Número de Milnor associado a curvas reduzidas

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

On the number of singularities in generic deformations of map germs

Let f:C-n, 0 --> C-p, 0 be a K-finite map germ, and let i = (i(1),..., i(k)) be a Boardman symbol such that Sigma(i) has codimension n in the corresponding jet space J(k)(n, p). When its iterated successors have codimension larger than n, the paper gives a list of situations in which the number of Sigma(i) points that appear in a generic deformation of f can be computed algebraically by means of Jacobian ideals of f. This list can be summarised in the following way: f must have rank n - i(1) and, in addition, in the case p = 6, f must be a singularity of type Sigma(i2.i2).

Analytic behavior of the QED polarizability function at finite temperature

We revisit the analytical properties of the static quasi-photon polarizability function for an electron gas at finite temperature, in connection with the existence of Friedel oscillations in the potential created by an impurity. In contrast with the zero temperature case, where the polarizability is an analytical function, except for the two branch cuts which are responsible for Friedel oscillations, at finite temperature the corresponding function is non analytical, in spite of becoming continuous everywhere on the complex plane. This effect produces, as a result, the survival of the oscillatory behavior of the potential. We calculate the potential at large distances, and relate the calculation to the non-analytical properties of the polarizability.

An operator formulation of the multiscale finite-volume method with correction function

The multiscale finite-volume (MSFV) method has been derived to efficiently solve large problems with spatially varying coefficients. The fine-scale problem is subdivided into local problems that can be solved separately and are coupled by a global problem. This algorithm, in consequence, shares some characteristics with two-level domain decomposition (DD) methods. However, the MSFV algorithm is different in that it incorporates a flux reconstruction step, which delivers a fine-scale mass conservative flux field without the need for iterating. This is achieved by the use of two overlapping coarse grids. The recently introduced correction function allows for a consistent handling of source terms, which makes the MSFV method a flexible algorithm that is applicable to a wide spectrum of problems. It is demonstrated that the MSFV operator, used to compute an approximate pressure solution, can be equivalently constructed by writing the Schur complement with a tangential approximation of a single-cell overlapping grid and incorporation of appropriate coarse-scale mass-balance equations.

Three-dimensional finite element analysis of MHD duct flow by the penalty function formulation

A numerical scheme based on the Finite Element Method (FEM) is presented to calculate the full solution of a three-dimensional steady magnetohydrodynamic (MHD) flow with moderately high Hartmann numbers and interaction parameters. An incompressible, viscous and electrically conducting liquid-metal is considered. Assuming a low magnetic Reynolds number, the solution method solves the coupled Navier-Stokes and Maxwell's equations through the use of a penalty function method. Results are presented for Hartmann numbers in the range 10(2)-10(3).

Pre-weighted homogeneous map germs finite determinacy and topological triviality

In this paper we introduce the notion of G-pre-weighted homogeneous map germ, (G is one of Mather's groups A or K.) and show that any G-pre-weighted homogeneous map germ is G-finitely determined. We also give an explicit order, based on the Newton polyhedron of a pre-weighted homogeneous germ of function, such that the topological structure is preserved after perturbations by terms of higher order.

Micromechanics of dentin/adhesive interface in function of dentin depth: 3d finite element analysis

Objectives: The aim of this study was to analyze the stress distribution on dentin/adhesive interface (d/a) through a 3-D finite element analysis (FEA) varying the number and diameter of the dentin tubules orifice according to dentin depth, keeping hybrid layer (HL) thickness and TAǴs length constant. Materials and Methods: 3 models were built through the SolidWorks software: SD - specimen simulating superficial dentin (41 x 41 x 82 μm), with a 3 μm thick HL, a 17 μm length Tag, and 8 tubules with a 0.9 μm diameter restored with composite resin. MD - similar to M1 with 12 tubules with a 1.2 μm diameter, simulating medium dentin. DD - similar to M1 with 16 tubules with a 2.5 μm diameter, simulating deep dentin. Other two models were built in order to keep the diameter constant in 2.5 μm: MS - similar to SD with 8 tubules; and MM - similar to MD with 12 tubules. The boundary condition was applied to the base surface of each specimen. Tensile load (0.03N) was performed on the composite resin top surface. Stress field (maximum principal stress in tension - σMAX) was performed using Ansys Wokbench 10.0. Results: The peak of σMAX (MPa) were similar between SD (110) and MD (106), and higher for DD (134). The stress distribution pathway was similar for all models, starting from peritubular dentin to adhesive layer, intertubular dentin and hybrid layer. The peak of σMAX (MPa) for those structures was, respectively: 134 (DD), 56.9 (SD), 45.5 (DD), and 36.7 (MD). Conclusions: The number of dentin tubules had no influence in the σMAX at the dentin/adhesive interface. Peritubular and intertubular dentin showed higher stress with the bigger dentin tubules orifice condition. The σMAX in the hybrid layer and adhesive layer were going down from superficial dentin to deeper dentin. In a failure scenario, the hybrid layer in contact with peritubular dentin and adhesive layer is the first region for breaking the adhesion. © 2011 Nova Science Publishers, Inc.

The group of invariants of an inner function with finite spectrum

This paper determines the group of continuous invariants corresponding to an inner function circle dot with finitely many singularities on the unit circle T; that is, the continuous mappings g : T -> T such that circle dot o g = circle dot on T. These mappings form a group under composition.

Thermal 2-loop master spectral function at finite momentum

When considering NLO corrections to thermal particle production in the “relativistic” regime, in which the invariant mass squared of the produced particle is K2 ~ (πT)2, then the production rate can be expressed as a sum of a few universal “master” spectral functions. Taking the most complicated 2-loop master as an example, a general strategy for obtaining a convergent 2-dimensional integral representation is suggested. The analysis applies both to bosonic and fermionic statistics, and shows that for this master the non-relativistic approximation is only accurate for K2 ~(8πT)2, whereas the zero-momentum approximation works surprisingly well. Once the simpler masters have been similarly resolved, NLO results for quantities such as the right-handed neutrino production rate from a Standard Model plasma or the dilepton production rate from a QCD plasma can be assembled for K2 ~ (πT)2.

Attenuated portal hypertension in germ-free mice: Function of bacterial flora on the development of mesenteric lymphatic and blood vessels

Intestinal bacterial flora may induce splanchnic hemodynamic and histological alterations that are associated with portal hypertension (PH). We hypothesized that experimental PH would be attenuated in the complete absence of intestinal bacteria. We induced prehepatic PH by partial portal vein ligation (PPVL) in germ-free (GF) or mice colonized with altered Schaedler's flora (ASF). After 2 or 7 days, we performed hemodynamic measurements, including portal pressure (PP) and portosystemic shunts (PSS), and collected tissues for histomorphology, microbiology, and gene expression studies. Mice colonized with intestinal microbiota presented significantly higher PP levels after PPVL, compared to GF, mice. Presence of bacterial flora was also associated with significantly increased PSS and spleen weight. However, there were no hemodynamic differences between sham-operated mice in the presence or absence of intestinal flora. Bacterial translocation to the spleen was demonstrated 2 days, but not 7 days, after PPVL. Intestinal lymphatic and blood vessels were more abundant in colonized and in portal hypertensive mice, as compared to GF and sham-operated mice. Expression of the intestinal antimicrobial peptide, angiogenin-4, was suppressed in GF mice, but increased significantly after PPVL, whereas other angiogenic factors remained unchanged. Moreover, colonization of GF mice with ASF 2 days after PPVL led to a significant increase in intestinal blood vessels, compared to controls. The relative increase in PP after PPVL in ASF and specific pathogen-free mice was not significantly different. CONCLUSION In the complete absence of gut microbial flora PP is normal, but experimental PH is significantly attenuated. Intestinal mucosal lymphatic and blood vessels induced by bacterial colonization may contribute to development of PH.

Incomplete penetrance of familial retinoblastoma linked to germ-line mutations that result in partial loss of RB function

To study the molecular basis for the clinical phenotype of incomplete penetrance of familial retinoblastoma, we have examined the functional properties of three RB mutations identified in the germ line of five different families with low penetrance. RB mutants isolated from common adult cancers and from classic familial retinoblastoma (designated as classic RB mutations) are unstable and generally do not localize to the nucleus, do not undergo cyclin-dependent kinase (cdk)-mediated hyperphosphorylation, show absent protein “pocket” binding activity, and do not suppress colony growth of RB(−) cells. In contrast, two low-penetrant alleles (661W and “deletion of codon 480”) retained the ability to localize to the nucleus, showed normal cdk-mediated hyperphosphorylation in vivo, exhibited a binding pattern to simian virus 40 large T antigen using a quantitative yeast two-hybrid assay that was intermediate between classic mutants (null) and wild-type RB, and had absent E2F1 binding in vitro. A third, low-penetrant allele, “deletion of RB exon 4,” showed minimal hyperphosphorylation in vivo but demonstrated detectable E2F1 binding in vitro. In addition, each low-penetrant RB mutant retained the ability to suppress colony growth of RB(−) tumor cells. These findings suggest two categories of mutant, low-penetrant RB alleles. Class 1 alleles correspond to promoter mutations, which are believed to result in reduced or deregulated levels of wild-type RB protein, whereas class 2 alleles result in mutant proteins that retain partial activity. Characterization of the different subtypes of class 2 low-penetrant genes may help to define more precisely functional domains within the RB product required for tumor suppression.

NOTCH1 Gain of Function in Germ Cells Causes Failure of Spermatogenesis in Male Mice

NOTCH1 is a member of the NOTCH receptor family, a group of single-pass trans-membrane receptors. NOTCH signaling is highly conserved in evolution and mediates communication between adjacent cells. NOTCH receptors have been implicated in cell fate determination, as well as maintenance and differentiation of stem cells. In the mammalian testis expression of NOTCH1 in somatic and germ cells has been demonstrated, however its role in spermatogenesis was not clear. To study the significance of NOTCH1 in germ cells, we applied a cre/loxP approach in mice to induce NOTCH1 gain- or loss-of function specifically in male germ cells. Using a Stra8-icretransgene we produced mice with conditional activation of the NOTCH1 intracellular domain (NICD) in germ cells. Spermatogenesis in these mutants was progressively affected with age, resulting in decreased testis weight and sperm count. Analysis of downstream target genes of NOTCH1 signaling showed an increased expression of Hes5, with a reduction of the spermatogonial differentiation marker, Neurog3 expression in the mutant testis. Apoptosis was significantly increased in mouse germ cells with the corresponding elevation of pro-apoptotic Trp53 and Trp63genes' expression. We also showed that the conditional germ cell-specific ablation of Notch1 had no effect on spermatogenesis or male fertility. Our data suggest the importance of NOTCH signaling regulation in male germ cells for their survival and differentiation.

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.

An Extension of the Invariance Principle for a Class of Differential Equations with Finite Delay

An extension of the uniform invariance principle for ordinary differential equations with finite delay is developed. The uniform invariance principle allows the derivative of the auxiliary scalar function V to be positive in some bounded sets of the state space while the classical invariance principle assumes that. V <= 0. As a consequence, the uniform invariance principle can deal with a larger class of problems. The main difficulty to prove an invariance principle for functional differential equations is the fact that flows are defined on an infinite dimensional space and, in such spaces, bounded solutions may not be precompact. This difficulty is overcome by imposing the vector field taking bounded sets into bounded sets.

Exact nonequilibrium work generating function for a small classical system

We obtain the exact nonequilibrium work generating function (NEWGF) for a small system consisting of a massive Brownian particle connected to internal and external springs. The external work is provided to the system for a finite-time interval. The Jarzynski equality, obtained in this case directly from the NEWGF, is shown to be valid for the present model, in an exact way regardless of the rate of external work.