A Classification of Homogeneous Operators in the Cowen-Douglas Class

A complete list of homogeneous operators in the Cowen-Douglas class B-n(D) is given. This classification is obtained from an explicit realization of all the homogeneous Hermitian holomorphic vector bundles on the unit disc under the action of the universal covering group of the bi-holomorphic automorphism group of the unit disc.

Characterization of a mercury-reducing Bacillus cereus strain isolated from the Pulicat Lake sediments, south east coast of India

Pulicat Lake sediments are often severely polluted with the toxic heavy metal mercury. Several mercury-resistant strains of Bacillus species were isolated from the sediments and all the isolates exhibited broad spectrum resistance (resistance to both organic and inorganic mercuric compounds). Plasmid curing assay showed that all the isolated Bacillus strains carry chromosomally borne mercury resistance. Polymerase chain reaction and southern hybridization analyses using merA and merB3 gene primers/probes showed that five of the isolated Bacillus strains carry sequences similar to known merA and merB3 genes. Results of multiple sequence alignment revealed 99% similarity with merA and merB3 of TnMERI1 (class II transposons). Other mercury resistant Bacillus species lacking homology to these genes were not able to volatilize mercuric chloride, indicating the presence of other modes of resistance to mercuric compounds.

Characterization of a mercury-reducing Bacillus cereus strain isolated from the Pulicat Lake sediments, south east coast of India

Pulicat Lake sediments are often severely polluted with the toxic heavy metal mercury. Several mercury-resistant strains of Bacillus species were isolated from the sediments and all the isolates exhibited broad spectrum resistance (resistance to both organic and inorganic mercuric compounds). Plasmid curing assay showed that all the isolated Bacillus strains carry chromosomally borne mercury resistance. Polymerase chain reaction and southern hybridization analyses using merA and merB3 gene primers/probes showed that five of the isolated Bacillus strains carry sequences similar to known merA and merB3 genes. Results of multiple sequence alignment revealed 99% similarity with merA and merB3 of TnMERI1 (class II transposons). Other mercury resistant Bacillus species lacking homology to these genes were not able to volatilize mercuric chloride, indicating the presence of other modes of resistance to mercuric compounds.

A classification of homogeneous operators in the Cowen-Douglas class

An explicit construction of all the homogeneous holomorphic Hermitian vector bundles over the unit disc D is given. It is shown that every such vector bundle is a direct sum of irreducible ones. Among these irreducible homogeneous holomorphic Hermitian vector bundles over D, the ones corresponding to operators in the Cowen-Douglas class B-n(D) are identified. The classification of homogeneous operators in B-n(D) is completed using an explicit realization of these operators. We also show how the homogeneous operators in B-n(D) split into similarity classes. (C) 2011 Elsevier Inc. All rights reserved.

Nitrogen and carbon flows through Belandur lake - Role of Bellandur lake as a natural wetland treating Bangalore wastewater

Much of the Bangalore sewage is treated in three streams namely Bellandur (K&C Valley),Vrishabhavati and Hebbal-Nagavara stream systems. Among these it is estimated that out of a total of about 500MLD of partially treated sewage is let into the Bellandur tank. We estimate that a total of about 77t N non-industrial anthropogenic nitrogen efflux (mainly urine and excreta) in Bangalore city. This is distributed between that handled by the three sewage streams, soak-pits and land deposition. About 17-24.5t N enters the Bellandur tank daily. This has been happening over few decades and our observations suggest that this approximately 380ha tank is functioning as a C and N removal system with reasonable efficiency. The ammoniacal and nitrate nitrogen content of the water at the discharge points were estimated and found that over 80% of the nitrogen influx and over 75% of the C influx is removed by this tank system. We observed that there are three nitrogen sinks namely bacterial, micro-algal and macrophytes. The micro-algal fraction is dominated by Microcystis and Euglenophyceae members and they appear to constitute a significant fraction. Water hyacinth represents the single largest representative of the macrophytes. This tank has been functioning in this manner for over three decades. We attempt to study this phenomenon from a material balance approach and show that it is functioning with a reasonable degree of satisfaction as a natural wetland. As the population served and concomitant influx into this wetland increases, there is a potential for the system to be overloaded and to collapse. Therefore a better understanding of its function and the need for maintenance is discussed in the paper.

Spatial Analysis and Characterisation of Lentic Ecosystems: A Case Study of Varthur Lake, Bangalore

Lentic ecosystems vital functions such as recycling of nutrients, purification of water, recharge of groundwater,augmenting and maintenance of stream flow and habitat provision for a wide variety of flora and fauna along with their recreation values necessitates their sustainable management through appropriate conservation mechanisms. Failure to restore these ecosystems will result in extinction of species or ecosystem types and cause permanent ecological damage. In Bangalore, lentic ecosystems (for example lakes) have played a prominent role serving the needs of agriculture and drinking water. But the burgeoning population accompanied by unplanned developmental activities has led to the drastic reduction in their numbers (from 262 in 1976 to 81). The existing water bodies are contaminated by residential, agricultural, commercial and industrial wastes/effluents. In order to restore the ecosystem, assessment of the level of contamination is crucial. This paper focuses on characterisation and restoration aspects of Varthur lake based on hydrological, morphometric, physical-chemical and socio-economic investigations for a period of six months covering post monsoon seasons. The results of the water quality analysis show that the lake is eutrophic with high concentrations of phosphorous and organic matter. The morphometric analysis indicates that the lake is shallow in relation to its surface area. Socio-economic analyses show dependence of local residents for irrigation, fodder, etc. These analyses highlight the need and urgency to restore the physical, chemical and biological integrity through viable restoration and sustainable watershed management strategies, which include pollution abatement, catchment treatment, desilting of the lake and educating all stakeholders on the conservation and restoration of lake ecosystems.

C:N ratio of Sediments in a sewage fed Urban Lake

C:N ratio of lake sediments provide valuable information about the source and proportions of terrestrial, phytogenic and phycogenic carbon and nitrogen. This study has been carried out in Varthur lake which is receiving sewage since many decades apart from large scale land cover changes. C:N profile of the surficial sediment layer collected in the rainy and the dry seasons revealed higher C:N values[43] due to the accumulation of autochthonous organic material mostly at the deeper portions of the lake. This also highlights N limitation in the sludge either due to uptake by micro and macro-biota or rapid volatilization, denitrification and possible leaching in water. Organic Carbon was lower towards the inlets and higher near the deeper zones. This pattern of Organic C deposition was aided by gusty winds and high flow conditions together with impacts by the land use land cover changes in the watershed. Spatial variability of C:N in surficial sediments is significant compared to its seasonal variability. This communication provides an insight to the pattern in which nutrients are distributed in the sludge/sediment and its variation across seasons and space impacted by the biotic process accompanied by the hydrodynamic changes in the lake.

Assessment of treatment capabilities of Varthur Lake, Bangalore, India

Manmade waterbodies have traditionally been used for domestic and irrigation purposes. Unplanned urbanization and ad-hoc approaches have led to these waterbodies receiving untreated sewage. This enriches and eutrophies the waterbody. A physicochemical and biological analysis of sewage-fed Varthur Lake in Bangalore was carried out and its treatment capabilities in terms of BOD removal, nutrient assimilation and self-remediation were assessed. Anaerobic conditions (0 mg/L) prevail at the inlet which improves towards the outlets due to algal aeration. This removed > 50% BOD in the monsoon season but was inhibited by floating macrophytes in all other seasons. Alkalinity, TDS, conductivity and hardness values were higher when compared to earlier studies. This study shows the lake behaves as an anaerobic~aerobic lagoon with a residence time of 4.8 d treating the wastewater to a considerable extent. Further research is required to optimise the system performance.

Infinitely divisible metrics and curvature inequalities for operators in the Cowen-Douglas class

The curvature (T)(w) of a contraction T in the Cowen-Douglas class B-1() is bounded above by the curvature (S*)(w) of the backward shift operator. However, in general, an operator satisfying the curvature inequality need not be contractive. In this paper, we characterize a slightly smaller class of contractions using a stronger form of the curvature inequality. Along the way, we find conditions on the metric of the holomorphic Hermitian vector bundle E-T corresponding to the operator T in the Cowen-Douglas class B-1() which ensures negative definiteness of the curvature function. We obtain a generalization for commuting tuples of operators in the class B-1() for a bounded domain in C-m.

Flag structure for operators in the Cowen-Douglas class

The explicit description of homogeneous operators and localization of a Hilbert module naturally leads to the definition of a class of Cowen-Douglas operators possessing a flag structure. These operators are irreducible. We show that the flag structure is rigid in the sense that the unitary equivalence class of the operator and the flag structure determine each other. We obtain a complete set of unitary invariants which are somewhat more tractable than those of an arbitrary operator in the Cowen-Douglas class. (C) 2014 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.

Homogeneous Hermitian holomorphic vector bundles and the Cowen-Douglas class over bounded symmetric domains

It is known that all the vector bundles of the title can be obtained by holomorphic induction from representations of a certain parabolic group on finite-dimensional inner product spaces. The representations, and the induced bundles, have composition series with irreducible factors. We write down an equivariant constant coefficient differential operator that intertwines the bundle with the direct sum of its irreducible factors. As an application, we show that in the case of the closed unit ball in C-n all homogeneous n-tuples of Cowen-Douglas operators are similar to direct sums of certain basic n-tuples. (c) 2015 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.