Spherical Tuples of Hilbert Space Operators

We introduce and study a class of operator tuples in complex Hilbert spaces, which we call spherical tuples. In particular, we characterize spherical multi-shifts, and more generally, multiplication tuples on RKHS. We further use these characterizations to describe various spectral parts including the Taylor spectrum. We also find a criterion for the Schatten $S_p$-class membership of cross-commutators of spherical $m$-shifts. We show, in particular, that cross-commutators of non-compact spherical $m$-shifts cannot belong to $S_p$ for $p \le m$. We specialize our results to some well-studied classes of multi-shifts. We prove that the cross-commutators of a spherical joint $m$-shift, which is a $q$-isometry or a $2$-expansion, belongs to $S_p$ if and only if $p > m$. We further give an example of a spherical jointly hyponormal $2$-shift, for which the cross-commutators are compact but not in $S_p$ for any $p <\infty$.Comment: a version close to final on

Stability and Equilibrium Analysis of Laneless Traffic with Local Control Laws

In this paper, a new model for traffic on roads with multiple lanes is developed, where the vehicles do not adhere to a lane discipline. Assuming identical vehicles, the dynamics is split along two independent directions: the Y-axis representing the direction of motion and the X-axis representing the lateral or the direction perpendicular to the direction of motion. Different influence graphs are used to model the interaction between the vehicles in these two directions. The instantaneous accelerations of each car, in both X and Y directions, are functions of the measurements from the neighbouring cars according to these influence graphs. The stability and equilibrium spacings of the car formation is analyzed for usual traffic situations such as steady flow, obstacles, lane changing and rogue drivers arbitrarily changing positions inside the formation. Conditions are derived under which the formation maintains stability and the desired intercar spacing for each of these traffic events. Simulations for some of these scenarios are included.Comment: 8 page

Extraction, purification and characterization of hyaluronic acid from Rooster comb

Hyaluronic acid, is extract by different procedures from various sources like pig, rabbit, oxes and human are available, but these processes have certain imitations like low yield, and also it requires the killing of these animals which is against the experimental ethics. In the present study, we have carried out the extraction of hyaluronic acid from cock’s comb which was further analyzed with qualitative test, viscosity, UV absorption, endotoxin detection assay. Also, the protein contamination of extracted hyaluronic acid was determined by using SDS-PAGE of hyaluronic acid was studied for checking the protein contaminants and it was noted that there were no bands observed in the well loaded with extracted hyaluronic acid sample indicating that the final extract of hyaluronic acid is not contaminated with the protein. The extraction and purification of hyaluronic acid by using the method reported here give pure hyaluronic acid. The viscosity of extracted hyaluronic acid was found to be 2.55 poise which is economical and can be used for industrial production of hyaluronic acid having clinical application

Landing of Rachycentron canadum(Linnaeus,1766)by the purse seines at New Ferry Wharf, Mumbai

On10-10-2003 Rachycentron canadum was caught along with Scomberomorus commerson and Euthynemus affinus at New Ferry Wharf by purse seines. estimated catch was 2t.The fishing area was about 50-70km.south west of Mumbai at adepth of 35-45 metres.Total catch of the purse seines was estimated at 3.5t

Record of complete albinism in marine catfish, Osteogeneiosus militaris (Linnaeus, 1758), landed at Mumbai

Albinism is due to one of several gene mutations that affect the normal pigmentation. There are various degrees of albinism. True albino or amelanistic animals lack melanin and are white with unpigmented pink eyes

Influence of Waterlogging on Carbohydrate Metabolism in Ragi and Rice Roots

Effect of different durations of waterlogging (4, 8 and 12 days) stress on carbohydrate status and activities of some related enzymes in ragi and rice roots was studied. In both ragi and rice roots there was decrease in starch and total sugar content in response to waterlogging conditions. Activity of α amylase was decrease in ragi roots while opposite trend was noticed in case of rice roots. The activity of pyruvate kinase was markedly increased due to 4, 8 and 12 days waterlogging in ragi roots while such increase was noticed in rice roots due to 12 days stress. Treatment of waterlogging caused enhancement in the activity of alkaline inorganic pyrophosphatase in the roots of both ragi and rice

Unusual landing of “Koth” Otolithoides biauritus by mini trawler at Versova, Mumbai.

A mini trawler landed an unusual catch of 103 numbers of “Koth” in the size range 770-1050mm each weighing between 2.5 to 5.0kg from a depth of 30 meters, at a distance of 25km off Mumbai, around the fishing grounds of Dahanu and Satpati

Unusual landing of Alepes djeddaba (Forskal) and Megalaspis cordyla (Linnaeus) by purse seiners at New Ferry Wharf Mumbai.

Carangids include 25 genera and 140 species. They are abundant in shallow water up to 60 meter depth along both coasts supporting fishery almost round the year.The fishery is constituted mainly by Megalaspis cordyla, Decapterus russelli,Alepes djeddaba, Selar crumenopthalamus,Carnax spp,Caragoides spp, and scomberoides spp. in Maharastra

Plastic menace faced by fishers of Satpati, Maharashtra

Small conical stationary bag nets (Bokshi) are operated by artisanal fishers mostly in creeks, with strong tidal currents in certain regions of Maharashtra. The net is set using wooden pole (Khunt) driven at creek bottom against the flood or ebb tide. At Satpati, Bokshi nets are operated in the near shore creek for about 16 days in a month at a rate of 2 hauls per day. Here, fishermen are concerned about the increasing quantity of plastic debris entering their nets during fishing operations adversely affecting their livelihood