial science.
The iterative method is necessary for estimating the point, since (3) is a nonlinear regression equation. This method, however, is more complicated than the algebraic method. Thus, this paper introduces the following two methods to obtain an approximate algebraic solution. One is to derive equation (7) from (3) using logarithmic linearization, and then to obtain an approximate value from (7) using linear regression analysis. This value is given by equations (12) and (13), where f=logd; z=x²+y²; S_fx=Σ(f_i-f)(x_i-x); and C_ij is a cofactor of the square matrix in equation (8). The other is to obtain a more approximate value from (7) using weighted regression analysis. This value is given by equations (15) and (16), where T_dfx=Σd_iΣd_if_ix_i-Σd_if_iΣd_ix_i; and C'_ij is a cofactor of the square matrix in equation (14). In this paper, the above three kinds of values calculated by nonlinear, linear, and weighted regression analysis are called the nonlinear solution, the linear solution, and the weighted solution respectively.
These solutions and the center of population are applied to the following areas: two hypothetical cities where population forms a concentric distribution (city A) or an elliptic distribution (city B); and three actual cities in 1970, 1975, and 1980 (Utsunomiya, Koriyama, and Yamagata). Figures 2 and 3 show the limits of these cities. Hypothetical cities A and B are delimited in two and four ways respectively, so that the city limits of A₀, A₁, B₀, B₁, B₂, and B₃ are established; the limits of the actual cities are established within each circle centered at the central station. In the hypothetical cities, the true value of the singular point of urban population is determined at the origin (0.0, 0.0); nevertheless in the actual cities

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