日本応用数理学会論文誌

表紙

原稿種別: 表紙
2003 年 13 巻 2 号 p. Cover1-
発行日: 2003/06/25
公開日: 2017/04/08

DOIhttps://doi.org/10.11540/jsiamt.13.2_Cover1

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目次

原稿種別: 表紙
2003 年 13 巻 2 号 p. Cover2-
発行日: 2003/06/25
公開日: 2017/04/08

DOIhttps://doi.org/10.11540/jsiamt.13.2_Cover2

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日本応用数理学会論文誌編集委員会

原稿種別: 付録等
2003 年 13 巻 2 号 p. App1-
発行日: 2003/06/25
公開日: 2017/04/08

DOIhttps://doi.org/10.11540/jsiamt.13.2_App1

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とびらの言葉

岡本龍明

原稿種別: 本文
2003 年 13 巻 2 号 p. i-
発行日: 2003/06/25
公開日: 2017/04/08

DOIhttps://doi.org/10.11540/jsiamt.13.2_i

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単調性保存スキームI : 定常移流・拡散方程式の局所厳密解に基づく有限可変差分法

木村功, 酒井勝弘

原稿種別: 本文
2003 年 13 巻 2 号 p. 139-157
発行日: 2003/06/25
公開日: 2017/04/08

DOIhttps://doi.org/10.11540/jsiamt.13.2_139

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We discuss a numerical scheme with monotonicity preserving properties without additionally introducing artificial diffusions for advection-diffusion equations. This paper proposes "Finite Variable Difference Method (FVDM)", in which the convection term is discretized by using locally optimized numerical fluxes so that the resulting difference equation may satisfy a locally exact solution of steady advection-diffusion equations. The present scheme ensures the monotnicity up to the cell Reynolds number Rm ≒ 3.4 in keeping the second-order accuracy, while the conventional central scheme and the QUICK scheme up to Rm = 2 and Rm = 8/3, respectively. For Rm > 3.4, though the present scheme has the first-order accuracy, the lowest order of its truncation error can be finite but arbitrary small. Numerical experiments show solutions with good quality.

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浮動小数点演算による4次方程式の解法(Brown法)

布広永示, 平野菅保

原稿種別: 本文
2003 年 13 巻 2 号 p. 159-179
発行日: 2003/06/25
公開日: 2017/04/08

DOIhttps://doi.org/10.11540/jsiamt.13.2_159

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When solving 4th order equation by floating decimal point operation, there is Ferrari method famous as a solution method of 4th order equation. In this paper, we apply Brown method that transform 4th order equation into the product of two 2nd order equations directly to floating point operation and propose the effective computation method. And from the relation of coefficient and solution of 4th order equation, we express coefficients and all numerical values in the middle calculation with four solutions, and by analyzing the information on the solutions contained in those coefficients, we show the validity of the Brown method.

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確率計画法による発電機起動停止問題

椎名孝之

原稿種別: 本文
2003 年 13 巻 2 号 p. 181-190
発行日: 2003/06/25
公開日: 2017/04/08

DOIhttps://doi.org/10.11540/jsiamt.13.2_181

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The unit commitment problem is an important problem for electric power utilities. The unit commitment problem is to determine the schedule of power generating units and the generating level of each unit. The decisions are which units to commit at each time period and at what level to generate power meeting the electricity demand. In this paper we propose a new stochastic programming programming model in which on/off scheduling of generators is made before the value of random demand is known. The solution approach is based on the Lagrangian relaxation method and dynamic programming.

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Swift-Hohenberg方程式の定常解大域分岐のConley指数を用いた検証

平岡裕章, 小川知之, Konstantin Mischaikow

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2003 年 13 巻 2 号 p. 191-211
発行日: 2003/06/25
公開日: 2017/04/08

DOIhttps://doi.org/10.11540/jsiamt.13.2_191

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This paper presents a numerical verification method for global bifurcation branches of the stationary solutions to dissipative partial differential equations. The key idea is combining verification method based on the Conley Index Theory with a branch chasing algorithm. In this paper, the verification algorithm is described in detail by taking the Swift-Hohenberg equation as an example. Some of the rigorous numerical results are also shown.

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方向性準単色波によって形成される包絡面の支配方程式の導出とその考察

野原勉

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2003 年 13 巻 2 号 p. 213-224
発行日: 2003/06/25
公開日: 2017/04/08

DOIhttps://doi.org/10.11540/jsiamt.13.2_213

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This paper focuses on the envelope surface of directional, nearly monochromatic waves and the governing equation of the envelope surface is reduced. The spectrum of nearly monochromatic waves is almost concentrated on a single frequency. Such waves create the envelope in a one-dimensional system. In a two-dimensional system, the envelope surface instead of the envelope in a one-dimensional system can be considered. Two-dimensional nearly monochromatic waves in the meaning of the frequency create the envelope surface. This is simply expanded to a two-dimensional system from a one-dimensional system. The author expands the frequency-based nearly monochromatic waves to the propagation-direction-based nearly monochromatic waves. We have the new concept of directional, nearly monochromatic waves, whose energy is almost concentrated in a single propagation direction. It is shown that directional, nearly monochromatic waves also create the envelope surface, which is featured by time-invariant in a linear system. However the fact that a non-linear system makes the envelope surface time-variant is presented.

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二重指数関数型数値積分公式の収束判定法の改良

大浦拓哉

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2003 年 13 巻 2 号 p. 225-230
発行日: 2003/06/25
公開日: 2017/04/08

DOIhttps://doi.org/10.11540/jsiamt.13.2_225

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The double exponential formula is well-known as a powerful numerical quadrature rule. The automatic quadrature routine of the double exponential formula is necessary for the procedure of checking the convergence, but the conventional method of estimating discretization error is too simple to have a reliable estimate. In this paper, we propose a new method which robustly estimates the discretization error quite effectively.

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代数曲線暗号

松尾和人, 有田正剛, 趙晋輝

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2003 年 13 巻 2 号 p. 231-243
発行日: 2003/06/25
公開日: 2017/04/08

DOIhttps://doi.org/10.11540/jsiamt.13.2_231

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This paper is a survey on the state-of-the-art of cryptosystems based on the discrete logarithm over algebraic curves on finite fields. The issue on security of these systems against various attacks are firstly considered. Then fast addition algorithms and efficient point counting algorithms for Jacobian varieties of algebraic curves are discussed. These algorithms, although are necessary for construction of algebraic curve cryptosystems, had not been available until very recently. This paper also surveys the known results and the recent advances of related number theoretic algorithms and new developments in construction of algebraic curve cryptosystems.

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有限体上の離散対数問題 : 数体ふるい法,関数体ふるい法

内山成憲

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2003 年 13 巻 2 号 p. 245-256
発行日: 2003/06/25
公開日: 2017/04/08

DOIhttps://doi.org/10.11540/jsiamt.13.2_245

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Since the invention of the public-key cryptosystem in the 1970's, some number theoretic problems such as the integer factoring and the discrete logarithm problem in finite fields have received a lot of attention. The number field sieve method is currently known as the asymptotically fastest integer factoring algorithm. It is also known that the number field sieve method can be made use of computing discrete logarithms in finite fields due to Gordon and Schirokauer. Besides, Adleman proposed a function field analogue of the number field sieve method, which is known as the function field sieve, to compute discrete logarithms in finite fields. This paper surveys recent results on these two methods, the number field sieve and the function field sieve, of computing discrete logarithms in finite fields.

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楕円曲線のMordell-Weil群について

木田雅成, 長尾孝一

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2003 年 13 巻 2 号 p. 257-271
発行日: 2003/06/25
公開日: 2017/04/08

DOIhttps://doi.org/10.11540/jsiamt.13.2_257

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This paper is intended for a survey on recent research on the group of rational points on elliptic curves. The first part is devoted for the recent progress on the computation of the group. The second part concerns on the constraction of elliptic curves with high rank Mordell-Weil group.

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有限体上の楕円曲線の位数計算アルゴリズム

佐藤孝和

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2003 年 13 巻 2 号 p. 273-288
発行日: 2003/06/25
公開日: 2017/04/08

DOIhttps://doi.org/10.11540/jsiamt.13.2_273

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rights: 日本応用数理学会rights: 本文データは学協会の許諾に基づきCiNiiから複製したものであるrelation: IsVersionOf: http://ci.nii.ac.jp/naid/110001878223/
This paper surveys recent advances of algorithms for computing order or elliptic curves over finite fields. Let p be the characteristic of the base field of a given elliptic curve. Following a usual convention, we denote a primo different from p by l. Then, for fields of large characteristic, l-adic method known as the SEA algorithm is efficient. Whereas, p-adic method runs much faster for fields of small characteristic.

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素因数分解の現状について

伊豆哲也, 木田祐司

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2003 年 13 巻 2 号 p. 289-303
発行日: 2003/06/25
公開日: 2017/04/08

DOIhttps://doi.org/10.11540/jsiamt.13.2_289

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This paper reports recent results of interger factorization from theoretic, algorithmic and experimental points of view. We also give introductions of major factorization algorithms, especially the (general) number field sieve (NFS) method.

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代数的計算数論の現状

中村憲

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2003 年 13 巻 2 号 p. 305-320
発行日: 2003/06/25
公開日: 2017/04/08

DOIhttps://doi.org/10.11540/jsiamt.13.2_305

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In this report, we shall give an illustration of recent research on computational algebraic number theory, mainly related to number fields and elliptic curves. The purpose of the paper is to describe the achievement of this area at present so that to what extent we can theoretically and practically compute on each field. We shall not go in detailed explanation of algorithms.

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複写される方へ

原稿種別: 付録等
2003 年 13 巻 2 号 p. App2-
発行日: 2003/06/25
公開日: 2017/04/08

DOIhttps://doi.org/10.11540/jsiamt.13.2_App2

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奥付

原稿種別: 付録等
2003 年 13 巻 2 号 p. App3-
発行日: 2003/06/25
公開日: 2017/04/08

DOIhttps://doi.org/10.11540/jsiamt.13.2_App3

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裏表紙

原稿種別: 表紙
2003 年 13 巻 2 号 p. Cover3-
発行日: 2003/06/25
公開日: 2017/04/08

DOIhttps://doi.org/10.11540/jsiamt.13.2_Cover3

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CONTENTS

原稿種別: 表紙
2003 年 13 巻 2 号 p. Cover4-
発行日: 2003/06/25
公開日: 2017/04/08

DOIhttps://doi.org/10.11540/jsiamt.13.2_Cover4

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