Simple currents and extensions of vertex operator algebras

We consider how a vertex operator algebra can be extended to an abelian interwining algebra by a family of weak twisted modules which aresimple currents associated with semisimple weight one primary vectors. In the case that the extension is again a vertex operator algebra, the rationality of the extended algebra is discussed. These results are applied to affine Kac-Moody algebras in order to construct all the simple currents explicitly (except forE ₈) and to get various extensions of the vertex operator algebras associated with integrable representations.Supported by NSF grant DMS-9303374 and a research grant from the Committee on Research, UC Santa Cruz.Supported by NSF grant DMS-9401272 and a research grant from the Committee on Research, UC Santa Cruz.     

Selective inversion in inhomogeneously broadened powder spectra

It is shown how amplitude-modulated radio-frequency pulses optimized for selective inversion of magnetization can be applied to static powder samples with inhomogeneously broadened spectra. Selective one-dimensional methods can in principle provide information similar to two-dimensional exchange spectroscopy, and they are often more efficient for determining the rates of dynamic processes. However, in systems where transverse magnetization is subject to significant homogeneous decay during the rf pulses, selective one-dimensional methods do not necessarily offer the expected advantages over two-dimensional spectroscopy.     

A family of graphs and the degree/diameter problem

We investigate a family of graphs relevant to the problem of finding large regular graphs with specified degree and diameter. Our family contains the largest known graphs for degree/diameter pairs (3, 7), (3, 8), (4, 4), (5, 3), (5, 5), (6, 3), (6, 4), (7, 3), (14, 3), and (16, 2). We also find a new bound for (3, 6) by an unrelated method. © 2001 John Wiley & Sons, Inc. J Graph Theory 37: 118–124, 2001     

Event shapes in e+e− annihilation

We present a complete set of rotationally invariant observables (H_l) which characterizes the ‘shapes’ of final states in e⁺e^? annihilation. They are infrared stable when calculated in QCD perturbation theory. We compare the ‘shapes’ of final states from the processes $\text{e}{}^{\mathrm{+}}\text{e}{}^{\mathrm{?}}\text{→}\text{q}\text{q}\text{,}\text{e}{}^{\mathrm{+}}\text{e}{}^{\mathrm{?}}\text{→}\text{q}\text{q}\text{(}\text{G}\text{)}$ and from the three-gluon decays of heavy vector mesons. We also consider the production and decay of heavy quarks and leptons. Using a realistic model for the development of hadron jets, we find that for c.m. energies above about 10 GeV, these processes may be clearly distinguished by their distributions in the H_l. We indicate how our analysis may be extended to deep inelastic lepton-hadron interactions and hadron-hadron collisions involving large transverse momenta.     

Regional concentration and efficiency in Mexican manufacturing

This paper explores the link between industrial location, concentration, and economic efficiency in Mexican manufacturing. Using a linear programming approach, the authors calculate indices of overall, technical, allocative, and scale efficiency for Mexican manufacturing industries by state to test whether, in 1985, those regions with high levels of industrial concentration were suffering from the costs of congestion. The evidence suggests that, at least at the aggregate level, there continued to be a positive relationship between industry concentration and efficiency in production. There is also evidence that overall efficiency was related to scale efficiency, although highly industrialized regions on the production frontier often operated at inefficient scales. In particular, the most concentrated regions (the Federal District, the state of Mexico, Jalisco, and Nuevo León) consistently display decreasing returns to scale, indicating that the process of industrial concentration may be leading to diseconomies of scale. Finally, an econometric analysis suggests that scale, urbanization, and agglomeration economies are positively related to overall and technical efficiency at the regional level, while foreign ownership is negatively related. Agglomeration economies at the industry level were not significant. The paper also makes a methodological contribution. It is the first application of a distance-function production methodology to measuring regional efficiency in a developing country. It demonstrates how to conduct distance-function efficiency analysis using the newly developed GAMS mathematical programming environment. These tools should be of considerable interest to applied microeconomists.