本論文の目的は不安定トラス構造のつりあい点の探索をきわめて単純な方法で行うことを提案することである。この種の研究にはこれまで、半谷らによる「一般逆行列」を用いた方法が提案されているが、ここではつりあい式に出てくるのみで容易に求まること示すとともに、仮想仕事の原理を用いながら、個々の部材力の算定方法を示す。それらの結果は、解析解の知られているカテナリー曲線などと比較することにより正しいことを確認する。また、それらの応用についても言及する。

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多次元(n-D)伝達関数からそのシステムの状態空間モデルを求める実現問題は, n-Dシステム理論の基礎的な問題であり,システムの不確かさのモデリングやセンサーネットワークの実現など多くの分野へ応用できる.しかし, n-D最小実現問題は極めて困難であるため,いかに低次数の実現を求めるかが特に重要となる.本論文は,行列基本変形を用いて,より低次数のFornasini-Marchesiniモデルを構築できる新しい実現法を提案する.

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Faculty of Engineering Yamaguchi continues the examination for students who study Engineering in the universities, EMaT, collaborating with the Faculty of Engineering Hiroshima University. The examination is open to all universities in Japan and has gained high estimate from many people in Japan concerning with the engineering education. The present paper describes the important information to people in the engineering education. It includes various matters about the examination.

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In this paper, we present a fraction-free algorithm for computing Rational Normal Forms of square matrices over the polynomial ring. The original algorithm is based on Danilevskii's method. Its principal transformations are similar to Gaussian elimination. When they are carried out exactly by computer algebra system, the difficulty lies in that the elements of intermediate matrices extremely swell and it requires much CPU-time to compute g.c.d.s and l.c.m.s for reducing rational expressions. In order to avoid such difficulty, we give a fraction-free algorithm analogous to Bareiss'single-step fraction-free elimination. We implement it on the computer algebra system REDUCE3.5. The experimental result shows the efficiency of our algorithm.

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The aim of Engineering Mathematics Test (EMaT) is to make sure what essentials in curriculum of Engineering Mathematics is, and to assess university students’ core academic competence and achievement of Engineering Mathematics, helping assurance of students’ academic ability. It is useful for professors to evaluate teaching effect of the classes, and this evaluation would help them improve curricula. Scores can be available for both graduate school entrance examinations and employment tests, leading to selecting persons with basic academic ability in Engineering Mathematics. The scope includes fundamentals in Calculus, Linear Algebra, Differential Equations, and Probability and Statistics. It is open to all students free of charge, and is annually given once in December. In 2007, 2,396 students from 35 universities took EMaT, and the total number of students who have taken EMaT in these 5 years is 6,240.

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In this paper, algorithms for computing Jordan Normal Forms of square matrices over the rational number field are elucidated. The computation is exactly carried out by computer algebra, and the result is free from any numerical errors. These algorithms are deduced from well-known mathematical theorems, but they have not been installed yet in most of computer algebra system. Basic algorithms contain the step of solution of algebraic equations, which limits the applicability of the program. Theorefore, the improvement of the defect is discussed. The result of experimental implementation on REDUCE3.3 shows that the improved algorithm works quite efficiently.

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3次元物体の復元と認識において, 物体の表現モデルとして, 従來主に単体モデルが用いられてきたが, 単体モデルは構築することが難しく, pyramidのような多重解像度モデルが実現不可能であった.また認識方法についても, ある変換に対して不変性のある認識方法が望まれている.本研究では, 3次元物体の表面データ及びポリュームデータについて, 拡張Kohonen's mapを用いた, 物体の立方特異単体複体モデルの構築方法を提案する.本方式は, 計算が簡単で, 多重解像度モデルとしてのpyramid構造も自然に構築できるため, 3次元物体の復元や符号化に応用できる.さらに, 本モデルによって, 物体の内在的な位相不変量としてホモロジー群を計算する.また, 物体の内在的な特徴量である結び目や絡み目など空間の埋め込み幾何学的な特徴についても考察を行なう.

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線形代数の知識は理工面への応用のみならず，算数・数学科の内容を正比例の視点から統合的に理解するためにも必要不可欠なものである．しかしながら，その存在意義は教員養成課程の学生には低く感じられがちである．本稿では理数系教員養成のための線形代数コースの開発にむけ，算数・数学科の教材研究の文脈から数学的活動を開始できる「アリスモゴン」という題材に注目し，その探究に自然に含まれうる線形代数の知識を特定する．そのために，教授人間学理論のプラクセオロジーを用いて，アリスモゴンを巡る数学的活動とその過程で生じる線形代数の知識を記述する．また，アリスモゴンを発展させた「アリスモヘドラ」や「アリスモグラフ」という題材を紹介・提案し，これらの題材から展開される多様な数学的活動が線形代数の知識の発生を促しうることを述べる．

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LQG approach is a useful metod for designing control systems in which disturbance effects should be alleviated. Although the order of the controller derived with LQG is generally equal to that of the controlled element, reduced-order controllers often give nearly the same performance index value as the optimal full-order controller gives. Since simple controllers are favorable in practical use, it is necessary to evaluate reduced-order controllers in the application of LQG. This paper presents an efficient algorithm to give sub-optimal and optimal reduced-order controllers. The algorithm consists of two processes. One is derivation of sub-optimal reduced-order controller, which is obtained by a chained aggregation model of the full-order controller. The model is given by Hessenberg representation of system matrix of the controller and diagonalization of covariance matrix of the controller states. Since diagonalization of the covariance matrix is equivalent to minimizing the residue of differencial equations, this chained aggregation model is suitable for the derivation of reduced-order models. The other is parameter optimization, which is obtained by using Gauss-Newton methed. Owing to this method, convergence characteristics are improved compared with ordinary gradient methods or Newton-Raphson method. An illustrative example is pretented. The algorithm is applied to an analysis of a basic windtunnel experiment model of an aircraft gust load alleviation system. The mathematical model of the experiment model is described by a 7th order system. In the case of suboptimal reduced-order controller, up to 3rd order controllers give similar performance indices as the optimal full-order controller gives, and in the optimized case, up to 2nd oder reduced-order controllers do so.

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This paper deals with a digital tracking control system subject to change in load condition. It is assumed that the plant is described by a discrete-time state-space model with a time delay and a direct forward link between control input and output. An optimal controller with state feedback plus integral and preview actions is derived by using the LQI technique. It is shown under the stabilizability and detectability conditions that the optimal closed-loop system is stable and achieves a complete output regulation. For a special case where the time delay is unilateral, we present an algorithm for computing feedback gain with less computational effort. The tracking performance of proposed optimal control law is evaluated through a numerical example for a heat exchanger model. Experimental studies using a pilot plant show that the controller gives acceptable tracking performance in the presence of load change.

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