An endomorphism of the Khovanov invariant

We construct an endomorphism of the Khovanov invariant to prove H-thinness and pairing phenomena of the invariants for alternating links. As a consequence, it follows that the Khovanov invariant of an oriented nonsplit alternating link is determined by its Jones polynomial, signature, and the linking numbers of its components.Comment: To appear in Adv. Math.; Brief summary of Khovanov invariant (math.QA/9908171) and previous result of the author (math.GT/0201105) adde

Absorption and Recoil of Fundamental String by D-String

Inclusive absorption cross section of fundamental IIB string to D-string is calculated perturbatively. The leading order result agrees with estimate based on stringy Higgs mechanism via Cremmer-Scherk coupling. It is argued that the subleading order correction is dominated by purely planar diagrams in the large mass limit. The correction represents conversion of binding energy into local recoil process of the fundamental string and D-string bound state. We show their presence explicitly in the next leading order.Comment: harvmac, 4 figures, 17 page

Detoxification of water by semiconductor photocatalysis

An overview of the use of semiconductor photocatalysis for water purification is given. The basic principles of semiconductor photocatalysis are described along with the current understanding of the underlying reaction mechanism(s) and how it fits in with the major features of the observed Langmuir-Hinshelwood-type kinetics of pollutant destruction. These features are illustrated based on literature on the destruction of aqueous solutions of 4-chlorophenol as a pollutant, using titanium dioxide as the photocatalyst. The range of organic and inorganic pollutants that can be destroyed by semiconductor photocatalysis are reported and discussed. The basic considerations that need to be made when designing a reactor for semiconductor photocatalysis are considered. These include: the nature of the reactor glass, the type of illumination source, and the nature and type of semiconductor photocatalyst. The key basic photoreactor designs are reported and discussed, including external illumination, annular, and circular photoreactors. Actual designs that have been used for fixed and thin falling film semiconductor photocatalyst reactors are illustrated and their different features discussed. Basic non-concentrating and concentrating solar photoreactors for semiconductor photocatalysis are also reported. The design features of the major commercial photocatalytic reactor systems for water purification are reported and illustrated. Several case studies involving commercial photocatalytic reactors for water purification are reported. An attempt is made briefly to compare the efficacy of semiconductor photocatalysis for water purification with that of other, more popular and prevalent water purification processes. The future of semiconductor photocatalysis as a method of purifying water is considered