We generalize the Gauss algorithm for the reduction of two–dimensional lattices from the l2-norm to arbitrary norms and extend Vallée’s analysis [J. Algorithms 12 (1991), 556-572] to the generalized algorithm.

Abstract We consider the critical spread-out contact process in Z with d ≥ 1, whose infection range is denoted by L ≥ 1. The two-point function τt(x) is the probability that x ∈ Z is infected at time t by the infected individual located at the origin o ∈ Z at time 0. We prove Gaussian behavior for the two-point function with L ≥ L0 for some finite L0 = L0(d) for d > 4. When d ≤ 4, we also perfo...

The generalized Higham matrix is a complex symmetric matrix A = B + iC, where both B ∈ Cn×n and C ∈ Cn×n are Hermitian positive definite, and i = √−1 is the imaginary unit. The growth factor in Gaussian elimination is less than 3 √ 2 for this kind of matrices. In this paper, we give a new brief proof on this result by different techniques, which can be understood very easily, and obtain some ne...

We solve the Kato problem for divergence form elliptic operators whose heat kernels satisfy a pointwise Gaussian upper bound. More precisely, given the Gaussian hypothesis, we establish that the domain of the square root of a complex uniformly elliptic operator L = −div(A∇) with bounded measurable coefficients in Rn is the Sobolev space H1(Rn) in any dimension with the estimate ‖ √ Lf‖2 ∼ ‖∇f‖2...

G aussian elimination is universally known as “the” method for solving simultaneous linear equations. As Leonhard Euler remarked, it is the most natural way of proceeding (“der natürlichste Weg” [Euler, 1771, part 2, sec. 1, chap. 4, art. 45]). Because Gaussian elimination solves linear problems directly, it is an important technique in computational science and engineering, through which it ma...

We show that the Sudakov factor from the resummation of double logarithms ln(s/k T ) contained in the distribution functions is responsible for the kT smearing mechanism employed in the next-to-leading-order QCD (αα 2 s) calculations of direct photon production. s is the center-of-mass energy, and kT the transverse momentum carried by a parton in a colliding hadron. This factor exhibits the app...

În această lucrare se prezintă o metodă eficientă de implementare a eliminării Gaussiene pentru o matrice de dimensiuni n·m (m≥n), folosind o arhitectură SIMD ce constă dintr-o matrice de n·m procesoare. Algoritmul descris constă în 2·n-1=O(n) iteraţii, oferind astfel o creştere de viteză optimă faţă de versiunea serială. O particularitate a algoritmului este că nu necesită realizarea operaţiei...

2 Discrete vector fields. 4 2.1 W-contractions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 Algebraic discrete vector fields. . . . . . . . . . . . . . . . . . . . . 6 2.3 V-paths and admissible vector fields. . . . . . . . . . . . . . . . . . 7 2.4 Reductions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.4.1 Definition. . . . . . . . . . . . . . . . . ...