Stochastic porous media equations and self-organized criticality: convergence to the critical state in all dimensions

If $X=X(t,\xi)$ is the solution to the stochastic porous media equation in $\cal O\subset\mathbb{R}^d$, $1\le d\le 3,$ modelling the self-organized criticaity and $X_c$ is the critical state, then it is proved that \int^\9_0m(\cal O\setminus\cal O^t_0)dt<\9, $\mathbb{P}{-a.s.}$ and \lim_{t\to\9}\int_{\cal O}|X(t)-X_c|d\xi=\ell<\9,\ \mathbb{P}{-a.s.} Here, $m$ is the Lebesgue measure and $\cal O^t_c$ is the critical region $\{\xi\in\cal O;$ $X(t,\xi)=X_c(\xi)\}$ and $X_c(\xi)\le X(0,\xi)$ a.e. $\xi\in\cal O$. If the stochastic Gaussian perturbation has only finitely many modes (but is still function-valued), \lim_{t\to\9}\int_K|X(t)-X_c|d\xi=0 exponentially fast for all compact $K\subset\cal O$ with probability one, if the noise is sufficiently strong. We also recover that in the deterministic case $\ell=0$

CORPORATE GOVERNANCE AND FIRM PERFORMANCE

Good corporate governance is an important step in building market confidence and encouraging more stable, long-term international investment flows. Many countries see better corporate governance practices as a way to improve economic dynamism and thus enhance overall economic performance. This paper sets out to further develop our understanding of corporate governance and its effects on corporate performance and economic performance. In doing so, it addresses some of the underlying factors that promote efficient corporate governance, and examines some of the economic implications associated with various corporate governance systems. I provide an framework for understanding how corporate governance can affect corporate performance. In the wake of a literature survey, I find that corporate governance matters for economic performance, insider ownership matters the most, outside ownership concentration destroys market value, direct ownership being superior to indirect.corporate governance, company performance

Retail store design and environment as branding support in the services marketing

The services are intangibles, therefore their quality is difficult to be evaluated by the client and building a strong brand image is a challenging task. The services are distributed using diverse channels such as: company retail stores, dealers, franchise. The service companies are interested in the environment of the location, not only to increase sells but also in order to boost the image of the company. The excitement that a retail store induces to a client can modify the perception of the brand. The client values more a brand that distributes its services in a luxury, high-tech retail environment than a discount store. In this paper we intended to investigate the techniques that a service company is using to enhance the brand image in a retail location. For this purpose, the various aspects of the retail store design and environment were analyzed in connection with the customer-based brand equity model. This original association will offer the services companies’ new perspectives on how to leverage brand image.retail environment, brand architecture, point of sale marketing

Probabilistic representation for solutions of an irregular porous media type equation: the degenerate case

We consider a possibly degenerate porous media type equation over all of $\R^d$ with $d = 1$, with monotone discontinuous coefficients with linear growth and prove a probabilistic representation of its solution in terms of an associated microscopic diffusion. This equation is motivated by some singular behaviour arising in complex self-organized critical systems. The main idea consists in approximating the equation by equations with monotone non-degenerate coefficients and deriving some new analytical properties of the solution

Convergence of invariant measures for singular stochastic diffusion equations

It is proved that the solutions to the singular stochastic $p$-Laplace equation, $p\in (1,2)$ and the solutions to the stochastic fast diffusion equation with nonlinearity parameter $r\in (0,1)$ on a bounded open domain $\Lambda\subset\R^d$ with Dirichlet boundary conditions are continuous in mean, uniformly in time, with respect to the parameters $p$ and $r$ respectively (in the Hilbert spaces $L^2(\Lambda)$, $H^{-1}(\Lambda)$ respectively). The highly singular limit case $p=1$ is treated with the help of stochastic evolution variational inequalities, where \mathbbm{P}-a.s. convergence, uniformly in time, is established. It is shown that the associated unique invariant measures of the ergodic semigroups converge in the weak sense (of probability measures).Comment: to appear in Stoch. Proc. Appl. (in press), 18 p

Dynamics of semi-flexible polymer solutions in the highly entangled regime

We present experimental evidence that the effective medium approximation (EMA), developed by D.C. Morse [Phys. Rev. E {\bf 63}, 031502, (2001)], provides the correct scaling law of the macroscopic plateau modulus $G^{0}\propto\rho^{4/3}L^{-1/3}_{p}$ (where $\rho$ is the contour length per unit volume and $L_{p}$ is the persistence length) of semi-flexible polymer solutions, in the highly entangled concentration regime. Competing theories, including a self-consistent binary collision approximation (BCA), have instead predicted $G^{0}\propto\rho^{7/5}L^{-1/5}_{p}$. We have tested both the EMA and BCA scaling predictions using actin filament (F-actin) solutions which permit experimental control of $L_p$ independently of other parameters. A combination of passive video particle tracking microrheology and dynamic light scattering yields independent measurements of the elastic modulus $G$ and $L_{p}$ respectively. Thus we can distinguish between the two proposed laws, in contrast to previous experimental studies, which focus on the (less discriminating) concentration functionality of $G$.Comment: 4 pages, 6 figures, Phys. Rev. Lett. (accepted

Event-based control of basic wastewater treatment plant control loops

[Abstract] This paper addresses the problem of basic control loops in wastewater treatment plants. By basic control loops we are referring to the traditional dissolved oxygen and nitrates. They are the basic controls more sophisticated control solutions can be based upon. Therefore it is important that these loops perform in an efficient way. The problem is addressed here within the framework provided by the Benchmark Simulation Model Number 1 (BSM1) and by the use of an event-based solution. It will be verified that the solution can slightly improve the performance of the already exiting controllers both at loop level as well as at plant operation level.[Resumen] Este documento aborda el problema de los bucles de control básicos en las plantas de tratamiento de aguas residuales. Por bucles de control básicos nos referimos a los tradicionales disueltos de oxígeno y nitratos. Son los controles básicos en los que se pueden basar las soluciones de control más sofisticadas. Por lo tanto, es importante que estos bucles funcionen de manera eficiente. El problema se aborda aquí dentro del marco provisto por el Número de modelo de simulación de referencia (BSM1) y por el uso de una solución basada en eventos. Se verificará que la solución puede mejorar ligeramente el rendimiento de los controladores que ya existen, tanto a nivel de bucle como a nivel de operación de la planta