Bi-Lipschitz A-triviality of map germs and Newton filtrations

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

Bi-Lipschitz G-triviality and Newton polyhedra, G = R, C, K, R-V, C-V, K-V

In this work we provide estimates for the bi-Lipschitz G-triviality, G = C or K, for a family of map germs satisfying a Lojasiewicz condition. We work with two cases: the class of weighted homogeneous map germs and the class of non-degenerate map germs with respect to some Newton polyhedron. We also consider the bi-Lipschitz triviality for families of map germs defined on an analytic variety V. We give estimates for the bi-Lipschitz G(V)-triviality where G = R,C or K in the weighted homogeneous case. Here we assume that the map germ and the analytic variety are both weighted homogeneous with respect to the same weights. The method applied in this paper is based in the construction of controlled vector fields in the presence of a suitable Lojasiewicz condition. In the last section of this work we compare our results with other results related to this work showing tables with all estimates that we know, including ours.

C(0) and bi-Lipschitz K-equivalence of mappings

In this paper we investigate the classification of mappings up to K-equivalence. We give several results of this type. We study semialgebraic deformations up to semialgebraic C(0) K-equivalence and bi-Lipschitz K-equivalence. We give an algebraic criterion for bi-Lipschitz K-triviality in terms of semi-integral closure (Theorem 3.5). We also give a new proof of a result of Nishimura: we show that two germs of smooth mappings f, g : R(n) -> R(n), finitely determined with respect to K-equivalence are C(0)-K-equivalent if and only if they have the same degree in absolute value.

A Schoenflies extension theorem for a class of locally bi-Lipschitz homeomorphisms

"Vegeu el resum a l'inici del document del fitxer adjunt."

K-bi-Lipschitz equivalence of real function-germs

In this paper we prove that the set of equivalence classes of germs of real polynomials of degree less than or equal to k, with respect to K-bi-Lipschitz equivalence, is finite.

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

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

On the Geometry of Rectifiable Sets with Carleson and Poincare-type inequlaities

Thesis (Ph.D.)--University of Washington, 2016-06

Correlação radiológica e histológica de lesões mamárias não-palpáveis em pacientes submetidas a marcação pré-cirúrgica, utilizando-se o sistema BI-RADS

OBJECTIVE: To evaluate the positive predictive value for BI-RADS (Breast Imaging Reporting and Data System) categories 3, 4 and 5, correlating mammographic and histological diagnosis in non-palpable breast lesions. MATERIALS AND METHODS: Analytical-descriptive study of 169 women submitted to stereotactic localization for surgical biopsy of non-palpable breast lesions. Mammographic and histological findings were correlated, analyzing the predictive positive value for each category. RESULTS: Forty-two (24.8%) cases were diagnosed with breast cancer - only one in category 3, 19 in category 4, and 22 in category 5. The positive predictive value for categories 3, 4A, 4B, 4C and 5 were, respectively, 3.4%, 10.3%, 11.3%, 36% and 91.7%. Microcalcifications were the most frequent finding related to malignancy, present in 61.5% of these cases. CONCLUSION: The present study has demonstrated that BI-RADS allows a safe prediction of high suspicion of malignancy in lesions category 5 and low suspicion for category 3. As regards the category 4, the positive predictive value has shown a progressive increase in subcategories A, B and C, demonstrating that this subclassification represents an invaluable contribution for a more detailed and accurate assessment of lesions suspicious for malignancy.

Photoluminescence enhancement by gold nanoparticles in Eu(3+) doped GeO(2)-Bi(2)O(3) glasses

We report large photoluminescence (PL) enhancement in Eu(3+)-doped GeO(2)-Bi(2)O(3) glasses containing gold nanoparticles (NPs). Growth of approximate to 1000% in the PL intensity corresponding to the Eu(3+) transition (5)D(0)->(7)F(2), at 614 nm, was observed in comparison with a reference sample that does not contain gold NPs. Other PL bands from 580 to 700 nm are also enhanced. The enhancement of the PL intensity is attributed to the increased local field in the Eu(3+) locations due to the presence of the NPs and the energy transfer from the excited NPs to the Eu(3+) ions.

LIPSCHITZ CLASSIFICATION OF FUNCTIONS ON A HOLDER TRIANGLE

The problem of semialgebraic Lipschitz classification of quasihomogeneous polynomials on a Holder triangle is studied. For this problem, the ""moduli"" are described completely in certain combinatorial terms.

Fault current test of a bifilar Bi-2212 bulk coil

A bifilar Bi-2212 bulk coil with parallel shunt resistor was tested under fault current condition using a 3 MVA single-phase transformer in a 220 V-60 Hz line achieving fault current peak of 8 kA. The fault current tests are performed from steady state peak current of 200 A by applying controlled short circuits up to 8 kA varying the time period from one to six cycles. The test results show the function of the shunt resistor providing homogeneous quench behavior of the HTS coil besides its intrinsic stabilizing role. The limiting current ratio achieves a factor 4.2 during 5 cycles without any degradation.

Electrophoretic deposition of ZrO(2)-Y(2)O(3): a bi-component study concerning self-assemblies

There are many industrial advantages of using mechanical multi-oxides mixtures to obtain ceramic parts by electrophoretic deposition (EPD). This is mainly because one could avoid complex chemical synthesis routes to achieve a desirable composition. However, EPD of these suspensions is not an easy task as well since many different surfaces are present, leading to unexpected suspension behavior. The particles surface potentials and interactions can, however, be predicted by an extension of the DLVO theory. Using this theory, one can control the suspension properties and particles distribution. The objective of this work was to apply the colloidal chemistry theories to promote the formation of a heterocoagulation between ZrO(2) and Y(2)O(3) particles in ethanol suspension to achieve a suitable condition for EPD. After identifying a condition where those particles had opposite surface charges and adequate relative sizes, heterocoagulation was observed at operational pH 7.5, generating an organized agglomerate with ZrO(2) particles surrounding Y(2)O(3), with a net zeta potential of -16.6 mV. Since the agglomerates were stable, EPD could be carried out and homogeneous deposits were obtained. The deposited bodies were sintered at 1600 A degrees C for 4 h and partially stabilized ZrO(2) could be obtained without traces of Y(2)O(3) second phases.

Light scattering in polycrystalline alumina with bi-dimensionally large surface grains

Alumina ceramics with high in-line transmittance at 0.5-1.0 mm-thickness were prepared with different doping additives by sintering at 1850 degrees C in vacuum for 1-8 h. Depending on the additive contents and sintering variables bi-dimensionally large surface grains, caused by surface evaporation of MgO, had grown parallel to the surface with similar to 100 mu m thickness and lateral sizes up to the millimeter range. The abnormal grain-growth process also resulted in the formation of pores entrapped inside the large surface grains within a narrow zone at 10-20 mu m distance from the surface. The fraction of these pores is thickness-invariant. Scattering factors associated to the pores entrapped inside the bi-dimensionally large surface grains, second-phase particles, grain-boundaries, and microstructural surface defects are derived from the results of in-line transmission (at 600 nm) and are used together with microstructural characteristics to explain the light transmittance in these materials. (C) 2008 Elsevier Ltd. All rights reserved.

Electrochemical study of modified cerium-silane bi-layer on Al alloy 2024-T3

In this paper, the performance of bis-1, 2-(triethoxysilyl) ethane (BTSE) as a pre-treatment to protect the AA 2024-T3 against corrosion has been investigated by electrochemical impedance spectroscopy (EIS), potentiodynamic polarization curves, and the scanning vibrating electrode technique (SVET). The microstructural and morphological characterizations were carried out via scanning electron microscopy and atomic force microscopy and the chemical composition evaluated using contact angle measurements and X-ray photoelectron spectroscopy (XPS). The electrochemical results showed that the additives improved the anticorrosion properties of the coating. The chemical characterization indicated that additives contribute to an increased degree of surface coverage, as well as to a more complete reticulation. The SVET results evidenced the self-healing abilities of Ce ions. (C) 2009 Elsevier Ltd. All rights reserved.

Corrosion behavior of carbon steel protected with single and bi-layer of silane films filled with silica nanoparticles

The electrochemical behaviour of carbon steel coated with bis-[trimethoxysilylpropyl]amine (BTSPA) filled with silica nanoparticles in naturally aerated 0.1 mol L-1 NaCl solutions was evaluated. The coating was prepared by adding different concentrations of silica nanoparticles (100, 200, 300, 400 and 500 ppm) to the hydrolysis solution and then a second layer without silica nanoparticles was applied. The electrochemical behavior of the coated steel was evaluated by means of open-circuit potential (E-OC), electrochemical impedance spectroscopy (EIS) and polarization curves. Surface characterization was made by atomic force microscopy (AFM), and its hydrophobicity assessed by contact angle measurements. EIS diagrams have shown an improvement of the barrier properties of the silane layer with the silica addition, which was further improved on the bi-layer system. However, a dependence on the filler concentration was verified, and the best electrochemical response was obtained for samples modified with 300 ppm of silica nanoparticles. AFM images have shown a homogeneous distribution of the silica nanoparticles on the sample surface; however particles agglomeration was detected, which degraded the corrosion protection performance. The results were explained on the basis of the improvement of the barrier properties of the coating due to the filler addition and on the onset of defective regions on the more heavily filled coatings allowing easier electrolyte penetration. (C) 2007 Elsevier B.V. All rights reserved.