Stable singularities of co-rank one quasi homogeneous map germs from (ℂn+1, 0) to (ℂn, 0), n = 2, 3

In this article, we investigate the geometry of quasi homogeneous corank one finitely determined map germs from (ℂn+1, 0) to (ℂn, 0) with n = 2, 3. We give a complete description, in terms of the weights and degrees, of the invariants that are associated to all stable singularities which appear in the discriminant of such map germs. The first class of invariants which we study are the isolated singularities, called 0-stable singularities because they are the 0-dimensional singularities. First, we give a formula to compute the number of An points which appear in any stable deformation of a quasi homogeneous co-rank one map germ from (ℂn+1, 0) to (ℂn, 0) with n = 2, 3. To get such a formula, we apply the Hilbert's syzygy theorem to determine the graded free resolution given by the syzygy modules of the associated iterated Jacobian ideal. Then we show how to obtain the other 0-stable singularities, these isolated singularities are formed by multiple points and here we use the relation among them and the Fitting ideals of the discriminant. For n = 2, there exists only the germ of double points set and for n = 3 there are the triple points, named points A1,1,1 and the normal crossing between a germ of a cuspidal edge and a germ of a plane, named A2,1. For n = 3, there appear also the one-dimensional singularities, which are of two types: germs of cuspidal edges or germs of double points curves. For these singularities, we show how to compute the polar multiplicities and also the local Euler obstruction at the origin in terms of the weights and degrees. © 2013 Pushpa Publishing House.

The use of elevation map histograms for topographic heterogeneity analysis

Surface defects are extremely important in mechanical characterization of several different materials. Therefore, the analysis of surface finishing is essential for a further simulation of surface mechanical properties in a customized project in materials science and technology. One of the methods commonly employed for such purpose is the statistical mapping of different sample surface regions using the depth from focus technique. The analysis is usually performed directly from the elevation maps which are obtained from the digital image processing. In this paper, the possibility of quantifying the surface heterogeneity of Silicon Carbide porous ceramics by elevation map histograms is presented. The advantage of this technique is that it allows the qualitative or quantitative verification of all surface image fields that cannot be done by using the Surface Plot plugin of image J™ platform commonly used in digital image processing. © 2012 Springer Science+Business Media, LLC.

A rescaling of the phase space for Hamiltonian map: Applications on the Kepler map and mappings with diverging angles in the limit of vanishing action

A rescale of the phase space for a family of two-dimensional, nonlinear Hamiltonian mappings was made by using the location of the first invariant Kolmogorov-Arnold-Moser (KAM) curve. Average properties of the phase space are shown to be scaling invariant and with different scaling times. Specific values of the control parameters are used to recover the Kepler map and the mapping that describes a particle in a wave packet for the relativistic motion. The phase space observed shows a large chaotic sea surrounding periodic islands and limited by a set of invariant KAM curves whose position of the first of them depends on the control parameters. The transition from local to global chaos is used to estimate the position of the first invariant KAM curve, leading us to confirm that the chaotic sea is scaling invariant. The different scaling times are shown to be dependent on the initial conditions. The universality classes for the Kepler map and mappings with diverging angles in the limit of vanishing action are defined. © 2013 Published by Elsevier Inc. All rights reserved.

A high-resolution radiation hybrid map of the river buffalo major histocompatibility complex and comparison with BoLA

The major histocompatibility complex (MHC) in mammals codes for antigen-presenting proteins. For this reason, the MHC is of great importance for immune function and animal health. Previous studies revealed this gene-dense and polymorphic region in river buffalo to be on the short arm of chromosome 2, which is homologous to cattle chromosome 23. Using cattle-derived STS markers and a river buffalo radiation hybrid (RH) panel (BBURH5000), we generated a high-resolution RH map of the river buffalo MHC region. The buffalo MHC RH map (cR5000) was aligned with the cattle MHC RH map (cR 12000) to compare gene order. The buffalo MHC had similar organization to the cattle MHC, with class II genes distributed in two segments, class IIa and class IIb. Class IIa was closely associated with the class I and class III regions, and class IIb was a separate cluster. A total of 53 markers were distributed into two linkage groups based on a two-point LOD score threshold of ≥8. The first linkage group included 32 markers from class IIa, class I and class III. The second linkage group included 21 markers from class IIb. Bacterial artificial chromosome clones for seven loci were mapped by fluorescence in situ hybridization on metaphase chromosomes using single- and double-color hybridizations. The order of cytogenetically mapped markers in the region corroborated the physical order of markers obtained from the RH map and served as anchor points to align and orient the linkage groups. © 2012 The Authors, Animal Genetics © 2012 Stichting International Foundation for Animal Genetics.

Integrated assessment for establishing an oil environmental vulnerability map: Case study for the Santos Basin region, Brazil

The growth of maritime transport and oil exploitation activities may increase the risk of oil spills. Thus, plans and actions to prevent or mitigate impacts are needed to minimize the effects caused by oil. However, tools used worldwide to support contingency plans have not been integrated, thus leading to failure in establishing priority areas. This investigation aimed to develop indices of environmental vulnerability to oil (IEVO), by combining information about environmental sensibility to oil and results of numerical modeling of spilled oil. To achieve that, a case study concerning to oil spills scenarios in a subtropical coastal area was designed, and IEVOs were calculated and presented in maps, in order to make the information about the areas' vulnerability more easily visualized. For summer, the extension of coastline potentially affected by oil was approximately 150. km, and most of the coastline presented medium to high vulnerability. For winter, 230. km coastline would be affected, from which 75% were classified as medium to high vulnerability. Thus, IEVO maps allowed a rapid and clearer interpretation of the vulnerability of the mapped region, facilitating the planning process and the actions in response to an oil spill. © 2013 Elsevier Ltd.

Topological K-classification of finitely determined map germs

We consider smooth finitely C 0-K-determined map germs f: (ℝn, 0) → (ℝp, 0) and we look at the classification under C 0-K-equivalence. The main tool is the homotopy type of the link, which is obtained by intersecting the image of f with a small enough sphere centered at the origin. When f -1(0) = {0}, the link is a smooth map between spheres and f is C 0-K-equivalent to the cone of its link. When f -1(0) ≠ {0}, we consider a link diagram, which contains some extra information, but again f is C 0-K-equivalent to the generalized cone. As a consequence, we deduce some known results due to Nishimura (for n = p) or the first named author (for n < p). We also prove some new results of the same nature. © 2012 Springer Science+Business Media Dordrecht.

Bi-Lipschitz A-equivalence of K-equivalent map-germs

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Covariant map between Ramond-Neveu-Schwarz and pure spinor formalisms for the superstring

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Escape through a time-dependent hole in the doubling map

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Dynamical properties of a dissipative discontinuous map: A scaling investigation

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Towards a Brazilian radon map: consortium radon Brazil

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Estimation of a preference map of new consumers for spatial load forecasting simulation methods using a spatial analysis of points

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Two-dimensional nonlinear map characterized by tunable Levy flights

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Experimental evidence of MAP kinase gene expression on the response of intestinal anti-inflammatory drugs

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)