Author Index, Volume 123 (2000)

Authors Index

Author Index, Volume 123 (2000)     

Painlevé test for the self-dual Yang-Mills equation

It is shown that the SU(2) self-dual Yang-Mills equation passes the Painlevé test for complete integrability.     

Soliton equations and fundamental representations of A 2l (2)

Fundamental representations of the Euclidean Lie algebra A _2l ⁽²⁾ is constructed by decomposing the vertex representations of gI(∞). For l=1 the multiplicities of highest weights are determined. Soliton equations associated with each of these representations are also discussed.     

Calculation of dielectric spectra of suspensions of rod-shaped cells using boundary element method

The boundary element method (BEM) has been applied to the calculation of dielectric spectra of suspensions of rod-shaped cells using two kinds of models: model-R consisting of a cylinder and two hemispheres and model-PU of prolate spheroid shape. Both models have an insulating shell phase of a uniform thickness. The calculations were compared with those using a conventional spheroidal model with a confocal shell (model-PC) and previous observations on rod-shaped yeast cells. The differences among the three models were not considerable and all the models succeeded in interpreting the observed data on yeast cells.     

Antigen�Cantibody interactions of influenza virus hemagglutinin revealed by the fragment molecular orbital calculation

Effective interactions between amino acid residues in antigen?Cantibody complex of influenza virus hemagglutinin (HA) protein can be evaluated in terms of the inter-fragment interaction energy (IFIE) analysis with the fragment molecular orbital (FMO) method, in which each fragment contains the side chain of corresponding amino acid residue. We have carried out the FMO-MP2 (second-order Moeller?CPlesset) calculation for the complex of HA antigen and Fab antibody of influenza virus H3N2 A/Aichi/2/68 and obtained the IFIE values between each amino acid residue in HA and the whole antibody as the sums over the residues contained in the latter. Combining this IFIE data with experimental data for hemadsorption activity of HA mutants, we succeeded in theoretically explaining the mutations in HA observed after the emergence of influenza virus H3N2 A/Aichi/2/68 in an earlier study, except for those of THR83. In the present study, we employ an alternative way of fragment division in the FMO calculation at the carbonyl C site of the peptide bond instead of the C_?? site used in the previous work, which provides revised IFIE values consistent with all the historical mutation data in the antigenic region E of HA including the case of THR83 in the present prediction scheme for probable mutations in HA.     

Extremal properties of t-SEEDs and recursive constructions

A t-spontaneous emission error design, called t-SEED for short, is a combinatorial design introduced by Beth et al. (Des Codes Cryptogr 29:51–70, 2003) in relation to a quantum jump code. In this article, firstly, it is shown that an optimal t-SEED attaining a given upper bound is a large set of Steiner t-designs. Secondly, we present some recursive constructions of t-SEEDs. Moreover, an application to secret sharing scheme by utilizing the properties of a t-SEED is also discussed.     

An algorithm for automatically selecting a suitable verification method for linear systems

Several methods have been proposed to calculate a rigorous error bound of an approximate solution of a linear system by floating-point arithmetic. These methods are called ‘verification methods’. Applicable range of these methods are different. It depends mainly on the condition number and the dimension of the coefficient matrix whether such methods succeed to work or not. In general, however, the condition number is not known in advance. If the dimension or the condition number is large to some extent, then Oishi–Rump’s method, which is known as the fastest verification method for this purpose, may fail. There are more robust verification methods whose computational cost is larger than the Oishi–Rump’s one. It is not so efficient to apply such robust methods to well-conditioned problems. The aim of this paper is to choose a suitable verification method whose computational cost is minimum to succeed. First in this paper, four fast verification methods for linear systems are briefly reviewed. Next, a compromise method between Oishi–Rump’s and Ogita–Oishi’s one is developed. Then, an algorithm which automatically and efficiently chooses an appropriate verification method from five verification methods is proposed. The proposed algorithm does as much work as necessary to calculate error bounds of approximate solutions of linear systems. Finally, numerical results are presented.     

Errata: A coset-type construction for the deformed Virasoro algebra,Lett. Math. Phys. 43(2) (1998), 173–185.

Letters in Mathematical Physics -     

A q-analog of the sixth Painlevé equation

A q-difference analog of the sixth Painlevé equation is presented. It arises as the condition for preserving the connection matrix of linear q-difference equations, in close analogy with the monodromy-preserving deformation of linear differential equations. The continuous limit and special solutions in terms of q-hypergeometric functions are also discussed.     

Monodromy perserving deformation of linear ordinary differential equations with rational coefficients. II

We continue our investigation on the newly introduced concept of the τ function [1], associated with monodromy preserving deformations of a linear differential equation $\text{dY}\text{dx}\text{= A(x)Y}$. In this paper a series of τ functions parametrized by integers are introduced. Their ratios to the original τ function are then shown to be explicit rational expressions in terms of the coefficients of A(x). We point out, and follow where possible, a close analogy between the theory of τ functions and that of classical theta functions.