本研究は, 一般ネットワークにおける経路・リンク接続を分析したものである. このは, ネットワーク・フロー問題に関わる種々の分析において重要な役割を果たすにもかかわらず, その基本特性が正確に知られていなかった. そこで, 本研究では, その階数をフロー保存則との関係から議論し, 一般的に, (全リンク数―ODノード数を除く全ノード数) によって求められることが結論される.

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平野と小池はLMSアルゴリズムを用いた線形結合型ステレオエコーキャンセラでの係数収束性について解析し,入力信号の拡大共分散行列の非正則性が係数の不定性の原因であることを指摘している。本報告では,同様のモデルのもとで入力信号が有色である場合にも平野らと同様の結果が得られることを示す。また,拡大共分散の上限についても明らかにする。

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磁気ディスクのヘッド位置決めの際に適用されるモード切り換え型制御系では，切り換え後の制御器の初期状態を再設定する初期値補償が行われている．本稿では最初に配置可能な零点のクラスについて考察を行う．次に配置すべき零点の数が制御器の次数よりも少ない場合，制御器の初期値の設定の際に自由度が存在するので，その自由度を用いた零入力応答の最適化について考察する．

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The measuring systems must be expressed by differential or difference equations and treated as dynamical systems, when the frequency ranges of the measuring systems cannot cover enough those of the measured values.
This paper shows first the necessary conditions and the necessary and sufficient conditions for the input observability of the linear time-discrete systems.
Comparing the conditions of controllability and obsrvability, the analogy between the time-continuous systems and the time-discrete systems are pointed out, concerning state controllability, state observability and output controllability. The principle of duality holds about the state values. It does not hold in general about the input and the output values. But the systems with one input or one output keep the principle of duality.
The time-discrete systems do not provide the sufficient informations with controllability and observability without the some numbers (n) of sampling and observation. But the time-continuous systems contain the same informations for only a little interval.
When we discretize the time-continuous systems, the controllability and observability of the time-continuous systems are the necessary conditions for those of the time-discrete systems. If we do not choose the proper sampling period when discretizing, we loose the controllability and observability. The rank of the linear coefficient matrix combining the time-continuous system with the time-discrete systems must be proper.
The condition which is very similar to the necessary and sufficient condition for the state observability is merely the necessary condition for the input observability.

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The Kronecker canonical form of matrix pencils plays an important role in various fields such as systems control and differential-algebraic equations. The Kronecker canonical form admits two characterizations: the highest degree of subdeterminants, which can be computed by combinatorial relaxation algorithms, and the ranks of larger constant matrices called expanded matrices. This article surveys the combinatorial approach to the analysis of the Kronecker canonical form.

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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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本論文では,多項式行列に対する小行列式の最大次数と展開がルジャンドル変換により関係づけられることを示し,さらに,それぞれに対応するグラフ論的な特徴量に関しても同様の関係が成り立つことを示す.これは,近年,室田によって得られた行列束に対する結果を拡張するものであり,有理関数行列に対する無限遠点におけるスミス・マクミラン標準形の組合せ論的解析への応用をもつ.

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A new simple method of identification for linear discrete systems has been developed, which is based on Kalman's Hankel matrix H formed by Markov parameters of the system.
By input random sequences generated by a computer, input Hankel type matrix U is formed. Matrix Y which is the product of matrices U and H, that is Y=U×H, plays the crucial roles in this identification method, because useful properties are transferred from Matrix H.
The identification for system dimension can be implemented by upper left sub-matrixY'. If system dimension is n₀, then Y' must be (2n₀-1)by n₀ matrix. After multiplying Y' by fundamental matrix chain S_n0-1, …, S₂, S₁ from the left, n₀ by n₀ matrix Y₀ can be obtained, the rank of which is equal to the system dimension. Increasing n₀ by one, the diagonalized matrix Y₀' becomes singular, but the parameters of the denominator of the transfer function appear on the (n₀+1)th column. So only n₀ iterations are required to complete system identification.

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画像を文書, 特徴ベクトルを単語とみなして潜在意味解析 (Latent Semantic Analysis, LSA) により画像の類似検索を行うことを考える.本論文では, LSAにおける低次元空間の次元数や特異値による重み付けが検索精度へどのように影響するか調べるためにLSAを一般化する.さらに, LSAにより低次元空間に射影された画像と圧縮された特徴ベクトルを対応分析で2次元空間に配置することにより, LSAの効果を視覚的に考察できるようにする.実験により, LSAにおけるパラメータの検索精度への影響や, 用いる特徴ベクトルによる効果の違いについて調べる.

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This paper deals with the input observability and the duality between inputs and outputs of the linear dynamic measuring system which is time-continuous and analytic.
First we introduce the necessary and sufficient conditions for the input observability of pulse and pulse series in the time varying system. We obtain slightly different conditions between time-fixed pulse series and time-free pulse series. The necessary and sufficient condition for the total input observability of pulse series is easily obtained from that of time-free pulse series.
In case of the time constant system, the necessary and sufficient condition for the input observability of power series is of the same form as that of pulse series.
The above necessary and sufficient conditions are analogous to those of state observability. Considering more general inputs capable of Laplace transformation, however, we need independent output variables of no smaller number than that of input variables.
If the system has the state observability, then the necessary and sufficient condition for the input obsevability is of much simpler form. This relation is similar to that between state controllability and output controllability.
At the end of this paper, it is shown that the pulse input observability is dual to the output controllability.

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Late Professor Yanai has contributed to many fields ranging from aptitude diagnostics, epidemiology, and nursing to psychometrics and statistics. This paper reviews some of his accomplishments in linear algebra and multivariate analysis through his collaborative work with the present author, along with some untold episodes for the inception of key ideas underlying the work. The various topics covered include constrained principal component analysis, extensions of Khatri’s lemma, the Wedderburn-Guttman theorem, ridge operators, decompositions of the total association between two sets of variables, and ideal instruments. A common thread running through all of them is projectors and singular value decomposition (SVD), which are the main subject matters of a recent monograph by Yanai, Takeuchi, and Takane (2011).

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Computational time for numerical simulation of transient incompressible viscous flow is governed by numerical methods to solve the Poisson equation of the pressure. In order to improve the computational efficiency of the SOR method, a mathematical analysis was conducted in the present study to derive the spectral radius, i. e., the maximum modulus of the eigenvalues of the iteration matrix for a discrete Poisson equation in staggered mesh system. The derived spectral radii for the point, line and area Jacobi iteration matrices are applicable to the Dirichlet, the mixed boundaryvalue and the Neumann problems in an n-dimensional rectangular region. The validity of the optimum relaxation parameter of the SOR method, which was calculated by the derived spectral radii, was confirmed by numerical experiments. Furthermore, a simple estimation method of the optimum relaxation parameter for the non-rectangular region was presented for transient flow analyses.

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