On the number of curves of genus 2 over a finite field

In this paper we compute the number of curves of genus 2 defined over a finite field k of odd characteristic up to isomorphisms defined over k; the even characteristic case is treated in an ongoing work (G. Cardona, E. Nart, J. Pujolàs, Curves of genus 2 over field of even characteristic, 2003, submitted for publication). To this end, we first give a parametrization of all points in , the moduli variety that classifies genus 2 curves up to isomorphism, defined over an arbitrary perfect field (of zero or odd characteristic) and corresponding to curves with non-trivial reduced group of automorphisms; we also give an explicit representative defined over that field for each of these points. Then, we use cohomological methods to compute the number of k-isomorphism classes for each point in .     

On the Cartan–Jacobson Theorem

The well-known Cartan–Jacobson theorem claims that the Lie algebra of derivations of a Cayley algebra is central simple if the characteristic is not 2 or 3. In this paper we have studied these two cases, with the following results: if the characteristic is 2, the theorem is also true, but, if the characteristic is 3, the derivation algebra is not simple. We have also proved that in this last case, there is a unique nonzero proper seven-dimensional ideal, which is a central simple Lie algebra of type A₂, and the quotient of the derivation algebra modulo this ideal turns out to be isomorphic, as a Lie algebra, to the ideal itself. The original motivation of this work was a series of computer-aided calculations which proved the simplicity of derivation algebras of Cayley algebras in the case of characteristic not 3. These computations also proved the existence of a unique nonzero proper ideal (which turns out to be seven-dimensional) in the algebra of derivations of split Cayley algebras in characteristic 3.     

2-Dimension from the Topological Viewpoint

In this paper we study the 2-dimension of a finite poset from the topological point of view. We use homotopy theory of finite topological spaces and the concept of a beat point to improve the classical results on 2-dimension, giving a more complete answer to the problem of all possible 2-dimensions of an n-point poset.      

Large area bolometers for millimeter-wave power calibration

An accurate monolithic power meter has been developed for millimeter-wave applications. The detector is a large-area Bismuth bolometer, integrated on a fused-Quartz substrate. It simply measures the temperature change caused by the absorption of millimeter-wave radiation. The power meter is simple to fabricate, inexpensive, and can be easily calibrated using a low-frequency network. The measured responsivity for a 50 bolometer, with an area of 1×1cm, at a bias of 1V. and a video modulation of 100Hz, is 1mV/W. The noise spectrum exhibits a 1/f rolloff till 1KHz, and is limited by the Johnson noise for higher frequencies. The NEP of the detector is 3WHz^–1/2 at a video modulation of 1KHz. It is possible to decrease the current NEP by fabricating bolometers with higher responsivities. Possible application areas are absolute power calibration and localized power density measurements at millimeter and submillimeter wavelengths.     

Influence of Temperature and Time on the Stability of Silver in Silica Sol-Gel Glasses

The darkening of silica sol-gel glasses doped with 0.05 mol% silver was studied. Six sols were prepared from TEOS and silver nitrate. Different additives were used, to influence the chemical and physical states of silver: oxidizing or reducing agents (H₂O₂, As₂O₅), colloid stabilizer (sodium citrate) and network modifiers (Li₂O, CaO). Sols were gelified at 60°C and densified at 600°C. The samples without additives and those prepared with H₂O₂ at room temperature even if they were protected from light. With increased temperature, the darkening became samples were heated above, 400°C, reversible bleaching took place. This darkening-bleaching is of thermal nature (“thermochromic effect”) and seems to be determined by a reversible aggregation-disaggregation of tiny silver particles. The presence of sodium citrate, as an additive delayed the darkening effect and the presence of CaO delayed it even further. Lithium oxide inhibited it totally.     

Multistep energy transfer in single molecular photonic wires

We demonstrate the synthesis and spectroscopic characterization of an unidirectional photonic wire based on four highly efficient fluorescence energy-transfer steps (FRET) between five spectrally different chromophores covalently attached to double-stranded DNA. The DNA-based modular conception enables the introduction of various chromophores at well-defined positions and arbitrary interchromophore distances. While ensemble fluorescence measurements show overall FRET efficiencies between 15 and 30%, single-molecule spectroscopy performed on four spectrally separated detectors easily uncovers subpopulations that exhibit overall FRET efficiencies of up to approximately 90% across a distance of 13.6 nm and a spectral range of approximately 200 nm. Fluorescence trajectories of individual photonic wires show five different fluorescence intensity patterns which can be ascribed to successive photobleaching events.     

Determination of lithium in human serum by electrothermal atomic absorption spectrometry

An efficient method was developed for the determination of nanogram levels of lithium in biological samples. Serum samples from human subjects from southeastern Spain, treated or not treated with lithium carbonate, were analyzed by electrothermal atomic absorption spectrometry. The samples were previously treated with a matrix modifier consisting of 0.1% Triton X-100 and injected through a graphite tube with L'vov platform. The Li concentrations measured by the procedure described for the 3 certified reference samples used were not significantly different (p > 0.05) than certified levels. Sample recoveries and variability during several days, with coefficients of variation from 4.00 to 14.8%, demonstrated the reliability and accuracy of this technique. Mean Li concentration determined in the serum of individuals with psychiatric disorders treated with Li (n = 117, 5.077 +/- 1.795 microg Li/mL) was significantly higher (p < 0.001) than that in individuals not treated with Li (n = 24, 1.902 +/- 2.054 ng Li/mL).     

Reactivity of 3d transition metal cations in diethylene glycol solutions. Synthesis of transition metal ferrites with the structure of discrete nanoparticles complexed with long-chain carboxylate anions

Study of the reactivity of 3d transition metal cations in diethylene glycol solutions revealed several key features that made it possible to develop a new method for synthesis of the nanocrystalline transition metal ferrites. The 3-7 nm particles of [MFe2O4]n[O2CR]m, where M = Mn, Fe, Co, Ni, and Zn, ligated on their surface with long-chain carboxylate anions, have been obtained in an isolated yield of 75-90%. The key features are the following. Complexation of the first-row transition metal cations with diethylene glycol at a presence of alkaline hydroxide is sufficient to enable control over the rate of their hydrolysis. The reaction of hydrolysis leads to the formation of metal oxide nanocrystals in colloidal solution. The nanoparticles growth is terminated by an added long-chain carboxylic acid, which binds to their surface and acts as a capping ligand. The isolated nanocrystalline powders are stable against agglomeration and highly soluble in nonpolar organic solvents.