A Bonnet theorem for isometric immersions into products of space forms

We prove a Bonnet theorem for isometric immersions of semi-Riemannian manifolds into products of semi-Riemannian space forms. Namely, we give necessary and sufficient conditions for the existence and uniqueness (up to an isometry of the ambient space) of an isometric immersion of a semi-Riemannian manifold into a product of semi-Riemannian space forms.     

Euclidean hypersurfaces with genuine deformations in codimension two

We classify hypersurfaces of rank two of Euclidean space ${\mathbb{R}^{n+1}}$ that admit genuine isometric deformations in ${\mathbb{R}^{n+2}}$ . That an isometric immersion ${\hat{f}\colon M^n \to \mathbb{R}^{n+2}}$ is a genuine isometric deformation of a hypersurface ${f\colon M^n\to\mathbb{R}^{n+1}}$ means that ${\hat f}$ is nowhere a composition ${\hat f=\hat F\circ f}$ , where ${\hat{F} \colon V\subset \mathbb{R}^{n+1} \to\mathbb{R}^{n+2}}$ is an isometric immersion of an open subset V containing the hypersurface.     

An Anionic Ring Locked into an Anionic Axle: A Metastable Rotaxane with Chemically Activated Electrostatic Stoppers

The use of the electrostatic stoppers concept in the field of mechanically interlocked molecules is reported; these stoppers are chemically sensitive end groups on a linear guest molecule that allows for the conversion of a pseudo-rotaxane species into a rotaxane complex by a change in the medium acidity. The chemical stimulus causes the appearance of negative charges on both ends of the linear component, passing from cationic to anionic, and causing a significant ring-to-axle electrostatic repulsion. This phenomenon has two different and simultaneous effects: 1) destabilizes the complex as a consequence of confining an anionic ring into an anionic axle, and 2) increases the dissociation energy barrier, thus impeding ring extrusion. This newly formed metastable rotaxane species is resistant to solvent and temperature effects and performs as a two-state degenerated molecular shuttle in solution.     

An analysis of X-ray absorption spectra in the XANES region of platinum-based electrocatalysts for low-temperature fuel cells

The knowledge of the electronic state of Pt-based electrocatalysts used in low temperature fuel cells is very important for the understanding of the activity of the material. Near-edge X-ray absorption spectroscopy (XANES), a particular region of the X-ray absorption spectra (XAS), can provide the desired information, but the analysis is not straightforward, particularly for the non-specialist. Mansour et al. (J. Phys. Chem., 88:2330, 1984) and Shukla et al. (J. Electroanal. Chem., 563:181, 2004) presented methods to obtain information on electronic states from XANES spectra. In this work, procedures to implement the two methods are presented in detail and applied to XANES results for Pt₂Sn₁/C and Pt/C electrocatalysts prepared in this laboratory. The scope and limitations of the two methods are also discussed. The results show that the presence of Sn in the Pt₂Sn₁/C material promotes a partial filling of the Pt 5d band, in comparison to Pt/C, which contributes to explain the better activity of the bimetallic material. This paper is dedicated to Prof. Francisco Nart, in memoriam.     

Modeling the Kinetics of Complex Systems: Enzymatic Hydrolysis of Lignocellulosic Substrates

Lignocellulosic biomass is mainly composed of cellulose, hemicellulose, and lignin. Fuzzy logic, in turn, is a branch of many-valued logic based on the paradigm of inference under vagueness. This paper presents a methodology, based on computational intelligence, for modeling the kinetics of a complex reactional system. The design of a fuzzy interpolator to model cellulose hydrolysis is reported, within the perspective of applying kinetic models in bioreactor engineering. Experimental data for various types of lignocellulosic materials were used to develop the interpolator. New experimental data from the enzymatic hydrolysis of a synthetic substrate, on the other hand, were used to validate the methodology. The accuracy of the results indicates that this is a promising approach to extend the application of models fitted for specific situations to different cases, thus enhancing their generality.     

Non-crossing matchings of points with geometric objects

Given an ordered set of points and an ordered set of geometric objects in the plane, we are interested in finding a non-crossing matching between point–object pairs. In this paper, we address the algorithmic problem of determining whether a non-crossing matching exists between a given point–object pair. We show that when the objects we match the points to are finite point sets, the problem is NP-complete in general, and polynomial when the objects are on a line or when their size is at most 2. When the objects are line segments, we show that the problem is NP-complete in general, and polynomial when the segments form a convex polygon or are all on a line. Finally, for objects that are straight lines, we show that the problem of finding a min-max non-crossing matching is NP-complete.     

The production of hydrocarbons from photoautotrophic growth ofDunaliella salina 1650

Microalga,Dunaliella salina 1650 was selected to produce hydrocarbons that may possibly substitute for fossil fuels in the near future. It can produce 0.22 (mg/L) of hydrocarbons over 20 d batch cultivation, maintaining 1.32 (g-dry wt./L) of cell density. Its productivity was similar to that fromBotryococcus braunii, which was known to economically produce liquid fuels. Optimal growth conditions for the alga were also determined as pH 7.2, 28°C, and 0.00034 (Kcal/cm²/h) of light intensity. It was shown that the hydrocarbon production from the alga was closely related to cell growth, except for the later periods of batch cultivation. Better hydrocarbon production was observed during light periods in light/dark cycle cultivation. Under chemostat conditions, maximum steady cell concentration was maintained as 1.1 (g-dry wt./L) at 0.12 (1/d) of dilution rate. The system reached to the steady state after 30 d of the cultivation. The maximum specific hydrocarbon production rate, 0.024 (mg/cell/d) was also obtained under this condition. It proves that the hydrocarbon production fromD. salina 1650 can compete with that fromB. braunii. Index Entries: Algal hydrocarbon production; photoautotrophic growth;Dunaliella salina