Second-degree Painlevé equations and their contiguity relations

We study second-order, second-degree systems related to the Painlevé equations which possess one and two parameters. In every case we show that by introducing a quantity related to the canonical Hamiltonian variables it is possible to derive such a second-degree equation. We investigate also the contiguity relations of the solutions of these higher-degree equations. In most cases these relations have the form of correspondences, which would make them non-integrable in general. However, as we show, in our case these contiguity relations are indeed integrable mappings, with a single ambiguity in their evolution (due to the sign of a square root).     

Triangle congruence and the Moulton plane

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Triangle congruence and the Moulton plane

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Development and Characterization of Microsatellite Markers (SSR) in Sesamum (Sesamum indicum L.) Species

Microsatellites, also known as simple sequence repeats (SSRs), are the class of repetitive DNA sequences present throughout the genome of many plant and animal species. Recent advances in molecular genetics had been the introduction of microsatellite markers to investigate the genetic structuring of natural plant populations. We have employed an enrichment strategy for microsatellite isolation by using multi-enzymes digestion, microsatellite oligoprobes, and streptavidin magnetic beads in Sesamum (Sesamum indicum L.). More than 200 SSR motifs were detected (SSR motifs ??2 repeat units or 6?bp); 80?% of the clones contained SSR motifs. When regarding SSRs with four or more repeat units and a minimum length of 10?bp, 132 of them showed repeats. Eighteen SSR markers were initially characterized for optimum annealing temperature using a gradient PCR technique. Among the 18 SSR markers characterized, five were found to be polymorphic and used to analyze 60 Sesamum germplasm accessions. The maximum number of alleles detected was four with a single primer and the least number of two alleles with three primers with an average PIC value of 0.77. SSRs are a valuable tool for estimating genetic diversity and analyzing the evolutionary and historical development of cultivars at the genomic level in sesame breeding programs.     

Mechanisms of antioxidant action: Antioxidant behaviour of nickel complex u.v. stabilisers

The antioxidant mechanisms involved in the u.v. stabilising activity of two nickel complexes, nickel dibutyl dithiocarbamate (NiDBC) and nickel acetophenone oxime (NiOx), have been investigated both by oxygen absorption measurements and in peroxide decomposition studies. NiDBC gives rise to a powerful catalyst for non-radical hydroperoxide decomposition; the rate of the reaction is faster in the presence than in the absence of light although the overall mechanisms appear to be very similar. NiOx is decomposed by hydroperoxides in a series of stoichiometric reactions which involve the consumption of at least six molecules of hydroperoxide per molecule of NiOx. Again the reaction is catalysed by light but the mechanism, which does not involve free-radical formation, is the same in the presence and absence of light. NiOx also appears to have weak radical trapping properties. Attempts to show that NiDBC and NiOx might interact sacrificially with photo-excited states of molecules (triplet carbonyl and singlet oxygen) were unsuccessful; the rates of photo-destruction of both complexes were unaffected by the presence of ketones both in the presence and absence of oxygen. This work confirms earlier conclusions that the nickel complex u.v. stabilisers function by auto-synergistic mechanisms involving u.v. screening and conventional chain-breaking and preventive antioxidant processes which operate during thermal processing operations as well as during environmental exposure. Although excited state quenching processes may occur, they appear to be less important in the overall scheme than the well established antioxidant mechanism.     

From Yang-Baxter Maps to Integrable Recurrences

Starting from known solutions of the functional Yang-Baxter equations, we construct a series of nonautonomous integrable recurrences, “median graphs”, and give their explicit solution.     

Numerical investigations of solution resistance effects on nonlinear electrochemical impedance spectra

The effect of solution resistance on the nonlinear electrochemical impedance spectra under quasi-potentiostatic conditions was investigated by numerical simulations. An electron transfer reaction, a reaction with an adsorbed intermediate and a reaction exhibiting negative resistance were chosen as the candidates and large amplitude perturbations were employed. The potential across the interface drifts initially and stabilizes after a certain time, which depends on the solution resistance and the kinetic parameter values. The fraction of the applied potential drop occurring across the metal–solution interface depends on the frequency and the amplitude of the perturbation as well as the value of solution resistance. This in turn leads to the possibility that, for a given conditions, a part of the spectrum may be acquired in the linear regime while the remaining part may be acquired in the nonlinear regime. The sensitivity of the Kramers Kronig transform (KKT) to identify these cases is evaluated. The results show that although the spectra are distorted by poorly conducting solution, the sensitivity of KKT to identify the nonlinear effects is not enhanced by the introduction of significant solution resistance.     

Biodegradable compositions by reactive processing of aliphatic polyester/polysaccharide blends

Commercially available biodegradable aliphatic polyesters, i.e., high molecular weight poly(ϵ-caprolactone) (PCL) and polylactide (PLA), were melt blended with a well-known natural and biodegradable polysaccharide: starch either as corn starch granules or as thermoplastic corn starch after plasticization with glycerol. Conventional melt blending yielded compositions with poor mechanical performances as a result of lack of interfacial adhesion between the rather hydrophobic polyester matrix and the highly hydrophilic and moisture sensitive starch phase. Interface compatibilization was achieved via two different strategies depending on the nature of the polyester chains. In case of PLA/starch compositions, PLA chains were grafted with maleic anhydride through a free radical reaction conducted by reactive extrusion. The maleic anhydride-grafted PLA chains (MAG-PLA) allowed for reinforcing the interfacial adhesion with granular starch as attested by TEM of cryofracture surface. As far as PCL/starch blends were concerned, the compatibilization was achieved via the interfacial localization of amphiphilic graft copolymers formed by grafting of PCL chains onto a polysaccharide backbone such as dextran. The PCL-grafted polysaccharide copolymers were synthesized by controlled ring-opening polymerization of ϵ-caprolactone proceeding via a coordination-insertion mechanism. These compatibilized PCL/starch compositions displayed much improved mechanical properties as determined by tensile testing as well as a much more rapid biodegradation as measured by composting testing.