Efficient synthesis of enantiomerically pure alpha-alkyl cyclopropanecarbonitrile derivatives from pyrazolines

[reaction: see text] Thermolysis of enantiopure sulfonyl pyrazolines 4 and 5, easily obtained from (Z)-3-p-tolylsulfinylacrylonitriles (1), afforded sulfonyl cyclopropanes (6, 7) in a completely stereoselective manner in almost quantitative yields. Both cyclopropanes and alkylidenecyclopropanes, containing one or two chiral carbon atoms, one of them being quaternary, were obtained by hydrogenolysis of the C-S bonding and under the conditions reported by Julia, respectively. The highly stereoselective extrusion of nitrogen suggests a concerted mechanism.     

Towards an understanding of the heat capacity of liquids. A simple two-state model for molecular association

A model for the temperature dependence of the isobaric heat capacity of associated pure liquids C(p,m)(o)(T) is proposed. Taking the ideal gas as a reference state, the residual heat capacity is divided into nonspecific C(p) (res,ns) and associational C(p) (res,ass) contributions. Statistical mechanics is used to obtain C(p)(res,ass) by means of a two-state model. All the experimentally observed C(p,m)(o)(T) types of curves in the literature are qualitatively described from the combination of the ideal gas heat capacity C(p)(id)(T) and C(p)(res,ass)(T). The existence of C(p,m)(o)(T) curves with a maximum is predicted and experimentally observed, for the first time, through the measurement of C(p,m)(o)(T) for highly sterically hindered alcohols. A detailed quantitative analysis of C(p,m)(o)(T) for several series of substances (n-alkanes, linear and branched alcohols, and thiols) is made. All the basic features of C(p,m)(o)(T) at atmospheric and high pressures are successfully described, the model parameters being physically meaningful. In particular, the molecular association energies and the C(p)(res,ns) values from the proposed model are found to be in agreement with those obtained through quantum mechanical ab initio calculations and the Flory model, respectively. It is concluded that C(p,m)(o)(T) is governed by the association energy between molecules, their self-association capability and molecular size.     

Synthesis of a cyclic peptide containing norlanthionine: effect of the thioether bridge on peptide conformation

Two diastereomeric analogues of ring C of nisin incorporating a novel norlanthionine residue have been synthesized via a triply orthogonal protecting group strategy. A full structural study was carried out by NMR, which elucidated the conformational properties of the two peptides and enabled the identity of each diastereoisomer to be proposed.     

Bridging fluorides and hard/soft mismatch in d6 and d8 complexes: the case of [Tl(mu-F)3Ru(PPh3)3

[RuCl2(PPh3)3] reacts with thallium(I) fluoride to give either [Tl(mu-F)3Ru(PPh3)3] (1) or [Tl(mu3-F)(mu2-Cl)2Ru2(mu2-Cl)(mu2-F)(PPh3)4] (2) depending on the excess of TlF used. Both 1 and 2 were fully characterized, including X-ray structure determinations. Complex 1 reacts with dihydrogen to form the known ruthenium hydride complex [Ru(H)2(H2)(PPh3)3] upon hydrogenolysis of the Ru-F bond. The reaction of 1 with activated alkyl bromides (R-Br) gives the corresponding alkyl fluorides and the trinuclear complex [Tl(mu3-F)(mu2-F)(mu2-X)Ru2(mu2-Br)(mu2-F)(PPh3)4] (X=Br, F) (3), whose structure closely resembles that of 2. However, 1 is not active as catalyst for the nucleophilic fluorination of R-Br in the presence of thallium fluoride. The effect of the bridging coordination mode of fluoride on the Ru-F bond is discussed in terms of the HSAB principle, which suggests a more general model for predicting the stability of d6 and d8 complexes containing hard ligands (such as fluoro, oxo, and amido).     

(Z)-3-p-tolylsulfinylacrylonitriles as chiral dipolarophiles: reactions with diazoalkanes

[reaction: see text] The dipolarophilic reactivity of enantiopure (Z)-3-p-tolylsulfinylacrylonitriles (1) has been evaluated with diazoalkanes. 3-Cyanopyrazoles are obtained when R = H, but with R = alkyl (Bn, n-Bu, and t-Bu) only one cycloadduct (4 or 5) is formed in high yield under mild conditions, therefore evidencing a complete control of the regioselectivity and the endo/exo and pi-facial selectivities. These reactions are a new straightforward entry to the synthesis of pyrazolines and related structures and reveal the excellent dipolarophilic features of (Z)-sulfinylacrylonitriles.     

Cosmological Two-Fluid Thermodynamics

We reveal unifying thermodynamic aspects of so different phenomena as the cosmological electron-positron annihilation, the evaporation of primordial black holes with a narrow mass range, and the "deflationary" transition from an initial de Sitter phase to a subsequent standard Friedmann–Lemaître–Robertson–Walker (FLRW) behavior.     

Multiresolution information measures applied to speech recognition

Considerable advances in automatic speech recognition have been made in the last decades, thanks specially to the use of hidden Markov models. In the field of speech signal analysis, different techniques have been developed. However, deterioration in the performance of the speech recognizers has been observed when they are trained with clean signal and tested with noisy signals. This is still an open problem in this field. Continuous multiresolution entropy has been shown to be robust to additive noise in applications to different physiological signals. In previous works we have included Shannon and Tsallis entropies, and their corresponding divergences, in different speech analysis and recognition systems. In this paper we present an extension of the continuous multiresolution entropy to different divergences and we propose them as new dimensions for the pre-processing stage of a speech recognition system. This approach takes into account information about changes in the dynamics of speech signal at different scales. The methods proposed here are tested with speech signals corrupted with babble and white noise. Their performance is compared with classical mel cepstral parametrization. The results suggest that these continuous multiresolution entropy related measures provide valuable information to the speech recognition system and that they could be considered to be included as an extra component in the pre-processing stage.     

Fractional diffusion models of option prices in markets with jumps

Most of the recent literature dealing with the modeling of financial assets assumes that the underlying dynamics of equity prices follow a jump process or a Lévy process. This is done to incorporate rare or extreme events not captured by Gaussian models. Of those financial models proposed, the most interesting include the CGMY, KoBoL and FMLS. All of these capture some of the most important characteristics of the dynamics of stock prices. In this article we show that for these particular Lévy processes, the prices of financial derivatives, such as European-style options, satisfy a fractional partial differential equation (FPDE). As an application, we use numerical techniques to price exotic options, in particular barrier options, by solving the corresponding FPDEs derived.     

Cohomogeneity One Einstein-Sasaki 5-Manifolds

We consider hypersurfaces in Einstein-Sasaki 5-manifolds which are tangent to the characteristic vector field. We introduce evolution equations that can be used to reconstruct the 5-dimensional metric from such a hypersurface, analogous to the (nearly) hypo and half-flat evolution equations in higher dimensions. We use these equations to classify Einstein-Sasaki 5-manifolds of cohomogeneity one.