Schlesinger transformations for elliptic isomonodromic deformations

Schlesinger transformations are discrete monodromy preserving symmetry transformations of the classical Schlesinger system. Generalizing well-known results from the Riemann sphere we construct these transformations for isomonodromic deformations on genus one Riemann surfaces. Their action on the system's tau-function is computed and we obtain an explicit expression for the ratio of the old and the transformed tau-function.Comment: 19 pages, LaTeX2

Critical Properties of the transition between the Haldane phase and the large-D phase of the spin-1/2 ferromagnetic-antiferromagnetic Heisenberg chain with on-site anisotropy"

We analytically study the ground-state quantum phase transition between the Haldane phase and the large-$D$ (LD) phase of the $S=1/2$ ferromagnetic-antiferromagnetic alternating Heisenberg chain with on-site anisotropy. We transform this model into a generalized version of the alternating antiferromagnetic Heisenberg model with anisotropy. In the transformed model, the competition between the transverse and longitudinal bond alternations yields the Haldane-LD transition. Using the bosonization method, we show that the critical exponents vary continuously on the Haldane-LD boundary. Our scaling relations between critical exponents very well explains the numerical results by Hida.Comment: text 12 pages (Plain TeX), LaTeX sourse files of a table and a figure on reques

Irregular conformal blocks, with an application to the fifth and fourth Painlev\'e equations

We develop the theory of irregular conformal blocks of the Virasoro algebra. In previous studies, expansions of irregular conformal blocks at regular singular points were obtained as degeneration limits of regular conformal blocks; however, such expansions at irregular singular points were not clearly understood. This is because precise definitions of irregular vertex operators had not been provided previously. In this paper, we present precise definitions of irregular vertex operators of two types and we prove that one of our vertex operators exists uniquely. Then, we define irregular conformal blocks with at most two irregular singular points as expectation values of given irregular vertex operators. Our definitions provide an understanding of expansions of irregular conformal blocks and enable us to obtain expansions at irregular singular points. As an application, we propose conjectural formulas of series expansions of the tau functions of the fifth and fourth Painlev\'e equations, using expansions of irregular conformal blocks at an irregular singular point.Comment: 26 page

A generalization of determinant formulas for the solutions of Painlev\'e II and XXXIV equations

A generalization of determinant formulas for the classical solutions of Painlev\'e XXXIV and Painlev\'e II equations are constructed using the technique of Darboux transformation and Hirota's bilinear formalism. It is shown that the solutions admit determinant formulas even for the transcendental case.Comment: 20 pages, LaTeX 2.09(IOP style), submitted to J. Phys.

A remark on the Hankel determinant formula for solutions of the Toda equation

We consider the Hankel determinant formula of the $\tau$ functions of the Toda equation. We present a relationship between the determinant formula and the auxiliary linear problem, which is characterized by a compact formula for the $\tau$ functions in the framework of the KP theory. Similar phenomena that have been observed for the Painlev\'e II and IV equations are recovered. The case of finite lattice is also discussed.Comment: 14 pages, IOP styl

Painleve equations from Darboux chains - Part 1: P3-P5

We show that the Painleve equations P3-P5 can be derived (in a unified way) from a periodic sequence of Darboux transformations for a Schrodinger problem with quadratic eigenvalue dependency. The general problem naturally divides into three different branches, each described by an infinite chain of equations. The Painleve equations are obtained by closing the chain periodically at the lowest nontrivial level(s). The chains provide ``symmetric forms'' for the Painleve equations, from which Hirota bilinear forms and Lax pairs are derived. In this paper (Part 1) we analyze in detail the cases P3-P5, while P6 will be studied in Part 2.Comment: 23 pages, 1 reference added + minor change

Challenges in achieving an integrative approach to people management in Japanese companies in Australia

University of Technology, Sydney. Faculty of Business.Japanese companies have always experienced challenges in managing white-collar local employees in their overseas subsidiaries (e.g. Byun & Ybema 2005; Hayashi 1994; Taga 2004; Tokusei 1994), as exemplified by the characteristic of a lack of integration which exists in overseas Japanese companies (e.g. Dedoussis 1994; Kidahashi 1987; Yoshihara 2001; Yoshimura & Anderson 1997). This is apparent in the demarcation between two groups of employees, local staff and Japanese expatriate staff, with the latter having close ties with the Head Office of the company. Elucidation on how to succeed in managing local staff in overseas Japanese companies is an important agenda. To attain this goal, the current study will examine the problems experienced by Japanese and local staff, and the strategies perceived as effective for the improvements by using Role Theory (Kahn et al. 1964; Katz & Kahn 1978) to understand the cross-cultural interactions within Japanese companies operating in Australia. This thesis has the following aims and objectives: (1) To explore the types of role stress experienced by Japanese and non-Japanese white-collar staff holding managerial and non-managerial positions in Japanese companies operating in Australia; and (2) To examine the strategies perceived as effective to relieve their role stress. In-depth interviews were conducted with 68 white collar employees of Japanese companies operating in Australia, including expatriates, local Japanese hires, and non-Japanese local staff. The qualitative data were analyzed using Nvivo software, according to thematic issues (Miles & Huberman 1994). There are four main findings. First, new types of role stress (that is, role ambiguity and role conflict) which have never been noted in the literature on role theory were identified. These new types of role ambiguity are lack of cultural understanding and communication problems. The communication problems involve language competency and the technique of ‘guessing’. With regard to role conflict, the current study identified two new types, namely, role exclusion and liaison role conflict. New types of coping strategy were also discovered. These are: hiring bicultural staff and indirect active coping. Among these new types of role stress and coping strategies, lack of cultural understanding, communication problems, and hiring bicultural staff are concerned with cultural issues. Thus, these are not found in a mono-cultural context but only in an inter-cultural context. These new types of role conflict illustrate a lack of integration among staff in companies. Second, the current study identified various sources of role stress. These are communication problems, work culture, cultural distance, and the position of expatriates. Similar to the new types of role stress types identified, the majority of these role stress sources are related to cultural issues. These types of role stress sources are, therefore, not relevant in a mono-cultural context but are applicable in an inter-cultural context. Third, the findings showed a link between role stress and coping strategies, indicating that role ambiguity, role conflict, and coping strategy are inter-related, which is consistent with an earlier finding by Stahl (2000). It suggests that selection of coping strategies should be made by taking into account employees’ role stress experiences. The findings led to a theoretical implication that role stress and the coping strategies found in a mono-cultural context are not necessarily applicable in an intercultural context. Further research is required in inter-cultural settings. Fourth, the results identify four different groupings of staff in Japanese companies in Australia. Staffing groups of Japanese companies in Australia are comprised of Japanese expatriate managers, non-Japanese local staff, local Japanese staff, and cultural integrators. This is contrary to past studies that state that overseas Japanese companies are composed of two groups, local staff and Japanese expatriate staff (e.g. Dedoussis 1994; White & Trevor, 1983; Kidahashi 1987; Yoshimura & Anderson 1997, p. 33). Overall, these findings lead to a theoretical implication that role stress and coping strategy developed in a mono-cultural context are not necessarily applicable in an intercultural context. Coping strategies perceived as effective to alleviate role stress in overseas Japanese companies are identified in this research. Implementation of these strategies, however, requires taking into consideration: types of role stress experienced by employees, their cultural background, and their corporate culture. Finally, the current study suggests development of positive relationships among staff is imperative to overcome a lack of integration among staff and establish successful white-collar management in overseas Japanese companies. Language and communication barriers are the long residing problems in overseas Japanese companies (e.g. Bamber et al. 1992; Tokusei 1994; Yoshihara 2001). The overall findings illustrate that removing these barriers, and enriching cultural understanding are the keys to improving integration among staff. In doing so, the ‘us and them’ mentality will be diminished and a shift will occur towards the growth of unity among staff. White collar management of overseas Japanese companies is acknowledged as the ‘dark side’ as opposed to their successful blue collar management recognized as ‘bright side’ (Yoshihara 1989). This doctoral research has opened the path to elevate white-collar management of overseas Japanese companies to reside in the ‘bright side’. Limitations exist in this research. First, some of the sample sizes of the respondent groups and thematic issues were small. The level of generalizability of the findings is, therefore, unconfirmed. Second, the current study did not examine the level of role stress from the point of view of both parties of the role sets (role sender and focal person). Third, all of the Japanese expatriate staff in the current study were male. The findings are, thus, limited to male expatriates. Future research should, therefore, consider these limitations. Furthermore, research in different intercultural settings should be carried out, such as in Japanese companies located in Asian countries. There has been a significant increase in recent years in Japan’s overseas direct investment in Asia (Ministry of Foreign Affairs of Japan 2005), and thus research in these countries is important. Finally, future research should be undertaken to discover how overseas Japanese companies can acquire valuable aspects of cultural diversity (e.g. Cox 1991; Cox & Blake 1991) and develop innovative and creative companies