Chiral de Rham complex on Riemannian manifolds and special holonomy

Interpreting the chiral de Rham complex (CDR) as a formal Hamiltonian quantization of the supersymmetric non-linear sigma model, we suggest a setup for the study of CDR on manifolds with special holonomy. We show how to systematically construct global sections of CDR from differential forms, and investigate the algebra of the sections corresponding to the covariantly constant forms associated with the special holonomy. As a concrete example, we construct two commuting copies of the Odake algebra (an extension of the N=2 superconformal algebra) on the space of global sections of CDR of a Calabi-Yau threefold and conjecture similar results for G_2 manifolds. We also discuss quasi-classical limits of these algebras.Comment: 49 pages, title changed, major rewrite with no changes in the main theorems, published versio

Numerical resolution of the hyperbolic heat equation using smoothed mathematical functions instead of Heaviside and Dirac delta distributions

The hyperbolic bioheat equation (HBE) has been used to model heating applications involving very short power pulses. This equation includes two mathematical distributions (Heaviside and Delta) which have to be necessarily substituted for smoothed mathematical functions when the HBE is solved by numerical methods. This study focuses on which type of smoothed functions would be suitable for this purpose, i.e. those which would provide solutions similar to those obtained analytically from the original Heaviside and Delta distributions. The logistic function was considered as a substitute for the Heaviside function, while its derivative and the probabilistic Gaussian function were considered as substitutes for the Delta distribution. We also considered polynomial interpolation functions, in particular, the families of smoothed functions with continuous second derivative without overshoot used by COMSOL Multiphysics. All the smoothed functions were used to solve the HBE by the Finite Element Method (COMSOL Multiphysics), and the solutions were compared to those obtained analytically from the original Heaviside and Delta distributions. The results showed that only the COMSOL smoothed functions provide a numerical solution almost identical to the analytical one. Finally, we demonstrated mathematically that in order to find a suitable smoothed function (f) that must adequately substitute any mathematical distribution (D) in the HBE, the difference D - f must have compact support. (c) 2013 Elsevier Ltd. All rights reserved.This work received financial support from the Spanish "Plan Nacional de I + D + I del Ministerio de Ciencia e Innovacion" Grant No. TEC2011-27133-C02-01 and from Universitat Politenica de Valencia (PAID-06-11 Ref. 1988). V. Romero Garcia is grateful for the support of "Programa de Contratos Post-Doctorales con Movilidad UPV del Campus de Excelencia (CEI-01-11)" and FEDER Project MAT2009-09438.Rivera Ortun, MJ.; Trujillo Guillen, M.; Romero García, V.; López Molina, JA.; Berjano Zanón, E. (2013). Numerical resolution of the hyperbolic heat equation using smoothed mathematical functions instead of Heaviside and Dirac delta distributions. International Communications in Heat and Mass Transfer. 46:7-12. https://doi.org/10.1016/j.icheatmasstransfer.2013.05.017S7124

Fluorosis risk from early exposure to fluoride toothpaste

Swallowed fluoride toothpaste in the early years of life has been postulated to be a risk factor for fluorosis, but the epidemiological evidence is weakened by the fact that most of the relevant studies were done in developed countries where an individual is exposed to multiple sources of fluoride. Objectives: To quantify the risk of fluorosis from fluoride toothpaste in a population whose only potential source of fluoride was fluoride toothpaste. Methods: Case-control analyses were conducted to test the hypothesis that fluoride toothpaste use before the age of 6 years increased an individual's risk of fluorosis. Data came from a cross-sectional clinical dental examination of schoolchildren and a self-administered questionnaire to their parents. The study was conducted in Goa, India. The study group consisted of 1189 seventh grade children with a mean age of 12.2 years. Results: The prevalence of fluorosis was 12.9% using the TF index. Results of the crude, stratified, and logistic regression analyses showed that use of fluoride toothpaste before the age of 6 years was a risk indicator for fluorosis (OR 1.83, 95% CI 1.05–3.15). Among children with fluorosis, beginning brushing before the age of 2 years increased the severity of fluorosis significantly ( P < 0.001). Other factors associated with the use of fluoride toothpaste, such as eating or swallowing fluoride toothpaste and higher frequency of use, did not show a statistically significant increased risk for prevalence or severity of fluorosis. Conclusions: Fluoride toothpaste use before the age of 6 years is a risk indicator for fluorosis in this study population.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/75437/1/j.1600-0528.1998.tb01957.x.pd

Photoproduction of pions and properties of baryon resonances from a Bonn-Gatchina partial wave analysis

Masses, widths and photocouplings of baryon resonances are determined in a coupled-channel partial wave analysis of a large variety of data. The Bonn-Gatchina partial wave formalism is extended to include a decomposition of t- and u-exchange amplitudes into individual partial waves. The multipole transition amplitudes for $\gamma p\to p\pi^0$ and $\gamma p\to n\pi^+$ are given and compared to results from other analyses.Comment: 18 pages, 14 figure