Grothendieck-Serre formula and bigraded Cohen-Macaulay Rees algebras

The Grothendieck-Serre formula for the difference between the Hilbert function and Hilbert polynomial of a graded algebra is generalized for bigraded standard algebras. This is used to get a similar formula for the difference between the Bhattacharya function and Bhattacharya polynomial of two m-primary ideals I and J in a local ring (A,m) in terms of local cohomology modules of Rees algebras of I and J. The cohomology of a variation of the Kirby-Mehran complex for bigraded Rees algebras is studied which is used to characterize the Cohen-Macaulay property of bigraded Rees algebra of I and J for two dimensional Cohen-Macaulay local rings.Comment: 23 page

Inherent properties of binary tetrahedral semiconductors

A new approach utilising the concept of ionic charge theory has been used to explain the inherent properties such as lattice thermal conductivity and bulk modulus of 3,5 and 2,6 semiconductors. The lattice thermal conductivity of these semiconductors exhibit a linear relationship when plotted on a log scale against the nearest neighbour distance but fall on two straight lines according to the product of the ionic charge of the compounds. On the basis of this result a simple relationship of lattice thermal conductivity with bulk modulus is proposed and used to estimate the bulk modulus of these semiconductors. A fairly good agreement has been found between the experimantal and calculated values of these parameters for zinc blende structured solids.Comment: 6 pages, 19 reference

Initial Condition Sensitivity of Global Quantities in Magnetohydrodynamic Turbulence

In this paper we study the effect of subtle changes in initial conditions on the evolution of global quantities in two-dimensional Magnetohydrodynamic (MHD) turbulence. We find that a change in the initial phases of complex Fourier modes of the Els\"{a}sser variables, while keeping the initial values of total energy, cross helicity and Alfv\'{e}n ratio unchanged, has a significant effect on the evolution of cross helicity. On the contrary, the total energy and Alfv\'{e}n ratio are insensitive to the initial phases. Our simulations are based on direct numerical simulation using the pseudo-spectral method.Comment: 12 pages LateX, 11 ps figures. Accepted for publication by Physics of Plasma