A structural theorem for co-commutative Hopf algebras

Lo scopo di questa tesi è studiare alcune proprietà di base delle algebre di Hopf, strutture algebriche emerse intorno agli anni ’50 dalla topologica algebrica e dalla teoria dei gruppi algebrici, e mostrare un collegamento tra esse e le algebre di Lie. Il primo capitolo è un’introduzione basilare al concetto di prodotto tensoriale di spazi vettoriali, che verrà utilizzato nel secondo capitolo per definire le strutture di algebra, co-algebra e bi-algebra. Il terzo capitolo introduce le definizioni e alcune proprietà di base delle algebre di Hopf e di Lie, con particolare attenzione al legame tra le prime e l’algebra universale inviluppante di un’algebra di Lie. Questo legame sarà approfondito nel quarto capitolo, dedicato allo studio di una particolare classe di algebre di Hopf, quelle graduate e connesse, che terminerà con il teorema di Cartier-Quillen-Milnor-Moore, un teorema strutturale che fornisce condizioni sufficienti affinché un’algebra di Hopf sia isomorfa all’algebra universale inviluppante dei suoi elementi primitivi.

Phylogenetics, Ancestral State Reconstruction, And A New Infrafamilial Classification Of The Pantropical Ochnaceae (medusagynaceae, Ochnaceae S.str., Quiinaceae) Based On Five Dna Regions.

Ochnaceae s.str. (Malpighiales) are a pantropical family of about 500 species and 27 genera of almost exclusively woody plants. Infrafamilial classification and relationships have been controversial partially due to the lack of a robust phylogenetic framework. Including all genera except Indosinia and Perissocarpa and DNA sequence data for five DNA regions (ITS, matK, ndhF, rbcL, trnL-F), we provide for the first time a nearly complete molecular phylogenetic analysis of Ochnaceae s.l. resolving most of the phylogenetic backbone of the family. Based on this, we present a new classification of Ochnaceae s.l., with Medusagynoideae and Quiinoideae included as subfamilies and the former subfamilies Ochnoideae and Sauvagesioideae recognized at the rank of tribe. Our data support a monophyletic Ochneae, but Sauvagesieae in the traditional circumscription is paraphyletic because Testulea emerges as sister to the rest of Ochnoideae, and the next clade shows Luxemburgia+Philacra as sister group to the remaining Ochnoideae. To avoid paraphyly, we classify Luxemburgieae and Testuleeae as new tribes. The African genus Lophira, which has switched between subfamilies (here tribes) in past classifications, emerges as sister to all other Ochneae. Thus, endosperm-free seeds and ovules with partly to completely united integuments (resulting in an apparently single integument) are characters that unite all members of that tribe. The relationships within its largest clade, Ochnineae (former Ochneae), are poorly resolved, but former Ochninae (Brackenridgea, Ochna) are polyphyletic. Within Sauvagesieae, the genus Sauvagesia in its broad circumscription is polyphyletic as Sauvagesia serrata is sister to a clade of Adenarake, Sauvagesia spp., and three other genera. Within Quiinoideae, in contrast to former phylogenetic hypotheses, Lacunaria and Touroulia form a clade that is sister to Quiina. Bayesian ancestral state reconstructions showed that zygomorphic flowers with adaptations to buzz-pollination (poricidal anthers), a syncarpous gynoecium (a near-apocarpous gynoecium evolved independently in Quiinoideae and Ochninae), numerous ovules, septicidal capsules, and winged seeds with endosperm are the ancestral condition in Ochnoideae. Although in some lineages poricidal anthers were lost secondarily, the evolution of poricidal superstructures secured the maintenance of buzz-pollination in some of these genera, indicating a strong selective pressure on keeping that specialized pollination system.

Fundamentos geometricos e algebricos da calibração e reconstrução tridimensional : aplicação na analise cinematica de movimentos humanos

Universidade Estadual de Campinas . Faculdade de Educação Física

Entropia, reversibilidade, irreversibilidade, equação de transporte e teorema H de Boltzmann e o teorema do retorno de Poincaré

Neste trabalho analisamos as conexões entre entropia, reversibilidade, irreversibilidade, teorema H e equação de transporte de Boltzmann e o teorema de retorno de Poincaré. Estes tópicos são estudados separadamente em muitos artigos e livros, mas não são em geral analisados em conjunto mostrando as relações entre eles como fizemos aqui. Procuramos redigir o artigo didaticamente seguindo um caminho que achamos ser o mais simples possível a fim de tornar o conteúdo acessível aos alunos de graduação de física.

Aging and fluctuation-dissipation ratio in a nonequilibrium q-state lattice model

A generalized version of the nonequilibrium linear Glauber model with q states in d dimensions is introduced and analyzed. The model is fully symmetric, its dynamics being invariant under all permutations of the q states. Exact expressions for the two-time autocorrelation and response functions on a d-dimensional lattice are obtained. In the stationary regime, the fluctuation-dissipation theorem holds, while in the transient the aging is observed with the fluctuation-dissipation ratio leading to the value predicted for the linear Glauber model.

Two dimensional analysis of inflatable structures by the positional FEM

This paper presents a, simple two dimensional frame formulation to deal with structures undergoing large motions due to dynamic actions including very thin inflatable structures, balloons. The proposed methodology is based on the minimum potential energy theorem written regarding nodal positions. Velocity, acceleration and strain are achieved directly from positions, not. displacements, characterizing the novelty of the proposed technique. A non-dimensional space is created and the deformation function (change of configuration) is written following two independent mappings from which the strain energy function is written. The classical New-mark equations are used to integrate time. Dumping and non-conservative forces are introduced into the mechanical system by a rheonomic energy function. The final formulation has the advantage of being simple and easy to teach, when compared to classical Counterparts. The behavior of a bench-mark problem (spin-up maneuver) is solved to prove the formulation regarding high circumferential speed applications. Other examples are dedicated to inflatable and very thin structures, in order to test the formulation for further analysis of three dimensional balloons.

Unconstrained Finite Element for Geometrical Nonlinear Dynamics of Shells

This paper presents a positional FEM formulation to deal with geometrical nonlinear dynamics of shells. The main objective is to develop a new FEM methodology based on the minimum potential energy theorem written regarding nodal positions and generalized unconstrained vectors not displacements and rotations. These characteristics are the novelty of the present work and avoid the use of large rotation approximations. A nondimensional auxiliary coordinate system is created, and the change of configuration function is written following two independent mappings from which the strain energy function is derived. This methodology is called positional and, as far as the authors' knowledge goes, is a new procedure to approximated geometrical nonlinear structures. In this paper a proof for the linear and angular momentum conservation property of the Newmark beta algorithm is provided for total Lagrangian description. The proposed shell element is locking free for elastic stress-strain relations due to the presence of linear strain variation along the shell thickness. The curved, high-order element together with an implicit procedure to solve nonlinear equations guarantees precision in calculations. The momentum conserving, the locking free behavior, and the frame invariance of the adopted mapping are numerically confirmed by examples. Copyright (C) 2009 H. B. Coda and R. R. Paccola.

Anomalous diffusion in non-Markovian walks having amnestically induced persistence

We report numerically and analytically estimated values for the Hurst exponent for a recently proposed non-Markovian walk characterized by amnestically induced persistence. These results are consistent with earlier studies showing that log-periodic oscillations arise only for large memory losses of the recent past. We also report numerical estimates of the Hurst exponent for non-Markovian walks with diluted memory. Finally, we study walks with a fractal memory of the past for a Thue-Morse and Fibonacci memory patterns. These results are interpreted and discussed in the context of the necessary and sufficient conditions for the central limit theorem to hold.

Ergonomic Aspects Related to Surgeon Position in Laparoscopic Radical Prostatectomy

Purpose: The aim is to evaluate the level of inclination of the surgeon's spinal column (ISSC) while performing laparoscopic radical prostatectomy (LRP) when using one trocar on each side of the patient abdomen (""torero"" position) in two scenarios: With and without a thin head supporter adapted to the table. Materials and Methods: Based on trigonometric principles, we elaborated a formula to calculate the ISSC for a determined surgeon and surgical table while performing LRP in the torero position. The parameters considered were the width of the surgical table (m), the distance between the surgeon's anterior superior iliac spines (q), and the distance from the central point between the surgeon's anterior superior iliac spines to the surgeon's head (h). We used the formula alpha = 90 degree-cos(-1)(b/h) (where b = q/2 + m/2) in an Excel sheet to calculate the angle of inclination of the surgeon's spinal column. We applied the measures of 12 surgeons with different biotypes of our staff to calculate the ISSC with and without the thin head supporter. Results: The use of a thin head supporter reduced the mean ISCC in the torero position from 36.1 +/- 3.73 degrees (range 31.3 to 49.8 degrees) to 22.1 +/- 4.9 degrees (range 18.7 to 32.9 degrees), which corresponds to a reduction of 38.8% in the mean angle of inclination. This difference was statistically significant (P < 0.001). Conclusion: The use of a thin head supporter adapted to the surgical table objectively reduces lateral inclination of the surgeon's spinal column in the torero position, making LRP a more comfortable procedure.

Origin of primordial magnetic fields

Magnetic fields of intensities similar to those in our galaxy are also observed in high redshift galaxies, where a mean field dynamo would not have had time to produce them. Therefore, a primordial origin is indicated. It has been suggested that magnetic fields were created at various primordial eras: during inflation, the electroweak phase transition, the quark-hadron phase transition (QHPT), during the formation of the first objects, and during reionization. We suggest here that the large-scale fields similar to mu G, observed in galaxies at both high and low redshifts by Faraday rotation measurements (FRMs), have their origin in the electromagnetic fluctuations that naturally occurred in the dense hot plasma that existed just after the QHPT. We evolve the predicted fields to the present time. The size of the region containing a coherent magnetic field increased due to the fusion of smaller regions. Magnetic fields (MFs) similar to 10 mu G over a comoving similar to 1 pc region are predicted at redshift z similar to 10. These fields are orders of magnitude greater than those predicted in previous scenarios for creating primordial magnetic fields. Line-of-sight average MFs similar to 10(-2) mu G, valid for FRMs, are obtained over a 1 Mpc comoving region at the redshift z similar to 10. In the collapse to a galaxy (comoving size similar to 30 kpc) at z similar to 10, the fields are amplified to similar to 10 mu G. This indicates that the MFs created immediately after the QHPT (10(-4) s), predicted by the fluctuation-dissipation theorem, could be the origin of the similar to mu G fields observed by FRMs in galaxies at both high and low redshifts. Our predicted MFs are shown to be consistent with present observations. We discuss the possibility that the predicted MFs could cause non-negligible deflections of ultrahigh energy cosmic rays and help create the observed isotropic distribution of their incoming directions. We also discuss the importance of the volume average magnetic field predicted by our model in producing the first stars and in reionizing the Universe.

An accurate distance to 2M1207Ab

Context. In April 2004, the first image was obtained of a planetary mass companion (now known as 2M 1207 b) in orbit around a self-luminous object different from our own Sun (the young brown dwarf 2MASSW J 1207334-393254, hereafter 2M 1207 A). That 2M 1207 b probably formed via fragmentation and gravitational collapse offered proof that such a mechanism can form bodies in the planetary mass regime. However, the predicted mass, luminosity, and radius of 2MI207 b depend on its age, distance, and other observables, such as effective temperature. Aims. To refine our knowledge of the physical properties of 2M 1207 b and its nature, we accurately determined the distance to the 2M 1207 A and b system by measuring of its trigonometric parallax at the milliarcsec level. Methods. With the ESO NTT/SUS12 telescope, we began a campaign of photometric and astrometric observations in 2006 to measure the trigonometric parallax of 2M 1207 A. Results. An accurate distance (52.4 +/- 1.1 pc) to 2M1207A was measured. From distance and proper motions we derived spatial velocities that are fully compatible with TWA membership. Conclusions. With this new distance estimate, we discuss three scenarios regarding the nature of 2M 1207 b: (1) a cool (1150 +/- 150 K) companion of mass 4 +/- 1 M-Jup (2) a warmer (1600 +/- 100 K) and heavier (8 +/- 2 M-Jup) companion occulted by an edge-on circumsecondary disk, or (3) a hot protoplanet collision afterglow.

Cosmic distance duality relation and the shape of galaxy clusters

Context. Observations in the cosmological domain are heavily dependent on the validity of the cosmic distance-duality (DD) relation, eta = D(L)(z)(1+ z)(2)/D(A)(z) = 1, an exact result required by the Etherington reciprocity theorem where D(L)(z) and D(A)(z) are, respectively, the luminosity and angular diameter distances. In the limit of very small redshifts D(A)(z) = D(L)(z) and this ratio is trivially satisfied. Measurements of Sunyaev-Zeldovich effect (SZE) and X-rays combined with the DD relation have been used to determine D(A)(z) from galaxy clusters. This combination offers the possibility of testing the validity of the DD relation, as well as determining which physical processes occur in galaxy clusters via their shapes. Aims. We use WMAP (7 years) results by fixing the conventional Lambda CDM model to verify the consistence between the validity of DD relation and different assumptions about galaxy cluster geometries usually adopted in the literature. Methods. We assume that. is a function of the redshift parametrized by two different relations: eta(z) = 1+eta(0)z, and eta(z) = 1+eta(0)z/(1+z), where eta(0) is a constant parameter quantifying the possible departure from the strict validity of the DD relation. In order to determine the probability density function (PDF) of eta(0), we consider the angular diameter distances from galaxy clusters recently studied by two different groups by assuming elliptical (isothermal) and spherical (non-isothermal) beta models. The strict validity of the DD relation will occur only if the maximum value of eta(0) PDF is centered on eta(0) = 0. Results. It was found that the elliptical beta model is in good agreement with the data, showing no violation of the DD relation (PDF peaked close to eta(0) = 0 at 1 sigma), while the spherical (non-isothermal) one is only marginally compatible at 3 sigma. Conclusions. The present results derived by combining the SZE and X-ray surface brightness data from galaxy clusters with the latest WMAP results (7-years) favors the elliptical geometry for galaxy clusters. It is remarkable that a local property like the geometry of galaxy clusters might be constrained by a global argument provided by the cosmic DD relation.

THE STELLAR CONTENT OF OBSCURED GALACTIC GIANT H II REGIONS. VII. W3

Spectrophotometric distances in the K band have been reported by different authors for a number of obscured Galactic H II regions. Almost 50% of them show large discrepancies compared to the classical method using radial velocities measured in the radio spectral region. In order to provide a crucial test of both methods, we selected a target that does not present particular difficulty for any method and which has been measured by as many techniques as possible. The W3 star-forming complex, located in the Perseus arm, offers a splendid opportunity for such a task. We used the Near-Infrared Integral Field Spectrograph on the Frederick C. Gillett Gemini North telescope to classify candidate ""naked photosphere"" OB stars based on Two Micron All Sky Survey photometry. Two of the targets are revealed to be mid-O-type main-sequence stars leading to a distance of d = 2.20 kpc. This is in excellent agreement with the spectrophotometric distance derived in the optical band (d = 2.18 pc) and with a measurement of the W3 trigonometric parallax (d = 1.95 kpc). Such results confirm that the spectrophotometric distances in the K band are reliable. The radio-derived kinematic distance, on the contrary, gives a distance twice as large (d = 4.2 kpc). This indicates that this region of the Perseus arm does not follow the Galactic rotation curve, and this may also be the case for other H II regions for which discrepancies have been found.

Origin of magnetic fields in galaxies

Microgauss magnetic fields are observed in all galaxies at low and high redshifts. The origin of these intense magnetic fields is a challenging question in astrophysics. We show here that the natural plasma fluctuations in the primordial Universe (assumed to be random), predicted by the fluctuation - dissipation theorem, predicts similar to 0.034 mu G fields over similar to 0.3 kpc regions in galaxies. If the dipole magnetic fields predicted by the fluctuation- dissipation theorem are not completely random, microgauss fields over regions greater than or similar to 0.34 kpc are easily obtained. The model is thus a strong candidate for resolving the problem of the origin of magnetic fields in less than or similar to 10(9) years in high redshift galaxies.

The young, tight, and low-mass binary TWA22AB: a new calibrator for evolutionary models? Orbit, spectral types, and temperature

Context. Tight binaries discovered in young, nearby associations are ideal targets for providing dynamical mass measurements to test the physics of evolutionary models at young ages and very low masses. Aims. We report the binarity of TWA22 for the first time. We aim at monitoring the orbit of this young and tight system to determine its total dynamical mass using an accurate distance determination. We also intend to characterize the physical properties (luminosity, effective temperature, and surface gravity) of each component based on near-infrared photometric and spectroscopic observations. Methods. We used the adaptive-optics assisted imager NACO to resolve the components, to monitor the complete orbit and to obtain the relative near-infrared photometry of TWA22 AB. The adaptive-optics assisted integral field spectrometer SINFONI was also used to obtain medium-resolution (R(lambda) = 1500-2000) spectra in JHK bands. Comparison with empirical and synthetic librairies were necessary for deriving the spectral type, the effective temperature, and the surface gravity for each component of the system. Results. Based on an accurate trigonometric distance (17.5 +/- 0.2 pc) determination, we infer a total dynamical mass of 220 +/- 21 M(Jup) for the system. From the complete set of spectra, we find an effective temperature T(eff) = 2900(-200)(+200) K for TWA22A and T(eff) = 2900(-100)(+200) for TWA22 B and surface gravities between 4.0 and 5.5 dex. From our photometry and an M6 +/- 1 spectral type for both components, we find luminosities of log(L/L(circle dot)) = -2.11 +/- 0.13 dex and log(L/L(circle dot)) = -2.30 +/- 0.16 dex for TWA22 A and B, respectively. By comparing these parameters with evolutionary models, we question the age and the multiplicity of this system. We also discuss a possible underestimation of the mass predicted by evolutionary models for young stars close to the substellar boundary.