Periodic solutions for nonautonomous second order differential inclusions systems with p- Laplacian

Using the nonsmooth variant of minimax point theorems, some existence results are obtained for periodic solutions of nonautonomous second-order differential inclusions systems with p-Laplacian.

Stabilized Petrov-Galerkin methods for the convection-diffusion-reaction and the Helmholtz equations

We present two new stabilized high-resolution numerical methods for the convection–diffusion–reaction (CDR) and the Helmholtz equations respectively. The work embarks upon a priori analysis of some consistency recovery procedures for some stabilization methods belonging to the Petrov–Galerkin framework. It was found that the use of some standard practices (e.g. M-Matrices theory) for the design of essentially non-oscillatory numerical methods is not feasible when consistency recovery methods are employed. Hence, with respect to convective stabilization, such recovery methods are not preferred. Next, we present the design of a high-resolution Petrov–Galerkin (HRPG) method for the 1D CDR problem. The problem is studied from a fresh point of view, including practical implications on the formulation of the maximum principle, M-Matrices theory, monotonicity and total variation diminishing (TVD) finite volume schemes. The current method is next in line to earlier methods that may be viewed as an upwinding plus a discontinuity-capturing operator. Finally, some remarks are made on the extension of the HRPG method to multidimensions. Next, we present a new numerical scheme for the Helmholtz equation resulting in quasi-exact solutions. The focus is on the approximation of the solution to the Helmholtz equation in the interior of the domain using compact stencils. Piecewise linear/bilinear polynomial interpolation are considered on a structured mesh/grid. The only a priori requirement is to provide a mesh/grid resolution of at least eight elements per wavelength. No stabilization parameters are involved in the definition of the scheme. The scheme consists of taking the average of the equation stencils obtained by the standard Galerkin finite element method and the classical finite difference method. Dispersion analysis in 1D and 2D illustrate the quasi-exact properties of this scheme. Finally, some remarks are made on the extension of the scheme to unstructured meshes by designing a method within the Petrov–Galerkin framework.

Velocity-jump instabilities in Hele-Shaw flow of associating polymer solutions

We study fracturelike flow instabilities that arise when water is injected into a Hele-Shaw cell filled with aqueous solutions of associating polymers. We explore various polymer architectures, molecular weights, and solution concentrations. Simultaneous measurements of the finger tip velocity and of the pressure at the injection point allow us to describe the dynamics of the finger in terms of the finger mobility, which relates the velocity to the pressure gradient. The flow discontinuities, characterized by jumps in the finger tip velocity, which are observed in experiments with some of the polymer solutions, can be modeled by using a nonmonotonic dependence between a characteristic shear stress and the shear rate at the tip of the finger. A simple model, which is based on a viscosity function containing both a Newtonian and a non-Newtonian component, and which predicts nonmonotonic regions when the non-Newtonian component of the viscosity dominates, is shown to agree with the experimental data.

Observation of a continuous interior crisis in the Hindmarsh-Rose neuron model.

Interior crises are understood as discontinuous changes of the size of a chaotic attractor that occur when an unstable periodic orbit collides with the chaotic attractor. We present here numerical evidence and theoretical reasoning which prove the existence of a chaos-chaos transition in which the change of the attractor size is sudden but continuous. This occurs in the Hindmarsh¿Rose model of a neuron, at the transition point between the bursting and spiking dynamics, which are two different dynamic behaviors that this system is able to present. Moreover, besides the change in attractor size, other significant properties of the system undergoing the transitions do change in a relevant qualitative way. The mechanism for such transition is understood in terms of a simple one-dimensional map whose dynamics undergoes a crossover between two different universal behaviors

Compromise solutions for bankruptcy situations: a note

Although classic bankruptcy problems take into account a single claims vector, Pulido et al. (2008) show that there are real bankruptcy situations where agents face more than one reference vector. In particular, they consider the claims and an additional reference vector. To analyze these situations, they propose the extreme and the diagonal approaches. Nonetheless, the former approach depends on the order of the vectors: if we interchange the claims and the reference vectors, the result changes. Moreover their study is limited to the case in which the reference vector is lower than the claims vector. In the present note, we propose an extension that solves these short- comings by introducing the idea of impartiality. Keywords: bankruptcy problems; reference point; compromise solution; impartiality.

Desenvolupament d'una tecnologia per a la millora de les recomanacions en la fertilització nitrogenada dels cereals d'hivern. (I) Cereals d'hivern a la Catalunya interior

Es va realitzar una sèrie d'assaigs d'adobat nitrogenat en diferents comarques de la Catalunya interior. En el conjunt d'aquests assaigs es varen comprovar tres mètodes diferents que es va considerar que eren prometedors per tal de millorar la fertilització nitrogenada. Els mètodes assajats eren el mètode del balanç de nitrogen, el del nitrogen mineral i el del contingut de nitrats al suc de la base de les tiges (CNSBT). Els sòls on es van realitzar els assaigs no presentaven cap limitació especial per al cultiu del blat i eren profunds, ben drenats, no salins i de textura mitjana; l'única excepció era un assaig sobre sòl moderadament profund. Per tant, i també pel que fa a la fertilitat química, els sòls s'han de considerar d'un potencial productiu mitjàalt. El mètode del balanç de nitrogen s'ha mostrat com a molt prometedor de cara a definir si cal la magnitud de l'adobat de cobertora per a les condicions estudiades. El mètode de nitrogen mineral també ha estat efectiu en aquest sentit, mentre que el del CNSBT s'ha revelat com a no aplicable en les condicions assajades, on en molts casos l'aigua és també factor limitant. Al llarg dels assaigs s'han identificat un seguit de factors que impedeixen ajustar la fertilitat nitrogenada. Entre aquests cal esmentar la mala estimació de la producció objectiu, la dificultat de predir el N disponible a partir dels adobs orgànics, dificultats de mostreig pel nitrogen nítric i l'efecte crític que té l'erràtica disponibilitat d'aigua que complica molt l'estratègia de fertilització nitrogenada a adoptar.

Highly eccentric hip-hop solutions of the 2N

We show the existence of families of hip-hop solutions in the equal-mass 2N-body problem which are close to highly eccentric planar elliptic homographic motions of 2N bodies plus small perpendicular non-harmonic oscillations. By introducing a parameter ϵ, the homographic motion and the small amplitude oscillations can be uncoupled into a purely Keplerian homographic motion of fixed period and a vertical oscillation described by a Hill type equation. Small changes in the eccentricity induce large variations in the period of the perpendicular oscillation and give rise, via a Bolzano argument, to resonant periodic solutions of the uncoupled system in a rotating frame. For small ϵ ≠ 0, the topological transversality persists and Brouwer's fixed point theorem shows the existence of this kind of solutions in the full system

On the structure of cooperative and competitive solutions for a generalized assignment game

We study cooperative and competitive solutions for a many- to-many generalization of Shapley and Shubik (1972)'s assignment game. We consider the Core, three other notions of group stability and two al- ternative definitions of competitive equilibrium. We show that (i) each group stable set is closely related with the Core of certain games defined using a proper notion of blocking and (ii) each group stable set contains the set of payoff vectors associated to the two definitions of competitive equilibrium. We also show that all six solutions maintain a strictly nested structure. Moreover, each solution can be identified with a set of ma- trices of (discriminated) prices which indicate how gains from trade are distributed among buyers and sellers. In all cases such matrices arise as solutions of a system of linear inequalities. Hence, all six solutions have the same properties from a structural and computational point of view.

Periodic solutions of second-order differential inclusions systems with p-Laplacian

Some existence results are obtained for periodic solutions of nonautonomous second-order differential inclusions systems with p-Laplacian

Growth, habit formation, and catching-up\ with the Joneses

When habits are introduced multiplicatively in a capital accumulation model, the consumers' objective function might fail to be concave. In this paper we provide conditions aimed at guaranteeing the existence of interior solutions to the consumers' problem. We also characterize the equilibrium path of two growth models with multiplicative habits: the internal habit formation model, where individual habits coincide with own past consumption, and the external habit formation (or catching-up with the Joneses) model, where habits arise from the average past consumption in the economy. We show that the introduction of external habits makes the equilibrium path inefficient during the transition towards the balanced growth path. We characterize in this context the optimal tax policy.

Lp-solutions to BSDEs with super-linear growth coefficient. Application to degenerate semilinear PDEs.

We consider multidimensional backward stochastic differential equations (BSDEs). We prove the existence and uniqueness of solutions when the coefficient grow super-linearly, and moreover, can be neither locally Lipschitz in the variable y nor in the variable z. This is done with super-linear growth coefficient and a p-integrable terminal condition (p & 1). As application, we establish the existence and uniqueness of solutions to degenerate semilinear PDEs with superlinear growth generator and an Lp-terminal data, p & 1. Our result cover, for instance, the case of PDEs with logarithmic nonlinearities.

Multiplicity of limit cycles and analytic m-solutions for planar differential systems

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

Stability of periodic solutions obtained via the averaging method for nonsmooth Lipschitz system

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

Degradació en planta pilot de colorants reactius mitjançant el procés de foto-Fenton assistit amb llum solar: aplicació del procés com a pre-tractament d'un procés biològic

Estudi elaborat a partir d’una estada a la Plataforma Solar de Almería entre desembre del 2006 i gener del 2007. S’ha dut a terme la degradació en planta pilot dels colorants reactius Procion Red H-E7B i Cibacron Red FN-R mitjançant el procés de foto-Fenton aplicat com a tractament únic i com a pretractament d’un procés biològic. El procés de foto-Fenton, assistit amb llum solar, es va realitzar en un fotoreactor solar tipus Col•lector Parabòlic Compost (CPC) i el tractament biològic en un Reactor de Biomassa Immobilitzada (RBI). Com a punt de partida, i amb l’objectiu d’estudiar la reproductibilitat del sistema, es van prendre resultats obtinguts d’experiments realitzats prèviament a escala de laboratori i amb llum artificial. El paràmetre Carboni Orgànic Total (COT) es va emprar com a indicador de l’eliminació dels colorants i dels seus intermedis. En aplicar únicament el procés de foto-Fenton com a tractament, concentracions de 10 mg•l-1 de Fe (II) i 250 mg•l-1 de H2O2 per degradar 250 mg•l-1 Procion Red H-E7B, i de 20 mg•l-1 de Fe (II) i 500 mg•l-1 de H2O2 per degradar 250 mg•l-1 Cibacron Red FN-R, van reproduir els resultants obtinguts al laboratori, amb uns nivells d’eliminació de COT del 82 i 86%, respectivament. A més, l’ús beneficiós de la llum solar en el procés de foto-Fenton, juntament amb la configuració del CPC, van incrementar la velocitat de degradació respecte als resultats previs, permetent la reducció de la concentració de Fe (II) de 10 a 2 mg•l-1 (Procion Red H-E7B) i de 20 a 5 mg•l-1 (Cibacron Red FN-R) sense pèrdues d’efectivitat. D’altre banda, el sistema combinat foto-Fenton/tractament biològic en planta pilot, unes concentracions d’oxidant de 225 mg•l-1 H2O2 per Cibacron Red FN-R i 65 mg•l-1 H2O2 per Procion Red H-E7B van ser suficients per generar solucions intermèdies biodegradables i alimentar així el RBI, millorant inclús els resultats obtinguts prèviament al laboratori.

Testing of stair climbing point-of-choice prompts in Barcelona at an outdoor set of stairs and scalators on the Montjuïc site

Regular stair climbing has well-documented health dividends, such as increased fitness and strength, weight loss and reduced body fat, improved lipid profiles and reduced risk of osteoporosis. The general absence of barriers to participation makes stair climbing an ideal physical activity (PA) for health promotion. Studies in the US and the UK have consistently shown that interventions to increase the accumulation of lifestyle PA by climbing stairs rather than using the escalators are effective. However, there are no previous in Catalonia. This project tested one message for their ability to prompt travelers on the Montjuïc site to choose the stairs rather than the escalator when climbing up the Monjuïc hill. One standard message, " Take the stairs! 7 minutes of stair climbing a day protects your heart" provided a comparison with previous research done in the UK. Translated into Catalan and Spanish, it was presented on a poster positioned at the point of choice between the stairs and the escalator. The study used a quasi-experimental, interrupted time series design. Travelers, during several and specific hours on two days of the week, were coded for stair or escalator use, gender, age, ethnic status, presence of accompanying children or bags by one observer. Overall, the intervention resulted in a 81% increase in stair climbing. In the follow-up period without messages, stair climbing dropped out to baseline levels. This preliminary study showed a significant effect on stair use. However, caution is needed since results are based on a small sample and, only a low percentage of the sample took the stairs at baseline or the intervention phase . Future research on stair use in Catalonia should focus on using bigger samples, different sites (metro stations, airports, shopping centers, etc) , different messages and techniques to promote stair climbing.