A characterization of the central shell-focusing singularity in spherical gravitational collapse

We give a characterization of the central shell-focusing curvature singularity that can form in the spherical gravitational collapse of a bounded matter distribution obeying the dominant energy condition. This characterization is based on the limiting behaviour of the mass function in the neighbourhood of the singularity. Depending on the rate of growth of the mass as a function of the area radius R, the singularity may be either covered or naked. The singularity is naked if this growth rate is slower than R, covered if it is faster than R, and either naked or covered if the growth rate is same as R.Comment: 12 pages, Latex, significantly revised version, including change of title. Revised version to appear in Classical and Quantum Gravit

Impact of Organic Farming on Yield and Quality of BASMATI Rice and Soil Properties

The management of soil organic matter is critical to maintain a productive organic farming system. No one source of nutrient usually suffices to maintain productivity and quality control in organic system. In addition, the inputs to supplement nutrient avail-ability are often not uniform presenting additional challenges in meeting the nutrient requirement of crops in organic systems. With this concept, a field experiment was conducted at the research farm of Indian Agricultural Research Institute, New Delhi, India during 2003-06 in rice-wheat-green gram cropping system. In this experiment, different treatments comprising organic amendments such as Blue Green Algae (BGA) 15kg/ha, Azolla 1.0 tonne/ha, Vermicompost and Farm Yard Manure (FYM) 5.0 tonne/ha each applied alone or in combination were tested in organic crop production. These treatments were compared with absolute control (N0P0K0) and recommended dose of chemical fertilizer (N80P40K40). In wheat crop Azotobacter replaced Azolla, but other treatments remained same. For rice, a scented variety ‘Pusa Basmati 1’ and for wheat and green gram HYVs were taken. Biomass of green gram was incorporated in soil after picking of pods and wheat was sown using zero tillage practice. The obser-vations on grain yield, contents of Fe, Zn, Mn and Cu in rice grains, insect pest inci-dence, soil nutrients and microbial activity were taken. Results revealed a significant enhancement in grain yield of rice over absolute control due to the application of different organic amendments applied alone or in combina-tions. Rice grain yield increased by 114 to 116.8% over absolute control when all the 4 organic amendments were applied altogether. The rice grain yield (4.0 t ha-1) obtained under combined application of four organic amendments was at par with the yield recorded under recommended dose of chemical fertilizer application. An interesting observation recorded was that there was no serious attack of any insect pest or dis-ease in organically grown crop. Soil microbial population (Actinomycetes, Bacteria, Fungi and BGA) enhanced due to the application of organic amendments in compari-son to absolute control as well as recommended fertilizer application that in turn re-sulted in a notable enhancement in soil dehydrogenase and phosphatase enzyme activity. Soil organic carbon and available phosphorus contents were also found to be significantly increased due to organic farming practice over control as well as chemical fertilizer application. Rice grain analysis for nutrients viz. Fe, Zn, Mn and Cu showed a significant increase in Fe and Mn content in the treatments having 2 or more organic amendments over control. Zn and Cu content also increased but the increment was significant with combined application of 3 or 4 organic amendments. The study revealed that addition of four organic amendments viz. BGA, Azolla, FYM and Vermicompost could give the optimum yield (4.05 t/ha) of organic Basmati rice and improve grain and soil quality

Crystallization of Simple Fluids: Relative Stability of f.c.c. and b.c.c Structures

A free-energy functional for a crystal that contains both the symmetry conserved and symmetry broken parts of the direct pair correlation function is developed. The free-energy functional is used to investigate the crystallization of fluids interacting via the inverse power potential ; $u(r)=\epsilon {(\sigma/r)}^n$. In agreement with simulation results we find that for $n=12$ the freezing is into close packed f.c.c structure while for soft repulsions $(n\leq 6)$ b.c.c phase is more stable.Comment: 9 pages, 2 figure

Properties of KCo2_2As2_2 and Alloys with Fe and Ru: Density Functional Calculations

Electronic structure calculations are presented for KCo$_2$As$_2$ and alloys with KFe$_2$As$_2$ and KRu$_2$As$_2$. These materials show electronic structures characteristic of coherent alloys, with a similar Fermi surface structure to that of the Fe-based superconductors, when the $d$ electron count is near six per transition metal. However, they are less magnetic than the corresponding Fe compounds. These results are discussed in relation to superconductivity.Comment: 5 page