Constraints on Non-Holomorphic correction in N=2 superspace

We study quantum corrections on four derivative term of vector multiplets in ${\cal{N}}=2$ supersymmetric Yang-Mills theory. We first show splitting of quantum correction on gauge neutral hypermultiplets from U(1) vector multiplets at four derivative order. We then revisit the non-renormalization theorem given by N. Seiberg and M. Dine and show the non-renormalization theorem in mixed (coulomb plus Higgs) branch even though gauge neutral hypermultiplet develops the vacuum expectation value.Comment: 6pages, no figure, eliminate statement for N=4 SYM theor

On subfactors arising from asymptotic representations of symmetric groups

We consider the infinite symmetric group and its infinite index subgroup given as the stabilizer subgroup of one element under the natural action on a countable set. This inclusion of discrete groups induces a hyperfinite subfactor for each finite factorial representation of the larger group. We compute subfactor invariants of this construction in terms of the Thoma parameter.Comment: to appear in Proc. AM

An Aspect of Spatial and Structural Changes in the Japanese Retail Market

The latest census of commerce shows that a drastic change is undergoing in Japanese retail market, especially in convenience goods market. This article is a case study, concernig the changes in the spatial and structural pattern of urban retail system in Japan. Some consideration on the new trends of market competition are also discussed