著者

曽 道智 茨木 俊秀

出版者

一般社団法人 日本応用数理学会

雑誌

応用数理 (ISSN:24321982)

巻号頁・発行日

vol.9, no.1, pp.12-27, 1999-03-15 (Released:2017-04-08)

参考文献数

31

---

We survey the recent research in the field of cake divisions and their procedures. The question is how to divide a cake among n players, so that a certain fairness is achieved, where players have individual measures on the cake, and each player only knows his own measure. The model has very wide applications, such as dividing up the property in an estate, and even in determining the border in an international dispute. We first review mathematical definitions of various concepts of fairness. Although the existence of fair divisions is proved under some mathematical conditions, their dividing procedures are not known for all cases. We summarize several existing division procedures and classify them according to their methods and purposes. Finally, we mention some related topics and describe possible future research directions.

著者

萩原 茂樹 米崎 直樹

出版者

一般社団法人 日本応用数理学会

雑誌

応用数理 (ISSN:24321982)

巻号頁・発行日

vol.17, no.4, pp.291-301, 2007-12-26 (Released:2017-04-08)

参考文献数

10

---

暗号プロトコルの解析は,確率的多項式時間チューリング機械を用いる計算論的手法と,Dolev-Yaoモデルに基づく記号論的手法がそれぞれ独立に研究されてきた.記号論による解析は,抽象レベルの解析とみなせ簡潔で分かりやすい一方,記号論による解析結果と計算論による解析結果の対応が明らかでなかった.この問題に対してAbadiとRogawayは,完全な対称鍵暗号方式を前提としてメッセージの見た目の等価性を記号論的に定義し,メッセージが等価ならばそれらは計算論的に識別不可能であること,すなわち記号論によるメッセージの識別不可能性の計算論的意味づけに対する健全性を示した.さらに,MicciancioとWarinschiはその完全性を示している.本稿では,これら内容を中心に関連する研究を含め紹介を行う.

著者

藤原 宏志 今井 仁司 竹内 敏己 磯 祐介

出版者

一般社団法人 日本応用数理学会

雑誌

日本応用数理学会論文誌 (ISSN:24240982)

巻号頁・発行日

vol.15, no.3, pp.419-434, 2005-09-25 (Released:2017-04-08)

---

A new method for the direct numerical computation of integral equations of the first kind, of which the integral kernels are analytic, is proposed. The basic idea of the method is based on combination of the spectral collocation method and the multiple precision computation. It gives good numerical results for the equations as far as we don't admit observation errors in the given inhomogeneous terms, and the results implies possibility of numerical analytic continuation on the multiple precision arithmetic. A new accurate rule for numerical integration is also introduced.

著者

藤井 宏

出版者

一般社団法人 日本応用数理学会

雑誌

応用数理 (ISSN:24321982)

巻号頁・発行日

vol.20, no.1, pp.10, 2010-03-25 (Released:2017-04-08)

著者

新井 朝雄

出版者

一般社団法人 日本応用数理学会

雑誌

応用数理 (ISSN:24321982)

巻号頁・発行日

vol.3, no.4, pp.292-306, 1993-12-15 (Released:2017-04-08)

参考文献数

46

---

Mathematical aspects of quantum field theory are reviewed. The topics included are: canonical quantization of classical fields, functional integral method, Schwinger's functional derivative equation, methods and results of constructive quantum field theory, Lamb shift in quantum electrodynamics, supersymmetric quantum field theory and related aspects.

著者

木村 英紀

出版者

一般社団法人 日本応用数理学会

雑誌

応用数理 (ISSN:24321982)

巻号頁・発行日

vol.1, no.1, pp.2-16, 1991-03-15 (Released:2017-04-08)

---

The relevance of mathematics in control theory is described. The role of mathematics in the early development of control theory is reviewed with the emphasis on the models of controlled objects. The relation between the operational calculus and the classical control theory is discussed. The contact between control theory and mathematics became more and more wider and deeper especially after the emergence of modern control theory in 1960. Some specific aspects of the mathematical problems posed by control theory are reviewed. Possible future directions of the mathematics/control interface is described in conjunction with robustness issues of control systems design.

著者

佐々木 宣介 梶原 羊一郎 飯田 弘之

出版者

一般社団法人 日本応用数理学会

雑誌

日本応用数理学会論文誌 (ISSN:24240982)

巻号頁・発行日

vol.10, no.4, pp.327-334, 2000-12-15 (Released:2017-04-08)

参考文献数

5

---

It is supposed that HEIAN SHOGI is an ancient variant of the MODERN SHOGI (Japanese CHESS). When two experienced players play a game of HEIAN SHOGI, they often reach a 'King-and-Gold vs King'endgame. This paper presents the results of computer analyses of this 'King-and-Gold vs King'endgame to explore the evolutionary changes of the characteristics of games. The analyses were done in the various sizes of square board. The loop positions, that are included neither in the winning position of 'King-and-Gold'side nor in the obvious draw positions, appear in larger than 11×11 board, and these loop positions account for above 80% of all positions. And the number of steps of the longest position-to-mate approach to a certain value. These results mean that the characteristics of games radically change in the different size of the board. It is hoped that these results give us important suggestion to suppose why the ancient SHOGI variant changes to 9×9 board (MODERN SHOGI).

著者

中根 和昭 Marcio Gameiro 鈴木 貴 松浦 成昭

出版者

一般社団法人 日本応用数理学会

雑誌

日本応用数理学会論文誌 (ISSN:24240982)

巻号頁・発行日

vol.22, no.3, pp.97-108, 2012-09-25 (Released:2017-04-08)

参考文献数

18

被引用文献数

1

---

病理診断とは,人体から採取された材料について顕微鏡で観察し,病理学の知識や手法を用いて病変の有無や種類について診断することである.日本では病理医の絶対数は症例数に比べ圧倒的に不足しているため,計算機による病理診断支援技術の開発は緊急の課題である.ここでは,位相幾何学的な概念を基にしたアルゴリズムを提案し,生体組織画像から病変部を抽出する手法と,大腸癌の組織に対して適用した結果を紹介する.

著者

川島 幸之助

出版者

一般社団法人 日本応用数理学会

雑誌

応用数理 (ISSN:24321982)

巻号頁・発行日

vol.4, no.4, pp.365-367, 1994-12-15 (Released:2017-04-08)

著者

室田 一雄

出版者

一般社団法人 日本応用数理学会

雑誌

応用数理 (ISSN:24321982)

巻号頁・発行日

vol.24, no.1, pp.37-40, 2014-03-25 (Released:2017-04-08)

著者

杉原 厚吉

出版者

一般社団法人 日本応用数理学会

雑誌

応用数理 (ISSN:09172270)

巻号頁・発行日

vol.5, no.3, pp.254-256, 1995

参考文献数

4

著者

小笠原 匡 多田野 寛人 櫻井 鉄也 伊藤 祥司

出版者

一般社団法人 日本応用数理学会

雑誌

日本応用数理学会論文誌 (ISSN:09172246)

巻号頁・発行日

vol.14, no.3, pp.193-205, 2004

参考文献数

8

被引用文献数

1

---

We consider a method to solve several shifted linear systems (A+σl)x = b with shift parameter σ. Krylov subspace for shifted linear systems is not depend on the parameter σ, therefore we can solve several shifted linear systems simultaneously without generating Krylov subspace for each parameter cr. In this paper, we show that shifted linear systems appear in an eigensolver using numerical integration. We applied Krylov subspace methods for shifted linear systems in this eigensolver. We have also presented some numerical examples illustrate the efficiency of the method.

著者

住井 英二郎

出版者

一般社団法人 日本応用数理学会

雑誌

応用数理 (ISSN:24321982)

巻号頁・発行日

vol.17, no.4, pp.280-290, 2007-12-26 (Released:2017-04-08)

参考文献数

15

---

This survey presents Abadi and Gordon's spi-calculus, which is a "process calculus" (i.e., a formal language of concurrent computation) for the verification of "cryptographic protocols" (i.e., procedures for secure communication in computer networks). First, we present process calculi before the spi-calculus (CCS and the pi-calculus), introducing the notion of reaction relation and structural congruence. We then define the spi-calculus and show an example of cryptographic ptotocols, represented as a class of spi-calculus processes. After discussing the formalization of security properties (secrecy and authenticity) and multiple sessions, we conclude by referring to generalizations of the spi-calculus (Abadi and Fournet's applied pi-calculus, and a recent result by Bruno Blanchet).

著者

斉藤 努

出版者

一般社団法人 日本応用数理学会

雑誌

応用数理 (ISSN:09172270)

巻号頁・発行日

vol.25, no.2, pp.72-76, 2015

著者

桧山 澄子 花田 孝郎 今井 仁司

出版者

一般社団法人 日本応用数理学会

雑誌

日本応用数理学会論文誌 (ISSN:09172246)

巻号頁・発行日

vol.3, no.2, pp.85-104, 1993

参考文献数

10

被引用文献数

2

---

We present here practical methods for reducing the data points composing a plane curve. This method is characterized that it works by specifying the rate or th number of the points to be reduced, not by giving the error tolerance. In this method we apply different algorithms according to the property of the original curve and the rate of reducing. This will give highly accurate result and less time in computing. In addition, the means how to estimate the obtained result are treated.

著者

緒方 秀教 杉原 正顯

出版者

一般社団法人 日本応用数理学会

雑誌

日本応用数理学会論文誌 (ISSN:09172246)

巻号頁・発行日

vol.8, no.2, pp.223-256, 1998

参考文献数

7

---

Quadrature formulae for oscillatory infinite integrals involving the Bessel functions are proposed. Those formulae are obtained by the so-called double exponential type of variable transformations followed by an application of quadrature formulae whose abscissae are the zeros of the Bessel functions, which are developed in [3]. Numerical examples are included.

著者

竹内 敏己 藤野 清次

出版者

一般社団法人 日本応用数理学会

雑誌

日本応用数理学会論文誌 (ISSN:09172246)

巻号頁・発行日

vol.5, no.1, pp.9-26, 1995

参考文献数

14

---

In this paper we study theoretically on some mathematical properties of the matrix of the linear system of equations which stems from discretization of n-dimensional Laplace equation by finite difference approximations. The mathematical properties, i.e., the maximum and minimum absolute eigenvalues, the eigenvectors and the condition numbers of the coefficient matrix A and the Jacobi matrix B of the iterative method are estimated. The discretization by the finite differences in n-dimensions is made using the nearest and skewed neighboring grid points. The effectiveness of the variants of the finite differences is shown throughout this study.

著者

平田 祥人

出版者

一般社団法人 日本応用数理学会

雑誌

応用数理 (ISSN:09172270)

巻号頁・発行日

vol.22, no.2, pp.105-114, 2012

---

In this paper, we review our recent developments of mathematical models for prostate cancer under intermittent androgen suppression. In the intermittent androgen suppression, androgen suppression, which is hormone therapy for prostate cancer, is intermittently stopped to delay the relapse of cancer. To optimize the protocol to each patient, we have proposed some mathematical models including ordinary differential equation models and partial differential equation models. Our most recent model is a three-dimensional piecewise linear model. One of the three variables of the model is for androgen dependent cancer cells and the other two variables are for androgen independent cancer cells. This piecewise linear model can not only fit clinical datasets of tumor marker called prostate specific antigen very well but also classify patients based on past time series of the tumor in a manner similar to medical doctors' classifications. We also discuss the future developments of mathematical methods for mathematical medicine including personalized treatment scheduling.

著者

野津 裕史 田端 正久

出版者

一般社団法人 日本応用数理学会

雑誌

日本応用数理学会論文誌 (ISSN:09172246)

巻号頁・発行日

vol.18, no.3, pp.427-445, 2008

参考文献数

29

---

Navier-Stokes方程式のための,圧力安定化有限要素法と時間刻み1次精度特性曲線法を組み合わせたスキームを提案する.P1/P1要素を用いており,現れる行列は対称である.2次元および3次元問題の数値計算結果を与える.

著者

甘利 俊一 川鍋 元明

出版者

一般社団法人 日本応用数理学会

雑誌

応用数理 (ISSN:09172270)

巻号頁・発行日

vol.6, no.2, pp.96-109, 1996

参考文献数

19

被引用文献数

10

---

The present paper studies estimation of the coefficient θ of a linear dependence relation y=θx between two variables x and y from n pairs (y_i, x_i), i=1, …, n, of noise-contaminated observations. This is an old problem where the maximum likelihood estimator or the least square estimator is known not to be a,symptotically optimal. A simple estimator which improves the above one is explicitly given. This is a typical example of semiparametric statistical estimation. The method of estimating functions is used to solve the problem. Information geometry is used for elucidating the set of all the estimating functions and the asymptotic efficiency of the related estimators. A fibre structure is composed on the manifold of a semiparametric model and a dual couple of parallel transports are introduced on the fibres.