On Some Infinite Convex Invariants

The present study on some infinite convex invariants. The origin of convexity can be traced back to the period of Archimedes and Euclid. At the turn of the nineteenth centaury , convexicity became an independent branch of mathematics with its own problems, methods and theories. The convexity can be sorted out into two kinds, the first type deals with generalization of particular problems such as separation of convex sets[EL], extremality[FA], [DAV] or continuous selection Michael[M1] and the second type involved with a multi- purpose system of axioms. The theory of convex invariants has grown out of the classical results of Helly, Radon and Caratheodory in Euclidean spaces. Levi gave the first general definition of the invariants Helly number and Radon number. The notation of a convex structure was introduced by Jamison[JA4] and that of generating degree was introduced by Van de Vel[VAD8]. We also prove that for a non-coarse convex structure, rank is less than or equal to the generating degree, and also generalize Tverberg’s theorem using infinite partition numbers. Compare the transfinite topological and transfinite convex dimensions

Structure Absorption Spectra Correlation in a Series of 2,6-Dimethyl-4-arylpyrylium Salts

A combined experimental and theoretical study of the absorption spectra of a group of closely related pyrylium perchlorates 1-11 are presented. Minor changes in the position of the substituents lead to drastic changes in the absorption spectra in this series of compounds. We have attempted to explain the observed changes using the x,y-band notation developed by Balaban and co-workers. Absorption spectra of all compounds are compared with results from time-dependent density functional theory (TDDFT) and Zerner’s intermediate neglect of differential overlap (ZINDO/S) level calculations. Results of the calculations are in good agreement with experimental observations and an interesting correlation between Balaban’s notations and the MO transitions are obtained for simple derivatives. It is suggested that for more complex systems such as R- and â-naphthyl substituted systems, the empirical method is not appropriate.

Detection and diversity of pathogenic Vibrio from Fiji

Here we investigate the diversity of pathogenic Vibrio species in marine environments close to Suva, Fiji. We use four distinct yet complementary analyses – biochemical testing, phylogenetic analyses, metagenomic analyses and molecular typing – to provide some preliminary insights into the diversity of vibrios in this region. Taken together our analyses confirmed the presence of nine Vibrio species, including three of the most important disease-causing vibrios (i.e. V. cholerae, V. parahaemolyticus and V. vulnificus), in Fijian marine environments. Furthermore, since toxigenic V. parahaemolyticus are present on fish for consumption we suggest these bacteria represent a potential public health risk. Our results from Illumina short read sequencing are encouraging in the context of microbial profiling and biomonitoring. They suggest this approach may offer an efficient and costeffective method for studying the dynamics of microbial diversity in marine environments over time.