A total order in [0,1] defined through a 'next' operator

A `next' operator, s, is built on the set R1=(0,1]-{ 1-1/e} defining a partial order that, with the help of the axiom of choice, can be extended to a total order in R1. Besides, the orbits {sn(a)}nare all dense in R1 and are constituted by elements of the samearithmetical character: if a is an algebraic irrational of degreek all the elements in a's orbit are algebraic of degree k; if a istranscendental, all are transcendental. Moreover, the asymptoticdistribution function of the sequence formed by the elements in anyof the half-orbits is a continuous, strictly increasing, singularfunction very similar to the well-known Minkowski's ?(×) function.

Solid phase crystallization under continuous heating: kinetic and microstructure scaling laws

The kinetics and microstructure of solid-phase crystallization under continuous heating conditions and random distribution of nuclei are analyzed. An Arrhenius temperature dependence is assumed for both nucleation and growth rates. Under these circumstances, the system has a scaling law such that the behavior of the scaled system is independent of the heating rate. Hence, the kinetics and microstructure obtained at different heating rates differ only in time and length scaling factors. Concerning the kinetics, it is shown that the extended volume evolves with time according to αex = [exp(κCt′)]m+1, where t′ is the dimensionless time. This scaled solution not only represents a significant simplification of the system description, it also provides new tools for its analysis. For instance, it has been possible to find an analytical dependence of the final average grain size on kinetic parameters. Concerning the microstructure, the existence of a length scaling factor has allowed the grain-size distribution to be numerically calculated as a function of the kinetic parameters

Color differences among feral pigeons (Columba livia) are not attributable to sequence variation in the coding region of the melanocortin-1 receptor gene (MC1R)

Genetic variation at the melanocortin-1 receptor (MC1R) gene is correlated with melanin color variation in many birds. Feral pigeons (Columba livia) show two major melanin-based colorations: a red coloration due to pheomelanic pigment and a black coloration due to eumelanic pigment. Furthermore, within each color type, feral pigeons display continuous variation in the amount of melanin pigment present in the feathers, with individuals varying from pure white to a full dark melanic color. Coloration is highly heritable and it has been suggested that it is under natural or sexual selection, or both. Our objective was to investigate whether MC1R allelic variants are associated with plumage color in feral pigeons.We sequenced 888 bp of the coding sequence of MC1R among pigeons varying both in the type, eumelanin or pheomelanin, and the amount of melanin in their feathers. We detected 10 non-synonymous substitutions and 2 synonymous substitution but none of them were associated with a plumage type. It remains possible that non-synonymous substitutions that influence coloration are present in the short MC1R fragment that we did not sequence but this seems unlikely because we analyzed the entire functionally important region of the gene.Our results show that color differences among feral pigeons are probably not attributable to amino acid variation at the MC1R locus. Therefore, variation in regulatory regions of MC1R or variation in other genes may be responsible for the color polymorphism of feral pigeons.

Generation of symmetric periodic orbits by a heteroclinic loop formed by two singular points and their invariant manifolds of dimension 1 and 2 in R3

In this paper we will find a continuous of periodic orbits passing near infinity for a class of polynomial vector fields in R3. We consider polynomial vector fields that are invariant under a symmetry with respect to a plane and that possess a “generalized heteroclinic loop” formed by two singular points e+ and e− at infinity and their invariant manifolds � and . � is an invariant manifold of dimension 1 formed by an orbit going from e− to e+, � is contained in R3 and is transversal to . is an invariant manifold of dimension 2 at infinity. In fact, is the 2–dimensional sphere at infinity in the Poincar´e compactification minus the singular points e+ and e−. The main tool for proving the existence of such periodic orbits is the construction of a Poincar´e map along the generalized heteroclinic loop together with the symmetry with respect to .

Differential pattern of glycogen accumulation after protein phosphatase 1 glycogen-targeting subunit PPP1R6 overexpression, compared to PPP1R3C and PPP1R3A, in skeletal muscle cells

Background PPP1R6 is a protein phosphatase 1 glycogen-targeting subunit (PP1-GTS) abundant in skeletal muscle with an undefined metabolic control role. Here PPP1R6 effects on myotube glycogen metabolism, particle size and subcellular distribution are examined and compared with PPP1R3C/PTG and PPP1R3A/GM. Results PPP1R6 overexpression activates glycogen synthase (GS), reduces its phosphorylation at Ser-641/0 and increases the extracted and cytochemically-stained glycogen content, less than PTG but more than GM. PPP1R6 does not change glycogen phosphorylase activity. All tested PP1-GTS-cells have more glycogen particles than controls as found by electron microscopy of myotube sections. Glycogen particle size is distributed for all cell-types in a continuous range, but PPP1R6 forms smaller particles (mean diameter 14.4 nm) than PTG (36.9 nm) and GM (28.3 nm) or those in control cells (29.2 nm). Both PPP1R6- and GM-derived glycogen particles are in cytosol associated with cellular structures; PTG-derived glycogen is found in membrane- and organelle-devoid cytosolic glycogen-rich areas; and glycogen particles are dispersed in the cytosol in control cells. A tagged PPP1R6 protein at the C-terminus with EGFP shows a diffuse cytosol pattern in glucose-replete and -depleted cells and a punctuate pattern surrounding the nucleus in glucose-depleted cells, which colocates with RFP tagged with the Golgi targeting domain of β-1,4-galactosyltransferase, according to a computational prediction for PPP1R6 Golgi location. Conclusions PPP1R6 exerts a powerful glycogenic effect in cultured muscle cells, more than GM and less than PTG. PPP1R6 protein translocates from a Golgi to cytosolic location in response to glucose. The molecular size and subcellular location of myotube glycogen particles is determined by the PPP1R6, PTG and GM scaffolding.