Modular Equations and Distortion Functions

Modular equations occur in number theory, but it is less known that such equations also occur in the study of deformation properties of quasiconformal mappings. The authors study two important plane quasiconformal distortion functions, obtaining monotonicity and convexity properties, and finding sharp bounds for them. Applications are provided that relate to the quasiconformal Schwarz Lemma and to Schottky's Theorem. These results also yield new bounds for singular values of complete elliptic integrals.Comment: 23 page

Photon Spectrum Produced by the Late Decay of a Cosmic Neutrino Background

We obtain the photon spectrum induced by a cosmic background of unstable neutrinos. We study the spectrum in a variety of cosmological scenarios and also we allow for the neutrinos having a momentum distribution (only a critical matter dominated universe and neutrinos at rest have been considered until now). Our results can be helpful when extracting bounds on neutrino electric and magnetic moments from cosmic photon background observations.Comment: RevTex, 14 pages, 3 figures; minor changes, references added. To appear in Phys. Rev.

Quantitative Treatment of Decoherence

We outline different approaches to define and quantify decoherence. We argue that a measure based on a properly defined norm of deviation of the density matrix is appropriate for quantifying decoherence in quantum registers. For a semiconductor double quantum dot qubit, evaluation of this measure is reviewed. For a general class of decoherence processes, including those occurring in semiconductor qubits, we argue that this measure is additive: It scales linearly with the number of qubits.Comment: Revised version, 26 pages, in LaTeX, 3 EPS figure

Effect of Investigator Disturbance in Experimental Forensic Entomology: Succession and Community Composition

Carrion insect succession studies have historically used repeated sampling of single or a few carcasses to produce data, either weighing the carcasses, removing a qualitative subsample of the fauna present, or both, on every visit over the course of decomposition and succession. This study, conducted in a set of related experimental hypotheses with two trials in a single season, investigated the effect that repeated sampling has on insect succession, determined by the number of taxa collected on each visit and by community composition. Each trial lasted at least 21 days, with daily visits on the first 14 days. Rat carcasses used in this study were all placed in the field on the same day, but then either sampled qualitatively on every visit (similar to most succession studies) or ignored until a given day of succession, when they were sampled qualitatively (a subsample) and then destructively sampled in their entirety. Carcasses sampled on every visit were in two groups: those from which only a sample of the fauna was taken and those from which a sample of fauna was taken and the carcass was weighed for biomass determination. Of the carcasses visited only once, the number of taxa in subsamples was compared to the actual number of taxa present when the carcass was destructively sampled to determine if the subsamples adequately represented the total carcass fauna. Data from the qualitative subsamples of those carcasses visited only once were also compared to data collected from carcasses that were sampled on every visit to investigate the effect of the repeated sampling. A total of 39 taxa were collected from carcasses during the study and the component taxa are discussed individually in relation to their role in succession. Number of taxa differed on only one visit between the qualitative subsamples and the actual number of taxa present, primarily because the organisms missed by the qualitative sampling were cryptic (hidden deep within body cavities) or rare (only represented by very few specimens). There were no differences discovered between number of taxa in qualitative subsamples from carcasses sampled repeatedly (with or without biomass determinations) and those sampled only a single time. Community composition differed considerably in later stages of decomposition, with disparate communities due primarily to small numbers of rare taxa. These results indicate that the methods used historically for community composition determination in experimental forensic entomology are generally adequate