On the Multiplicity of Algebraic Limit Cycles

In the present paper we tackle the problem of determining the multiplicity of periodic orbit as limit cycle of a planar differential system. We consider the particular case of a circumference as periodic orbit. We show that the conditions of multiplicity can be almost algebraically solvable. There are parameters in which these conditions depend transcendentally, as happens in the degenerate center-focus problem. Even though this difficulty, these transcendental dependence can be, in some sense, controlled because only a basis of fundamental functions appear. The appearance of this fundamental basis opens the path to approach these types of problems. We present several examples of families for which these conditions can be computed.     

Mechanism of Thermal Degradation of an Inorganic-Organic Hybrid Based on an Epoxy-POSS

A novel inorganic-organic hybrid material, belonging to the family of polyhedral oligomeric silsesquioxanes (POSS), was used to reduce the trend of a conventional epoxy-amine system to undergo combustion. The mixtures with different percentages in weight of POSS, and equal number of equivalents between of epoxy and amino groups were tested by thermogravimetic analysis (TGA) in both, argon and oxygen atmospheres. The results indicated that the char/ceramic yield values increase with the content of POSS and therefore, fire resistance is enhanced. Activation energies of degradation processes were obtained by Kissinger-Akahira-Sunose method. An empirical kinetic model satisfactorily explained the degradation mechanism of different blends.     

Thermodynamic Analysis of Phase Separation of a Thermoplastic in the Precursors of Different Epoxy-Amine Systems

The miscibility of a thermoplastic, polystyrene (PS), with the precursors of several epoxy-amine systems has been studied thermodynamically and experimentally. The epoxy-amine systems were different only in the origin of amino groups, which were provided by a monoamine (MA) and a diamine (DA) in different proportions. Cloud-point curves (CPC) at conversion zero were reported for five modified systems with different MA-DA proportion. All CPCs showed an UCST behaviour. CPC shifted to lower temperatures when the ratio of MA/DA in the system increased, meaning that the MA produces an increase in the miscibility of the system. A model based on the Flory-Huggins theory was used for the thermodynamic analysis, in which the dependence of interaction parameter on temperature and composition, χ(T,ϕ), and the polydispersity of components were considered. A general equation for χ(T,ϕ) also depending on the MA-DA proportion was reached and used to obtain the phase diagram of the different systems. A high level of agreement between theoretical and experimental CPCs was obtained.     

Magnetic and transport studies of σ-phase Fe50V50 alloys with different thermal history

The influence of the formation conditions of the sigma phase in an equiatomic FeV alloy on the magnetic and electric transport properties is studied. It is found that a sigma phase sample with higher resistivity (subject to a previous long annealing) has a much sharper magnetic transition than one formed after a shorter heat treatment and quenching, although both have very similar magnetic moments and ferromagnetic transition temperatures (T_c ～ 15 K from minimum dM/dT).     

Substrate promiscuity in DNA methyltransferase M.PvuII. A mechanistic insight

M.PvuII is a DNA methyltransferase from the bacterium Proteus vulgaris that catalyzes methylation of cytosine at the N4 position. This enzyme also displays promiscuous activity catalyzing methylation of adenine at the N6 position. In this work we use QM/MM methods to investigate the reaction mechanism of this promiscuous activity. We found that N6 methylation in M.PvuII takes place by means of a stepwise mechanism in which deprotonation of the exocyclic amino group is followed by the methyl transfer. Deprotonation involves two residues of the active site, Ser53 and Asp96, while methylation takes place directly from the AdoMet cofactor to the target nitrogen atom. The same reaction mechanism was described for cytosine methylation in the same enzyme, while the reversal timing, that is methylation followed by deprotonation, has been described in M.TaqI, an enzyme that catalyzes the N6-adenine DNA methylation from Thermus aquaticus. These mechanistic findings can be useful to understand the evolutionary paths followed by N-methyltransferases.     

Glycation and oxidation of histones H2B and H1: in vitro study and characterization by mass spectrometry

Among the post-translational modifications, oxidation and glycation are of special interest, especially in diseases such as diabetes, and in aging. The synergistic interaction between glycation and oxidation, also known as “glycoxidation” is highly relevant due to its involvement in the production of deleterious changes at the molecular level. Non-enzymatic damage to nuclear proteins has potentially severe consequences for the maintenance of genomic integrity [54]. In this report, we study glycated histones and its in vitro oxidation. Data concerning the modifications that occurred in the histones were obtained by analysis of enzymatic digests (Glu-C and Arg-C) of unmodified and glycated histones, obtained before and after oxidation. Analysis was then performed using a MALDI-MS/MS-based approach combined with nano liquid chromatography. This approach allowed us to identify histone H2B and H1 specific-sites of oxidation and to distinguish the most affected residues for each histone. The results showed the occurrence of a cumulative effect of oxidative damage in the glycated histones when subjected to in vitro oxidation, suggesting that structural changes caused by glycation induces histones to a pro-oxidant state. Comparing the data of oxidized glycated histones with data from unmodified oxidized histones, using the same model of oxidation, the results clearly show that these oxidative modifications occur earlier and more extensively in glycated histones. Furthermore, the results pointed to an increased oxidative damage in the vicinity of the glycated residues.     

Electrical conductivity of PUR/MWCNT nanocomposites in the molten state, during crystallization and in the solid state

The electrical conductivity of a nanocomposite constituted of multiwalled carbon nanotubes (MWCNT) dispersed in a semicrystalline polyurethane matrix, is investigated during cooling from the melt to the solid state. The same percolation threshold, ?_c = 0.85 wt.%, is obtained in the molten and in the solid state, although the exponent t of the percolation equation is significantly higher in the solid state. A remarkable increase of the conductivity during crystallization is observed for nanocomposites of MWCNT content above ?_c, but for contents below ?_c the conductivity decreases. Combined conductivity and PVT results, lead us to discard the hypothesis of an increase of the density of the conductive network (associated with volume shrinkage) as being the cause of the conductivity enhancement during crystallization. Instead, the analysis of the parameters of the percolation equation for the molten and the solid state, suggests a transition from a less effective conductive network to a more performing three dimensional network.     

Photovoltaic activity of Ti/MCM‐41

Ti/MCM‐41 is a well‐known heterogeneous catalyst for alkene epoxidation with organic peroxides. This titanosilicate contains isolated titanium atoms forming part of a framework of mesoporous silica whose structure is formed by parallel hexagonal channels 3.2 nm in diameter. The surface area and porosity of Ti/MCM‐41 are about 880 m² g^?1 and 0.70 cm³ g^?1, respectively. These values are among the highest for any material. Herein, we show that Ti/MCM‐41 exhibits photovoltaic activity. Dye‐sensitized solar cells using mesoporous Ti/MCM‐41 (2.8–5.7 % Ti content) as active layer, black dye N3 as photosensitizer and I₃^?/I^? in methoxyacetonitrile as electrolyte exhibit a V_OC, J_SC and FF of 0.44 V, 0.045 mA cm^?2 and 0.33, respectively. These values compare well against 0.75 V, 4.1 mA cm^?2 and 0.64, respectively, measured for analogous solar cells using conventional P‐25 TiO₂. However, the specific current density (J_SC/Ti atom) for the Ti/MCM‐41 is very similar to that of P25 TiO₂.