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Article type: Cover
1993 Volume 3 Issue 4 Pages
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Published: December 15, 1993
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Article type: Cover
1993 Volume 3 Issue 4 Pages
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[in Japanese]
Article type: Article
1993 Volume 3 Issue 4 Pages
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Published: December 15, 1993
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Shin-ichi Nakano, Takao Nishizeki, Nobuji Saito
Article type: Article
1993 Volume 3 Issue 4 Pages
279-307
Published: December 15, 1993
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An f-coloring of a multigraph G = (V, E) is a coloring of edges such that each color appeares at each vertex υ at most f(υ)times. It is known that every multigraph G can be f-colored with at most max_<υ, ω∈V>⌈(d(υ)+p(υω))/(f(υ))⌉ colors, where d(υ) denotes the degree of vertex υ, and p(υω) the cardinality of the set of multiple edges joining vertices υ and ω. A straightforward algorithms such an f-coloring in time O(|E|^2). This paper presents two more efficient algorithms which run in time O(|E|Δ_flog|E|) or O(|E|√<|E|log|E|>) where Δ_f = max_<υ∈V>⌈d(υ)/f(υ)⌉.
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Hidenori Ogata, Masaaki Sugihara, Masatake Mori
Article type: Article
1993 Volume 3 Issue 4 Pages
309-322
Published: December 15, 1993
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A Double exponential-type(DE-type)quadrature formula is proposed for evaluating the Cauchy principal-value integral:p.v.∫^1_<-1>F(x)(x-λ)^(-1)dx, and the Hadamard finite-part integral:f.p.∫^1_<-1>F(x)(x-λ)^<-n>dx, whereF(x) is a given analytic function, λ is a constant such that -1 < λ < 1, and n is an integer n = 2, 3, ・・・. This formula is theoretically based on the "Sinc method"[4], [6]. This quadrature error is of the order O(exp(-c_λN/logN)), where N is the number of nodes used, and c_λ is a positive constant which depends on λ. Numerical examples are presented.
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Hiroshi Kai, Matu-Tarow Noda
Article type: Article
1993 Volume 3 Issue 4 Pages
323-336
Published: December 15, 1993
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Hybrid Rational Function Approximation(HRFA) is a rational function approximation using approximate GCD algorithm. Properties of HRFA are considerd in details. HRFA is used for approximating a set of discrete data and gives satisfactory results. It is also shown that HRFA is powerful to smooth data which contains some large noises. HRFA is compared with "least square approximation" and "best rational approximation" and it shows various superiorities over others.
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Toshiaki Itoh, DongSheng Cai
Article type: Article
1993 Volume 3 Issue 4 Pages
337-351
Published: December 15, 1993
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We found the symplectic structures in the first, second and third discrete Painleve equations, which were constructed using the singularity confinement method. Moreover, we also construct the discrete version of their Hamiltonian functions using the symplectic integration method.
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Hirobumi Mizuno, Iwao Sato
Article type: Article
1993 Volume 3 Issue 4 Pages
353-365
Published: December 15, 1993
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In this paper we study switching classes of alternating functions on the arc set of a complete symmetric digraph. Let KD be a complete symmetric digraph on a finite set X and L a switching class of alternating functions on the arc set A(KD). We discuss two cohomological invariants associated with a group of automorphisms of L. We determine whether for an automorphism g of L, two cohomological invariants of the cyclic group <g> and L are zero. Finally, we consider switching classes of alternating functions without non-identity automorphism.
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Itaru Hataue
Article type: Article
1993 Volume 3 Issue 4 Pages
367-386
Published: December 15, 1993
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In this paper we want to analyze the characteristic behavior in a numerical solution of a nonlinear partial differential equation by utilizing the nonlinear dynamics approach such as a bifurcation diagram and the Lyapunov Exponent. To investigate the typical feature of spurious asymptotes(periodic points, limit cycles, tori and chaotic motions), and to discuss the speed of convergence to the steady-state solution could contribute new suggestions in the interpretation of numerical results. Some kinds of space discretization formulas such as a central difference, an upwind difference and so on, and the Euler forward difference scheme in time are applied to the one-dimensional Burgers' equation. Furthermore, we have a discussion about the first bifurcation point where the ghost solution appeares by applying the linear stability analysis.
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Susumu Ono
Article type: Article
1993 Volume 3 Issue 4 Pages
387-424
Published: December 15, 1993
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Wire ropes are analyzed by assuming that the central lines of these wires are threedemensional spatial curves, and their surfaces are canal surfaces. These central lines are also curves on other inner canal surfaces. To study them it is very important to use the most suitable frame as a basis. In general, for the treatment of the curve Frenet frame is used, and for the surface Gauss' frame is used. However, it will be found that two other new frames should be set up and used to analyze the curves on surfaces and other surfaces such as wire rope. Then the analysis of these surfaces and curves are devided in several steps. At first, being set the frame of central line, more complicated canal surfaces will be achieved step by step. In this paper, the above mentioned theoretical development of analysis in wire rope will be described, the principal geometrical quantities calculated and then the projection of configuration of wires will be made for the case that the central line of the rope is straight or circular for example.
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Yasushi Kikuchi, Nobuyoshi Asai, Yoshinori Miyazaki, DongSheng Cai, Is ...
Article type: Article
1993 Volume 3 Issue 4 Pages
425-437
Published: December 15, 1993
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Consider the problem of computing a given number N of the smallest positive zeros j_<ν, 1>・・・, j_<ν, N> of Bessel function j_ν(z) of a given nonnegative order ν with a given relative accurasy ε > 0. In this paper, we describe how to implement our matrix algorithm developed earlier for this purpose for the case 0 ≤ ν ≤ 30, ε ≥ 10^<-24> and N ≤ 15. The algorithm can be extended to the case where ν is negative. However, if ν is close to a negative integer then the problem turns out to be ill-conditioned.
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Lei LI, Tatuo TORII, Tadao NAKAMURA
Article type: Article
1993 Volume 3 Issue 4 Pages
439-444
Published: December 15, 1993
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In this paper, we unify and generalize two fast algorithms for the evaluation of polynomials and their higher-order differential coefficients.
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Noboru Nakanishi, Mitsuo Abe
Article type: Article
1993 Volume 3 Issue 4 Pages
445-450
Published: December 15, 1993
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The Heaviside-Mikusinski operational calculus for constant-coefficient linear ordinary differential equations is extended to the case in which the unknown function is noncommutative with the coefficients in the differential equation.
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Kazufumi Ozawa
Article type: Article
1993 Volume 3 Issue 4 Pages
451-464
Published: December 15, 1993
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We propose a simple procedure for setting the efficient starting values of the Durand-Kerner iteration, which finds all zeros α_i(i = 1, ・・・, n) of a polynomial of degree n simultaneously. In our new procedure, the starting values are located on the circle centered at β with radius γ_<gm>where β = 1/nΣ^^n__<i=1>α_i, and γ_<gm> is the geometric mean of the deviations |α_i - β|. The computational cost for this procedure is extremely cheap compared with that for Aberth's procedure. Moreover, the various numerical examples show that our new method reduces the number of iterations tremendously over any other ones, particularly when some of the deviations |α_i - β| are large.
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Article type: Index
1993 Volume 3 Issue 4 Pages
Toc1-
Published: December 15, 1993
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Article type: Index
1993 Volume 3 Issue 4 Pages
Index1-
Published: December 15, 1993
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Article type: Appendix
1993 Volume 3 Issue 4 Pages
App1-
Published: December 15, 1993
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Article type: Cover
1993 Volume 3 Issue 4 Pages
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Published: December 15, 1993
Released on J-STAGE: April 08, 2017
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Article type: Cover
1993 Volume 3 Issue 4 Pages
Cover4-
Published: December 15, 1993
Released on J-STAGE: April 08, 2017
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