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Article type: Cover
2006 Volume 16 Issue 3 Pages
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Article type: Cover
2006 Volume 16 Issue 3 Pages
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Article type: Index
2006 Volume 16 Issue 3 Pages
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Article type: Appendix
2006 Volume 16 Issue 3 Pages
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[in Japanese]
Article type: Article
2006 Volume 16 Issue 3 Pages
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Masayuki Ishii, Ken Hayami
Article type: Article
2006 Volume 16 Issue 3 Pages
135-147
Published: September 25, 2006
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This paper presents a numerical algorithm for solving systems of algebraic equations arising in a MEG inverse problem. First, we derive the system of algebraic equations which relate the position and moment of current dipoles in the brain to the magnetic field and its derivatives at the surface of the head. Then, we present a homotopy algorithm for complex variables in order to solve the system of algebraic equations and determine the current dipoles. Finally, we show the effectiveness of the proposed algorithm by numerical experiments.
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Yi-Bin LU, Taku ITOH, Tetsuya SAKURAI
Article type: Article
2006 Volume 16 Issue 3 Pages
149-164
Published: September 25, 2006
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In this paper, we present a charge points-location method for numerical conformal mappings of a bounded doubly-connected domain and an unbounded multiply-connected domain, using Pade approximation. This method is based on the method for numerical conformal mapping of simply-connected domains using Pade approximation. In this method, we reduce calculations of the charge points by Pade approximation to some generalized eigenvalue problems. Using the charge points obtained by solving the generalized eigenvalue problems, we compute the conformal mappings by applying the charge simulation method. Some numerical examples illustrate the efficiency of our method.
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Masahiro Kainaga, Yugo Kashiwagi
Article type: Article
2006 Volume 16 Issue 3 Pages
165-176
Published: September 25, 2006
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This paper proposes a function approximation algorithm with reduced rounding mistakes for single precision IEEE format, without using double or higher intermediate data. The algorithm is suited for embedded micro-controllers without double precision floating-point hardware. With the new algorithm, 3-9 extra cycles reduces the ration of rounding mistakes to around 1%.
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Hiroshi Ono
Article type: Article
2006 Volume 16 Issue 3 Pages
177-186
Published: September 25, 2006
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The explicit Runge-Kutta method is one of the numerical solutions of the initial value problem of an ordinary differential equation. This method is proposed up to the 10th formula. E.Hairer showed the 17 stage 10th order formula. It is shown that the method is extended and 25 stage the 12th order formula can be determined. It is shown using a numerical example that the formulas is 12th order. And it was also shown that high precision calculation can do the formula efficiently.
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Yasuo Ohno, Takeshi Goto
Article type: Article
2006 Volume 16 Issue 3 Pages
187-195
Published: September 25, 2006
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Jenkins recently showed that an odd perfect number must be divisible by a prime greater than 10^7. The aim of this article is to give a new algorithm to obtain such a lower bound. The theory of cyclotomic numbers plays an important role in the algorithm. We also discuss some relation between cyclotomic numbers and ABC conjecture.
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Hidetomo Nagai, Daisuke Takahashi, Junta Matsukidaira
Article type: Article
2006 Volume 16 Issue 3 Pages
197-210
Published: September 25, 2006
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A new method to construct a higher-order integrable difference equations generated from second-order ones is proposed. Using this method, we can obtain third or higher-order integrable difference equations from Quispel-Roberts-Thompson(QRT) systems. Moreover, we can obtain third-order integrable equations from discrete Painleve I equations. The higher-order equation can also be separated into a set of second-order integrable equations on separated lattices. Especially, a pair of discrete Painleve II equations on even and odd lattices are obtained via the third-order equation derived from a pair of discrete Painleve I equations.
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Masahiro Kanai, Katsuhiro Nishinari, Tetsuji Tokihiro
Article type: Article
2006 Volume 16 Issue 3 Pages
211-220
Published: September 25, 2006
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In the present paper, we investigate the asymmetric simple exclusion process with parallel dynamics on a ring of finite sites. We focus on the correspondence between the asymmetric exclusion process and the zero-range process, and exploit the recursion formula for the partition function of the zero-range process. Then, we find that the explicit formulas for the partition function and the average velocity (or the flux) in the steady state are expressed by the Gauss hypergeometric functions.
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Hideki SATO, Takashi SAKAJO
Article type: Article
2006 Volume 16 Issue 3 Pages
221-235
Published: September 25, 2006
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It is quite difficult to show the existence and uniqueness of solution for the 3-D Navier-Stokes equations. The difficulty arises from the quadratic two nonlilnear terms, the vortex stretching term and the convection term. In order to see how these two terms affect the existence of the solution, De Gregorio proposed a 1-D model equation for the 3-D vorticity equation. However, in spite of its simple formulation, mathematical analysis of the model is not so easy. Thus, in this article, we investigate the model equation by numerical means, and discuss the property of the solution.
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Kentarou Touda, Takashi Kako
Article type: Article
2006 Volume 16 Issue 3 Pages
237-253
Published: September 25, 2006
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In this paper, we propose a numerical method for the voice generation process based on some mathematical model. As the model, we use Webster's horn equation for the 1D case. We then discretize this equation by FEM and calculate the frequency response function. We consider the complex eigenvalue problem corresponding to Webster's horn equation and give a variational formula for the complex eigenvalue with respect to the variation of vocal tract shape. We numerically confirm that the complex eigenvalue is closely related to the frequency response function, and propose a vocal tract shape design algorithm using variational formula and confirm its efficiency numerically.
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Masaaki Suzuki, Hiroshi Okuda
Article type: Article
2006 Volume 16 Issue 3 Pages
255-264
Published: September 25, 2006
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The native structure of protein corresponds to the global minimum of free energy. Replica-exchange method (REM) has been recently used to search the energy minimum in a huge conformation space of a protein. For large systems, however, applying REM can be costly since the number of replicas required for the conformation sampling increases. We have developed a variant REM called fragment REM (FREM), which is based on the existence of correlation between the local amino acid sequence and the local structure. Equilibrium distributions for poly-alanine were computed by the conventional MD, REM and the proposed FREM simulations. We have found that FREM successfully reduces the number of replicas needed for the simulation.
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Tetsuo Ichimori
Article type: Article
2006 Volume 16 Issue 3 Pages
265-276
Published: September 25, 2006
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This paper discusses two apportionment methods taking account of dispersion. The first one minimizes the variance of per capita shares of a representative of 47 prefectures. And the second one minimizes the coeffcient of variation of those shares of a representative of 47 prefectures. We observe that these methods give reasonable allocations of 300 seats to 47 prefectures and also reasonable allocations of 180 to 11 blocks in Japan.
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Satoshi KAIZU, Hideyuki AZEGAMI
Article type: Article
2006 Volume 16 Issue 3 Pages
277-290
Published: September 25, 2006
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In shape optimization, in which partial differential equations are defined and the shape with minimum cost is searched, an admissible family of shapes are given as being compact in some topology. Then minimizing of shapes for a cost implies an optimal shape, which we desire. The traction method is a power way to construct minimizing sequence of shapes for a cost, which guarantees the smoothness of shapes of the sequence. A reason of why the smoothness of shape is guaranteed is given from the point of view of mathematics.
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Yasuhiro Kawanishi
Article type: Article
2006 Volume 16 Issue 3 Pages
291-303
Published: September 25, 2006
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In this paper, we introduce a new type of barrier options, that is, Lizard Option. The most brand-new point is that its payoff explicitly includes stock prices in the first passage time to a given barrier level and right before this time. Then, basing on the risk-neutral valuation, we analytically price Lizard Option under the Variance Gamma model. At the same time, we also obtain an analytical valuation of one touch barrier option.
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Misao Endo, Shiwei Zuo, Kazuo Kishimoto
Article type: Article
2006 Volume 16 Issue 3 Pages
305-316
Published: September 25, 2006
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This paper develops a new model describing intraday price changes in the Tokyo Stock Exchange and the Osaka Securities Exchange. The price changes are specified by the repetition of one tick price moves, each of which is caused by the termination of a continuous double auction system described by the classic queuing theory. This model predicts that the one tick price move follows the first order Markov process. We test the null hypothesis of this Markov property for the tick-by-tick data of Nikkei225 Futures on the Osaka Securities Exchange, to find the null hypothesis is not rejected.
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Takuya KANEKO, Hidetoshi NAKAGAWA
Article type: Article
2006 Volume 16 Issue 3 Pages
317-343
Published: September 25, 2006
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In this paper, we propose a bank loan pricing model for non-listed companies. At first, we present a pricing formula for a principal-equal-repayment loan and obtain the corresponding formula of relevant loan interest rate, which is sufficiently tractable. Indeed, the pricing model is specified by the distribution of recovery rate estimated from Balance Sheet(B/S), the term structure of default probability and the default-risk-premium structure. Discussing how to compute the parameter called B/S-adjusted asset-debt coverage ratio that specifies the distribution of recovery rate, we give some numerical results based on real accounting data of non-listed companies.
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Masato Kimura, Isao Wakano
Article type: Article
2006 Volume 16 Issue 3 Pages
345-358
Published: September 25, 2006
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We study general mathematical framework for rigorous derivation of the energy release rate which plays an important role in the theory of fracture mechanics. Applying a technique of the shape sensitivity analysis, we formulate this as a variational problem with a parameter. Key points of our theory are a new parameter variational principle and the classical implicit function theorem in Banach spaces.
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Article type: Appendix
2006 Volume 16 Issue 3 Pages
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Article type: Appendix
2006 Volume 16 Issue 3 Pages
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Article type: Appendix
2006 Volume 16 Issue 3 Pages
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Article type: Index
2006 Volume 16 Issue 3 Pages
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Article type: Cover
2006 Volume 16 Issue 3 Pages
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Article type: Cover
2006 Volume 16 Issue 3 Pages
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