Working group report: Flavor physics and model building

This is the report of flavor physics and model building working group at WHEPP-9. While activites in flavor physics have been mainly focused on B-physics, those in model building have been primarily devoted to neutrino physics. We present summary of working group discussions carried out during the workshop in the above fields, and also briefly review the progress made in some projects subsequently.     

Hubbard-type solution in the planar approximation

The Hubbard solution to the Hubbard model showed a non-trivial metal-insulator transition. The value of the one-particle density of states at the Fermi energy in that solution decreased continuously with increasing value of the Hubbard interaction and vanished at a critical value of the interaction. Such a solution is derived from a planar model, as an approximation to the exact construction of the model's one-particle Green function.     

Design,synthesis, and characterization of main‐chain,aromatic polyesters based on 3,4‐ethylenedioxythiophene

A series of new thermoplastic polyesters based on 3,4‐ethylenedioxythiophene (EDOT) with flexible aliphatic spacers have been synthesized and characterized for the first time. The thermal properties of these polyesters based on EDOT are comparable to those of conventional polyesters based on the 1,4‐phenyl unit, indicating that EDOT is a viable replacement for the phenyl units. The glass‐transition and melting‐transition temperatures decrease monotonically with an increase in the spacer length. Theoretical calculations have revealed that the core angle for EDOT is comparable to that of unsubstituted thiophene and hence should be compatible with the formation of the mesophase. This has been confirmed experimentally by the synthesis of a main‐chain, thermotropic, liquid‐crystalline polyester based on EDOT that exhibits fluid birefringence. In fact, this is the first report in which a main‐chain, liquid‐crystalline polymer based on 3,4‐disubstituted thiophene has been successfully designed and synthesized. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 3479–3486, 2006     

Corrigendum to the paper ``Adjoining an Order Unit to a Matrix Ordered Space'

An error has been detected (and also corrected) in Theorem 2.8 of the paper entitled “Adjoining an Order Unit to a Matrix Ordered Space” (Positivity, (2005)9: 207–223; DOI ). Accordingly, some of the results of the paper have been modified. Also, a notion of C*-matricially, Riesz normed spaces has been introduced.     

Dimensional reduction for Helmholtz's equation on a bounded domain

Summary. The dimensional reduction method for solving boundary value problems of Helmholtz's equation in domain by replacing them with systems of equations in dimensional space are investigated. It is proved that the existence and uniqueness for the exact solution and the dimensionally reduced solution of the boundary value problem if the input data on the faces are in some class of functions. In addition, the difference between and in is estimated as and are fixed. Finally, some numerical experiments in a domain are given in order to compare theretical results. Received April 2, 1996 / Revised version received July 30, 1990