On the Asymptotic Optimality of a Low-Complexity Coding Strategy for WSS,MA, and AR Vector Sources

In this paper, we study the asymptotic optimality of a low-complexity coding strategy for Gaussian vector sources. Specifically, we study the convergence speed of the rate of such a coding strategy when it is used to encode the most relevant vector sources, namely wide sense stationary (WSS), moving average (MA), and autoregressive (AR) vector sources. We also study how the coding strategy considered performs when it is used to encode perturbed versions of those relevant sources. More precisely, we give a sufficient condition for such perturbed versions so that the convergence speed of the rate remains unaltered.     

Solution of a Riemann problem for elasticity

This paper describes a numerical algorithm for the Riemann solution for nonlinear elasticity. We assume that the material is hyperelastic, which means that the stress-strain relations are given by the specific internal energy. Our results become more explicit under further assumptions: that the material is isotropic and that the Riemann problem is uniaxial. We assume that any umbilical points lie outside the region of physical relevance. Our main conclusion is that the Riemann solution can be obtained by the iterative solution of functional equations (Godunov iterations) each defined in one- or two-dimensional spaces.Supported in part by AFOSR-88-0025.     

Optimisation of focused ultrasound extraction (FUSE) and microwave-assisted extraction (MAE) of hydrocarbons in geological chert samples

The analysis of hydrocarbons in chert rocks provides a worthwhile source of information regarding the geochemical features of a depositional setting. Since the typical analytical procedure requires long Soxhlet extractions and the use of large quantities of sample (30-50 g), in this work we have optimised the focused ultrasound extraction (FUSE) and the microwave-assisted extraction (MAE) to make available a less severe procedure. In both cases a full experimental design including solvent mixture composition (Dichloromethane/Hexane/Acetone) and process variables (sonication time and cycles, and extraction temperature and time) by means of D-optimal designs. In the extracted fractions hydrocarbons (C₁₆-C₄₀) were analysed by gas-chromatography-mass spectrometry. In the case of FUSE the process variables were the most sensitive variables and the optimum conditions were defined at 60:40 DCM/Hex mixture and a sonication time of 30 min and 9 cycles. In the case of MAE all the variables shown a significant effect on the extraction yield and the most adequate conditions (60:30:10 DCM/Hex/Ace mixture and an irradiation time of 15 min at 110 °C) were established from the analysis of the response surface. Both methods were systematically applied with different chert samples collected in Cucho (Trebiño County, Burgos, Spain) and we were able to assure quantitative extractions (>85%) in the first extraction. Additionally, from the distribution patterns of n-alkanes obtained in the different chert samples (nodular chert, laminar chert and massive-brechoid chert) collected in Cucho, we were able to distinguish different origins and diagenetic history.     

Magnetic endohedral transition-metal-doped semiconducting-nanoclusters

Endohedral first-row transition-metal-doped TM@Zn(i)S(i) nanoclusters, in which TM stands for the first-row transition-metals from Sc to Zn, and i=12, 16, have been characterized. In these structures the dopant metals are trapped inside spheroidal hollow semiconducting nanoclusters. It is observed that some of the transition metals are trapped in the center of mass of the cluster, whereas others are found to be displaced from that center, leading to structures in which the transition metals display a complex dynamical behavior upon encapsulation. This fact was confirmed by quantum molecular dynamics calculations, which further confirmed the thermal stability of endohedral compounds. In the endohedrally-doped nanoclusters in which the transition-metal atom sits on the center of mass, the host hollow cluster structure remains undistorted after dopant encapsulation. Conversely, if the encapsulated transition-metal atom is displaced from the center of mass, the host hollow cluster structure suffers a very tiny distortion. Additionally, it is found that there is negligible charge transfer between the dopant transition-metal atom and its hollow cluster host and, after encapsulation, the spin densities remain localized on the transition-metal atom. This allows for the atomic-like behavior of the trapped transition-metal atom, which gives rise to their atomic-like magnetic properties. The encapsulation free energies are negative, suggesting that these compounds are thermodynamically stable.     

Trans-stereoselectivity in the reaction between homophthalic anhydride and imines

The reaction between homophthalic anhydride and imines in the presence of TiCl4 and diisopropyl ethyl amine is trans-selective. Under these conditions, the reaction using homochiral imines can be highly diastereoselective, thus allowing the synthesis of enantiopure 1,2,3,4-tetrahydro-1-oxoquinoline-4-carboxylic acids.     

Theoretical studies on the hydrolysis of phosphate diesters in the gas phase,solution, and RNase A

Density functional theory, polarizable continuum models and semiempirical hybrid quantum mechanical/molecular mechanical (QM/MM) calculations were applied to the hydrolysis of phosphate diesters in the gas phase, in solution, and in the enzyme RNase A. Neutralization of the negative charge of the pentacovalent phosphorane intermediates provides a substantial stabilization of the transition‐state structures in the gas phase. Inclusion of solvent effects on the phosphate/phosphorane species was critical to reproducing the trends in reactivity observed experimentally. Finally, the catalytic mechanism for the hydrolysis of uridine 2′,3′‐cyclic phosphate by RNase A was studied by QM/MM calculations. Our results suggest that the rate‐limiting transition state of the reaction corresponds to the approach of a water molecule to the phosphate and its activation by His119. Thus, His119 acts as a generalized base for the reaction. The water attack leads to a pentacovalent phosphorane transition state of formal charge ?2; this excess of negative charge in the transition state is stabilized by a number of positively charged residues including His12 and Lys41. In the second stage of the reaction, the phosphorane is converted into products. This part of the reaction proceeds without a detectable barrier, and it is facilitated by a proton transfer from Lys41 to the departing O_2′. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

The extended Koopmans' theorem: vertical ionization potentials from natural orbital functional theory

The Piris natural orbital functional, PNOF5, has been used to predict vertical ionization potentials of a selected set of 30 organic and inorganic spin-compensated molecules by means of the extended Koopmans' theorem. Electron affinities of 10 selected radicals have also been estimated as the inverse of the ionization potentials of the anionic species, calculated at the experimental geometries of the neutral radicals. The basis set limit effects have been assessed by inspecting the data obtained for the Dunning's basis set series cc-pVXZ and aug-cc-pVXZ (X = D, T, Q, 5). The performance of the PNOF5 is established by carrying out a statistical analysis of the mean absolute errors (MAEs) with respect to the experiment values. The calculated PNOF5 ionization potentials and electron affinities agree satisfactorily with the corresponding experimental data, with MAEs smaller than 0.5 eV.