Inverse Problems for multiple invariant curves

Planar polynomial vector fields which admit invariant algebraic curves, Darboux integrating factors or Darboux first integrals are of special interest. In the present paper we solve the inverse problem for invariant algebraic curves with a given multiplicity and for integrating factors, under generic assumptions regarding the (multiple) invariant algebraic curves involved. In particular we prove, in this generic scenario, that the existence of a Darboux integrating factor implies Darboux integrability. Furthermore we construct examples where the genericity assumption does not hold and indicate that the situation is different for these.

Inverse problems for invariant algebraic curves: explicit computations

Given an algebraic curve in the complex affine plane, we describe how to determine all planar polynomial vector fields which leave this curve invariant. If all (finite) singular points of the curve are nondegenerate, we give an explicit expression for these vector fields. In the general setting we provide an algorithmic approach, and as an alternative we discuss sigma processes.

Environmental Kuznets Curves for Carbon Emissions: A Critical Survey

The empirical finding of an inverse U-shaped relationship between per capita income and pollution, the so-called Environmental Kuznets Curve (EKC), suggests that as countries experience economic growth, environmental deterioration decelerates and thus becomes less of an issue. Focusing on the prime example of carbon emissions, the present article provides a critical review of the new econometric techniques that have questioned the baseline polynomial specification in the EKC literature. We discuss issues related to the functional form, heterogeneity, “spurious” regressions and spatial dependence to address whether and to what extent the EKC can be observed. Despite these new approaches, there is still no clear-cut evidence supporting the existence of the EKC for carbon emissions. JEL classifications: C20; Q32; Q50; O13 Keywords: Environmental Kuznets Curve; Carbon emissions; Functional form; Heterogeneity; “Spurious” regressions; Spatial dependence.Residential satisfaction is often used as a barometer to assess the performance of public policy and programmes designed to raise individuals' well-being. However, the fact that responses elicited from residents might be biased by subjective, non-observable factors casts doubt on whether these responses can be taken as trustable indicators of the individuals' housing situation. Emotional factors such as aspirations or expectations might affect individuals' cognitions of their true residential situation. To disentangle this puzzle, we investigated whether identical residential attributes can be perceived differently depending on tenure status. Our results indicate that tenure status is crucial not only in determining the level of housing satisfaction, but also regarding how dwellers perceive their housing characteristics. Keywords: Housing satisfaction, subjective well-being, homeownership. JEL classification: D1, R2.

A computational and geometric approach to phase resetting curves and surfaces

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

On hyperbolic once-punctured-torus bundles IV: automata for lightning curves

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

Destruction of invariant curves in the restricted circular planar three body problem using comparison of action

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

On rigid analytic uniformizations of Jacobians of Shimura curves

The main goal of this article is to give an explicit rigid analytic uniformization of the maximal toric quotient of the Jacobian of a Shimura curve over Q at a prime dividing exactly the level. This result can be viewed as complementary to the classical theorem of Cerednik and Drinfeld which provides rigid analytic uniformizations at primes dividing the discriminant. As a corollary, we offer a proof of a conjecture formulated by M. Greenberg in hispaper on Stark-Heegner points and quaternionic Shimura curves, thus making Greenberg's construction of local points on elliptic curves over Q unconditional.

Equations of hyperelliptic Shimura curves

We describe an algorithm that computes explicit models of hyperelliptic Shimura curves attached to an indefinite quaternion algebra over Q and Atkin-Lehner quotients of them. It exploits Cerednik-Drinfeld’s nonarchimedean uniformisation of Shimura curves, a formula of Gross and Zagier for the endomorphism ring of Heegner points over Artinian rings and the connection between Ribet’s bimodules and the specialization of Heegner points, as introduced in [21]. As an application, we provide a list of equations of Shimura curves and quotients of them obtained by our algorithm that had been conjectured by Kurihara.

A new automated method versus continuous positive airway pressure method for measuring pressure-volume curves in patients with acute lung injury

Objective: To compare pressure–volume (P–V) curves obtained with the Galileo ventilator with those obtained with the CPAP method in patients with ALI or ARDS receiving mechanical ventilation. P–V curves were fitted to a sigmoidal equation with a mean R2 of 0.994 ± 0.003. Lower (LIP) and upper inflection (UIP), and deflation maximum curvature (PMC) points calculated from the fitted variables showed a good correlation between methods with high intraclass correlation coefficients. Bias and limits of agreement for LIP, UIP and PMC obtained with the two methods in the same patient were clinically acceptable.

Statistical treatment of grain-size curves and empirical distributions: densities as compositions?

The preceding two editions of CoDaWork included talks on the possible considerationof densities as infinite compositions: Egozcue and D´ıaz-Barrero (2003) extended theEuclidean structure of the simplex to a Hilbert space structure of the set of densitieswithin a bounded interval, and van den Boogaart (2005) generalized this to the setof densities bounded by an arbitrary reference density. From the many variations ofthe Hilbert structures available, we work with three cases. For bounded variables, abasis derived from Legendre polynomials is used. For variables with a lower bound, westandardize them with respect to an exponential distribution and express their densitiesas coordinates in a basis derived from Laguerre polynomials. Finally, for unboundedvariables, a normal distribution is used as reference, and coordinates are obtained withrespect to a Hermite-polynomials-based basis.To get the coordinates, several approaches can be considered. A numerical accuracyproblem occurs if one estimates the coordinates directly by using discretized scalarproducts. Thus we propose to use a weighted linear regression approach, where all k-order polynomials are used as predictand variables and weights are proportional to thereference density. Finally, for the case of 2-order Hermite polinomials (normal reference)and 1-order Laguerre polinomials (exponential), one can also derive the coordinatesfrom their relationships to the classical mean and variance.Apart of these theoretical issues, this contribution focuses on the application of thistheory to two main problems in sedimentary geology: the comparison of several grainsize distributions, and the comparison among different rocks of the empirical distribution of a property measured on a batch of individual grains from the same rock orsediment, like their composition

Estudi de la distribució de components i recobriment en comprimits farmacèutics mitjançant NIR-CI

La qualitat d’un producte elaborat és un factor important, tant pels consumidors, com pels òrgans reguladors que en defineixen normatives cada cop més estrictes. Iniciatives com la del PAT (Process Analytical Technology) en el sector farmacèutic, responen a aquestes necessitats. El PAT afavoreix la implantació de noves tècniques analítiques que facilitin el monitoratge i el control de paràmetres clau in-/on-line durant els processos de producció. En aquest sentit, el NIR-CI (Near Infrarred-Chemical Imaging) podria ser una eina molt útil en la millora de la qualitat de la indústria farmacèutica, ja que aprofita les avantatges del NIR com a tècnica analítica (ràpid, no invasiu, no destructiu) i les aplica a tota la superfície espacial de la mostra. És una tècnica capaç de proporcionar una gran quantitat d’informació, tant espectral com espacial, en una sola imatge. L’objectiu d’aquest treball és avaluar la capacitat de la tècnica NIR-CI, com a eina pel control de paràmetres de qualitat de comprimits farmacèutics. Concretament, s’han analitzat quantitativament la concentració i la distribució dels components (principi actiu i excipients) d’un comprimit farmacèutic amb i sense recobriment. A més, també s’ha determinat el gruix de la pel·lícula de laca de recobriment i la seva distribució a la superfície del comprimit. Per obtenir aquesta informació, es parteix d’imatges NIR-CI hiperespectrals dels comprimits. Per a l’extracció de les dades d’interès s’ha usat l’algoritme PLS en les diferents versions dels softwares Isys 5.0 i Unscrambler 9.8. La versió de l’Isys permet determinar la contribució de cada component pur a cada punt de la imatge, emprant únicament l’espectre del component en estudi. Amb la de l’Unscrambler, en canvi, es construeix un model de calibratge que, a partir d’unes mostres de referència, prediu la distribució del gruix de recobriment sobre la superfície del comprimit.

Principal curves and principal oriented points

Principal curves have been defined Hastie and Stuetzle (JASA, 1989) assmooth curves passing through the middle of a multidimensional dataset. They are nonlinear generalizations of the first principalcomponent, a characterization of which is the basis for the principalcurves definition.In this paper we propose an alternative approach based on a differentproperty of principal components. Consider a point in the space wherea multivariate normal is defined and, for each hyperplane containingthat point, compute the total variance of the normal distributionconditioned to belong to that hyperplane. Choose now the hyperplaneminimizing this conditional total variance and look for thecorresponding conditional mean. The first principal component of theoriginal distribution passes by this conditional mean and it isorthogonal to that hyperplane. This property is easily generalized todata sets with nonlinear structure. Repeating the search from differentstarting points, many points analogous to conditional means are found.We call them principal oriented points. When a one-dimensional curveruns the set of these special points it is called principal curve oforiented points. Successive principal curves are recursively definedfrom a generalization of the total variance.

Wage curves for Spain evidence from the family budget survey

This study explores the existence of a wage curve for Spain. To quantify this relationship for the Spanish economy, we used individual datafrom the EPF 1990-1991. The results show the presence of a wage curve with an elasticity of -0.13. The availability of very detailed information on wages and unemployment has also shown that less protected labour market groups -young workers, manual workers and building sector workers- have a higher elasticity of wages to local unemployment. These results could be interpreted as a greater facility of firms in these segments to settle wages as a function ofthe unemployment rate

Wage curves for Spain evidence from the family budget survey

This study explores the existence of a wage curve for Spain. To quantify this relationship for the Spanish economy, we used individual datafrom the EPF 1990-1991. The results show the presence of a wage curve with an elasticity of -0.13. The availability of very detailed information on wages and unemployment has also shown that less protected labour market groups -young workers, manual workers and building sector workers- have a higher elasticity of wages to local unemployment. These results could be interpreted as a greater facility of firms in these segments to settle wages as a function ofthe unemployment rate