Transactions of the Japan Society for Industrial and Applied Mathematics

Online ISSN : 2424-0982
ISSN-L : 0917-2246

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Volume 18, Issue 1

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[title in Japanese]

Article type: Cover
2008 Volume 18 Issue 1 Pages Cover1-
Published: March 25, 2008
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.18.1_Cover1

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[title in Japanese]

Article type: Cover
2008 Volume 18 Issue 1 Pages Cover2-
Published: March 25, 2008
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.18.1_Cover2

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[title in Japanese]

Article type: Index
2008 Volume 18 Issue 1 Pages Toc1-
Published: March 25, 2008
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.18.1_Toc1

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[title in Japanese]

Article type: Appendix
2008 Volume 18 Issue 1 Pages App1-
Published: March 25, 2008
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.18.1_App1

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[title in Japanese]

[in Japanese]

Article type: Article
2008 Volume 18 Issue 1 Pages A1-
Published: March 25, 2008
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.18.1_A1

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[title in Japanese]

Article type: Appendix
2008 Volume 18 Issue 1 Pages i-xxviii
Published: March 25, 2008
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.18.1_i

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Computing reciprocals for constant divisors without searching(Practice)

Masahiro Kainaga, Yugo Kashiwagi

Article type: Article
2008 Volume 18 Issue 1 Pages 1-16
Published: March 25, 2008
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.18.1_1

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It has been studied to speed up constant division by replacing it with an exact algorithm using multiplication with the approximation of the divisor's reciprocal. The existing algorithm computes the approximate reciprocal by a simple calculation, or by searching a better reciprocal which makes the run-time algorithm optimal. This paper shows that the optimal reciprocal value can be computed directly, without searching.

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A Study of Dilemma-Solving Effects by the Co-evolution of Both Social Networks and Strategy in a 2×2 Symmetry Game(Practice)

Jun Tanimoto

Article type: Article
2008 Volume 18 Issue 1 Pages 17-27
Published: March 25, 2008
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.18.1_17

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A 2×2 symmetry game model implemented by a co-evolution mechanism of both networks and strategy, inspired by Zimmermann & Eguiluz's work is established. A Series of numerical experiments, considering various 2×2 game structures, reveals that the proposed co-evolution mechanism can solve dilemmas in several game classes. The effect of solving a dilemma means the mutual-cooperation reciprocity (R reciprocity), which is brought about by emerging several cooperative hub agents who have plenty of links. The co-evolution mechanism, however, seems counterproductive for game classes of Leader and Hero, where the alternating reciprocity (ST reciprocity) is meaningful.

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Riemann zeta function and the best constants of three series of Sobolev inequalities(Theory,Applied Integrable Systems,<Special Issue>Joint Symposium of JSIAM Activity Groups 2007)

Yoshinori Kametaka, Hiroyuki Yamagishi, Kohtaro Watanabe, Atsushi Naga ...

Article type: Article
2008 Volume 18 Issue 1 Pages 29-40
Published: March 25, 2008
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.18.1_29

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We clarified the variational meaning of the special values ζ(2M)(M=1,2,3,…) of Riemann zeta function ζ(s). These are essentially the best constants of three series of Sobolev inequalities. In the background we have three kind of boundary value problem (periodic, Dirichlet, Neumann) for the simplest differential operator (-1)^M(d/dx)^<2M>. Green functions for these boundary value problems can be given by Bernoulli polynomials. Sobolev energy of G(x,y) with respect to x is its diagonal value G(y,y). Its maximum max__<|y|≤1> G(y,y) is equal to the best constant for corresponding Sobolev inequality.

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The best constant of Sobolev inequality corresponding to the free boundary value problem for (-1)^M(d/dx)^<2M>(Theory,Applied Integrable Systems,<Special Issue>Joint Symposium of JSIAM Activity Groups 2007)

Kazuo Takemura, Atsushi Nagai, Yoshinori Kametaka, Kohtaro Watanabe, H ...

Article type: Article
2008 Volume 18 Issue 1 Pages 41-64
Published: March 25, 2008
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.18.1_41

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M=1,2,3,…. For any function u(x) which satisfy u(x), u^<(M)>(x)∈L^2(-1,1), ∫^1_<-1>u(x)x^idx=0(0≤i≤M-1), there exists a positive constant C independent of u(x) such that the Sobolev inequality [numerical formula] hold. If M≤5, the best constant C(M) among such C is given as follows. C(M)=2<2M-1>(2(M-1))!(2M)!/(((M-1)!)^2(4M-1)!)(M≤5) Although the above equality is expected to hold for M≥6, its proof remains be unsolved.

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CA simulation of Railroad traffic and Automatic Restoration of Delayed Schedule(Application,Applied Integrable Systems,<Special Issue>Joint Symposium of JSIAM Activity Groups 2007)

Kensuke Fujii, Shinji Iida, Katsuhiro Nishinari

Article type: Article
2008 Volume 18 Issue 1 Pages 65-85
Published: March 25, 2008
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.18.1_65

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In present railway systems, the restoration of delayed schedules due to accidents or breakdowns, etc, relies solely on human efforts. Automatic restoration by a computer seems necessary in the near future, although at present it is believed to be impossible because of the complexity and the request of real time and absolutely accurate operations. This paper gives simulations of railway traffic by using cellular automaton (CA). The temporal signal breakdown is introduced to trigger off the delay whose time evolution is studied. We propose a set of rules which restores the delayed schedule to its normal state.

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A neural network model for cognition of the order relation among sequential input patterns : A basic idea on forecast and abstraction(Application,Scientific Computation and Numerical Analysis,<Special Issue>Joint Symposium of JSIAM Activity Groups 2007)

Kazuho Tanaka, Shinichiro Yano, Nobito Yamamoto

Article type: Article
2008 Volume 18 Issue 1 Pages 87-105
Published: March 25, 2008
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.18.1_87

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We propose a neural network model which commits the order relation among sequential input patterns to memory, using associative memory for sequential patterns. The network is constructed by association of Leaky Integrate and Fire neuron models. The model may give the basic concept to some functions of the brain, especially the functions of forecast and abstraction. We implement our model to computer and investigate the numerical results in order to consider what the model gives to the concept of forecast and abstraction.

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On Convergence of dqds Algorithm that Uses Ostrowski and Brauer Type Lower Bounds as Shifts(Theory,Algorithms for Matrix/Eigenvalue Problems and their Applications,<Special Issue>Joint Symposium of JSIAM Activity Groups 2007)

Yusaku Yamamoto, Takafumi Miyata

Article type: Article
2008 Volume 18 Issue 1 Pages 107-134
Published: March 25, 2008
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.18.1_107

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Recently, Aishima et al. proved that the dqds algorithm that uses the Johnson bound for the smallest singular value as shifts is globally convergent and its asymptotic convergence rate is 1.5/ In this paper, we study the convergence of the dqds algorithm when Ostrowski and Brauer type bounds, which are stronger lower bounds than the Johnson bound, are used as shifts. Both shifting strategies satisfy the conditions for global convergence. The asymptotic convergence rate is shown to be 1.5 for the Ostrowski bound and super-1.5 for the Brauer bound. Numerical experiments support our theoretical analysis.

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Image Feature Extraction Based on Complex Moments(Application,Algorithms for Matrix/Eigenvalue Problems and their Applications,<Special Issue>Joint Symposium of JSIAM Activity Groups 2007)

Nobutaka Ito, Takaaki Nara, Tetsuya Sakurai

Article type: Article
2008 Volume 18 Issue 1 Pages 135-153
Published: March 25, 2008
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.18.1_135

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In this paper, we propose image feature extraction methods based on complex moments. Edges, corners, and circular (un)symmetrical points are extracted by the proposed methods. We derive operators to calculate the complex moments accurately for discrete images. It is shown by numerical simulations (1) that our edge extraction method is more robust than the Sobel and SUSAN operators, and as robust as the Canny operator; and (2) that the threshold in our edge extraction method is very little dependent on SNR.

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An AOR-base Variable Preconditioned GCR Method(Algorithms for Matrix/Eigenvalue Problems and their Applications,<Special Issue>Joint Symposium of JSIAM Activity Groups 2007)

Shouhei Maeda, Kuniyoshi Abe, Tomohiro Sogabe, Shao-Liang Zhang

Article type: Article
2008 Volume 18 Issue 1 Pages 155-170
Published: March 25, 2008
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.18.1_155

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It is commonly known that Generalized Conjugate Residual(GCR) method with the variable preconditioning using Successive Over-Relaxation(SOR) method is an efficient iterative method for solving large and sparse linear systems. In the present paper, we consider using of Accelerated Over-Relaxation (AOR) method instead of SOR method as a variable preconditioning. Since AOR method is a natural extension of SOR method, our approach includes the previous one. It is experimentally shown by reducing the computational cost of AOR method that the present method can be very promising.

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On Stability of the Order of the Estimated Locations of Parties(Application,Mathematical Politics,<Special Issue>Joint Symposium of JSIAM Activity Groups 2007)

Mitsuyo Yamamoto, Kazuo Kishimoto

Article type: Article
2008 Volume 18 Issue 1 Pages 171-184
Published: March 25, 2008
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.18.1_171

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This paper proposes an efficient method for testing the stability of the orders of the parties in the policy space estimated by the approach in Kishimoto et al.. Its application to Japanese national elections during 1983-2004 shows that the orders are stable in most cases while in some cases they are unstable. These facts show that the approach by Kishimoto et al. is useful if it is used with the test presented in this paper.

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On key generation of OTU2000 and related problems(Algorithmic Number Theory and Its Application,<Special Issue>Joint Symposium of JSIAM Activity Groups 2007)

Keiichiro Nishimoto, Ken Nakamula

Article type: Article
2008 Volume 18 Issue 1 Pages 185-197
Published: March 25, 2008
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.18.1_185

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In Crypto2000, the concept of quantum public key cryptosystems and its concrete scheme OTU2000 were first proposed. We actually implemented the key generation, encryption and decryption for the rational number field and imaginary quadratic fields, and then performed numerical experiments about key generation. For actual key generation, it was necessary to consider the choice and the order of parameters. Taking this into account, we propose a concrete algorithm of key generation. Intending to increase the density of the generated knapsack problem, we also propose a slightly extended scheme of OTU2000.

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[title in Japanese]

Article type: Appendix
2008 Volume 18 Issue 1 Pages App2-
Published: March 25, 2008
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.18.1_App2

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[title in Japanese]

Article type: Appendix
2008 Volume 18 Issue 1 Pages App3-
Published: March 25, 2008
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.18.1_App3

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[title in Japanese]

Article type: Appendix
2008 Volume 18 Issue 1 Pages App4-
Published: March 25, 2008
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.18.1_App4

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[title in Japanese]

Article type: Index
2008 Volume 18 Issue 1 Pages Toc2-
Published: March 25, 2008
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.18.1_Toc2

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[title in Japanese]

Article type: Cover
2008 Volume 18 Issue 1 Pages Cover3-
Published: March 25, 2008
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.18.1_Cover3

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[title in Japanese]

Article type: Cover
2008 Volume 18 Issue 1 Pages Cover4-
Published: March 25, 2008
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.18.1_Cover4

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