Uniqueness of signature for simple curves

We propose a topological approach to the problem of determining a curve from its iterated integrals. In particular, we prove that a family of terms in the signature series of a two dimensional closed curve with finite p-variation, 1≤p<2, are in fact moments of its winding number. This relation allows us to prove that the signature series of a class of simple non-smooth curves uniquely determine the curves. This implies that outside a Chordal SLEκ null set, where 0<κ≤4, the signature series of curves uniquely determine the curves. Our calculations also enable us to express the Fourier transform of the n-point functions of SLE curves in terms of the expected signature of SLE curves. Although the techniques used in this article are deterministic, the results provide a platform for studying SLE curves through the signatures of their sample paths.

Simple piecewise geodesic interpolation of simple and Jordan curves with applications

We explicitly construct simple, piecewise minimizing geodesic, arbitrarily fine interpolation of simple and Jordan curves on a Riemannian manifold. In particular, a finite sequence of partition points can be specified in advance to be included in our construction. Then we present two applications of our main results: the generalized Green’s theorem and the uniqueness of signature for planar Jordan curves with finite p -variation for 1⩽p<2.

Transcendental Brauer groups of products of CM elliptic curves

Let L be a number field and let E/L be an elliptic curve with complex multiplication by the ring of integers O_K of an imaginary quadratic field K. We use class field theory and results of Skorobogatov and Zarhin to compute the transcendental part of the Brauer group of the abelian surface ExE. The results for the odd order torsion also apply to the Brauer group of the K3 surface Kum(ExE). We describe explicitly the elliptic curves E/Q with complex multiplication by O_K such that the Brauer group of ExE contains a transcendental element of odd order. We show that such an element gives rise to a Brauer-Manin obstruction to weak approximation on Kum(ExE), while there is no obstruction coming from the algebraic part of the Brauer group.

Bad reduction of genus three curves with complex multiplication

Let C be a smooth, absolutely irreducible genus 3 curve over a number field M. Suppose that the Jacobian of C has complex multiplication by a sextic CM-field K. Suppose further that K contains no imaginary quadratic subfield. We give a bound on the primes p of M such that the stable reduction of C at p contains three irreducible components of genus 1.

Shadow lines in the arithmetic of elliptic curves

Let E/Q be an elliptic curve and p a rational prime of good ordinary reduction. For every imaginary quadratic field K/Q satisfying the Heegner hypothesis for E we have a corresponding line in E(K)\otimes Q_p, known as a shadow line. When E/Q has analytic rank 2 and E/K has analytic rank 3, shadow lines are expected to lie in E(Q)\otimes Qp. If, in addition, p splits in K/Q, then shadow lines can be determined using the anticyclotomic p-adic height pairing. We develop an algorithm to compute anticyclotomic p-adic heights which we then use to provide an algorithm to compute shadow lines. We conclude by illustrating these algorithms in a collection of examples.

Corrosion behavior of pure titanium in artificial saliva solution

The biocompatibility of commercially pure (cp) titanium stems from its chemical stability within an organism, due to a fine film of impermeable titanium oxide covering the metal surface, which guarantees its resistance to corrosion. Despite its biocompatible characteristic, this material does not promote the formation of a hydroxyapatite layer, therefore, many research groups have sought to alter the material`s surface, introducing modifications that might influence corrosion resistance. The electrochemical behavior of cp Ti, with hydroxyapatite coating and without hydroxyapatite coating, commonly used in implant materials, was investigated using an artificial saliva solution at 25 degrees C and pH=7.4. In the conditions of the study it was observed that the hydroxyapatite layer influences the properties of corrosion resistance. This study of the behavior of cp Ti with and without hydroxyapatite coating, in naturally aerated artificial saliva solution at 25 degrees C, was based on open circuit potential measurements and potentiodynamic polarization curves. At approximately 1x10(-6) A/cm(2) the potential for cp Ti with and without hydroxyapatite coating begins to increase at a faster rate, but at -74mV (SCE) for coated cp Ti and at 180mV (SCE) for uncoated cp Ti the increase in potential begins to slow. This behavior, characterized by a partial stabilization of current density, indicates that in those potential ranges a protective passive film is formed.

Supercritical fluid extracts from the Brazilian cherry (Eugenia uniflora L.): Relationship between the extracted compounds and the characteristic flavour intensity of the fruit

Supercritical carbon dioxide (SC-CO(2)) extractions of Brazilian cherry (Eugenia uniflora L.) were carried out under varied conditions of pressure and temperature, according to a central composite 2(2) experimental design, in order to produce flavour-rich extracts. The composition of the extracts was evaluated by gas chromatography coupled with mass spectrometry (GC/MS). The abundance of the extracted compounds was then related to sensory analysis results, assisted by principal component and factorial discriminant analysis (PCA and FDA, respectively). The identified sesquiterpenes and ketones were found to strongly contribute to the characteristic flavour of the Brazilian cherry. The extracts also contained a variety of other volatile compounds, and part of the fruit wax contained long-chain hydrocarbons that according to multivariate analysis, contributed to the yield of the extracts, but not the flavour. Volatile phenolic compounds, to which antioxidant properties are attributed, were also present in the extracts in high proportion, regardless of the extraction conditions. (C) 2010 Elsevier Ltd. All rights reserved.

The SARS algorithm: detrending CoRoT light curves with Sysrem using simultaneous external parameters

Surveys for exoplanetary transits are usually limited not by photon noise but rather by the amount of red noise in their data. In particular, although the CoRoT space-based survey data are being carefully scrutinized, significant new sources of systematic noises are still being discovered. Recently, a magnitude-dependant systematic effect was discovered in the CoRoT data by Mazeh et al. and a phenomenological correction was proposed. Here we tie the observed effect to a particular type of effect, and in the process generalize the popular Sysrem algorithm to include external parameters in a simultaneous solution with the unknown effects. We show that a post-processing scheme based on this algorithm performs well and indeed allows for the detection of new transit-like signals that were not previously detected.

Indecomposable and noncrossed product division algebras over function fields of smooth p-adic curves

We construct indecomposable and noncrossed product division algebras over function fields of connected smooth curves X over Z(p). This is done by defining an index preserving morphism s: Br(<(K(X))over cap>)` --> Br(K(X))` which splits res : Br(K (X)) --> Br(<(K(X))over cap>), where <(K(X))over cap> is the completion of K (X) at the special fiber, and using it to lift indecomposable and noncrossed product division algebras over <(K(X))over cap>. (C) 2010 Elsevier Inc. All rights reserved.

C(k)-solvability near the characteristic set for a class of planar complex vector fields of infinite type

This paper deals with semi-global C(k)-solvability of complex vector fields of the form L = partial derivative/partial derivative t + x(r) (a(x) + ib(x))partial derivative/partial derivative x, r >= 1, defined on Omega(epsilon) = (-epsilon, epsilon) x S(1), epsilon > 0, where a and b are C(infinity) real-valued functions in (-epsilon, epsilon). It is shown that the interplay between the order of vanishing of the functions a and b at x = 0 influences the C(k)-solvability at Sigma = {0} x S(1). When r = 1, it is permitted that the functions a and b of L depend on the x and t variables, that is, L = partial derivative/partial derivative t + x(a(x, t) + ib(x, t))partial derivative/partial derivative x, where (x, t) is an element of Omega(epsilon).

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.

Gevrey solvability near the characteristic set for a class of planar complex vector fields of infinite type

We study the Gevrey solvability of a class of complex vector fields, defined on Omega(epsilon) = (-epsilon, epsilon) x S(1), given by L = partial derivative/partial derivative t + (a(x) + ib(x))partial derivative/partial derivative x, b not equivalent to 0, near the characteristic set Sigma = {0} x S(1). We show that the interplay between the order of vanishing of the functions a and b at x = 0 plays a role in the Gevrey solvability. (C) 2008 Elsevier Inc. All rights reserved.

On the dominance of roots of characteristic equations for neutral functional differential equations

We present a sufficient condition for a zero of a function that arises typically as the characteristic equation of a linear functional differential equations of neutral type, to be simple and dominant. This knowledge is useful in order to derive the asymptotic behaviour of solutions of such equations. A simple characteristic equation, arisen from the study of delay equations with small delay, is analyzed in greater detail. (C) 2009 Elsevier Inc. All rights reserved.

Fitting Lorenz curves

This paper presents a functional form, linear in the parameters, to deal with income distribution and Lorenz curves. The function is fitted to the Brazilian income distribution. Data standard deviations were estimated from year-to-year variation of the income share. (C) 2010 Elsevier B.V. All rights reserved.