9,143 research outputs found
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
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