Topological invariants of isolated complete intersection curve singularities

In this paper we present some formulae for topological invariants of projective complete intersection curves with isolated singularities in terms of the Milnor number, the Euler characteristic and the topological genus. We also present some conditions, involving the Milnor number and the degree of the curve, for the irreducibility of complete intersection curves.

Finite determinacy and Whitney equisingularity of map germs from C(n) to C(2n-1)

We show that a holomorphic map germ f : (C(n), 0) -> (C(2n-1), 0) is finitely determined if and only if the double point scheme D(f) is a reduced curve. If n >= 3, we have that mu(D(2)(f)) = 2 mu(D(2)(f)/S(2))+C(f)-1, where D(2)(f) is the lifting of the double point curve in (C(n) x C(n), 0), mu(X) denotes the Milnor number of X and C(f) is the number of cross-caps that appear in a stable deformation of f. Moreover, we consider an unfolding F(t, x) = (t, f(t)(x)) of f and show that if F is mu-constant, then it is excellent in the sense of Gaffney. Finally, we find a minimal set of invariants whose constancy in the family f(t) is equivalent to the Whitney equisingularity of F. We also give an example of an unfolding which is topologically trivial, but it is not Whitney equisingular.

Precession and nutation in the eta Carinae binary system: evidence from the X-ray light curve

It is believed that eta Carinae is actually a massive binary system, with the wind-wind interaction responsible for the strong X-ray emission. Although the overall shape of the X-ray light curve can be explained by the high eccentricity of the binary orbit, other features like the asymmetry near periastron passage and the short quasi-periodic oscillations seen at those epochs have not yet been accounted for. In this paper we explain these features assuming that the rotation axis of eta Carinae is not perpendicular to the orbital plane of the binary system. As a consequence, the companion star will face eta Carinae on the orbital plane at different latitudes for different orbital phases and, since both the mass-loss rate and the wind velocity are latitude dependent, they would produce the observed asymmetries in the X-ray flux. We were able to reproduce the main features of the X-ray light curve assuming that the rotation axis of eta Carinae forms an angle of 29 degrees +/- 4 degrees with the axis of the binary orbit. We also explained the short quasi-periodic oscillations by assuming nutation of the rotation axis, with an amplitude of about 5 degrees and a period of about 22 days. The nutation parameters, as well as the precession of the apsis, with a period of about 274 years, are consistent with what is expected from the torques induced by the companion star.

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).

The doodle of a finitely determined map germ from R(2) to R(3)

Let f : U subset of R(2) -> R(3) be a representative of a finitely determined map germ f : (R(2), 0) -> (R(3), 0). Consider the curve obtained as the intersection of the image of the mapping f with a sufficiently small sphere s(epsilon)(2) centered at the origin in R(3), call this curve the associated doodle of the map germ f. For a large class of map germs the associated doodle has many transversal self-intersections. The topological classification of such map germs is considered from the point of view of the associated doodles. (C) 2009 Elsevier Inc. All rights reserved.

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.