Stationary polarons in discrete molecular chains

Properties of the large acoustic polarons in discrete molecular chains have been investigated within the adiabatic approximation. It turns out that practically all the polaron features are determined by the single parameter‐coupling constant which represents the ratio between the small polaron binding energy and the electron bandwidth. Three different types of stationary solutions were found corresponding to weak, intermediate, and strong coupling limits, respectively. In the weak coupling regime, that is, for the values of coupling constant exceeding the limit of the applicability of continuum approximation but lower than the critical one ( $g_C$ ), we observe symmetric bond‐centered solution corresponding to the polaron positioned in the middle between the adjacent lattice sites. When coupling constant overgrows, this critical value transition toward the site‐centered state occurs. It takes place continuously through the intermediate asymmetric state whose position gradually approaches lattice site as coupling constant increases. One of the main consequences of the lattice discreteness is the emergence of the periodic potential, Peierls‐Nabarro potential relief, through which polarons have to pass to transfer along the chain. The conditions for the polaron propagation are formulated in terms of the threshold velocity. © 2012 Wiley Periodicals, Inc.     

Grapevine as a Rich Source of Polyphenolic Compounds

Grapes are rich in primary and secondary metabolites. Among the secondary metabolites, polyphenolic compounds are the most abundant in grape berries. Besides their important impacts on grape and wine quality, this class of compounds has beneficial effects on human health. Due to their antioxidant activity, polyphenols and phenolic acids can act as anti-inflammatory and anticancerogenic agents, and can modulate the immune system. In grape berries, polyphenols and phenolic acids can be located in the pericarp and seeds, but distribution differs considerably among these tissues. Although some classes of polyphenols and phenolic acids are under strict genetic control, the final content is highly influenced by environmental factors, such as climate, soil, vineyard, and management. This review aims to present the main classes of polyphenolic compounds and phenolic acids in different berry tissues and grape varieties and special emphasis on their beneficial effect on human health.     

New insight into solid-state molecular dynamics: mechanochemical synthesis of azobenzene/triphenylphosphine palladacycles

Solid-state reactions of dicyclopalladated azobenzenes and triphenylphosphine lead to the thermodynamically favorable bridged complexes. It was demonstrated for the first time that very complex molecular dynamics involving a series of structural transformations is also feasible in the solid state.     

Atomic absorption background of Ba in EXAFS analysis of BaFe12O19 nanoparticles

The approximate barium X‐ray atomic absorption in the energy region of L‐edges is reconstructed from the absorption spectrum of an aqueous solution of BaCl₂. The result is corroborated by comparison with pure atomic absorption spectra of neighbour elements Xe and Cs. The application of the atomic absorption signal as a proper EXAFS background is demonstrated and discussed in the analysis of Ba hexaferrite nanoparticles with a very weak structural signal. The essential gain is found in the decrease of uncertainty intervals of structural parameters and their correlations. A simple analytical model of the absorption background for the practical EXAFS analysis is demonstrated.     

Magnon energy renormalization and low-temperature thermodynamics of O(3) Heisenberg ferromagnets

We present the perturbation theory for lattice magnon fields of the D$D$-dimensional O(3) Heisenberg ferromagnet. The effective Hamiltonian for the lattice magnon fields is obtained starting from the effective Lagrangian, with two dominant contributions that describe magnon–magnon interactions identified as a usual gradient term for the unit vector field and a part originating in the Wess–Zumino–Witten term of the effective Lagrangian. Feynman diagrams for lattice scalar fields with derivative couplings are introduced, on the basis of which we investigate the influence of magnon–magnon interactions on magnon self-energy and ferromagnet free energy. We also comment appearance of spurious terms in low-temperature series for the free energy by examining magnon–magnon interactions and internal symmetry of the effective Hamiltonian (Lagrangian).     

Sorbent-excluding sample preparation method for GC–MS pesticide analysis in apple peel

Apple peel is frequently exposed to pesticides, especially in the last stages of the pesticide treatment practice. For a certain period, peel retains most of the applied pesticides, which precisely indicates the presence of pesticide residues. This study was conducted to establish and evaluate the method for the residue analysis of pyrimethanil, cyprodinil, trifloxystrobin, bifenthrin and boscalid by GC–MS in peel of Granny Smith, Golden Delicious and Idared varieties. The method consisted of few steps, without the routine usage of sorbents, and resulted in efficient removal of waxes, targeted as main interferences in GC–MS analysis. The matrix effect, boscalid selectivity issue, trend of lower trueness for bifenthrin in all matrices and for all analytes in Granny Smith matrix were in some way associated with the waxes. Finally, the method was applied to the analysis of three varieties of apple orchard samples, after 9 and 5 months of treatment with commercial formulations that contain pyrimethanil, cyprodinil and boscalid as active ingredients. Since the developed method consisted of few steps and used nontoxic and economic reagents, it could be implemented as a fast, economic and reliable screening method.     

STRONG COMPACTNESS OF APPROXIMATE SOLUTIONS TO DEGENERATE ELLIPTIC-HYPERBOLIC EQUATIONS WITH DISCONTINUOUS FLUX FUNCTION

Under a non-degeneracy condition on the nonlinearities we show that sequences of approximate entropy solutions of mixed elliptic-hyperbolic equations are strongly precompact in the general case of a Caratheodory flux vector. The proofs are based on deriving localization principles for H-measures associated to sequences of measurevalued functions. This main result implies existence of solutions to degenerate parabolic convection-diffusion equations with discontinuous flux. Moreover, it provides a framework in which one can prove convergence of various types of approximate solutions, such as those generated by the vanishing viscosity method and numerical schemes.     

On Compactness of Commutators of Multiplications and Fourier Multipliers

We generalise results on compactness of commutators of multiplications and Fourier multiplier operators by Cordes (J Funct Anal 18:115–131, 1975) with respect to the smoothness of multiplication function. Our prime motivation has been a particular case known as the first commutation lemma—the basic tool for defining H-measures and H-distributions. We review and improve the known results in the \(\mathrm{L}^p\) setting, with \(1<p<\infty \), illustrating these results with an application, obtaining a generalised compactness by compensation result.     

Coherent orientation of mixed moduli spaces in Morse-Floer theory

We give the coherent orientation for the spaces of intersections of gradient trajectories and holomorphic disks in cotangent bundle. This construction provides the Piunikhin-Salamon-Schwarz isomorphism between Morse homology and Floer homology for Lagrangian intersections in cotangent bundles, with integer coefficients. This work is partially supported by Ministry of Science and Environmental Protection of Republic of Serbia Project #144020.