Approximating multi-dimensional Hamiltonian flows by billiards

Consider a family of smooth potentials $V_{\epsilon}$, which, in the limit $\epsilon\to0$, become a singular hard-wall potential of a multi-dimensional billiard. We define auxiliary billiard domains that asymptote, as $\epsilon\to0$ to the original billiard, and provide asymptotic expansion of the smooth Hamiltonian solution in terms of these billiard approximations. The asymptotic expansion includes error estimates in the $C^{r}$ norm and an iteration scheme for improving this approximation. Applying this theory to smooth potentials which limit to the multi-dimensional close to ellipsoidal billiards, we predict when the separatrix splitting persists for various types of potentials

Sistema Estadual de Pesquisa Agropecuária - SEPA: revitalização de um mecanismo de integração e parceria institucional.

SEPA; Abordagem conceitual; Importância; Objetivo geral; Diretrizes; Organização e operacionalização; O papel da EMBRAPA em relação ao SNPA e aos SEPAs.bitstream/item/120249/1/Sistema-Estadual-de-Pesquisa-Agropecuaria-SEPA.pd

Convergence of invariant densities in the small-noise limit

This paper presents a systematic numerical study of the effects of noise on the invariant probability densities of dynamical systems with varying degrees of hyperbolicity. It is found that the rate of convergence of invariant densities in the small-noise limit is frequently governed by power laws. In addition, a simple heuristic is proposed and found to correctly predict the power law exponent in exponentially mixing systems. In systems which are not exponentially mixing, the heuristic provides only an upper bound on the power law exponent. As this numerical study requires the computation of invariant densities across more than 2 decades of noise amplitudes, it also provides an opportunity to discuss and compare standard numerical methods for computing invariant probability densities.Comment: 27 pages, 19 figures, revised with minor correction

In vitro production of bovine embryos derived from individual donors in the Corral® dish

Background: Since the identity of the embryo is of outmost importance during commercial in vitro embryo production, bovine oocytes and embryos have to be cultured strictly per donor. Due to the rather low yield of oocytes collected after ovum pick-up (OPU) per individual cow, oocyte maturation and embryo culture take place in small groups, which is often associated with inferior embryo development. The objective of this study was to improve embryonic development in small donor groups by using the Corral (R) dish. This commercial dish is designed for human embryo production. It contains two central wells that are divided into quadrants by a semi-permeable wall. In human embryo culture, one embryo is placed per quadrant, allowing individual follow-up while embryos are exposed to a common medium. In our study, small groups of oocytes and subsequently embryos of different bovine donors were placed in the Corral (R) dish, each donor group in a separate quadrant. Results: In two experiments, the Corral (R) dish was evaluated during in vitro maturation (IVM) and/or in vitro culture (IVC) by grouping oocytes and embryos of individual bovine donors per quadrant. At day 7, a significantly higher blastocyst rate was noted in the Corral (R) dish used during IVM and IVC than when only used during IVM (12.9% +/- 2.10 versus 22.8% +/- 2.67) (P < 0.05). However, no significant differences in blastocyst yield were observed anymore between treatment groups at day 8 post insemination. Conclusions: In the present study, the Corral (R) dish was used for in vitro embryo production (IVP) in cattle; allowing to allocate oocytes and/or embryos per donor. As fresh embryo transfers on day 7 have higher pregnancy outcomes, the Corral (R) dish offers an added value for commercial OPU/IVP, since a higher blastocyst development at day 7 is obtained when the Corral (R) dish is used during IVM and IVC

Track billiards

We study a class of planar billiards having the remarkable property that their phase space consists up to a set of zero measure of two invariant sets formed by orbits moving in opposite directions. The tables of these billiards are tubular neighborhoods of differentiable Jordan curves that are unions of finitely many segments and arcs of circles. We prove that under proper conditions on the segments and the arcs, the billiards considered have non-zero Lyapunov exponents almost everywhere. These results are then extended to a similar class of of 3-dimensional billiards. Finally, we find that for some subclasses of track billiards, the mechanism generating hyperbolicity is not the defocusing one that requires every infinitesimal beam of parallel rays to defocus after every reflection off of the focusing boundary.Comment: 7 figure

Oxidation and magnetic states of chalcopyrite CuFeS2: a first principles calculation

The ground state band structure, magnetic moments, charges and population numbers of electronic shells of Cu and Fe atoms have been calculated for chalcopyrite CuFeS2 using density functional theory. The comparison between our calculation results and experimental data (X ray photoemission, X ray absorption and neutron diffraction spectroscopy) has been made. Our calculations predict a formal oxidation state for chalcopyrite as Cu1+Fe3+S. However, the assignment of formal valence state to transition metal atoms appears to be oversimplified. It is anticipated that the valence state can be confirmed experimentally by nuclear magnetic and nuclear quadrupole resonance and Mössbauer spectroscopy methods

Highly efficient separation of actinides from lanthanides by a phenanthroline-derived bis-triazine ligand

The synthesis, lanthanide complexation, and solvent ex- traction of actinide(III) and lanthanide(III) radiotracers from nitric acid solutions by a phenanthroline-derived quadridentate bis-triazine ligand are described. The ligand separates Am(III) and Cm(III) from the lanthanides with remarkably high efficiency, high selectivity, and fast extraction kinetics compared to its 2,2'-bipyridine counterpart. Structures of the 1:2 bis-complexes of the ligand with Eu(III) and Yb(III) were elucidated by X-ray crystallography and force field calculations, respec-tively. The Eu(III) bis-complex is the first 1:2 bis-complex of a quadridentate bis-triazine ligand to be characterized by crystallography. The faster rates of extraction were verified by kinetics measurements using the rotating membrane cell technique in several diluents. The improved kinetics of metal ion extraction are related to the higher surface activity of the ligand at the phase interface. The improvement in the ligand's properties on replacing the bipyridine unit with a phenanthroline unit far exceeds what was anticipated based on ligand design alone

Potential Role for Peptidylarginine Deiminase 2 (PAD2) in Citrullination of Canine Mammary Epithelial Cell Histones

Peptidylarginine Deiminases (PADs) convert arginine residues on substrate proteins to citrulline. Previous reports have documented that PAD2 expression and activity varies across the estrous cycle in the rodent uterus and pituitary gland, however, the expression and function of PAD2 in mammary tissue has not been previously reported. To gain more insight into potential reproductive roles for PAD2, in this study we evaluated PAD2 expression and localization throughout the estrous cycle in canine mammary tissue and then identified possible PAD2 enzymatic targets. Immunohistochemical and immunofluorescence analysis found PAD2 expression is low in anestrus, limited to a distinct, yet sparse, subset of epithelial cells within ductal alveoli during estrus/early diestrus, and encompasses the entire epithelium of the mammary duct in late diestrus. At the subcellular level, PAD2 is expressed in the cytoplasm, and to a lesser extent, the nucleus of these epithelial cells. Surprisingly, stimulation of canine mammary tumor cells (CMT25) shows that EGF, but not estrogen or progesterone, upregulates PAD2 transcription and translation suggesting EGF regulation of PAD2 and possibly citrullination in vivo. To identify potential PAD2 targets, anti-pan citrulline western blots were performed and results showed that citrullination activity is limited to diestrus with histones appearing to represent major enzymatic targets. Use of site-specific anti-citrullinated histone antibodies found that the N-terminus of histone H3, but not H4, appears to be the primary target of PAD activity in mammary epithelium. This observation supports the hypothesis that PAD2 may play a regulatory role in the expression of lactation related genes via histone citrullination during diestrus