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Article, 指導法・実践報告

複素数連立一次方程式およびエルミート固有値問題を数値計算によって解いた場合の誤差の分析に必要なデータ取得を支援するサブルーチンを開発した。複素数連立一次方程式については、残差ベクトルのノルム、係数行列の条件数、解の誤差限界を計算する。エルミート行列固有値問題については、Korn-Katoの公式に基づいて、固有値の存在範囲を計算する。上記それぞれについて、逐次計算機用と並列計算機用が用意されている。本報告書は、サブルーチンで使用している精度評価公式の要点と、サブルーチンの利用方法についてまとめたものである。, 著者所属: 日本原子力研究開発機構(JAEA)

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We study projections of matrix algebras over complex or real numbers, to (partially) classify the (generically non-degenerate) projections (in our sense) and their spaces algebraically and geometrically, in the three by three, and four by four matrix cases, and in the general matrix case., 紀要論文

I consider the graphs of the functions of a complex variable in this paper. I cannot draw it directly, the functions from complex number to complex number. Because a thought method to look around the perspective from the part is necessary, high content will be found mathematically. If it can be visualized in a part easily, I become able to understand the total picture by putting them on top of one another in imagination. And this is regarded as typical mathematical activity. Therefore I decided to use an information appliance to be able to perform visualization instantly. I calculated the theoretical numerical value by C language and used drawing software Gnuplot with practice numerical value. We are dealing with fluid dynamics as a specific example. I really report the contents which let a university student test it by a class here.

application/pdf, 論文(Article), The purpose of this study is to survey learning context at Elementary Mathematic Practice A in the Department of Electrical Engineering. Elementary Mathematic Practice A is a required course which includes trigonometric function and complex number on a high school level. The content of the lecture provides basic knowledge for understanding specialized courses. However,the numbers of students who have limited insight into the content have been increasing. This is partly because many students have little study habits. The students take mini-exam and evaluate their studying context by themselves at every lecture. Analysis of the self-evaluations and mini-exam results shows that there are gaps in perception between their real academic abilities and self-assumptive academic abilities. We think the gaps would prevent the students from studying continuously.

21, KJ00004869432, 論文, Article

Let k be a field of characteristic zero. Let G be a connected &-split linear algebraic group, p: G^GL(X) with X=Affra a &-homomorphism. If there exists a Zariski-dense p(G)-orbit Y, we say that (G, p, X) is a prehomogeneous vector space (abbrev. P. V.). When each irreducible component is castling equivalent to a non-trivial reduced irreducible prehomogeneous vector space or each irreducible component is a regular prehomogeneous vector space, we have completed a classification of reductive prehomogeneous vector spaces over a complex number field C (see [4], [5]). Put G = p(G). Let / be the number of G(£)-orbits in Y(k), i. e., /= | G(k)\Y(k)\. We say that Y is a universally transitive open orbit if l=\G(k)\Y(k)\=l for all k satisfying H\k, Aut(SL2))=£0, i.e., there exists a nonsplit quaternion kalgebra. This condition is satisfied by every local field k other than C. Actually our classification depends on the transitivity of G(k) on Y(k) for just one k satisfying H\k, Aut(SL2))^0 (see Remarks 2.13 and 3.5). In [1] and [2], allirreducible regular prehomogeneous vector spaces with universally transitive open orbits are classified. In [10], we have classified simple or 2-simple prehomogeneous vector spaces with universally transitive open orbits. In this paper, we shall classify reductive prehomogeneous vector spaces with universally transitive open orbits when each irreducible component is castling equivalent to a non-trivial reduced irreducible prehomogeneous vector space or each irreducible component is a regular prehomogeneous vector space. This paper consists of the following three sections. §1. Preliminaries. §2, Reductive P.V.'s with universally transitive open orbits: the case I. §3. Reductive P.V.'s with universally transitive open orbits: the case II. The results are given in Theorems 2.11, 3.4 and Corollary 2.12.

Distribution patterns of grand wire current along transmission lines have been analyzed by a experts in order to find the fault location. Various types of fault location methods using multi-layered feed forward type neural network models have been proposed and these efficiencies have been shown in several papers. The amplitudes and the phase angles are used as the input data of the neural network. If we use complex number for the neural network, we can relate the amplitude and the phase angle to each other. In this paper, we propose a fault location method using the multi-layered feed forward type neural network model. In the proposed method, the neurons are expressed by the sigmoid functions which are extend to the complex number and we use the complex back propagation learning algorithm.

We show that if a cubic hypersurface with positive dual defect over the complex number field is not a cone, then either the hypersurface coincides with the secant variety of the singular locus, or the hypersurface contains a linear subvariety of dimension greater than the dual defect such that the intersection of the singular locus and a general contact locus is contained in the linear subvariety., 於 城崎国際アートセンター(2018年10月22日-10月26日), 平成30年度科学研究費補助金 基盤研究(S)(課題番号15H05738, 代表 金銅誠之), 平成30年度科学研究費補助金 基盤研究(S)(課題番号17H06127, 代表 齋藤政彦), 平成30年度科学研究費補助金 基盤研究(S)(課題番号16H06337, 代表 高橋篤史), Date : Oct. 22, 2018 (Mon) - Oct. 26, 2018 (Fri). Venue : Kinosaki International Arts Center., Kinosaki Algebraic Geometry Symposium 2018 is partially supported by Grantin-Aid for Scientific Research (S) 15H05738, (S) 17H06127, and (S) 16H06337. Organizers: Hokuto Uehara (Tokyo Metropolitan University), Kiwamu Watanabe (Saitama University), Atsushi Kanazawa (Kyoto University)

We give an example of vector-valued analogue of the theory of the Heckman-Opdam hypergeometric function associated with a root system. We construct matrix-valued commuting differential operators associated with root system of type A_{2} and their joint eigenfunctions. In group case, the differential operators are radial parts of invariant differential operators on a certain homogeneous vector bundle over a Riemannian symmetric space and the radial part of a matrix coefficient of a principal series representation gives a joint eigenfunction that is analytic at the origin. Allowing the root multiplicity to be an arbitrary complex number, we give matrix-valued commuting differential operators and connection coefficients (c-functions) for their joint eigenfunctions given by power series.

フィルタ対角化法を用いて, 実対称定値一般固有値問題の指定区間に固有値がある固有対の近似を求める. 単一のレゾルベントの多項式をフィルタとして用いることで, 複数のレゾルベントの線形結合を用いる場合に比べて演算量と記憶量が低減できることが期待できる. 固有値分布の内側の固有値を持つ固有対を求める場合にはレゾルベントのシフトには虚数を選ぶが, 固有値分布の端にある固有値を持つ固有対を求める場合にはシフトに実数を選ぶことができる. シフトに実数を選ぶと, すべての計算を実数演算だけを用いて複素数を用いずに行なえるので, 演算量と記憶量が減らせて有利になる. 単一のレゾルベントの多項式をフィルタとして採用する場合, その多項式を特にチェビシエフ多項式とすると, 阻止域では伝達率の大きさの上限を容易に小さく抑えることができる. しかし通過域では伝達率の最大最小比が小さくないため, 必要な近似対の精度は均一性が良くない可能性がある. そこでフイルタに用いる単一のレゾルベントの多項式を, 一つのチェビシェフ多項式で表わされるものから, 複数のチェビシエフ多項式の和で表わされるチェビシェフ展開形へと拡張することにより阻止域に於ける減衰率を十分に確保しながら, 通過域に於ける伝達率の最大最小比をできるだけ抑えることを試みた., For a real symmetric definite generalized eigenproblem, by using the filter diagonalization method, we solve approximations of those eigenpairs whose eigenvalues are in a specified interval. We can expect to reduce both amounts of computation and memory space when we use a filter which is a polynomial of a single resolvent rather than to use a hnear combination of many resolvents. When we solve eigenpairs with interior eigenvalues for the shift of the resolvent we choose a complex number. We can choose a real number for the shift when we solve pairs with exterior eigenvalues. If a real number is chosen for the shift, the calculation is be made only by real arithmetics rather than complex ones, we have an advantage to reduce both amounts of computation and memory space. When a filter is a polynomial of a single resolvent, if the polynomial is chosen as a Chebyshev polynomial then it is easy to obtain a small upper-bound for the magnitude of the transfer rate of the filter in the stopband. However, for such a filter, the ratio of the maximum and the minimum of the magnitude of the transfer rates in the passband cannot be made so small, it is likely that the uniformity of approximations of required eigenpairs is not so good. Therefore, in this report of research, to reduce the ratio, we tried to extend the polynomial for the filter from a single Chebyshev polynomial of a certain degree to a sum of Chebyshev polynomials up to a certain degree.

本論では、既に提示した3 つの組織モデル（フローモデル、ストックモデル、共振モデル）の実用性に関する考察を行う。まず、単位系に関する整合性の議論を行い、次に、財務分析として広く用いられている比率分析との比較として、フローとストックの複素数表示と実数表示を用いた再定義を行う。さらに、プロダクト・ポートフォリオ・マネジメント（ＰＰＭ）の各セグメントついて共振モデルの変数を用いた再記述を試みる, In this paper, we examine the practical ability of three organizational models (flow model, stock model, resonance model) already reported. First, we discuss on the consistency of the unit system, next, as a comparison with Ratio Analysis Method which is widely used for the finance data, we re-define each index of Ratio Analysis Method by complex number and real number of flow and stock. Furthermore, we redescribe the each segment of Product Portfolio Management (PPM) with the parameter of resonance model.

The purpose of this paper is to present a numerical method for shape optimization problems related to frequency response problems of linear elastic continuum.Following the previous report in which no damping eas assumed, proportional viscous damping is considered in this paper. Minimization problems of strain energy,kinetic energy and absolute value of mean compliance are treated.A variational form of an equation of motion is obtained with complex number of displacement amplitude. Sensitivity function,that is called shape gradiant function, is derived using the Lagrange multiplier method.A technique using modal parameters for calculation of Lagrange multiplier function,that is called adjoint function,is shown.The traction method is applied for numerical analysis.Beamlike plate problems are analyzed to show the validity of this approach.

application/pdf, Experimental analysis of stresses around reentrant corners as lying in such a plate as in the title, encounters very often difficulty of finding exact values or at least considerably reliable one, due to the principle, capacity, mechanism or externals of the measuring apparatus, or to the manufacture or preparation of the tested specimen. Theoretical one exercises its power on such a stress system with more exact solution, clearing up most of the speculative constitution of the problem, which could be expected to do some in future for the stereotyped theory. It is studied and described in this paper, in what inference and procedure the analysis can be made theoretically about such a boundary of a plate by the method of Muskhelisvili’s type，treating the problem as the complex stress boundary one. It might be why overall and concrete analysis or numerical calculation thereabout has not yet been found out in the former papers, that the stress condition there has been considered not so critical in the main, and furthermore numerical calculation by the complex in6nite series, very hard to carry through,. This study has confirmed this safety and unsafety about stress numerically and is hoped to help some the analysis and application of the kind. As to the computation, it was done by both a common and an electronic computer, and the description refers to the number of the terms of the infinite series to be expanded, and the mode of the convergence of the results is plotted in relation with this number of the known coefficients, and it has come clear : the more the number, the more exact values ; an electronic computer does not always detest the complex number calculation as long as the programming is adquate and the amount of data to work by or memorize, within its capability.