Fast computation of a rational point of a variety over a finite field

We exhibit a probabilistic algorithm which computes a rational point of an absolutely irreducible variety over a finite field defined by a reduced regular sequence. Its time-space complexity is roughly quadratic in the logarithm of the cardinality of the field and a geometric invariant of the input system. This invariant, called the degree, is bounded by the Bézout number of the system. Our algorithm works for fields of any characteristic, but requires the cardinality of the field to be greater than a quantity which is roughly the fourth power of the degree of the input variety.

     

A simple model for magnetic after-effects in magnetite at room temperature

Magnetic after-effects in vacancy-doped magnetite at room temperature are considered on the basis of a statistical thermodynamic treatment. In this paper we study the kinetics of a very small vacancy concentration distributed on the four non-equivalent octahedral sites of the inverse spinel structure. It is to be noted that satisfactory agreement is found between recent experimental results and the theoretical model.     

On conservative approximation by linear polynomial operators an extension of the Bernstein's operator

In this work we study linear polynomial operators preserving some consecutive i-convexities and leaving invariant the polynomials up to a certain degree. First, we study the existence of an incom patibility between the conservation of certain i-convexities and the invariance of a space of polynomials. Interpolation properties are obtained and a theorem by Berens and DeVore about the Bernstein's operator is extended. Finally, from these results a generalized Bernstein's operator is obtained. This work was supported by Junta de Andalucia. Grupo de investigación: Matemática Aplicada. Código: 1107     

Some Questions of Heinrich on Ultrapowers of Locally Convex Spaces

In this note we treat some open problems of Heinrich on ultrapowers of locally convex spaces. In section 1 we investigate the localization of bounded sets in the full ultrapower of a locally convex space, in particular the coincidence of the full and the bounded ultrapower, mainly concentrating in the case of (DF)-spaces. In section 2 we provide a partial answer to a question of Heinrich on commutativity of strict inductive limits and ultrapowers. In section 3 we analyze the relation between some natural candidates for the notion of superreflexivity in the setting of Fréchet spaces. We give an example of a Fréchet-Schwartz space which is not the projective limit of a sequence of superreflexive Banach spaces.     

Complex surfaces polarized by an ample and spanned line bundle of genus three

Let X be a complex connected projective nonsingular algebraic surface endowed with an ample line bundle L, which is spanned by its global sections. Pairs (X, L) as above, with sectional genus g(X, L)=1+(L·(K _X L))/2=3 are classified by means of the main techniques of adjunction theory.     

Geometries of type Cn and F4 with flag-transitive automorphism groups

Let be a finite thick geometry of type C_n (n 4) or F₄. We prove that is a building iff Aut() is flag-transitive.     

New extraction method for the analysis of linear alkylbenzene sulfonates in marine organisms. Pressurized liquid extraction versus Soxhlet extraction

A new method has been developed for the determination of linear alkylbenzene sulfonates (LAS) from various marine organisms, and compared with Soxhlet extraction. The technique applied includes the use of pressurized liquid extraction (PLE) for the extraction stage, preconcentration of the samples, purification by solid-phase extraction (SPE) and analysis by liquid chromatography with fluorescence detection. The spiked concentrations were added to the samples (wet mass of the organisms: Solea senegalensis and Ruditapes semidecussatus), which were homogenized and agitated continuously for 25 h. The samples were extracted by pressurized hot solvent extraction using two different extraction temperatures (100 and 150 degrees C) and by traditional Soxhlet extraction. The best recoveries were obtained employing pressurized hot solvent extraction at 100 degrees C and varied in the range from 66.1 to 101.3% with a standard deviation of between 2 and 13. Detection limit was between 5 and 15 microg kg(-1) wet mass using HPLC-fluorescence detection. The analytical method developed in this paper has been applied for LAS determination in samples from a Flow-through exposure system with the objective of measuring the bioconcentration of this surfactant.     

Crystal and molecular structure of nitrosyl(1,10-phenanthroline)-bis(triphenylphosphine)iridium(I) Dihexafluorophosphate, [Ir(NO)(phen)(PPh3)2][PF6]2

Summary The structure of [Ir(NO)(phen)(PPh₃)₂][PF₆]₂ has been determined from x-ray diffractometer data. The compound crystallizes in space groupPnam with four molecules in a unit cell witha = 19.924(12),b = 14.793(9) andc = 16.348(9) A. Full-matrix least-squares refinement has led to a final R value of 0.061 for the 4796 observed reflections. The structure consists of well-separated ions, and the geometry around the metal is trigonal bipyramidal with nitrosyl and bidentate 1,10-phenanthroline (in spite of the very narrow bite angle of 75.8°) ligands occupying the equatorial positions and the triphenylphosphine ligands the axial positions. The cation has an imposed crystallographicm symmetry. Important bond lengths are as follows: Ir-P, 2.391(3): Ir-N (nitrosyl) 1.700(12): Ir-N (1,10-phenanthroline) 2.103(12) and 2.142(11): N-O, 1.201(18)A. The nitrosyl ligand is linear [Ir-N-O = 179.9(9)°] so that this complex can be formulated as an NO⁺ complex of iridium(I).     

Synthesis and properties of perchlorobi-9-fluorenylidene,An exceptionally twisted ethylene

The synthesis and properties of perchlorobi-9-fluorenylidene, a highly twisted ethylene, are reported. It is a diamagnetic chlorocarbon.