Allophane: a natural gel in volcanic soils with interesting environmental properties

Volcanic (allophanic) soils are interesting in terms of the control of the greenhouse effect and the knowledge of the porous features is of importance to understand the mechanism of C and N sequestration. These soils contain a peculiar clay: allophane aggregates quite close to the synthetic mineral gels aggregates. These volcanic materials behave as gels during drying with a large irreversible shrinkage that can modify the soil physical properties. Consequently, as for silica gels, we use the CO₂ supercritical drying procedure (SD) to control the drying step and to preserve the structural and textural properties of the soils. The experimental results show that the N and C content in the soils is clearly dependent on the allophane content. We also show that the textural properties, such as specific surface area, are higher for the supercritically dried samples, compared to the classically dried samples, and SAXS results confirm the preserving effect of the SD. With these data, we propose possible effects of the specific surface area on the C and N content of the allophanic soils.     

Newtonian limits of warp drive spacetimes

We find a class of warp drive spacetimes possessing Newtonian limits, which we then determine. The same method is used to compute Newtonian limits of the Schwarzschild solution and spatially flat Friedmann-Robertson-Walker cosmological models. This work was partially supported by FCT/POCTI/FEDER.     

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.     

Existence of standing waves for dirac fields with singular nonlinearities

We prove the existence of stationary states for nonlinear Dirac equations of the form (E) $$i\sum\limits_{\mu = 0}^3 {\gamma ^\mu \partial _\mu \psi - M\psi + F\left( {\bar \psi \psi } \right)\psi = 0,} $$ whereM>0 andF is a singular self-interaction. In particular, in the model case whereF(s)=?s ^?α, for some 0<α<1, and for every ω>M, there exists a solution of (E) of the form ψ(t, x)=e ^iωt?(x), wherex ₀=t andx=(x ₁,x ₂,x ₃), such that ? has compact support. IF 0<α<1/3, then ? is of classC ¹. If 1/3<α<1, then ? is continuously differentiable, except on some sphere {|x|=R}, where |??| is infinite.     

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.     

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.