On the structure of framed vertex operator algebras and their pointwise frame stabilizers

In this paper, we study the structure of a general framed vertex operator algebra. We show that the structure codes (C,D) of a framed VOA V satisfy certain duality conditions. As a consequence, we prove that every framed VOA is a simple current extension of the associated binary code VOA V_C. This result would give a prospect on the classification of framed vertex operator algebras. In addition, the pointwise frame stabilizer of V is studied. We completely determine all automorphisms in this pointwise stabilizer, which are of order 1, 2 or 4. The 4A-twisted sector and the 4A-twisted orbifold theory of the famous Moonshine VOA are also constructed explicitly. We verify that the top module of this twisted sector is of dimension 1 and of weight 3/4 and the VOA obtained by 4A-twisted orbifold construction of the moonshine VOA is isomorphic to the moonshine VOA itself.Comment: Version 3: 59 pages. Corrected version. 54 pages on my LaTeX system version 2: We add Theorem 5.16 in which we give a necessary and sufficient condtion for a code to be a structure code of a holomorphic framed VOA. "hyperref" style is also introduce

Measures of Prices and Price Competitiveness in International Trade in Manufactured Goods

The purpose of this paper is to present, and to explain the construction of, a set of price indexes relating to international trade in manufactured goods. These include: 1. Indexes of export prices for the U.S., Germany, and Japan, based on their weights, and indexes of competitors' prices for each of those countries based on the sane set of weights; 2. Indexes of domestic prices for the U. S., Germany, and Japan based on export weights; 3. Indexes for developed country exports of manufactures based on weights of developed country exports of manufactures to developing countries and of total developed country exports of manufactures, and indexes for exports of the U.S., Germany, and Japan on the sane sets of weights. The indexes for developed country exports make use of a method for estimating missing prices that takes account not only of contemporaneous price changes in the same country within the sane community groups, but also of price changes for the particular commodity in other countries. Comparisons are made between movements of domestic and export prices and between price indexes based on weights of early and late base years. In addition, an attempt is made to correct the price indexes for changes in the quality of some manufactured goods not usually taken account of in measures of export or import prices.

A simple model for NN correlations in quasielastic lepton-nucleus scattering

We present a covariant extension of the relativistic Fermi gas model which incorporates correlation effects in nuclei. Within this model, inspired by the BCS descriptions of systems of fermions, we obtain the nuclear spectral function and from it the superscaling function for use in treating high-energy quasielastic electroweak processes. Interestingly, this model has the capability to yield the asymmetric tail seen in the experimental scaling function.Comment: 11 pages, 6 figures, Proceedings of the Twenty Seventh International Workshop on Nuclear Theory, June 23 - 28, 2008, Rila mountains, Bulgari