Synthesis and reactivity of η-tetramethylcyclopentadienyl-propenyl rhenium complexes: Molecular structure of [(η:η-C5Me4CH2CHCH2)Re(CO)2]

The fulvene complexes [(η⁶-C₅Me₄CH₂)Re(CO)₂(R)] (1a, RI; 1b, RC₆F₅) react at the exocyclic methylene carbon with a vinylmagnesium bromide solution to produce the anionic species [(η⁵-C₅Me₄CH₂CHCH₂)Re(CO)₂(R)]⁻. Protonation with HCl at 0 °C produces the hydride complexes [trans-(η⁵-C₅Me₄CH₂CHCH₂)Re(CO)₂(R)(H)] (2a, RI; 2b, RC₆F₅). Thermolysis of an hexane solution of the iodo-hydride (2a) under a CO atmosphere yields the complex [(η⁵-C₅Me₄CH₂CHCH₂)Re(CO)₃] (3) and [Re(CO)₅I] as by-product. Thermolysis of 2b produced three new products, mainly the chelated complex [(η⁵:η²-C₅Me₄CH₂CHCH₂)Re(CO)₂] (4) and complex 3, with a non-coordinated olefin group, in moderated yield, and traces of [Re(CO)₅(C₆F₅)]. Thermolysis of an hexane solution of 2 in presence of an excess of PMe₃, afforded the phosphine derivative [(η⁵-C₅Me₄CH₂CHCH₂)Re(CO)₂(PMe₃)] (5). All the complexes were characterized by IR, ¹H, ¹³C and ³¹P NMR spectroscopies and mass spectrometry. The molecular structure of 4 has also been determined. The molecule exhibits a formal three-legged piano-stool structure, with two CO groups, and the third position corresponding to the η²-coordination of the propenyl side arm of the η⁵-C₅Me₄ ring.     

Kinetics of autocatalytic acid hydrolysis of cellulose with crystalline and amorphous fractions

The acid hydrolysis of cellulose with crystalline and amorphous fractions is analyzed on the basis of autocatalytic model with a positive feedback of acid production from the degraded biopolymer. In the condition of low acid rate production compared with hydrolysis rate, both fraction of cellulose decrease exponentially with linear and cubic time dependence, and the normalized number of scissions per cellulose chain follows a sigmoid behavior with reaction time. The model predicts that self generated acidic compounds from cellulose accelerate the degradation of the biopolymer. However, if the acidic compounds produced are volatile species, then their release under low pressure will reduce the global rate of degradation of cellulose toward its intrinsic rate value determined by the residual acid catalyst present in the starting material.     

Modeling and analysis of laminate composite plates with embedded active-passive piezoelectric networks

The objective of this work is to present the finite element modeling of laminate composite plates with embedded piezoelectric patches or layers that are then connected to active-passive resonant shunt circuits, composed of resistance, inductance and voltage source. Applications to passive vibration control and active control authority enhancement are also presented and discussed. The finite element model is based on an equivalent single layer theory combined with a third-order shear deformation theory. A stress-voltage electromechanical model is considered for the piezoelectric materials fully coupled to the electrical circuits. To this end, the electrical circuit equations are also included in the variational formulation. Hence, conservation of charge and full electromechanical coupling are guaranteed. The formulation results in a coupled finite element model with mechanical (displacements) and electrical (charges at electrodes) degrees of freedom. For a Graphite-Epoxy (Carbon-Fibre Reinforced) laminate composite plate, a parametric analysis is performed to evaluate optimal locations along the plate plane (xy) and thickness (z) that maximize the effective modal electromechanical coupling coefficient. Then, the passive vibration control performance is evaluated for a network of optimally located shunted piezoelectric patches embedded in the plate, through the design of resistance and inductance values of each circuit, to reduce the vibration amplitude of the first four vibration modes. A vibration amplitude reduction of at least 10 dB for all vibration modes was observed. Then, an analysis of the control authority enhancement due to the resonant shunt circuit, when the piezoelectric patches are used as actuators, is performed. It is shown that the control authority can indeed be improved near a selected resonance even with multiple pairs of piezoelectric patches and active-passive circuits acting simultaneously.     

Spatial distribution of AT- and GC-rich DNA within interphase cell nuclei of Triatoma infestans Klug

Heterochromatin bodies in single- and multichromocentered interphase cell nuclei of Triatoma infestans, a vector of Chagas disease, have been suggested to contain AT-rich DNA, based on their positive response to Q-banding and Hoechst 33248 treatment. No information exists on whether GC-rich DNA is also present in these nuclei and whether it plays a role on chromatin condensation. Considering that methodologies more precise than those previously used to determine DNA base composition in situ are currently available, and that the spatial distribution of chromatin areas differing in composition in interphase cell nuclei of different species is a matter of interest, the localization of AT- and GC-rich DNA in T. infestans nuclei is revisited here. The methodologies used included DAPI/AMD and CMA(3)/Distamycin differential staining, Feulgen-DNA image analysis following Msp I and Hpa II enzymatic digestion, 5-methylcytidine immunodetection, AgNOR response, confocal microscopy, and the 5-aza-2'-deoxycytidine (5-AZA) demethylation assay. The results identified the presence of AT-rich/GC-poor DNA in chromocenters and evenly distributed AT and GC sequences in euchromatin. A GC-rich DNA zone encircling the chromocenters was also found but it could not be associated with NOR regions. To corroborate the DNA AT-richness in T. infestans nuclei, bioinformatic analyses were also performed. Methylated cytosine was evident at some points of the chromocenters' edge in single- and multichromocentered nuclei and at the euchromatin of multichromocentered nuclei and could be transiently affected by the 5-AZA treatment. The present results suggest that in the particular case of chromocenters of the hemipteran T. infestans, cytosine methylation is not a relevant factor involved in chromatin condensation.     

Time-periodic perturbation of a Liénard equation with an unbounded homoclinic loop

We consider a quadratic Liénard equation with an unbounded homoclinic loop, which is a solution tending in forward and backward time to a non-hyperbolic equilibrium point located at infinity. Under small time-periodic perturbation, this equilibrium becomes a normally hyperbolic line of singularities at infinity. We show that the perturbed system may present homoclinic bifurcations, leading to the existence of transverse intersections between the stable and unstable manifolds of such a normally hyperbolic line of singularities. The global study concerning the infinity is performed using the Poincaré compactification in polar coordinates, from which we obtain a system defined on a set equivalent to a solid torus in R³, whose boundary plays the role of the infinity. The transversality of the manifolds is proved using the Melnikov method and implies, via the Birkhoff-Smale Theorem, a complex dynamical behaviour of the perturbed system solutions in the finite part of the phase space. Numerical simulations are performed in order to illustrate this behaviour, which could be called “the chaos arising from infinity”, since it depends on the global structure of the Liénard equation, including the points at infinity. Although applied to a particular case, the analysis presented provides a geometrical approach to study periodic perturbations of homoclinic (or heteroclinic) loops to infinity of any planar polynomial vector field.     

Nonlinear perturbations of a ‐Laplacian equation with critical growth in

We prove the existence of solution for a class of ‐Laplacian equations where the nonlinearity has a critical growth. Here, we consider two cases: the first case involves the situation where the variable exponents are periodic functions. The second one involves the case where the variable exponents are nonperiodic perturbations.     

Radical of submodules and symmetric algebra

A prime ideal of the symmetric algebra of an R-module N is associated to every prime submodule M ?N and this assignment is then used to obtain a new characterization of the radical of a submodule. Several applications of these results are also included.