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

Calculation of renormalized viscosity and resistivity in magnetohydrodynamic turbulence

A self-consistent renormalization (RG) scheme has been applied to nonhelical magnetohydrodynamic turbulence with normalized cross helicity $\sigma_c =0$ and $\sigma_c \to 1$. Kolmogorov's 5/3 powerlaw is assumed in order to compute the renormalized parameters. It has been shown that the RG fixed point is stable for $d \ge d_c \approx 2.2$. The renormalized viscosity $\nu^*$ and resistivity $\eta^*$ have been calculated, and they are found to be positive for all parameter regimes. For $\sigma_c=0$ and large Alfv\'{e}n ratio (ratio of kinetic and magnetic energies) $r_A$, $\nu^*=0.36$ and $\eta^*=0.85$. As $r_A$ is decreased, $\nu^*$ increases and $\eta^*$ decreases, untill $r_A \approx 0.25$ where both $\nu^*$ and $\eta^*$ are approximately zero. For large $d$, both $\nu^*$ and $\eta^*$ vary as $d^{-1/2}$. The renormalized parameters for the case $\sigma_c \to 1$ are also reported.Comment: 19 pages REVTEX, 3 ps files (Phys. Plasmas, v8, 3945, 2001

INPOP new release: INPOP13b

Based on the use of MESSENGER radiotracking data in the construction of new Mercury ephemerides (Verma et al. 2014) a new planetary ephemerides INPOP13b was built including Mercury improvements but also improvements on the Mars orbit and on the tie of INPOP planetary ephemerides to ICRF in general.Comment: INPOP sources available http://www.imcce.fr/inpo

Universal Scaling in Mixing Correlated Growth with Randomness

We study two-component growth that mixes random deposition (RD) with a correlated growth process that occurs with probability p. We find that these composite systems are in the universality class of the correlated growth process. For RD blends with either Edwards-Wilkinson of Kardar-Parisi-Zhang processes, we identify a nonuniversal parameter in the universal scaling in p.Comment: 4 pages, 6 figures, 11 references; under revie