Core structure of eremophilanes and bakkanes through niobium catalyzed Diels-Alder reaction: synthesis of (+/-)-bakkenolide A

A suitable intermediate for the synthesis of eremophilanes and bakkanes was prepared by a highly regioselective and stereoselective one-step synthesis through a niobium catalyzed Diels-Alder reaction. As a demonstration of the versatility of this intermediate, a total synthesis of (+/-)-bakkenolide A is described.     

Analysis of a cycloheptenone derivative: an experimental and theoretical approach

A detailed analysis with total assignment of (1)H and (13)C NMR spectral data for a cycloheptenone derivative, a key intermediate for the synthesis of perhydroazulene terpenoids, is related. These assignments are based on 1D (1)H and (13)C NMR and on 2D NMR techniques including gCOSY, gHSQC, gHMBC, J-resolved and NOEDIF experiments. The unequivocal assignments were supported by theoretical chemical shifts and scalar coupling constant calculations at GIAO B3LYP/cc-pVDZ level from optimized structures at the same level of theory.     

Connection between scale-free networks and nonextensive statistical mechanics

The degree distribution of the so-called scale-free networks exhibits, quite often, the form p(k) ∝1/(k₀+k)^γ (with γ>0 and k₀>0), in the limit of large networks. It happens that this form precisely coincides with the q-exponential p(k) ∝exp _q(-k/κ) (q ≥1 and κ>0), with γ=1/(q-1) and k₀=κ/(q-1). It optimises the nonadditive entropy with mathematically the same constraints that yield the stationary (or quasi-stationary) distribution in nonextensive statistical mechanics. In other words, the most ubiquitous form of the degree distribution of scale-free networks is a realisation of the hypothesis involved within the q-generalisation of Boltzmann-Gibbs statistical mechanics. In addition to this, we show that growth is not a necessary condition for having scale-free networks, in contrast with a widely spread belief.     

Synthesis of 1-methyl-3-oxo-7-oxabicyclo[2.2.1]hept-5-ene-2-carboxylic acid methyl ester

A simple and efficient method for the preparation of 1-methyl-3-oxo-7- oxabicyclo[2.2.1]hept-5-en-2-carboxylic acid methyl ester (1) is described. The first step is a highly regioselective Diels-Alder reaction between 2-methylfuran and methyl-3-bromo- propiolate. A remarkably difficult ketal hydrolysis reaction was effected by treatment with HCl, a simple reagent that was shown to be more efficient, in this case, than commonly used more elaborate methods.     

Numerical calculation of the dielectric and electrokinetic properties of vesicle suspensions

The dielectric and electrokinetic properties of aqueous suspensions of vesicles (unilamellar liposomes) are numerically calculated in the 1 Hz to 1 GHz frequency range using a network simulation method. The model consists of a conducting internal medium surrounded by an insulating membrane with fixed surface charges on both sides. Without an applied field, the internal medium is in electric equilibrium with the external one, so that it also bears a net volume charge. Therefore, in the presence of an applied ac field, there is fluid flow both in the internal and in the external media. The obtained results are qualitatively different from those corresponding to suspensions of charged homogeneous particles, mainly due to the existence of an additional length scale (the membrane thickness) and the corresponding dispersion mechanism, charging of the membrane. Because of this dispersion, the shapes of the spectra change with the size of the particles (at constant zeta potential and particle radius to Debye length ratio) instead of merely shifting along the frequency axis. A comparison between the numerical results and those obtained using approximate analytical expressions shows deviations that are, in general, sufficiently large enough to show the necessity to use numerical results in order to interpret broad frequency range dielectric and electrokinetic measurements of vesicle suspensions.     

Anomalous diffusion with absorption: exact time-dependent solutions

Recently, analytical solutions of a nonlinear Fokker-Planck equation describing anomalous diffusion with an external linear force were found using a nonextensive thermostatistical Ansatz. We have extended these solutions to the case when an homogeneous absorption process is also present. Some peculiar aspects of the interrelation between the deterministic force, the nonlinear diffusion, and the absorption process are discussed.     

Critical surface of the quenched bond-diluted cubic model in self-dual lattice: Renormalization group approach

Summary We propose a quite simple real-space renormalization group, which enables us to calculate (for the first time, as far as we know, and presumably with high precision) the critical surface of the quenched bond-diluted discreteN-vector ferromagnet in a self-dual lattice.     

Ionization state and bound level populations in hot,dense plasmas

The ionization state and bound level populations in hot, dense plasmas are studied in the average atom approximation. Bound level energies are fixed self-consistently with the complete set of population numbers, using pre-existent Hartree-Fock calculations. We present a pressure- ionization scheme that gradually merges bound electrons into the continuum. To solve the nonlinear algebraic system of equations of the model, we have derived an efficient iterative algorithm. Results are shown for aluminum and iron.     

An equation for diffusion in shrinking or swelling bodies

The differential equation that describes the mass balance of a solvent which diffuses in a shrinking or swelling body is transformed in order to fix the domain of integration and a numerical solution is given. The numerical results obtained differ significantly from the solution of the equation without volume change commonly used in literature. Hence, the new equation could affect substantially the fields of drying, dyeing ion exchange, diffusion in polymers, and solid-liquid extraction.     

Dimerization in the magnetostrictive one-dimensional XY model

We discuss the one-dimensional first-neighbor $\text{1}\text{2}$-spin magnetostrictive XY model (where the crystalline degrees of freedom are assumed to be three- dimensional), and exhibit that, for all temperatures below T_c, no other contributions to the structural order appear than the pure dimerization one. The influences of temperature and elastic constant on the order parameter and sound velocity are analyzed as well.