Rigorous derivation of a nonlinear diffusion equation as fast-reaction limit of a continuous coagulation-fragmentation model with diffusion

Weak solutions of the spatially inhomogeneous (diffusive) Aizenmann-Bak model of coagulation-breakup within a bounded domain with homogeneous Neumann boundary conditions are shown to converge, in the fast reaction limit, towards local equilibria determined by their mass. Moreover, this mass is the solution of a nonlinear diffusion equation whose nonlinearity depends on the (size-dependent) diffusion coefficient. Initial data are assumed to have integrable zero order moment and square integrable first order moment in size, and finite entropy. In contrast to our previous result [CDF2], we are able to show the convergence without assuming uniform bounds from above and below on the number density of clusters.

Lp theory for the multidimensional aggregation equation

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

A one-dimensional Keller-Segel equation with a drift issued from the boundary

We investigate in this note the dynamics of a one-dimensional Keller-Segel type model on the half-line. On the contrary to the classical configuration, the chemical production term is located on the boundary. We prove, under suitable assumptions, the following dichotomy which is reminiscent of the two-dimensional Keller-Segel system. Solutions are global if the mass is below the critical mass, they blow-up in finite time above the critical mass, and they converge to some equilibrium at the critical mass. Entropy techniques are presented which aim at providing quantitative convergence results for the subcritical case. This note is completed with a brief introduction to a more realistic model (still one-dimensional).

A functional equation related to the product in a quadratic number field

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

Gaussian estimates for the density of the non-linear stochastic heat equation in any space dimension

In this paper, we establish lower and upper Gaussian bounds for the probability density of the mild solution to the stochastic heat equation with multiplicative noise and in any space dimension. The driving perturbation is a Gaussian noise which is white in time with some spatially homogeneous covariance. These estimates are obtained using tools of the Malliavin calculus. The most challenging part is the lower bound, which is obtained by adapting a general method developed by Kohatsu-Higa to the underlying spatially homogeneous Gaussian setting. Both lower and upper estimates have the same form: a Gaussian density with a variance which is equal to that of the mild solution of the corresponding linear equation with additive noise.

Existence and uniqueness of viscosity solution for Hamilton-Jacobi equation with discontinuous coefficients dependent on time

The main result is a proof of the existence of a unique viscosity solution for Hamilton-Jacobi equation, where the hamiltonian is discontinuous with respect to variable, usually interpreted as the spatial one. Obtained generalized solution is continuous, but not necessarily differentiable.

Diseño de filtros Bulk Acoustic Wave con topología en escalera de altas prestaciones

Degut als avenços als dispositius de telecomunicacions durant l’última dècada, els filtres integrats en aquests dispositius requereixen de millors prestacions, baix cost i, per sobre de tot, requereixen unes dimensions el més reduïdes possibles. Tot i que avui dia encara s’utilitzen el filtres SAW en aquests dispositius, cada cop més s’estan substituint pels filtres amb tecnologia BAW, ja que tenen millors prestacions. En l’actualitat la topologia BAW més extensa i utilitzada és la topologia en escala. En aquest projecte s’ha portat a terme un estudi en profunditat de les limitacions dels filtres en escala. A partir de les limitacions detectades s’ha presentat una nova estructura de disseny per aquest tipus de filtres que redueix les dimensions d’aquests i millora considerablement algunes de les limitacions de l’estructura convencional. Paral·lelament s’ha desenvolupat una metodologia sistemàtica pròpia pel disseny de la nova estructura.

Confounding effects of heart rate on pulse wave velocity in paced patients with a low degree of atherosclerosis.

BACKGROUND: Pulse wave velocity (PWV), an index of arterial wall stiffness, is modulated by blood pressure (BP). Whether heart rate (HR) is also a modulator of PWV is controversial. Recent research involving mainly patients with high aortic PWV have found either no change or a positive correlation between the two. Given that PWV is increasingly being measured in cardiovascular studies, the relationship between HR and PWV should be known in patients with preserved arterial wall elasticity. OBJECTIVE: The aim of this study was to evaluate the importance of HR as a determinant of the variability in PWV in patients with a low degree of atherosclerosis. DESIGN AND METHODS: Fourteen patients (five female, nine male; aged 68 +/- 8 years) were evaluated post pacemaker implantation due to sick sinus or carotid hypersensitivity syndromes. Carotid-femoral PWV was measured at rest and during atrial pacing at 80, 90 and 100 bpm (paced HR). Arterial femoral blood flow (AFBF) was measured by echodoppler. RESULTS: PWV increased from 6.2 +/- 1.5 m/s (mean +/- SD) during resting sinus rhythm (HR 62 +/- 8 bpm; mean +/- SD) to 6.8 +/- 1.0, 7.0 +/- 0.9, and 7.6 +/- 1.1 m/s at pacing rates of 80, 90 and 100 bpm, respectively (P < 0.0001). Systolic (SBP) and mean blood pressure (MBP) remained constant at all HR levels, whereas AFBF increased in a linear fashion. CONCLUSIONS: These results demonstrate that even in patients with a low degree of atherosclerosis, HR is a potential modulator of carotid-femoral PWV.

Wellposedness of a nonlinear, logarithmic Schrödinger equation of Doebner-Goldin type modeling quantum dissipation

This paper is concerned with the modeling and analysis of quantum dissipation phenomena in the Schrödinger picture. More precisely, we do investigate in detail a dissipative, nonlinear Schrödinger equation somehow accounting for quantum Fokker–Planck effects, and how it is drastically reduced to a simpler logarithmic equation via a nonlinear gauge transformation in such a way that the physics underlying both problems keeps unaltered. From a mathematical viewpoint, this allows for a more achievable analysis regarding the local wellposedness of the initial–boundary value problem. This simplification requires the performance of the polar (modulus–argument) decomposition of the wavefunction, which is rigorously attained (for the first time to the best of our knowledge) under quite reasonable assumptions.

Parametric estimation of pulse arrival time: a robust approach to pulse wave velocity.

Pulse wave velocity (PWV) is a surrogate of arterial stiffness and represents a non-invasive marker of cardiovascular risk. The non-invasive measurement of PWV requires tracking the arrival time of pressure pulses recorded in vivo, commonly referred to as pulse arrival time (PAT). In the state of the art, PAT is estimated by identifying a characteristic point of the pressure pulse waveform. This paper demonstrates that for ambulatory scenarios, where signal-to-noise ratios are below 10 dB, the performance in terms of repeatability of PAT measurements through characteristic points identification degrades drastically. Hence, we introduce a novel family of PAT estimators based on the parametric modeling of the anacrotic phase of a pressure pulse. In particular, we propose a parametric PAT estimator (TANH) that depicts high correlation with the Complior(R) characteristic point D1 (CC = 0.99), increases noise robustness and reduces by a five-fold factor the number of heartbeats required to obtain reliable PAT measurements.

Predicting random level and seasonality of hotel prices. A structural equation growth curve approach

This article examines the effect on price of different characteristics of holiday hotels in the sun-and-beach segment, under the hedonic function perspective. Monthly prices of the majority of hotels in the Spanish continental Mediterranean coast are gathered from May to October 1999 from the tour operator catalogues. Hedonic functions are specified as random-effect models and parametrized as structural equation models with two latent variables, a random peak season price and a random width of seasonal fluctuations. Characteristics of the hotel and the region where they are located are used as predictors of both latent variables. Besides hotel category, region, distance to the beach, availability of parking place and room equipment have an effect on peak price and also on seasonality. 3- star hotels have the highest seasonality and hotels located in the southern regions the lowest, which could be explained by a warmer climate in autumn

Simultaneous estimation of indirect and interaction effects using structural equation models

Interaction effects are usually modeled by means of moderated regression analysis. Structural equation models with non-linear constraints make it possible to estimate interaction effects while correcting formeasurement error. From the various specifications, Jöreskog and Yang's(1996, 1998), likely the most parsimonious, has been chosen and further simplified. Up to now, only direct effects have been specified, thus wasting much of the capability of the structural equation approach. This paper presents and discusses an extension of Jöreskog and Yang's specification that can handle direct, indirect and interaction effects simultaneously. The model is illustrated by a study of the effects of an interactive style of use of budgets on both company innovation and performance

Explaining Fiscal Balances with a Simultaneous Equation Model of Revenue and Expenditure : A Case Study of Swiss Cantons Using Panel Data

Empirical literature on the analysis of the efficiency of measures for reducing persistent government deficits has mainly focused on the direct explanation of deficit. By contrast, this paper aims at modeling government revenue and expenditure within a simultaneous framework and deriving the fiscal balance (surplus or deficit) equation as the difference between the two variables. This setting enables one to not only judge how relevant the explanatory variables are in explaining the fiscal balance but also understand their impact on revenue and/or expenditure. Our empirical results, obtained by using a panel data set on Swiss Cantons for the period 1980-2002, confirm the relevance of the approach followed here, by providing unambiguous evidence of a simultaneous relationship between revenue and expenditure. They also reveal strong dynamic components in revenue, expenditure, and fiscal balance. Among the significant determinants of public fiscal balance we not only find the usual business cycle elements, but also and more importantly institutional factors such as the number of administrative units, and the ease with which people can resort to political (direct democracy) instruments, such as public initiatives and referendum.

Estimation de la fonction rénale par l'equation MDRD: intérêt et limites pour l'adaptation des doses de médicaments [Renal function estimation by MDRD equation: interest and limitations for drug dosing].

The MDRD (Modification of diet in renal disease) equation enables glomerular filtration rate (GFR) estimation from serum creatinine only. Thus, the laboratory can report an estimated GFR (eGFR) with each serum creatinine assessment, increasing therefore the recognition of renal failure. Predictive performance of MDRD equation is better for GFR < 60 ml/min/1,73 m2. A normal or near-normal renal function is often underestimated by this equation. Overall, MDRD provides more reliable estimations of renal function than the Cockcroft-Gault (C-G) formula, but both lack precision. MDRD is not superior to C-G for drug dosing. Being adjusted to 1,73 m2, MDRD eGFR has to be back adjusted to the patient's body surface area for drug dosing. Besides, C-G has the advantage of a greater simplicity and a longer use.

Doppler ultrasound in the measurement of pulse wave velocity: agreement with the Complior method

Aortic stiffness is an independent predictor factor for cardiovascular risk. Different methods for determining pulse wave velocity (PWV) are used, among which the most common are mechanical methods such as SphygmoCor or Complior, which require specific devices and are limited by technical difficulty in obtaining measurements. Doppler guided by 2D ultrasound is a good alternative to these methods. We studied 40 patients (29 male, aged 21 to 82 years) comparing the Complior method with Doppler. Agreement of both devices was high (R = 0.91, 0.84-0.95, 95% CI). The reproducibility analysis revealed no intra-nor interobserver differences. Based on these results, we conclude that Doppler ultrasound is a reliable and reproducible alternative to other established methods for themeasurement of aortic PWV