Elastic waves in quasiperiodic structures

We study the transverse and sagittal elastic waves in different quasiperiodic structures by means of the full transfer-matrix technique and surface Green-function matching method. The quasiperiodic structures follow Fibonacci, Thue-Morse and Rudin-Shapiro sequences, respectively. We consider finite structures having stress-free bounding surfaces and different generation orders, including up to more than 1000 interfaces. We obtain the dispersion relations for elastic waves and spatial localization of the different modes. The fragmentation of the spectrum for different sequences is evident for intermediate generation orders, in the case of transverse elastic waves, whereas, for sagittal elastic waves, higher generation orders are needed to show clearly the spectrum fragmentation. The results of Fibonacci and Thue-Morse sequences exhibit similarities not present in the results of Rudin-Shapiro sequences.     

Diastereoselective Approach to cis-4-Methyl/thiol-Pipecolic Esters Based on RCM Reaction and Conjugate Michael Addition

A synthetic route for the access to enantiopure cis-4-methyl/thiol-pipecolic esters is presented. It is based on the ring-closing metathesis reaction to build the α,β-unsaturated piperidin-2-one derived from (S)-(–)-phenylethylamine, followed by either diastereoselective conjugate addition of methylorganocuprate allowing access to cis-4-methyl pipecolic ester or by tandem diastereoselective hydrosulforization–thionization reaction providing access to cis-4-thiol pipecolic ethyl esters.     

Relativistic scalar and spin-orbit density functional calculations of the electronic structure, NICS index and ELF function of the [Re2(CO)8(μ-BiPh)2] and [Re2(CO)8(μ-BiPh2)2] clusters

Relativistic scalar and spin-orbit density functional calculations of the electronic structure, Nucleus-Independent Chemical Shift (NICS) index and ELF function of the [Re₂(CO)₈(μ-BiPh)₂] and [Re₂(CO)₈(μ-BiPh₂)₂] clusters are reported. We show here that the [Re₂(CO)₈(μ-BiPh)₂] cluster has large negative NICS values in the region defined by the Re-Bi-Re-Bi four-membered ring and the ELF function shows significant electron delocalization density in the center of the metallic ring, thus indicating an aromatic cluster. In contrast the Re-Bi-Re-Bi four-membered ring in the [Re₂(CO)₈(μ-BiPh₂)₂] cluster has negligible paratropic ring currents and the ELF function shows a low-density region within the metallic ring indicating that aromaticity is switched off. However, the phenyl ligands in both clusters show the expected aromatic character.     

Crystal and molecular structure of [Zn(II)]2(diacetoamidoglutarate)2 hexaaquo·2H2O,an unusual macrocyclic dimer with pentacoordinated Zn in a slightly distorted trigonal bipyramid

The crystal and molecular structure of the title compound, [Zn(II)]₂(DAG)₂, were determined and the results compared with those obtained for similar N-protected amino acids. In the crystalline state, 16-membered macrocyclic dimers are held together by hydrogen bridges in a triclinic lattice. The Zn(II) ions are pentacoordinated to oxygens in a slightly distorted trigonal bipyramid. The trigonal plane is formed by two carboxylic oxygens and an oxygen atom from a water molecule, whereas the apical positions are occupied by two other oxygens from the remaining coordinated water molecules. The ligands form bridges between cations providing the cyclic dimers, whereas similar but shorter systems form pseudo polymer sheets.     

Combining optimization with simulation to obtain credible models for intensive care units

In this paper we develop a simulation model to study bed occupancy levels in an Intensive Care Unit (ICU). The main contributions of this study are: (1) A proposal for generalized regression models to fully capture the high variability of patients’ length of stay; (2) Proof that a simulation model that does not incorporate the management decisions by clinical staff cannot be considered valid; (3) The development of a mathematical model to represent these management decisions, and (4) A proposal for a method combining optimization with simulation to estimate the model parameters. This provides a valid simulation model that includes the physician management of an ICU. Validation is accomplished by comparing distribution patterns in daily bed occupancy records against simulated bed occupancy data. The methodology is tested using data provided by the Hospital of Navarre in Spain.     

Dependence of Cm on the composition of solid binary propellants in ablative laser propulsion

Propulsion pellets of different metal/salt (Zn/CaCO₃) composition have been prepared. The impulse imparted to the pellet by the laser has been measured using two different methods: a torsion pendulum and a piezoelectric sensor. The dependence of the coupling coefficient, C_m, on the composition of the solid binary propellants in ablative laser propulsion has been investigated under different experimental conditions: in vacuum and at atmospheric pressure as well as with two different wavelengths, IR and UV. The composition of the Zn/CaCO₃ propellant mixture that optimizes the coupling coefficient, C_m, has been determined.     

A Note on Semilocal Reciprocity Laws on Curves

The aim of this work is to offer a definition of the Contou-Carrère symbol associated with a closed point of an algebraic curve and with a local ring of dimension zero, first, and then with a semilocal ring of dimension zero, from the commutator of a certain central extension. When the curve is complete, we deduce the reciprocity law in both cases. Moreover, we give some applications to the residues, and obtain explicit relations between the classic residue and the Witt residue.

Communicated by C. Pedrini.