FREE GROUP ALGEBRAS IN DIVISION RINGS

Let k be an algebraically closed field of characteristic zero and let L be an algebraic function field over k. Let sigma : L -> L be a k-automorphism of infinite order, and let D be the skew field of fractions of the skew polynomial ring L[t; sigma]. We show that D contains the group algebra kF of the free group F of rank 2.

Polynomial and Poisson dependence in free Poisson algebras and free Poisson fields

We prove that any two Poisson dependent elements in a free Poisson algebra and a free Poisson field of characteristic zero are algebraically dependent, thus answering positively a question from Makar-Limanov and Umirbaev (2007) [8]. We apply this result to give a new proof of the tameness of automorphisms for free Poisson algebras of rank two (see Makar-Limanov and Umirbaev (2011) [9], Makar-Limanov et al. (2009) [10]). (C) 2011 Elsevier Inc. All rights reserved.

Seven-membered Rings Through Metal-free Rearrangement Mediated By Hypervalent Iodine.

A versatile and metal-free approach for the synthesis of carbocycles and of heterocycles bearing seven- and eight-membered rings is described. The strategy is based on ring expansion of 1-vinylcycloalkanols (or the corresponding silyl or methyl ether) mediated by the hypervalent iodine reagent HTIB (PhI(OH)OTs). Reaction conditions can be easily adjusted to give ring expansion products bearing different functional groups. A route to medium-ring lactones was also developed.

Direct Computation of Operational Matrices for Polynomial Bases

Several numerical methods for boundary value problems use integral and differential operational matrices, expressed in polynomial bases in a Hilbert space of functions. This work presents a sequence of matrix operations allowing a direct computation of operational matrices for polynomial bases, orthogonal or not, starting with any previously known reference matrix. Furthermore, it shows how to obtain the reference matrix for a chosen polynomial base. The results presented here can be applied not only for integration and differentiation, but also for any linear operation.

Ring chromosome instability evaluation in six patients with autosomal rings

Ring chromosomes are often associated with abnormal phenotypes due to loss of genomic material and also because of ring instability at mitosis after sister chromatid exchange events. We investigated ring chromosome instability in six patients with ring chromosomes 4, 14, 15, and 18 by examining 48- and 72-h lymphocyte cultures at the first, second and subsequent cell divisions after bromodeoxyuridine incorporation. Although most cells from all patients showed only one monocentric ring chromosome, ring chromosome loss and secondary aberrations were observed both in 48-and 72-h lymphocyte cultures and in metaphase cells of the different cell generations. We found no clear-cut correlation between ring size and ring instability; we also did not find differences between apparently complete rings and rings with genetic material loss. The cytogenetic findings revealed secondary aberrations in all ring chromosome patients. We concluded that cells with ring chromosome instability can multiply and survive in vivo, and that they can influence the patient's phenotype.

Artificial molecular quantum rings under magnetic field influence

The ground states of a few electrons confined in two vertically coupled quantum rings in the presence of an external magnetic field are studied systematically within the current spin-density functional theory. Electron-electron interactions combined with inter-ring tunneling affect the electronic structure and the persistent current. For small values of the external magnetic field, we recover the zero magnetic field molecular quantum ring ground state configurations. Increasing the magnetic field many angular momentum, spin, and isospin transitions are predicted to occur in the ground state. We show that these transitions follow certain rules, which are governed by the parity of the number of electrons, the single-particle picture, Hund's rules, and many-body effects. (C) 2009 American Institute of Physics. [doi:10.1063/1.3223360]

Control of the persistent currents in two interacting quantum rings through the Coulomb interaction and interring tunneling

The persistent current in two vertically coupled quantum rings containing few electrons is studied. We find that the Coulomb interaction between the rings in the absence of tunneling affects the persistent current in each ring and the ground-state configurations. Quantum tunneling between the rings alters significantly the ground state and the persistent current in the system.

Characterization of tree-rings of Pinus caribaea var. hondurensis Barr. et Golf. trees by X ray densitometry

This work aimed to determining the anatomical structure of wood, through methodology of histology and X-ray densitometry, of resin-tapped and not resin-tapped Pinus caribaea var. hondurensis trees samples, of three diameter classes. Pine trees, in forest plantation established in 1969, in the Ecological Experimental Station of Itirapina, from the Forestry Institute of Sao Paulo State, were measured and stratified into three classes of trunk diameter. The pine trees were resin-tapped since 2004, with the opening of two simultaneous and opposing panels. Sixty samples of pine wood trees were extracted from the tree trunk through a non-destructive method and in the laboratory. Tree rings were determined in the laboratory and wood apparent density by X-ray densitometry. The test results showed that: (i) false tree rings occur in the early wood and late wood of the tree rings due to climate change; (ii) the X-ray densitometry allowed the demarcation of the tree rings limits; (iii) the wood apparent density average was significantly different between the trees in high class diameter and in the medium-low class; (iv) the wood characteristics from the resin-tapped and non resin-tapped faces did not show significant differences.

Annual growth rings in the mangrove Laguncularia racemosa (Combretaceae)

Stem discs from trees of known age were used to determine the periodic nature of the growth rings formed in Laguncularia racemosa and to describe the anatomical features of these rings. The growth rings were scarcely distinct on microscopic examination, but they were well distinguishable macroscopically, with alternating light brown and dark brown layers. Cross-dating analysis revealed the occurrence of annual growth rings in L. racemosa. The existence of annual growth rings in L. racemosa suggests that it may have great potential for dendrochronology and should encourage age-related studies on the dynamics of mangrove forests. These studies can be important for the evaluation of climate change impact on mangrove ecosystems, as well as for the analysis of effects related to climate variability on plant communities.

Self-assembly in chains, rings, and branches: a single component system with two critical points

Agências financiadoras: FCT - PEstOE/FIS/UI0618/2011; PTDC/FIS/098254/2008 ERC-PATCHYCOLLOIDS e MIUR-PRIN