Central Invariants and Higher Indicators for Semisimple Quasi-Hopf Algebras

In this paper, we define the higher Frobenius-Schur (FS-)indicators for finite-dimensional modules $V$ of a semisimple quasi-Hopf algebra $H$ via the categorical counterpart developed in \cite{NS05}. We prove that this definition of higher FS-indicators coincides with the higher indicators introduced by Kashina, Sommerh\"auser, and Zhu when $H$ is a Hopf algebra. We also obtain a sequence of canonical central elements of $H$, which is invariant under gauge transformations, whose values, when evaluated by the character of an $H$-module $V$, are the higher Frobenius-Schur indicators of $V$. As an application, we show that FS-indicators are sufficient to distinguish the four gauge equivalence classes of semisimple quasi-Hopf algebras of dimension eight corresponding to the four fusion categories with certain fusion rules classified by Tambara and Yamagami. Three of these categories correspond to well-known Hopf algebras, and we explicitly construct a quasi-Hopf algebra corresponding to the fourth. We also derive explicit formulae for FS-indicators for some quasi-Hopf algebras associated to group cocycles.Comment: The higher Frobenius-Schur indicators for certain quasi-Hopf algebras associated with finite groups and their 3-cocycles have been computed in section

Higher Frobenius-Schur Indicators for Pivotal Categories

We define higher Frobenius-Schur indicators for objects in linear pivotal monoidal categories. We prove that they are category invariants, and take values in the cyclotomic integers. We also define a family of natural endomorphisms of the identity endofunctor on a $k$-linear semisimple rigid monoidal category, which we call the Frobenius-Schur endomorphisms. For a $k$-linear semisimple pivotal monoidal category -- where both notions are defined --, the Frobenius-Schur indicators can be computed as traces of the Frobenius-Schur endomorphisms.Comment: A paragraph which describes the organization of the paper has been added to the introduction. Some observations have been added to Theorems 5.1 and 7.

CR-Invariants and the Scattering Operator for Complex Manifolds with Boundary

The purpose of this paper is to describe certain CR-covariant differential operators on a strictly pseudoconvex CR manifold $M$ as residues of the scattering operator for the Laplacian on an ambient complex K\"{a}hler manifold $X$ having $M$ as a `CR-infinity.' We also characterize the CR $Q$-curvature in terms of the scattering operator. Our results parallel earlier results of Graham and Zworski \cite{GZ:2003}, who showed that if $X$ is an asymptotically hyperbolic manifold carrying a Poincar\'{e}-Einstein metric, the $Q$-curvature and certain conformally covariant differential operators on the `conformal infinity' $M$ of $X$ can be recovered from the scattering operator on $X$. The results in this paper were announced in \cite{HPT:2006}.Comment: 32 page

One-step and two-step estimation of the effects of exogenous variables on technical efficiency levels

Consider a stochastic frontier model with one-sided inefficiency u, and suppose that the scale of u depends on some variables (firm characteristics) z. A one-step model specifies both the stochastic frontier and the way in which u depends on z, and can be estimated in a single step, for example by maximum likelihood. This is in contrast to a two-step procedure, where the first step is to estimate a standard stochastic frontier model, and the second step is to estimate the relationship between (estimated) u and z. In this paper we propose a class of one-step models based on the scaling property that u equals a function of z times a one-sided error u * whose distribution does not depend on z. We explain theoretically why two-step procedures are biased, and we present Monte Carlo evidence showing that the bias can be very severe. This evidence argues strongly for one-step models whenever one is interested in the effects of firm characteristics on efficiency levels.technical efficiency; stochastic frontiers

Review of the Proposed Reserve Markets in New England

ISO New England proposes reserve markets designed to improve the existing forward reserve market and improve pricing during real-time reserve shortages. We support all of the main elements of the proposal. For example, we agree that little is gained by allowing reserve availability bids in the day-ahead market. Doing so greatly increases the complexity of the market without the prospect of more efficient pricing. Rather, offline reserves are most efficiently priced and awarded well in advance, as is done by the improved forward reserve market.Auctions; Multiple Object Auctions; Electricity Auctions

Autonomous response of a third-order digital filter with two’s complement arithmetic realized in cascade form

In this letter, results on the autonomous response of a third-order digital filter with two’s complement arithmetic realized as a first-order subsystem cascaded by a second-order subsystem are reported. The behavior of the second-order subsystem depends on the pole location and the initial condition of the first-order subsystem, because the transient behavior is affected by the first-order subsystem and this transient response can be viewed as an excitation of the original initial state to another state. New results on the set of necessary and sufficient conditions relating the trajectory equations, the behaviors of the symbolic sequences, and the sets of the initial conditions are derived. The effects of the pole location and the initial condition of first-order subsystem on the overall system are discussed. Some interesting differences between the autonomous response of second-order subsystem and the response due to the exponentially decaying input are reported. Some simulation results are given to illustrate the analytical results

Properties and partial purification of pectin methyl esterase in vegetable-type soybeans

The purpose of this work was to study the effect of sodium chloride, pH, temperature and maturity on soybean pectin methyl esterase activity, to determine enzyme kinetic constants and to describe the inhibition of PME by tannic acid. The enzyme was partially purified. The source of FM£ was a slurry of the soybeans which were raised on the University of Tennessee Plant Science Farm at Knoxville. Beckman Autotitrator was used for enzyme assay. The data reflecting effects of salt concentration, pH, temperature and maturity on PME activity were analyzed by the analysis of variance. The Duncan\u27s Multiple Range Test was employed to determine significant differences among means. In the study of enzyme kinetics, the Lineweaver-Burk double reciprocal form of the Michaelis-Menten was utilized. A FORTRAN computer program was written to determine Km, Vmax, regression coefficient, b,/u\u3e, and the corre-lation coefficient, r, on the IBM 7040 computer. Progressive purification steps for this enzyme were made by acetone-dried powders, salt extraction, ammonium sulfate precipitation, dialysis, and DEAE-cellulose ion-exchange column chromatography. Maximum activity for the PME occurred between 0.25 and 0.40 M concentrations of NaCl, between pH 7.5 and 8.5, and at 50°C. The mean Q10 value was 1.23. The more mature the soybeans were, the lower the total PME activity. The Km value for soybean PME of the first harvest was 0.052 percent pectin and for the third, 0.057 percent pectin. The amount of inhibition of PME by tannic acid was related to inhibitor and substrate concentrations. An increase in PME specific activity of about 140-fold was ob-tained by the purification methods. There were at least two isoenzymes of the soybean FME. This hypothesis is based on the elution behavior of the enzyme on the DEAE-cellulose ion-exchange column