In 2003 Cohn and Umans introduced a group-theoretic approach to fast matrix multiplication. This involves finding large subsets S, T and U of a group G satisfying the Triple Product Property (TPP) as a means to bound the exponent ω of the matrix multiplication. We show that S, T and U may be be assumed to contain the identity and be otherwise disjoint. We also give a much shorter proof of the u...

OBJECTIVE Teeth discoloration is a rare orthodontic complication. The aim of this study was to report the clinical progression of discoloration during orthodontic treatment. METHODS Discolored teeth, detected during orthodontic treatment between January 2003 and December 2012 by a single dentist using similar techniques and appliances, were analyzed. RESULTS The total number of teeth that s...

The degradation of the AB1 dye by electro-generated species using a BDD electrode was performed. The results were explained by the generation of OH radical, S2O8 in the presence of sulfate, and active halide species in the presence of halide salt. The discoloration rate increases in this order: sulfate, KCl, KBr. In the presence of KCl, the discoloration is affected by the current density, init...

OBJECTIVE To evaluate the relationship between early white discoloration of infantile hemangioma (IH) and ulceration. DESIGN Retrospective cohort study. SETTING Tertiary referral center. PATIENTS A case series of 11 infants with early white discoloration of IH are described. An additional 55 infants with IH, aged 3 months, were evaluated retrospectively from a photograph archive to furthe...

Bacterial, mechanical, or chemical irritation to the pulp may result in tissue necrosis and release of disintegration by-products that may penetrate tubules and discolor the surrounding dentin. The degree of discoloration is directly related to how long the pulp has been necrotic. The longer the discoloration compounds are present in the pulp chamber, the greater the discoloration. Such discolo...

Although supporters of vegetarianism (and animals' interests in general) come in many varieties, we may distinguish two groups. First, utilitarians such as Singer base their argument on the suffering that factory farming causes to nonhumans and the absence of comparable benefits to humans. l Second, the animal rights view, as expressed by Regan, extends Kant's respect for persons principle to i...

INTRODUCTION The American Association of Endodontists clinical considerations for regenerative therapy (April 2015) advise of the risk of the possible adverse effect of staining of teeth. It is widely acknowledged that before these guidelines were developed there was no standardized protocol for regenerative therapy, and different approaches using different materials have been reported. The pur...

Three different reactive dyes Reactive Blue 19, Reactive Orange 16 and Reactive Red 180 were dissolved in water separately in concentration 0.04g/l as model pollutants for contaminated wastewaters from textile industry. Every wastewater sample was treated by ozone with concentration 2000 ppm for 30 minutes at ambient temperature and the effect of discoloration was traced after 5, 10, 20 and 30 ...