On Szegö’s Type Theorems

This study is to look the effect of change in the ordering of the Fourier system on Szegö’s classical observations of asymptotic distribution of eigenvalues of finite Toeplitz forms.This is done by checking proofs and Szegö’s properties in the new set up.The Fourier system is unconditional [19], any arbitrary ordering of the Fourier system forms a basis for the Hilbert space L2 [-Π, Π].Here study about the classical Szegö’s theorem.Szegö’s type theorem for operators in L2(R+) and check its validity for certain multiplication operators.Since the trigonometric basis is not available in L2(R+) or in L2(R) .This study discussed about the classes of orderings of Haar System in L2 (R+) and in L2(R) in which Szegö’s Type TheoreT Am is valid for certain multiplication operators.It is divided into two sections. In the first section there is an ordering to Haar system in L2(R+) and prove that with respect to this ordering, Szegö’s Type theorem holds for general class of multiplication operators Tƒ with multiplier ƒ ε L2(R+), subject to some conditions on ƒ.Finally in second section more general classes of ordering of Haar system in L2(R+) and in L2(R) are identified in such a way that for certain classes of multiplication operators the asymptotic distribution of eigenvalues exists.

Biochemical and molecular characterization of pathogenic vibrios from hatcheries and aquaculture farms

Vibrio are important during hatchery rearing. aquaculture phase and post-harvest quality of shrimps. Vibrio spp are of concern to shrimp farmers and hatchery operators because certain species can cause Vibriosis. Vibrio species are of concern to humans because certain species cause serious diseases.With the progress in aquaculture, intensive systems used for shrimp aquaculture create an artificial environment that increases bacterial growth. To maintain the productivity of such an intensive aquaculture, high inputs of fish protein have to be employed for feeding together with high levels of water exchange and the massive use of antibiotics/ probiotics / chemicals. It seems that the combination of these conditions favours the proliferation of vibrios and enhances their virulence and disease prevalence. The risk of a microbial infection is high, mainly at larval stages. The effect and severity are related to Vibrio species and dose, water, feed, shrimp quality and aquaculture management.Consumption of seafood can occasionally result in food-bome illnesses due to the proliferation of indigenous pathogens like Vibrio.Of the l2 pathogenic Vibrio species, 8 species are known to be directly food associated. Strict quality guidelines have been laid by the importing nations, for the food products that enter their markets. The microbiological quality requirement for export of frozen shrimp products is that V.cholerae, V.parahaemolyticus and V. vulnificus should be absent in 25g of the processed shrimp (Export Inspection Council of India, 1995). The mere presence of these pathogenic Vibrios is sufficient for the rejection of the exported product.The export rejections cause serious economic loss to the shrimp industry and might harm the brand image of the shrimp products from the countiy.There is a need for an independent study on the incidence of different pathogenic vibrios in shrimp aquaculture and investigate their biochemical characteristics to have a better understanding about the growth and survival of these organisms in the shrimp aquaculture niche. PCR based methods (conventional PCR, duplex PCR, multiplex-PCR and Real Time PCR) for the detection of the pathogenic Vibrios is important for rapid post-harvest quality assessment. Studies on the genetic heterogeneity among the specific pathogenic vibrio species isolated from shrimp aquaculture system provide; valuable information on the extent of genetic diversity of the pathogenic vibrios, the shrimp aquaculture system.So the present study was undertaken to study the incidence of pathogenic Vibrio spp. in Penaeus monodon shrimp hatcheries and aquaculture farms, to carry out biochemical investigations of the pathogenic Vibrio spp isolated from P. monodon hatchery and. aquaculture environments, to assess the effect of salt (NaCl) on the growth and enzymatic activities of pathogenic Vibrio spp., to study the effect of preservatives, and chemicals on the growth of pathogenic Vibrio spp. and to employ polymerase chain reaction (PCR) methods for the detection of pathogenic V ibrio spp.Samples of water (n=7) and post-larvae (n=7) were obtained from seven Penaeus monodon hatcheries and samples of water (n=5), sediment (n=5) and shrimp (n=5) were obtained from five P. monodon aquaculture farms located on the East Coast of lndia. The microbiological examination of water, sediment, post-larvae and shrimp samples was carried out employing standard methods and by using standard media.The higher bacterial loads were obtained in pond sediments which can be attributed to the accumulation of organic matter at the pond bottom which stimulated bacterial growth.Shrimp head. (4.78 x 105 +/- 3.0 x 104 cfu/g) had relatively higher bacterial load when compared to shrimp muscle 2.7 x 105 +/- 1.95 x 104 cfu/g). ln shrimp hatchery samples, the post-larvae (2.2 x 106 +/- 1.9 x 106 cfu/g) had higher bacterial load than water (5.6 x 103 +/- 3890 cfu/ml).The mean E.coli counts were higher in aquaculture pond sediment (204+/-13 cfu/g) and pond water (124+/-88 cfu/ml). Relatively lower Escherichia coli counts were obtained from shrimp samples (12+/-11 to 16+/-16.7 cfu/g). The presence of E.coli in aquaculture environment might have been from the source water. E.coli was not detected in hatchery waters and post-larvae.

Chemistry of molecular and supramolecular structures of vanadium(IV) and dioxygen-bridged V(V) complexes incorporating tridentate hydrazone ligands

Four hydrazone ligands: 2-benzoylpyridine benzoyl hydrazone (HBPB), di-2-pyridyl ketone nicotinoyl hydrazone (HDKN), quinoline-2-carbaldehyde benzoyl hydrazone (HQCB), and quinoline-2-carbaldehyde nicotinoyl hydrazone (HQCN) and four of their complexes with vanadyl salts have been synthesized and characterized. Single crystals of HBPB and complexes [VO(BPB)(l2-O)]2 (1) and [VO(DKN)(l2-O)]2 ½H2O (2) were isolated and characterized by X-ray crystallography. Each of the complexes exhibits a binuclear structure where two vanadium(V) atoms are bridged by two oxygen atoms to form distorted octahedral structures within cis-N2O4 donor sets. In most complexes, the uninegative anions function as tridentate ligands, coordinating through the pyridyl- and azomethine-nitrogen atoms and enolic oxygen whereas in complex [VO(HQCN)(SO4)]SO4 4H2O (4) the ligand is coordinated in the keto form. Complexes [VO(QCB)( OMe)] 1.5H2O (3) and 4 are found to be EPR active and showed well-resolved axial anisotropy with two sets of eight line pattern