A note on the acyclicity of the Koszul complex of a module

We prove the vanishing of the Koszul homology group H _μ(Kos(M)_μ), where μ is the minimal number of generators of M. We give a counterexample that the Koszul complex of a module is not always acyclic and show its relationship with the homology of commutative rings.     

A topological characterization of classical BRST cohomology

The recent identification of classical BRST cohomology with the vertical cohomology of a certain fibration is used to compute it in terms of the classical observables and the topology of the gauge orbits. When the gauge orbits are compact and orientable, a duality theorem is exhibited.     

Interpolatory properties of best rationalL 1-approximations

In this paper the distribution of the zeros of the error function for bestL ₁-approximation by rational functions fromR _n,m is considered. It is shown that the maximal distance between such zeros isO(1/(n–m)), ifn > m.Communicated by Edward B. Saff.     

A confidence interval for the slope of a truncated regression

Summary Bhattacharya, Chernoff and Yang (1983) proposed a nonparametric estimate for the slope of a regression lineY = _o X + V subjected to the truncationYy ₀. The estimate corresponds to the zero-crossing of a random functionS _n (). In this paper an estimate for the asymptotic variance of the estimate of the slope is proposed and the rate of convergence is given. The proofs rest heavily on the local behavior ofS _n () in the neighborhood of the true value _o.     

On the permanence of the null character of Maxwell fields

A critical review of known results about the permanence conditions for the null character of the solutions to the (vacuum) Maxwell equations, is presented. Concomitants of the electromagnetic field and the metric tensor are constructed, which give the principal directions of the field in covariant form. The known permanence conditions are generalized in order to includeall the (local) null fields; the above concomitants allow these conditions to be explicitly formulated in terms of the electromagnetic field.Supported in part by Conselleria de Cultura, Educació i Ciència de la Generalitat Valenciana.     

Determination of gallium by anodic stripping square-wave voltammetry Detection of a GaZn intermetallic compound and its destruction by Sb in an NaSCNNaClO(4) supporting electrolyte

Reproducibility for successive determinations with a hanging mercury drop electrode is assessed in relation to solution stirring, drop size and back-diffusion to the mercury thread. The effect of experimental parameters such as drop size, deposition time and gallium concentration on the observed stripping current is investigated. The interference of zinc present in a 0.5M NaSCN + 4.2M NaClO(4) supporting electrolyte on the gallium detection limit and calibration plots is described. Formation of an intermetallic compound with a Zn:Ga ratio of 2:3 and its destruction by co-deposition of zinc with Sb are reported. A detection limit of 10(-8)M gallium was obtained in the presence of 10(-5)M Sb(III).