与えられたAにランク１の行列を加えた行列に対して、一般基本行列のすでに証明されている処々の性質を利用することにより、Aにランク１を加えた行列の性質を統一的に解明する試みを紹介する。またそのほか２，３の応用例や分類についても言及する。

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 古典力学３体問題８の字解の分岐解析に必要な点群の既約直交表現を，Mathematicaを使って，直接，1)生成元の関係式と直交条件を行列の方程式として解くことで直交表現を得て，2)同値な表現の定義を行列の方程式として解くことで同値な表現を取り除き，3)可換な対称行列かを調べることで既約判定して導出する。

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The present paper describes the flow characteristics of multiple round air jets with square arrangement at a relatively low-Reynolds number (Re = 4.1×10³). The diameter of a round nozzle was d = 6 mm. To investigate the influence of number of nozzles on the flow characteristics, the number of nozzles was varied 4×4, 6×6 and 8×8 with the nozzle spacing ratio of l/d = 3 where l was the nozzle spacing. To investigate the influence of nozzle spacing, the nozzle spacing ratio l/d was varied from 1.5 to 5 for the multiple round jets with the number of nozzles of 6×6. The mean and fluctuating velocities were measured using constant-temperature anemometer with the normal and reflected image layout cross-wire probes. In case of 6×6 and 8×8 square matrix nozzles, the shape of round jets which were located at the side of the ambient fluid were stretched into elliptical shape by the secondary flow caused by entrainment of the multiple round jets. The combined point of the multiple round jets issuing from square nozzle arrangement was x/d ≈ 16 without relation to the number of nozzles. At the downstream, the flow field of multiple round jets with square matrix arrangement has similarity for the dimensionless parameters of y/D_e, u/U_b, and u'_rms /U_b, without relation to the nozzle number. The multiple round jets with 6×6 matrix arrangement merged easily when the nozzle spacing ratio became small. Thus, the centreline velocity of the combined flow formed by the confluence of the multiple round jets increased with decreasing the spacing ratio. At x/l ≥ 12, the multiple round jets developed as a single jet, and the flow field has similarity for the dimensionless parameters of y/l, u/U_b, and u'_rms /U_b without relation to the nozzle spacing ratio.

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This note investigates the characteristic of a coefficient matrix, which is derived from governing equations used in a discrete vortex method. When singular points on a body are arranged symmetrically, the rank of the coefficient matrix is reduced. Namely, the matrix is singular. When Kelvin's theorem is introduced in order to avoid the reduction of rank, that becomes regular. Then, governing equations can be solved by using a suitable method. When those are arranged asymmetrically, another unknown parameter should be introduced.

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In this note, we define the determinant of matrices by induction on the (horizontal or vertical) dimension and the elementary row and column operations. We also present some class practice examples which use the definition and show that definition is strictly suitable for classes on determinant.

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The group theoretical model of symmetry cognition (Hamada et al., 2016) was tested based on goodness and complexity judgments of dot patterns in a matrix framework. These patterns were divided into cyclic group patterns, determined by the number of rotations, and dihedral group patterns, determined by the number of reflection axes. The former have rotational symmetries and the latter reflectional and rotational symmetries. Undergraduates (N=104) rated the goodness or complexity of 21-dot compound patterns. The goodness and simplicity of these patterns in both their original form and with partially expanded frameworks increased monotonously with the number of transformations. Partially expanding a pattern influenced the goodness of cyclic groups with one transformation, but not the goodness of dihedral groups. Partially expanding a pattern did have an effect on the complexity of both groups, but only with a large number of transformations. For patterns with 4 transformations, the goodness and simplicity of dihedral patterns were higher than those of cyclic group patterns. Furthermore, grouping effects influenced complexity but not goodness judgments.

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The radiant heat transfer problem in an enclosure with both of diffuse radiation at surfaces and non-radiative medium can be analized using the radiant transport function, which is useful to express the radiant transfer characteristics in the enclosure and to get the solution corresponding to any surface temperature. The radiant transport function should be analytically solved, because which has at least two variables. The generalized formula for the radiant transport function is composed of the integral equation. Thereby, an approximate method getting the analytical solution is indicated, using the separated kernel for the integral equation. Regarding the two-dimensional rectangular space, the approximate solution and the error estimation for the radiant transport function are presented, substituting the normal orthogonal function for the kernel. In a square space a calculation is performed to get the solution of the radiant transport function, using the Legendre polynomial as the normal orthogonal function. The result shows that the solution is reasonable and the error estimation is not so large excluding the points close to the end of both sides probably owing to the quality of the Legendre polynomial.

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逐次的にユーザ・アイテムのファジィ共クラスターを抽出することでユーザに個人化した推薦を提示するための協調フィルタリングモデルが提案され，購買履歴のような0-1型の履歴データにおいて高い推薦性能が示されたが，ユーザ数＋アイテム数のの固有値問題を解く必要があることから，計算効率の面で問題があった．本研究では，データ行列の特性を考慮した計算の効率化アプローチについて考察する．

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 For the input-output analyses using non-square matrix, we propose the method of repeated calcu- lation including the processing of wastes and by-products. Row values which have no counterparts of that of columns are divided proportionally. The proportion is decided beforehand.

 We show that errors occur in the estimation of the products which relates to the wastes and the by-products, when the wastes and by-products are added with the major products to make the square input-output matrix.

 With the proposed method, the industry of the columns of the input-output analyses can be agents.

 We show that the agent-based input-output analyses are possible, using the case of the electric power generation and the paddy rice tillage.

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As a basic study for the establishment of the methodology for computer aided or automated design of machine structures, this report deals with an algorithm and a computer program for the automated generation of the functional structures of power transmitting or motion transmitting machines, such as machine tools, measuring apparatuses. The machines are considered as the aggregation of motion transmitting elements, such as gear mechanism, screw driving mechanism, cam mechanism, and their functional structures are generated automatically using these elements. In computer the functional structure of a machine is described by an adjacency matrix and transformation vectors of all motion transmitting elements. In the adjacency matrix, each matrix element corresponds to the relation between two elements such as fixed, sliding or motion transmitting.

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