著者

青木 繁 天谷 賢治

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.10, no.2, pp.121-129, 2000-06-15 (Released:2017-04-08)

参考文献数

10

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After a brief description about the ill-posed inverse problems which are discretized with the finite element method etc., a method for solving such problems is presented with a practical example. This method consists of the following procedures. 1. The singular value decomposition of the coefficient matrix is performed, and then the rank is appropriately reduced. 2. A set of solutions is represented by Moore-Penrose's solution and the null space. 3. The solution is obtained by fuzzy reasoning using the set of solutions and sets of fuzzy priori information. Following three studies are presented: a study which the Kalman filtering technique is applied to estimate the material parameters of two nonlinear constitutive equations, A method for obtaining the optimal experimental/measurement procedure for general estimation problems, and a method (GA filter) for non-linear state space estimation using genetic algorithm.

著者

三宅 茂樹

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.8, no.2, pp.133-146, 1998-06-15 (Released:2017-04-08)

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In most cases treated in information theory, stationary memoryless/ergodic property on the system are assumed. In this paper, source coding theorems on the general information sources, which means neither stationary memoryless nor stationary ergodic property are conditioned, are considered. We clarify the following two issues: 1) What quantity can be essential in source coding problems under the general sources? 2) What are the differences between theorems under conventional stationary memoryless/ergodic condition and ones under the general sources?

著者

梅野 健

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.32, no.3, pp.160-169, 2022-09-22 (Released:2022-12-26)

参考文献数

14

著者

松宮 徹

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.59-62, 1991-03-15 (Released:2017-04-08)

被引用文献数

1

著者

武藤 雅基

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.32, no.2, pp.87-92, 2022-06-24 (Released:2022-09-30)

参考文献数

3

著者

高津 飛鳥

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.32, no.2, pp.69-79, 2022-06-24 (Released:2022-09-30)

参考文献数

17

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This paper is concerned with a variational problem on the space of probability measures over either ℝ2 or a finite set, the so-called optimal transport problem. We discussed three ways to formulate the optimal transport problem on ℝ2 as follows: the use of a probability measure (transport plan) on ℝ2 × ℝ2, a map (transport map) from ℝ2 to ℝ2, and a family of paths (transport path) on ℝ2. The definition of transport path requires the property that each pair of points in ℝ2 should be connected by a length minimizing curve. To define transport paths on a finite set, we explained how to modify the optimal transport problem on a finite set.

著者

梅野 健

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.32, no.2, pp.99-108, 2022-06-24 (Released:2022-09-30)

参考文献数

12

著者

小林 健太 土屋 卓也

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.28, no.1, pp.18-25, 2018-03-23 (Released:2018-06-30)

参考文献数

14

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We describe recent development of finite element error analysis. In finite element error analysis, estimating errors of Lagrange interpolation on triangles is very important. To obtain error estimations of Lagrange interpolation, it is believed that triangles or triangulations must satisfy a certain geometric conditions such as minimum or maximum angle conditions. The authors have found that the circumradius condition of triangles or triangulations is more essential than the minimum and maximum angle conditions. To show our claim, the authors extended techniques presented by Babuška-Aziz and Liu-Kikuchi. Our method can be applied to the case of Lagrange interpolation on tetrahedrons and Crouzeix-Raviart interpolation on triangles.

著者

真貝 寿明 米田 元

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.15, no.1, pp.2-15, 2005-03-25 (Released:2017-04-08)

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We review recent efforts to re-formulate the Einstein equations for fully relativistic numerical simulations in general relativity. The so-called "numerical relativity" is a promising research field matching with ongoing astrophysical observations such as gravitational wave astronomy. Many trials for longterm stable and accurate simulations of binary compact objects have revealed that mathematically equivalent sets of evolution equations show different numerical stability in free evolution schemes. After reviewing the efforts of the community in the decade, we introduce our idea for understanding all the efforts in a unified way using eigenvalue analysis of the constraint propagation equations. The modifications of (or adjustments to) the evolution equations change the character of constraint propagation, and several particular adjustments using constraints are expected to diminish the constraint-violating modes. We propose several new adjusted evolution equations, and present some numerical demonstrations.

著者

山田 道夫

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.11, no.2, pp.141-151, 2001-06-15 (Released:2017-04-08)

参考文献数

16

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Weakly nonlinear theory of fluid motion is discussed in relation with pattern formation phenomena in fluids. In nonlinear stability theory of parallel flows, Landau-type equation is obtained by growth-rate expansion method around the critical point, while in subcritical case it is obtained by amplitude expansion method in which the solvability condition is replaced by an exact definition of the 'amplitude'. In the case of falling film flow, amplitude equations derived so far do not agree well with experiments, and a new expansion method of Pade type proposed by Ooshida is successful although the method is not yet fully understood in mathematical sense. In the Benard convection problem, an order-parameter equation describes the weakly nonlinear stage, and some reduced amplitude equations are derived from this equation. Even in strongly nonlinear stage, pattern formation phenomena are often observed as in the two-dimensional turbulence on a rotating sphere where a circumpolar jet appears from a turbulent initial flow field.

著者

三輪 哲二

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.11, no.2, pp.170-171, 2001-06-15 (Released:2017-04-08)

著者

中村 直俊

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.31, no.1, pp.32-37, 2021-03-25 (Released:2021-06-30)

参考文献数

19

著者

関根 順

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.29, no.1, pp.35-40, 2019-03-26 (Released:2019-06-30)

参考文献数

4

著者

中村 直俊

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.31, no.3, pp.28-33, 2021-09-22 (Released:2021-12-26)

参考文献数

19

著者

萩原 一郎

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.31, no.3, pp.34-37, 2021-09-22 (Released:2021-12-26)

著者

吉田 善章

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.29, no.3, pp.6-13, 2019-09-25 (Released:2019-12-26)

参考文献数

12

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The creation of macroscopic hierarchy (such as fluids or plasmas) is studied in the context of noncanonical Hamiltonian systems. We study the origin of noncanonicality in two perspectives; (1) the reductions from canonical systems, (2) the Lie-Poisson algebras and their deformations, and show how the dynamics of macro-systems can be different from those of microscopic canonical systems.

著者

片桐 孝洋

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.21, no.2, pp.152-153, 2011-06-24 (Released:2017-04-08)

著者

中村 直俊

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.31, no.2, pp.28-33, 2021-06-24 (Released:2021-09-30)

参考文献数

23

著者

矢島 美寛

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.11, no.4, pp.281-294, 2001-12-14 (Released:2017-04-08)

参考文献数

53

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This paper provides a survey of long memory models and their applications in economic and financial time series. Section 2 describes the definition of long memory models, particularly two popular models, ARFIMA and FGN. Section 3 describes unit roots tests and cointegration, two major topics of the recent decades in theoretical and applied econometrics. Section 4 discusses a generalization of unit roots tests and cointegration to long memory models. Section 5 describes ARCH models and SV models which have been paid much attention to analyze volatility in actual financial data. Section 6 considers a generalization of these volatility models to those with long memory properties. Finally Section 7 considers some problems to be solved in future.

著者

山口 昌哉

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.7, no.2, pp.143-146, 1997-06-16 (Released:2017-04-08)