The curve selection lemma and the Morse-Sard theorem

We use an inequality due to Bochnak and Lojasiewicz, which follows from the Curve Selection Lemma of real algebraic geometry in order to prove that, given a C(r) function f : U subset of R(m) -> R, we have lim(y -> xy is an element of crit(f)) vertical bar f(y) - f(x)vertical bar/vertical bar y - x vertical bar(r) = 0, for all x is an element of crit(f)` boolean AND U, where crit( f) = {x is an element of U vertical bar df ( x) = 0}. This shows that the so-called Morse decomposition of the critical set, used in the classical proof of the Morse-Sard theorem, is not necessary: the conclusion of the Morse decomposition lemma holds for the whole critical set. We use this result to give a simple proof of the classical Morse-Sard theorem ( with sharp differentiability assumptions).

Plane curve diagrams and geometrical applications

We look at plane curve diagrams (f,alpha), which are given by a plane curve multigerm alpha : (R, S) -> R(2) and a function on it f : (R, S) -> R. We obtain a classification of all such diagrams, where alpha has e-codimension <= 2 and f has finite order. Then we define an equivalence between plane curves which we call Ah(alpha)-equivalence and which is determined by the class of the diagram (h(alpha), alpha). Here, h alpha denotes the height function of alpha with respect to its normal vector. This is an equivalence which not only takes into account the topology of the singularity of alpha, but also its flat geometry. Finally, we apply our results in order to obtain a classification of all the plane projections of a generic space curve gamma embedded in R(3).

Magnetic interaction in exchange-biased bilayers: a first-order reversal curve analysis

The distributions of coercivities and magnetic interactions in a set of polycrystalline Ni(0.8)Fe(0.2)/FeMn bilayers have been determined using the first-order reversal curve (FORC) formalism. The thickness of the permalloy (Py) film was fixed at 10 nm (nominal), while that of the FeMn film varied within the range 0-20 nm. The FORC diagrams of each bilayer displayed two clearly distinguishable regions. The main region was generated by Py particles whose coercivities were enhanced in comparison with those in which the FeMn film was absent (sample O). The minor region was produced by Py particles with coercivities similar to or slightly higher than those of particles in the Py film of sample O. Each sample presented two distributions of interaction fields, one for each region, and both were centred slightly below the exchange-bias field, thus indicating a prevalence of magnetizing interactions. These results are consistent with a grain size distribution in the Py layer and the presence of uncompensated antiferromagnetic moments.

First-order-reversal-curve analysis of Pr-Fe-B-based exchange spring magnets

Ribbons of nominal composition (Pr(9.5)Fe(84.5)B(6))(0.96)Cr(0.01)(TiC)(0.03) were produced by arc-melting and melt-spinning the alloys on a Cu wheel. X-ray diffraction (XRD) reveals two main phases, one based upon alpha-Fe and the other upon Pr(2)Fe(14)B. The ribbons show exchange spring behavior with H (c) = 12.5 kOe and (BH)(max) = 13.6 MGOe when these two phases are well coupled. Transmission electron microscopy revealed the coupled behavior is observed when the microstructure consists predominantly of alpha-Fe grains (diameter similar to 100 nm.) surrounded by hard material containing Pr(2)Fe(14)B. The microstructure is discussed in terms of a calculation by Skomski and Coey. A first-order-reversal-curve (FORC) analysis was performed for both a well-coupled sample and a poorly coupled sample. The FORC diagrams show two strong peaks for both the poorly coupled sample and for the well-coupled material. In both cases, the localization of the FORC probability suggests magnetizing interactions between particles. Switching field distributions were calculated and are consistent with the sample microstructure.

First-order-reversal-curve analysis of Pr-Fe-B-based nanocomposites

Ribbons of nominal composition (Pr(9.5)Fe(84.5)B(6))(0.96)Cr(0.01)(TiC)(0.03) were produced by arc-melting and melt-spinning the alloys on a Cu wheel. X-ray diffraction reveals two main phases, one based upon alpha-Fe and the other upon Pr(2)Fe(14)B. The ribbons show exchange spring behavior with H(c)=12.5 kOe and (BH)(max)= 13.6 MGOe when these two phases are well coupled. Transmission electron microscopy revealed that the coupled behavior is observed when the microstructure consists predominantly of alpha-Fe grains(diameter similar to 100 nm.) surrounded by hard material containing Pr(2)Fe(14)B. A first-order-reversal-curve (FORC) analysis was performed for both a well-coupled sample and a partially-coupled sample. The FORC diagrams show two strong peaks for both the partially-coupled sample and for the well coupled material. In both cases, the localization of the FORC probability suggests demagnetizing interactions between particles. Switching field distributions were calculated and are consistent with the sample microstructure. (C) 2009 Elsevier B.V. All rights reserved.

First order reversal curve analysis of nanocrystalline Pd(80)Co(20) alloy films

Films of isotropic nanocrystalline Pd(80)Co(20) alloys were obtained by electrodeposition onto brass substrate in plating baths maintained at different pH values. Increasing the pH of the plating bath led to an increase in mean grain size without inducing significant changes in the composition of the alloy. The magnetocrystalline anisotropy constant was estimated and the value was of the same order of magnitude as that reported for samples with perpendicular magnetic anisotropy. First order reversal curve (FORC) analysis revealed the presence of an important component of reversible magnetization. Also, FORC diagrams obtained at different sweep rate of the applied magnetic field, revealed that this reversible component is strongly affected by kinetic effect. The slight bias observed in the irreversible part of the FORC distribution suggested the dominance of magnetizing intergrain exchange coupling over demagnetizing dipolar interactions and microstructural disorder. (c) 2009 Elsevier B.V. All rights reserved.

Chemostratigraphy of the Tamengo Formation (Corumba Group, Brazil) A contribution to the calibration of the Ediacaran carbon-isotope curve

The Corumba Group cropping out in the southern Paraguay Belt in Brazil is one of the most complete Ediacaran sedimentary archives of palaeogeographic climatic biogeochemical and biotic evolution in southwestern Gondwana The unit hosts a rich fossil record including acritarchs vendotaenids (Vendo taenia Eoholynia) soft-bodied metazoans (Corumbella) and skeletal fossils (Cloudina Titanotheca) The Tamengo Formation made up mainly of limestones and marls provides a rich bio- and chemostratigraphic record Several outcrops formerly assigned to the Cuiaba Group are here included in the Tamengo Formation on the basis of lithological and chemostratigraphical criteria High-resolution carbon isotopic analyses are reported for the Tamengo Formation showing (from base to top) (1) a positive delta(13)C excursion to +4 parts per thousand PDB above post-glacial negative values (2) a negative excursion to -3 5 parts per thousand associated with a marked regression and subsequent transgression (3) a positive excursion to +5 5 parts per thousand and (4) a plateau characterized by delta(13)C around +3 parts per thousand A U-Pb SHRIMP zircon age of an ash bed Interbedded in the upper part of the delta(13)C positive plateau yielded 543 +/- 3 Ma which is considered as the depositional age (Babinski et al 2008a) The positive plateau in the upper Tamengo Formation and the preceding positive excursion are ubiquitous features in several successions worldwide including the Nama Group (Namibia) the Dengying Formation (South China) and the Nafun and Ara groups (Oman) This plateau is constrained between 542 and 551 Ma thus consistent with the age of the upper Tamengo Formation The negative excursion of the lower Tamengo Formation may be correlated to the Shuram-Wonoka negative anomaly although delta(13)C values do not fall beyond -3 5 parts per thousand in the Brazilian sections Sedimentary breccias occur just beneath this negative excursion in the lower Tamengo Formation One possible interpretation of the origin of these breccias is a glacioeustatic sea-level fall but a tectonic interpretation cannot be completely ruled out Published by Elsevier B V

U-curve: A branch-and-bound optimization algorithm for U-shaped cost functions on Boolean lattices applied to the feature selection problem

This paper presents the formulation of a combinatorial optimization problem with the following characteristics: (i) the search space is the power set of a finite set structured as a Boolean lattice; (ii) the cost function forms a U-shaped curve when applied to any lattice chain. This formulation applies for feature selection in the context of pattern recognition. The known approaches for this problem are branch-and-bound algorithms and heuristics that explore partially the search space. Branch-and-bound algorithms are equivalent to the full search, while heuristics are not. This paper presents a branch-and-bound algorithm that differs from the others known by exploring the lattice structure and the U-shaped chain curves of the search space. The main contribution of this paper is the architecture of this algorithm that is based on the representation and exploration of the search space by new lattice properties proven here. Several experiments, with well known public data, indicate the superiority of the proposed method to the sequential floating forward selection (SFFS), which is a popular heuristic that gives good results in very short computational time. In all experiments, the proposed method got better or equal results in similar or even smaller computational time. (C) 2009 Elsevier Ltd. All rights reserved.

A simple relation between the Leimkuhler curve and the mean residual life

In this paper, a simple relation between the Leimkuhler curve and the mean residual life is established. The result is illustrated with several models commonly used in informetrics, such as exponential, Pareto and lognormal. Finally, relationships with some other reliability concepts are also presented. (C) 2010 Elsevier Ltd. All rights reserved.

DIAGNOSTIC TECHNIQUES OF LOCAL INFLUENCE IN SPATIAL ANALYSIS OF SOYBEAN YIELD

Modeling of spatial dependence structure, concerning geoestatistics approach, is an indispensable tool for fixing parameters that define this structure, applied on interpolation of values in places that are not sampled, by kriging techniques. However, the estimation of parameters can be greatly affected by the presence of atypical observations on sampled data. Thus, this trial aimed at using diagnostics techniques of local influence in spatial linear Gaussians models, applied at geoestatistics in order to evaluate sensitivity of maximum likelihood estimators and restrict maximum likelihood to small perturbations in these data. So, studies with simulated and experimental data were performed. Those results, obtained from the study of real data, allowed us to conclude that the presence of atypical values among the sampled data can have a strong influence on thematic maps, changing, therefore, the spatial dependence. The application of diagnostics techniques of local influence should be part of any geoestatistic analysis, ensuring that the information from thematic maps has better quality and can be used with greater security by farmers.

Protoporphyrin IX Nanoparticle Carrier: Preparation, Optical Properties, and Singlet Oxygen Generation

The present study is focused on developing a nanoparticle carrier for the photosensitizer protoporphyrin IX for use in photodynamic therapy. The entrapment of protoporphyrin IX (Pp IX) in silica spheres was achieved by modification of Pp IX molecules with an organosilane reagent. The immobilized drug preserved its optical properties and the capacity to generate singlet oxygen, which was detected by a direct method from its characteristic phosphorescence decay curve at near-infrared and by a chemical method using 1,3-diphenylisobenzofuran to trap singlet oxygen. The lifetime of singlet oxygen when a suspension of Pp IX-loaded particles in acetonitrile was excited at 532 nm was determined as 52 mu s, which is in good agreement with the value determined for methylene blue in acetonitrile solution under the same conditions. The Pp IX-loaded silica particles have an efficiency of singlet oxygen generation (eta Delta) higher than the quantum yield of free porphyrins. This high efficiency of singlet oxygen generation was attributed to changes on the monomer-dimer equilibrium after photosentisizer immobilization.

Genetic studies of body mass index yield new insights for obesity biology

Obesity is heritable and predisposes to many diseases. To understand the genetic basis of obesity better, here we conduct a genome-wide association study and Metabochip meta-analysis of body mass index (BMI), a measure commonly used to define obesity and assess adiposity, in upto 339,224 individuals. This analysis identifies 97 BMI-associated loci (P < 5 x 10(-8)), 56 of which are novel. Five loci demonstrate clear evidence of several independent association signals, and many loci have significant effects on other metabolic phenotypes. The 97 loci account for similar to 2.7% of BMI variation, and genome-wide estimates suggest that common variation accounts for >20% of BMI variation. Pathway analyses provide strong support for a role of the central nervous systemin obesity susceptibility and implicate new genes and pathways, including those related to synaptic function, glutamate signalling, insulin secretion/action, energy metabolism, lipid biology and adipogenesis.

The Determinants of Recovery Rates on Defaulted Corporate Securities: Why do Fallen Angels recover more than Original High Yield Issues?

Regression analysis has shown that recovery rates are determined by a variety of conditions at the time of default. These conditions can be broken into five major categories: (1) a security's seniority within the capital structure of the defaulting firm, (2) the type of default event, (3) firm-specific factors, (4) industry-specific factors, and (5) macroeconomic factors. Expectations of these inputs determine the expected recovery rate if default were to occur, thereby determining credit ratings and security prices. Although it is widely understood how recovery rate estimates influence credit rating assignments (the higher the expected recovery rate, the higher the assigned credit rating), no research, to the best of my knowledge, has investigated the reasons why higher rated securities recover more than lower rated securities in the event of default. Specifically, this paper will empirically investigate why securities originally rated investment grade, fallen angels, recover more than securities originally rated high yield in the event of default.

Dividend yield e persistência de retornos anormais das ações : evidência do mercado brasileiro

Analisamos, empiricamente, o comportamento dos preços das ações após o anúncio do pagamento de dividendos. Nossa amostra foi constituída de 163 eventos, incluindo as ações mais negociadas na Bolsa de Valores de São Paulo, no período de 1998 a 2000. Encontramos uma relação direta entre o dividend yield e o retomo anormal acumulado destas ações no período pós-pagamento de dividendos, dividindo a amostra em três subamostras, em função do dividend yield. Obtivemos um retomo anormal acumulado, nos 90 dias após o evento, de 21,97% para as empresas que pagaram dividendos mais altos, 5,16% para as companhias que pagaram dividendos intermediários, e -15,50% para as empresas que pagaram dividendos mais baixos. Isto demonstra a persistência dos retornos anormais das ações no período pós-evento. Esta relação foi confirmada quando analisamos os eventos por tipo de controlador da empresa (fundos, estatais ou fanu1ias) e as companhias privatizadas, e quando pesquisamos o retomo acumulado das ações em função do percentual do lucro líquido distribuído sob a forma de dividendos.

A structuralist Philips curve

This paper presents a structuralist model of the Philips curve and applies it to the US and Brazilian economies. The theoretical model starts from a simple markup rule to build a Philips curve based on the assumptions that firms have a desired rate of profit and wokers have a target real wage. Inflation expectations are modeled in terms of current inflation and the governments’ target, and the model shows that relative prices can have both a short-run and long-run influence on inflation. When applied to the US, the structuralist Philips curve results in a nonlinear model in which there are two steady states for inflation, and where the wageshare of income becomes the main instrument to drive inflation to the governments’ target. When applied to Brazil, the structuralist Philips curve reveals a nonlinear relationship between long-run inflation and the real exchange rate, so that the same inflation target can be consistent with more than one value of the exchange rate. The main conclusion of the paper is that a structuralist specification of the Philips curve is a useful instrument to model many macroeconomic topics as well as alternative theoretical closures.