Curvature calculations for a class of homogeneous operators

For an operator $T$ in the class ${\mathrm B}_n(\Omega)$, introduced in \cite{CD}, the simultaneous unitary equivalence class of the curvature and the covariant derivatives up to a certain order of the corresponding bundle $E_T$ determine the unitary equivalence class of the operator $T$. In the paper \cite{CD2}, the authors ask if there exists some pair of inequivalent oprators $T_1$ and $T_2$ for which the simultaneous unitary equivalence class of the curvature along with all the covariant derivatives coincide except for the derivative of the highest order. Here we show that some of the covariant derivatives are necessary to determine the unitary equivalence class of the operators in ${\mathrm B}_n(\Omega)$. Our examples consist of homogeneous operators. For homogeneous operators, the simultaneous unitary equivalence class of the curvature and all its covariant derivatives are determined from the simultaneous unitary equivalence class of these at 0. This shows that it is enough to calculate all the invariants and compare them at just one point, say 0. These calculations are then carried out in number of examples

Sustainable Agriculture And Food Security In West Bengal

Cropping intensity in West Bengal is 185%, one of the highest in our country. Intensity of fertilizer use has been consistently increasing. The state ranked seventh in fertilizer use (172 Kg) per hectare of gross cropped area by size of holding in 2010-11. There is an inverse relationship between farm size and intensity of fertilizer use. Soil recharging pulse crops occupied slightly more than 3% of the gross cropped area under rice cultivation in 2009-10. Mono-cropping, indiscriminate and increasing trend in use of pesticides, increasing cost of inputs and labour and changes in climate change has resulted in agrarian stress. FAO in its guide book “Save and Grow”, 2011 points out that the present paradigm of intensive crop production cannot meet the challenges of the new millennium. Dr MS Swaminathan recommends for evergreen revolution for increase in productivity in perpetuity, without ecological harm. There is growing consciousness about benefits of organic agriculture as resilient and can ensure true food security in long run, i.e. sufficient, chemical free (safe) and nutritious food to maintain a healthy and active life. More and more farmers are adopting sustainable agriculture and the area under organic farming increased many folds from 42 thousand hectares in 2003-04 to 4430 thousand hectares of cultivated land under certification in 2010-11, accounting for 6 lakhs farmers, mainly small and marginal. The population of India increased at an exponential rate of 1.64% year on year (YoY) during 2001-11 and for West Bengal it’s 1.31%. On continuing with conventional production, the per capita availability of cereals would be 390 grams per day in 2032 for West Bengal and 568 grams per day for India. The adjusted R2 of fit is 78% for West Bengal and 96% for India. There is a steady decline in growth of cereal production in India and the decline is more striking in West Bengal. On converting 5% of the total cultivated land under cereals production in West Bengal from conventional into sustainable agricultural practices for the next 20 years, per capita availability of cereals would be 450 grams for West Bengal and 564 grams for India in 2032 (see Figure). Under sustainable methods, cereal production was reduced by 30% on first year and increased by 10% from next year upto three years, thereon cereal production was increased by 3% YoY. Besides, the cost of production under sustainable agricultural methods is comparatively much less than conventional agriculture. Support Needed for Promoting Sustainable Agriculture in West Bengal: 1. Review the present state agricultural policies and subsidies, especially those that act as barrier to development of sustainable agriculture 2. Favourable policy support – to integrate sustainable agriculture as state mission with explicit policy and strategic plan for extension, adequate funding support and set goals 3. Create an innovation Centre of Excellence in West Bengal to promote sustainable agriculture development, particularly in Eastern India. The centre may be setup in strategic collaboration with state government, national and international institutions, universities involving experts and farmers for research and innovation, PG studies, training, extension, knowledge repository and advocacy 4. Support innovation, capacity building and information to farmers 5. Ensure availability of organic inputs: seeds, bio-fertilizers and bio-pesticides etc. 6. Ensure availability of farm advisory services and innovative institutional and funding support for organic certification, labeling and inspection 7. Provide market support 8. Support and create consumer awareness 9. Integrate and promote the efforts of NGOs, private organizations and entrepreneurs

Vacuum Stability Constraints on the Minimal Singlet TeV Seesaw Model

We consider the minimal seesaw model in which two gauge singlet right handed neutrinos with opposite lepton numbers are added to the Standard Model. In this model, the smallness of the neutrino mass is explained by the tiny lepton number violating coupling between one of the singlets with the standard left-handed neutrinos. This allows one to have the right handed neutrino mass at the TeV scale as well as appreciable mixing between the light and heavy states. This model is fully reconstructible in terms of the neutrino oscillation parameters apart from the overall coupling strengths. We show that the overall coupling strength $y_\nu$ for the Dirac type coupling between the left handed neutrino and one of the singlets can be restricted by consideration of the (meta)stability bounds on the electroweak vacuum. In this scenario the lepton flavor violating decays of charged leptons can be appreciable which can put further constraint on $y_\nu$, for right-handed neutrinos at TeV scale. We discuss the combined constraints on $y_\nu$ for this scenario from the process $\mu \rightarrow e \gamma$ and from the consideration of vacuum (meta)stability constraints on the Higgs self coupling. We also briefly discuss the implications for neutrinoless double beta decay and possible signatures of the model that can be expected at colliders.Comment: One loop effective potential due to heavy neutrino included, 20 pages, 9 figure

Electric propulsion device for high power applications

An electric propulsion device is disclosed having an anode and a cathode. The propulsion device includes a discharge annulus having the anode adjacent an end region thereof. At least one inlet aperture is adjacent the anode, the aperture(s) having propellant gas flow therethrough into the discharge annulus. The propellant gas has an ionization potential. Opposed, dielectric walls define the annulus, with at least one of the opposed dielectric walls having pores therein, the pores having cooling gas flow therethrough into the discharge annulus and substantially adjacent the opposed dielectric wall(s). The cooling gas has an ionization potential higher than the ionization energy of the propellant gas. The cooling gas is adapted to substantially prevent at least one of secondary electron emission and sputtering of the dielectric walls

Recovery Improvement of Fine Iron Ore Particles by Multi Gravity Separation

Conventional gravity separation process of iron mineral fines is not very effective. In present work Multi Gravity Separation (MGS) process has been studied. This study was performed on a low-grade iron ore namely goethiticlateritic ore (GLO) from Eastern India. Detailed mineralogical, physical and chemical characteristics of a goethiticlateritic iron ore showed that the sample contained porous and friable oxides and hydroxides of iron. The ore sample had a feed grade of 54.43% total Fe, 9.27% SiO2 and 8.02% Al2O3. Hematite and goethite are main iron-bearing minerals while kaolinite and gibbsite are the major gangue mineral constituents. Considering the characterization data, these ores were ground separately to three size fractions, namely -300 μm, -250 μm and -150 μm sizes and subjected to flowing film concentration in Wilfley Table. As revealed by the liberation study, higher concentration was obtained by the processing of -150 μm crushed sample. The grade of the ore was improved from 54.43% Fe to 65.71% Fe. However, significant amount of fine iron ore particles were lost during the processing of -150 μm size ore, because it is not very effective for particles less than 15 μm. Thus, fine hematite and goethite particles are usually not recovered resulting in the loss of valuable iron ore fines. To recover this fine, Multi Gravity Separator was used in place of Wilfley Table and was found to be effective in reducing loss of fine iron particles and increasing the grade of the concentrate. The MGS process improved the Fe from 54.43% to 66.5% along with decreasing the alumina from 8.02% to 1.17%

Magnetic Separation - Principles and Application in Beneficiation of Iron Ores

Magnetic Separation is one of the physical concentration processes that utilizes the differences in magnetic properties of various minerals present in the ore body. The magnetic fraction may be valuable or gangue depending upon its end use in a particular process and so also the non-magnetic fraction, e.g., separation of magnetite (magnetic) from quartz (non-magnetic), separation of tin bearing mineral cassiterite (non-magnetic) from magnetite (magnetic) impurity etc