The Poincaré Map of Randomly Perturbed Periodic Motion

A system of autonomous differential equations with a stable limit cycle and perturbed by small white noise is analyzed in this work. In the vicinity of the limit cycle of the unperturbed deterministic system, we define, construct, and analyze the Poincaré map of the randomly perturbed periodic motion. We show that the time of the first exit from a small neighborhood of the fixed point of the map, which corresponds to the unperturbed periodic orbit, is well approximated by the geometric distribution. The parameter of the geometric distribution tends to zero together with the noise intensity. Therefore, our result can be interpreted as an estimate of the stability of periodic motion to random perturbations. In addition, we show that the geometric distribution of the first exit times translates into statistical properties of solutions of important differential equation models in applications. To this end, we demonstrate three distinct examples from mathematical neuroscience featuring complex oscillatory patterns characterized by the geometric distribution. We show that in each of these models the statistical properties of emerging oscillations are fully explained by the general properties of randomly perturbed periodic motions identified in this paper.     

Application of multiple quench parameters for confirmation of radionuclide identity in radioanalytical quality control

Journal of Radioanalytical and Nuclear Chemistry - Robust and reliable radiochemical analysis is the key factor in the appropriate disposal and management of radioactive wastes arising from the...     

Correction to: Foreword to the memorial issue for Professor Roberto Marassi

Journal of Solid State Electrochemistry -     

Late-Stage Functionalization by Chan–Lam Amination: Rapid Access to Potent and Selective Integrin Inhibitors

A late-stage functionalization of the aromatic ring in amino acid derivatives is described. The key step is a copper-catalysed diversification of a boronate ester by amination (Chan–Lam reaction) that can be carried out on a complex β-aryl-β-amino acid scaffold. This not only considerably extends the substrate scope of amination partners, but also delivers an array of potent and selective integrin inhibitors as potential treatment agents of idiopathic pulmonary fibrosis (IPF). This versatile chemical strategy, which is amenable to high-throughput-array protocols, allows the installation of pharmaceutically valuable heteroaromatic fragments at a late stage by direct coupling to NH heterocycles, leading to compounds with drug-like attributes. It thus constitutes a useful addition to the medicinal chemist's repertoire.     

The influence of compression conditions on the peculiarities of self-propagating exothermal reaction in Al–Ni powder reactive materials

The paper deals with the effect of the compression conditions on the propagation front velocity of exothermal reaction and the specific heat release in Al–Ni powder reactive materials with mean particle sizes of 70–110 nm. It was shown that the velocity increases from 2.7 to 8 cm s^?1 and comes to saturation with the lowering of the porosity (η) from 0.91 to 0.34, while the dependence of the specific heat release has its maximum for η?=?0.5. The results of the X-ray diffraction analysis obtained in situ during the sample heating suggest that the sequence of phase transformations in the system does not depend on the porosity. In all cases, first in the temperature range of ~?500–540 °C the NiAl compound is formed. With the further heating up to ~?640 °C, the Ni₃Al, Ni₂Al₃ and NiAl₃ compounds are additionally formed. The calculation of kinetic parameters was performed using the obtained curves of the differential scanning calorimetry: activation energy, pre-exponential factor and reaction model. The comparison of the calculated results and the scanning electron microscopy data has shown that such behavior of the Al–Ni system with the porosity lowering occurs due to the growth of the transformation degree and is associated with the presence in the final powder mixture of mutually non-contacting Al and Ni agglomerates with the dimensions of over 10 μm.     

A Characterization of Finitely Decidable Congruence Modular Varieties

For every finitely generated, congruence modular variety of finite type we find a finite family of finite rings such that the variety is finitely decidable if and only if is congruence permutable and residually small, all solvable congruences in finite algebras from are Abelian, each congruence above the centralizer of the monolith of a subdirectly irreducible algebra from is comparable with all congruences of , each homomorphic image of a subdirectly irreducible algebra with a non-Abelian monolith has a non-Abelian monolith, and, for each ring from , the variety of -modules is finitely decidable.

     

DFT study of Co-C bond cleavage in the neutral and one-electron-reduced alkyl-cobalt(III) phthalocyanines

Density functional theory (DFT) has been applied to the analysis of the structural and electronic properties of the alkyl-cobalt(III) phthalocyanine complexes, [CoIIIPc]-R (Pc = phthalocyanine, R = Me or Et), and their pyridine adducts. The BP86/6-31G(d) level of theory shows good reliability for the optimized axial bond lengths and bond dissociation energies (BDEs). The mechanism of the reductive cleavage was probed for the [CoIIIPc]-Me complex which is known as a highly effective methyl group donor. In the present analysis, which follows a recent study on the reductive Co-C bond cleavage in methylcobalamin (J. Phys. Chem. B 2007, 111, 7638-7645), it is demonstrated that addition of an electron and formation of the pi-anion radical [CoIII(Pc*)]-Me- significantly lowers the energetic barrier required for homolytic Co-C bond dissociation. Such BDE lowering in [CoIII(Pc*)]-Me- arises from the involvement of two electronic states: upon electron addition, a quasi-degenerate pi*Pc state is initially formed, but when the cobalt-carbon bond is stretched, the unpaired electron moves to a sigma*Co-C state and the final cleavage involves the three-electron (sigma)2(sigma*)1 bond. As in corrin complexes, the pi*Pc-sigma*Co-C states crossing does not take place at the equilibrium geometry of [CoIII(Pc*)]-Me- but only when the Co-C bond is stretched to approximately 2.3 A. The DFT computed Co-C BDE of 23.3 kcal/mol in the one-electron-reduced phthalocyanine species, [CoIII(Pc*)]-Me-, is lowered by approximately 37% compared to the neutral Py-[CoIIIPc]-Me complex where BDE = 36.8 kcal/mol. A similar comparison for the corrin-containing complexes shows that a DFT computed BDE of 20.4 kcal/mol for [CoIII(corrin*)]-Me leads to approximately 45% bond strength reduction, in comparison to 37.0 kcal/mol for Im-[CoIII(corrin)]-Me+. These results suggest some preference by the alkylcorrinoids for the reductive cleavage mechanism.     

The origin of open circuit voltage of porphyrin-sensitised TiO(2) solar cells

Electron lifetime and diffusion coefficient measurements in highly efficient porphyrin-sensitised TiO(2) solar cells showed reduced electron lifetime, and consequently, lower photo-induced electron density under illumination compared to commonly used ruthenium dye (N719)-sensitised solar cells, which is proposed to be the origin of the generally lower open circuit voltage.     

Direct catalytic asymmetric three-component Mannich reactions with dihydroxyacetone: enantioselective synthesis of amino sugar derivatives

Highly enantioselective, amino acid-catalyzed, one-pot three-component asymmetric Mannich reactions between dihydroxyacetone, p-anisidine, and aldehydes are presented. The reactions proceeded with high chemo- and stereoselectivity and furnished the corresponding α,α′-dihydroxy-β-aminoketones in high yields with 82-95% ee.     

The study of the lipophilicity of alpha-(4-phenylpiperazin-1-yl)-gamma-phthalimidobutyramides using chromatographic and computational methods

The lipophilicity of the series of alpha-(4-phenylpiperazin-1-yl)-gamma-phthalimido-butyramides (1-8) has been investigated. Several methods, like reversed-phase thin-layer chromatography and high-performance liquid chromatography using reversed-phase RP18 and IAM.DD2 columns, were applied to determine RMO, log k0 and log k(0IAM) factors. The RP-TLC investigations were performed in mixtures of acetone-water and acetonitrile-water. For RP-HPLC method mixtures of acetonitrile, water and 0.01% TFA were used as the mobile phases while for IAM.DD2 investigations mixtures of acetonitrile and water were applied. The partition coefficients of compounds (1-8) were also calculated with the Pallas and CAChe programs. All the obtained data, both from experimental methods and computational calculations, were compared and a suitable conclusion was reached.