A fractional approach to the Sturm-Liouville problem

The objective of this paper is to show an approach to the fractional version of the Sturm-Liouville problem, by using different fractional operators that return to the ordinary operator for integer order. For each fractional operator we study some of the basic properties of the Sturm-Liouville theory. We analyze a particular example that evidences the applicability of the fractional Sturm-Liouville theory.     

The unusual ability of α‐angelicalactone to form adducts: A kinetic approach

Since α‐angelicalactone (AAL) substantially inhibits the formation of tumors, here its chemical reactivity was compared with that of carcinogenic lactones. Investigation of the electrophilic potential of AAL was carried out by studying the capacity of this lactone to form adducts with NBP, 4‐(p‐nitrobenzyl)pyridine, a substrate with nucleophilic characteristics similar to DNA bases. The formation of the AAL–NBP adduct occurs about 900,000‐fold faster than with β‐propiolactone, the most effective carcinogenic lactone (ΔG^#₃₅ = 52 and 87 kJ mol^?1, respectively). A stopped‐flow technique was required for this reaction to be monitored. It was concluded that the formation of AAL–NBP adducts takes place through an entropy‐strain‐catalyzed mechanism caused by early lactone ring cleavage. The kinetic results are consistent with the AAL potential as a chemoprotective agent. © 2007 Wiley Periodicals, Inc. Int J Chem Kinet 39: 591–594, 2007     

Solar heterogeneous and homogeneous photocatalysis as a pre-treatment option for biotreatment

In this paper, we present pilot-scale solar Photo-Fenton and TiO₂ treatment of a model compound (α-methylphenylglycine) dissolved in 500 mg/l concentration in water. Not only contaminant disappearance and mineralisation were evaluated, but also enhancement of biodegradability. The solar photoreactors, composed of 4.16 m² of compound parabolic collectors, had a total volume of 82 l (44.6 l illuminated). Treatment was successful with both Advanced Oxidation Processes (AOPs) tested, but photo-Fenton was shown to be by far more efficient from the kinetic and practical point of view. To find out the conditions for biocompatibility using the AOPs as a pre-treatment, waste water after certain degradation time, unacclimated municipal sludge and mineral nutrients were placed together and evaluated by the Zahn-Wellens (Z-W) test. Biodegradability was enhanced (70% biodegradable) by both AOPs, but photo-Fenton was demonstrated to be more efficient, requiring a treatmen time one order of magnitude shorter than TiO₂. Hydrogen peroxide management for reduced consumption and elimination prior to discharging water to the biotreatment step is also discussed in detail.     

The effect of chain architecture on “sharkskin” of metallocene polyethylenes

Dynamic viscoelastic and extrusion capillary results of metallocene based polyethylenes are analyzed. Three samples show very high viscosities at low frequencies and large relaxation times, which is a symptom of the presence of small amounts of long chain branching (LCB). A linear correlation is found between the sharkskin dynamics (periodicity) and a characteristic entanglement‐disentanglement time. It is found that this correlation does not hold for samples suspected of LCB.     

Autoacceleration and inhibition: Free volume. Epoxy-amine kinetics

The epoxy-diamine cure process was studied. We found that the mechanism can be described in three steps: (i) initiation up to 20–25% of conversion. (ii) autoacceleration and (iii) inhibition. It has been observed that after the initiation there is a clear autoacceleration effect which has been explained in terms of free volume, considerations: the volume occupied by the products of reaction diminishes the available volume increasing the “local concentration” of the reactants and therefore the rate of reaction. The reaction was followed by FTIR (near infrared) as the main technique. We used a purified epoxy resin as well as phenyl glycidyl ether cured with m-xylenediamine. © 1998 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 36: 1001–1016, 1998     

Enthalpy relaxation in polymethyl(α-n-alkyl)acrylates: Effect of length of alkyl chain

In this work, we have investigated by DSC the structural relaxation of amorphous polymethyl(α-n-alkyl)acrylates in which it is possible to change the length of the alkyl chain. We have evaluated the Narayanaswamy parameter, x, which controls the relative contribution of temperature and of structure to the relaxation time, the apparent activation energy, Δh*, and the nonexponentiality parameter, β, of the stretched exponential response function. The results suggest that x increases while Δh* decreases and β remains constant as the length of the side chain increases. This allows us to comment on the effect of chemical modification on the relaxation kinetics. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 583–593, 1998     

The Infestation of Olive Fruits by Bactrocera oleae (Rossi) Modifies the Expression of Key Genes in the Biosynthesis of Volatile and Phenolic Compounds and Alters the Composition of Virgin Olive Oil

Bactrocera oleae, the olive fruit fly, is one of the most important pests affecting the olive fruit, causing serious quantitative and qualitative damage to olive oil production. In this study, the changes induced by B. oleae infestation in the biosynthesis of volatile and phenolic compounds in olive (cvs. Picual, Manzanilla, and Hojiblanca) have been analyzed. Despite cultivar differences, the oils obtained from infested fruits showed a significant increase in the content of certain volatile compounds such as (E)-hex-2-enal, ethanol, ethyl acetate, and β-ocimene and a drastic decrease of the phenolic contents. The impact of those changes on the inferred quality of the oils has been studied. In parallel, the changes induced by the attack of the olive fly on the expression of some key genes in the biosynthesis of volatile and phenolic compounds, such as lipoxygenase, β-glucosidase, and polyphenol oxidase, have been analyzed. The strong induction of a new olive polyphenol oxidase gene (OePPO2) explains the reduction of phenolic content in the oils obtained from infested fruits and suggest the existence of a PPO-mediated oxidative defense system in olives.