We review the properties of classical p-brane solutions to supergravity theories, i.e. solutions that may be interpreted as Poincaré-invariant hyperplanes in space-time. Topics covered include the distinction between elementary/electric and soli-tonic/magnetic solutions, examples of singularity and global structure, relations between mass densities, charge densities and the preservation of unbr...

We use a diagonal matrix for getting the Binet’s formula for k-Pell sequence Also the n power of the generating matrix for k-Pell-Lucas sequence is established and basic properties involving the determinant allow us to obtain its Cassini’s identity. Mathematics Subject Classification: 11B37, 05A15, 11B83.

A novel method of function minimization that combines the power of the diagonal approximation to the normal matrix with conjugate directions is described. This method approaches closer to the local minimum than the methods that are commonly used in macromolecular refinement. The weakness of the current methods are analyzed to explain the advantage of the conjugate-direction method.

We describe a divide-and-conquer tridiagonalizationapproach for matrices with repeated eigenvalues. Our algorithmhinges on the fact that, under easily constructivelyveriiable conditions,a symmetricmatrix with bandwidth b and k distinct eigenvalues must be block diagonal with diagonal blocks of size at most bk. A slight modiication of the usual orthogonal band-reduction algorithm allows us to re...

The ScaLAPACK library contains a pair of routines for solving banded linear systems which are strictly diagonally dominant by rows. Mathematically, the algorithm is complete block cyclic reduction corresponding to a particular block partitioning of the system. In this paper we extend Heller’s analysis of incomplete cyclic reduction for block tridiagonal systems to the ScaLAPACK case. We obtain ...

SSOR preconditioning of fermion matrix inversions which is parallelized using a locally-lexicographic lattice sub-division has been shown to be very efficient for standard Wilson fermions. We demonstrate here the power of this method for the Sheikholeslami-Wohlert improved fermion action and for a renormalization group improved action incorporating couplings of the lattice fermion fields up to ...