Regular Moebius transformations of the space of quaternions

Let H be the real algebra of quaternions. The notion of regular function of a quaternionic variable recently presented by G. Gentili and D. C. Struppa developed into a quite rich theory. Several properties of regular quaternionic functions are analogous to those of holomorphic functions of one complex variable, although the diversity of the quaternionic setting introduces new phenomena. This paper studies regular quaternionic transformations. We first find a quaternionic analog to the Casorati-Weierstrass theorem and prove that all regular injective functions from H to itself are affine. In particular, the group Aut(H) of biregular functions on H coincides with the group of regular affine transformations. Inspired by the classical quaternionic linear fractional transformations, we define the regular fractional transformations. We then show that each regular injective function from the Alexandroff compactification of H to itself is a regular fractional transformation. Finally, we study regular Moebius transformations, which map the unit ball B onto itself. All regular bijections from B to itself prove to be regular Moebius transformations.Comment: 12 page

BORDER COLLISION OF NON-HYPERBOLIC FIXED POINTS

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Thermodynamics of beta-amyloid fibril formation

Amyloid fibers are aggregates of proteins. They are built out of a peptide called $\beta$--amyloid (A$\beta$) containing between 41 and 43 residues, produced by the action of an enzyme which cleaves a much larger protein known as the Amyloid Precursor Protein (APP). X-ray diffraction experiments have shown that these fibrils are rich in $\beta$--structures, whereas the shape of the peptide displays an $\alpha$--helix structure within the APP in its biologically active conformation. A realistic model of fibril formation is developed based on the seventeen residues A$\beta$12--28 amyloid peptide, which has been shown to form fibrils structurally similar to those of the whole A$\beta$ peptide. With the help of physical arguments and in keeping with experimental findings, the A$\beta$12--28 monomer is assumed to be in four possible states (i.e., native helix conformation, $\beta$--hairpin, globular low--energy state and unfolded state). Making use of these monomeric states, oligomers (dimers, tertramers and octamers) were constructed. With the help of short, detailed Molecular Dynamics (MD) calculations of the three monomers and of a variety of oligomers, energies for these structures were obtained. Making use of these results within the framework of a simple yet realistic model to describe the entropic terms associated with the variety of amyloid conformations, a phase diagram can be calculated of the whole many--body system, leading to a thermodynamical picture in overall agreement with the experimental findings. In particular, the existence of micellar metastable states seem to be a key issue to determine the thermodynamical properties of the system

k-Dirac operator and parabolic geometries

The principal group of a Klein geometry has canonical left action on the homogeneous space of the geometry and this action induces action on the spaces of sections of vector bundles over the homogeneous space. This paper is about construction of differential operators invariant with respect to the induced action of the principal group of a particular type of parabolic geometry. These operators form sequences which are related to the minimal resolutions of the k-Dirac operators studied in Clifford analysis

Brazilian Atlantic Forest Lato Sensu: The Most Ancient Brazilian Forest, And A Biodiversity Hotspot, Is Highly Threatened By Climate Change.

After 500 years of exploitation and destruction, the Brazilian Atlantic Forest has been reduced to less the 8% of its original cover, and climate change may pose a new threat to the remnants of this biodiversity hotspot. In this study we used modelling techniques to determine present and future geographical distribution of 38 species of trees that are typical of the Brazilian Atlantic Forest (Mata Atlântica), considering two global warming scenarios. The optimistic scenario, based in a 0.5% increase in the concentration of CO2 in the atmosphere, predicts an increase of up to 2 °C in the Earth's average temperature; in the pessimistic scenario, based on a 1% increase in the concentration of CO2 in the atmosphere, temperature increase may reach 4 °C. Using these parameters, the occurrence points of the studied species registered in literature, the Genetic Algorithm for Rule-set Predictions/GARP and Maximum entropy modeling of species geographic distributions/MaxEnt we developed models of present and future possible occurrence of each species, considering Earth's mean temperature by 2050 with the optimistic and the pessimistic scenarios of CO2 emission. The results obtained show an alarming reduction in the area of possible occurrence of the species studied, as well as a shift towards southern areas of Brazil. Using GARP, on average, in the optimistic scenario this reduction is of 25% while in the pessimistic scenario it reaches 50%, and the species that will suffer the worst reduction in their possible area of occurrence are: Euterpe edulis, Mollinedia schottiana, Virola bicuhyba, Inga sessilis and Vochysia magnifica. Using MaxEnt, on average, in the optimistic scenario the reduction will be of 20% while in the pessimistic scenario it reaches 30%, and the species that will suffer the worst reduction are: Hyeronima alchorneoides, Schefflera angustissima, Andira fraxinifolia and the species of Myrtaceae studied.70697-70

Understanding the determinants of stability and folding of small globular proteins from their energetics

The results of minimal model calculations suggest that the stability and the kinetic accessibility of the native state of small globular proteins are controlled by few "hot" sites. By mean of molecular dynamics simulations around the native conformation, which simulate the protein and the surrounding solvent at full--atom level, we generate an energetic map of the equilibrium state of the protein and simplify it with an Eigenvalue decomposition. The components of the Eigenvector associated with the lowest Eigenvalue indicate which are the "hot" sites responsible for the stability and for the fast folding of the protein. Comparison of these predictions with the results of mutatgenesis experiments, performed for five small proteins, provide an excellent agreement

Percutaneous mitral valve repair procedures

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XMM-Newton and Chandra observations of G272.2-3.2. Evidence of stellar ejecta in the central region

We aim to study the spatial distribution of the physical and chemical properties of the X-ray emitting plasma of the supernova remnant G272.2-3.2, in order to get important constraints on its ionization stage, on the progenitor supernova explosion, and the age of the remnant. We report combined XMM-Newton and Chandra images, median photon energy map, silicon and sulfur equivalent width maps, and a spatially resolved spectral analysis for a set of regions of the remnant. Complementary radio and H{\alpha} observations, available in the literature, are also used to study the multi-wavelength connection of all detected emissions. The X-ray morphology of the remnant displays an overall structure with an almost circular appearance, a centrally brightened hard region, with a peculiar elongated hard structure oriented along the northwest-southeast direction of the central part. The X-ray spectral study of the regions shows distinct K{\alpha} emission-line features of metal elements, confirming the thermal origin of the emission. The X-ray spectra are well represented by an absorbed VNEI thermal plasma model, which produces elevated abundances of Si, S, and Fe in the circular central region, typical of ejecta material. The values of abundances found in the central region of the SNR favor a Type Ia progenitor for this remnant. The outer region shows abundances below the solar value, as expected if the emission arises from the shocked ISM. The relatively low ionization timescales suggests non-equilibrium ionization. We identify the location of the contact discontinuity. Its distance to the outer shock is higher than expected for expansion in a uniform media, what suggests that the remnant spent most of its time in a more dense medium.Comment: 9 pages, 7 figures. Accepted for publication in A&