Kolmogorov Theorem revisited

Kolmogorov Theorem on the persistence of invariant tori of real analytic Hamiltonian systems is revisited. In this paper we are mainly concerned with the lower bound on the constant of the Diophantine condition required by the theorem. From the existing proofs in the literature, this lower bound turns to be of O(ε1/4), where ε is the size of the perturbation. In this paper, by means of careful estimates on Kolmogorov's method, we show that this lower bound can be weakened to be of O(ε1/2). This condition coincides with the optimal one of KAM Theorem. Moreover, we also obtain optimal estimates for the distance between the actions of the perturbed and unperturbed tori. We believe that some ideas contained in this paper may be used for improving several estimates in the general KAM context.     

Excess charge delocalization in organic and biological molecules: some theoretical notions

Theoretical and computational investigations of the excess charge distribution (ECD) in molecular complexes have attracted considerable attention as ECD is closely related to electronic properties of organic semiconductors, such as the efficiency of photoinduced charge separation in organic solar cells and charge transport in DNA and proteins. In this paper, we analyze the ECD in several representative models on the basis of ab initio and DFT calculations. We consider how changes in the reorganization energy, electronic coupling and charge transfer energy affect the ECD in the systems. In particular, we compare ECD in π stacks of polycyclic aromatic hydrocarbons and DNA nucleobases. While the π interaction between subunits in the systems is similar in both cases, ECD is quite different: the excess charge is found to be completely delocalized over the hydrocarbon stacks but strongly confined to a single nucleobase in DNA stacks. We also discuss the effects of conformational fluctuations on ECD in the stacks. Finally, ECD in amino acids and its dependence on the conformational changes are briefly considered.     

Selecting and adapting weekly work schedules with working time accounts: A case of a retail clothing chain

A case of selection and adaptation of weekly work schedules is presented. Weekly work schedules in two franchises of an important retail clothing chain have to be established. Working time accounts are used: each week, an employee can owe the company a certain number of hours or vice versa. Nevertheless, over a certain threshold, the hours have to be paid for by the company and the account balance returns to zero. A minimum and desired level of capacity of employees is contemplated. Hierarchically, the planned capacity must attempt to reach the minimum level; then it must fit a desired level as much as possible. At present, the task of allocation and the final adjustment of schedules is done manually, which is difficult, ineffective and often inaccurate. The procedure proposed is divided into two phases. Firstly, a work schedule, selected from a list, is assigned to each worker; a mixed linear program, followed by a local optimization process, is used. In the second phase, the work schedules are modified according to predefined rules: if there is a surplus of capacity, work schedules are reduced, and if there is a shortage, work schedules are extended. The company considers the results to be satisfactory.     

Studies on the Toxic Oil Syndrome: proposal of a mechanism for the thermal conversion of 3-N-phenylamino-1,2-propanediol esters into anilides under deodorisation conditions

A study on the reaction mechanism for the conversion of title esters, the species recognised as toxic biomarkers of the oil batches responsible for the Toxic Oil Syndrome, into the corresponding anilides under the thermal conditions of an oil deodorisation process was performed using experimental and computational techniques. The results obtained suggest a reaction course that includes two basic steps: an intramolecular process involving the reaction of the amine group of the diester derivative with the secondary ester of the same compound, followed by the attack of an aniline molecule to form the (E)-isomer of an imidic acid, which would finally tautomerise to give the final anilide.     

N,N′‐Butane‐1,4‐diylbis­(bromo­acetamide)

The title compound, C₈H₁₄Br₂N₂O₂, lies about an inversion centre and adopts a pleated conformation, with the C(O)—NH—CH₂—CH₂ and NH—CH₂—CH₂—CH₂ torsion angles of the butane­diamine residue being −89.5 (6) and −62.1 (7)°, respectively. These data are useful in discerning the structure of polymers containing such a unit. A skew conformation is found for the Br—CH₂—C(O)—NH torsion angle [−124.2 (4)°]. The mol­ecular packing is stabilized by strong hydrogen bonds between amide groups and also by weak CH₂⋯OC inter­actions. In this way, each mol­ecule inter­acts with its six closest neighbours through eight hydrogen bonds.     

Nucleating and retarding effects of nanohydroxyapatite on the crystallization of poly(butylene terephthalate-co-alkylene dicarboxylate)s with different lengths

Journal of Thermal Analysis and Calorimetry - New biodegradable and biocompatible composites are continuously developed for biomedical applications (e.g., from drug delivery devices to tissue...     

Anionic organic guests incorporated in zeolites: adsorption and reactivity of a Meisenheimer complex in faujasites

Zeolites are suitable microporous hosts for positively charged organic species, but it is believed that they cannot adsorb organic anions. Pure Meisenheimer complex, derived from reduction of 2,4-dinitroaniline with NaBH4, was adsorbed inside faujasite cavities. Evidence for the internal incorporation of this negatively charged reaction intermediate comes from 1) XPS elemental analysis as a function of the depth of penetration into the particle, 2) the remarkable blue shift in lambda(max) of the Meisenheimer complex adsorbed on zeolite (ca. 470 nm) as compared to that in acetonitrile (580 nm) and 3) from the lack of reactivity with size-excluded hydride-acceptor reagents. Evidence is provided in support of an adsorption mechanism in which a neutral ion pair (alkali metal ion + Meisenheimer anion) is the actual species being adsorbed. In fact it appears that there is remarkable increase in the association constant for the ion-pair complex within the zeolite cavities as compared to DMF solution. Although this mechanism of adsorption as an ion-pair complex has precedents in the adsorption of some inorganic salts, what is novel is the notable increase in the stability and persistence of the Meisenheimer anion (a anionic reaction intermediate) as a result of zeolite inclusion. Adsorbed Meisenheimer complex exhibits much lower reactivity towards electron acceptors, oxygen, and water. Cyclic voltammetry of zeolite-modified electrodes reveals for the Meisenheimer complex adsorbed on LiY a reversible redox peak that is not observed in solution and has been interpreted as arising from site isolation and stabilisation of the electrochemically generated species.     

Structural analysis of chiral complexes of palladium(0) with 15-membered triolefinic macrocyclic ligands

The complete structural analysis of the palladium complexes of the triolefinic macrocycles (E,E,E)-1,6,11-tris(arylsulfonyl)-1,6,11-triazacyclopentadeca-3,8,13-trienes, which featured from three identical to three different aryl groups, was achieved by performing X-ray diffraction studies, NMR spectroscopy, and other calculations. The stereochemical complexity is determined by the different isomers formed through complexation of the metal to one or other face of each of the three olefins involved. The palladacyclopropane formulation of the palladium-olefin interaction offers a clear picture of the stereogenicity of the olefin carbon atoms that are complexed to the metal. The energetically favorable isomers were identified in the solid-state and in solution by performing X-ray diffraction and NMR spectroscopic analysis, respectively.     

A theoretical study of the competitive homolytic/heterolytic aniomesolytic cleavages of C-O alkyl ether bonds

Density functional theory electronic structure calculations of the homolytic/heterolytic aniomesolytic C-O fragmentations in the gas phase of a series of radical anions of substituted-phenyl benzyl ethers and substituted-benzyl phenyl ethers have been carried out. Along the series, the electron-withdrawing strength of the substituents increases. An intramolecular electron transfer from the pi system to the sigma molecular orbital of the scissile C-O bond is required to produce the fragmentation. As the electron-withdrawing strength of the substituents increases, the transition-state structures appear later with higher potential energy and Gibbs free energy barriers. The homolytic mesolytic cleavages are always thermodynamically favored versus the corresponding heterolytic mesolytic ones. The heterolytic mesolytic fragmentations in radical anions containing only weak electron-withdrawing groups are faster than the corresponding homolytic mesolytic ones. Conversely, in radical anions supporting strong electron-withdrawing groups the homolytic mesolytic fragmentations are faster in terms of potential energy barriers. However, the entropic contribution makes it comparable the homolytic and the heterolytic Gibbs free energy barriers in this case. The main factors that determine the relative rates of those kind of aniomesolytic cleavages are discussed.     

Photoinduced molecular reorientation dynamics in confined domains of Langmuir monolayers

In a photoresponsive Langmuir monolayer comprised of smectic-C-like domains of mesogenic trans-azobenzene derivative embedded within an isotropic matrix of its cis isomer counterpart, several structurally differing circular droplets were irradiated with linearly polarized light. This report describes the structural rearrangements that occurred in these droplets upon illumination followed by Brewster angle microscopy analysis. Starting from initial well-characterized and symmetric states, final photoaligned situations were reached in which the azimuth angles of the rod-shaped elongated molecules were found to be perpendicular to the electric component of the excitation light. The dynamical aspects of the photoalignments, including their transient patterns, are captured by a theoretical model that couples a relaxational principle incorporating long-range elastic forces with a kinetic formalism presenting an anisotropic rate law.