Binary quadratic residue codes of length p + 1 produce via construction B and density doubling type II lattices like the Leech. Recently, quaternary quadratic residue codes have been shown to produce the same lattices by construction A modulo 4. We prove in a direct way the equivalence of these two constructions for p ~ 31. In dimension 32, we obtain an extremal lattice of type II not isometric...

Rational and algebraic Pad e approximants are applied to MMller-Plesset (MP) perturbation expansions of energies for a representative sample of atoms and small molecules. These approximants can converge to the full connguration-interaction result even when partial summation diverges. At order MP2 (the rst order beyond the Hartree-Fock approximation) best results are obtained from the rational 0...

ON THE BASIC CHARACTER OF RESIDUE CLASSES P . HILTON, J . HOOPER AND J . PEDERSEN Let t, b be mutually prime positive integers . We say that the residue class t mod b is basic if theie exists n such that ta -1 mod b; otherwise t is not basic. In this paper we relate the basic character of t mod b to the quadratic character of t modulo the prime factors of b. If all prime factors p of b satisfy ...

Strong asymptotics on the whole complex plane of a sequence of monic Jacobi polynomials P (αn,βn) n is studied, assuming that lim n→∞ αn n = A , lim n→∞ βn n = B , with A and B satisfying A > −1, B > −1, A + B < −1. The asymptotic analysis is based on the non-Hermitian orthogonality of these polynomials, and uses the Deift/Zhou steepest descent analysis for matrix Riemann-Hilbert problems. As a...

The quadratic matrix equation AX2 + B X +C = 0 in n ×n matrices arises in applications and is of intrinsic interest as one of the simplest nonlinear matrix equations. We give a complete characterization of solutions in terms of the generalized Schur decomposition and describe and compare various numerical solution techniques. In particular, we give a thorough treatment of functional iteration m...

For problems of linear control system synthesis, an apparatus of polynomial equations (for single-variable case) and of matrix polynomial equations (for multivariable case) was successfully developed in recent times, cf. [1]. In connection with quadratic criteria, we are led to equations of special type, containing an operation of conjugation ah-* a* representing a(s) i-> a( — s) for continuous...

in this paper, we solve the quadratic $alpha$-functional equations $2f(x) + 2f(y) = f(x + y) + alpha^{-2}f(alpha(x-y)); (0.1)$ where $alpha$ is a fixed non-archimedean number with $alpha^{-2}neq 3$. using the fixed point method and the direct method, we prove the hyers-ulam stability of the quadratic $alpha$-functional equation (0.1) in non-archimedean banach spaces.