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.

On locally finite transitive two-ended digraphs

Projecte de recerca elaborat a partir d’una estada al Department de Matemàtica Aplicada de la Montanuniversität Leoben, Àustria, entre agost i desembre del 2006. L’ objectiu ha estat fer recerca sobre digrafs infinits amb dos finals, connexos i localment finits, i, en particular, en digrafs amb dos finals i altament arc-transitius. Malnic, Marusic et al. van introduir un nou tipus de relació d’equivalència en els vèrtexs d’un dígraf, anomenades relacions d’assolibilitat, que generalitzen i tenen el seu origen en un problema posat per Cameron et al., on les classes de la relació d’equivalència eren vèrtexs que pertanyien a un camí alternat del dígraf . Malnic et al. en el mencionat article van establir connexions ben estretes entre aquestes relacions d’assolibilitat i l'estructura de finals i creixement dels digrafs localment finits i transitius. En aquest treball, s’ha caracteritzat per complet aquestes relacions d’assolibitat en el cas de dígrafs localment finits i transitius amb exactament dos finals, en termes de la descomposició en números primers del número de línies que genera el digraf amb dos finals. A més, es nega la Conjectura 1 sostinguda per Seifter que afirmava que un digraf connex localment finit amb més d’un final era necessàriament o be 0-, 1- o altament arc-transitiu. Seifer havia donat una solució parcial a la conjectura pel cas de digrafs regulars amb grau primer que tinguin un conjunt de tall connex. En aquest treball, es descriu una família infinita de dígrafs regulars de grau dos, amb dos finals, exactament 2-arc transitius i no 3-arc transitius. Així, es nega la Conjectura de Seifter en el cas general, fins i tot per grau primer. Tot i així, la solució parcial donada per Seifter en el seu article és en cert sentit la millor possible i l'existència un conjunt de tall connex essencial.

Locally univalent functions, VMOA, and the Dirichlet space

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

A Schoenflies extension theorem for a class of locally bi-Lipschitz homeomorphisms

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

Rethinking economy-wide rebound measures: an unbiased proposal

In spite of having been first introduced in the last half of the ninetieth century, the debate about the possible rebound effects from energy efficiency improvements is still an open question in the economic literature. This paper contributes to the existing research on this issue proposing an unbiased measure for economy-wide rebound effects. The novelty of this economy-wide rebound measure stems from the fact that not only actual energy savings but also potential energy savings are quantified under general equilibrium conditions. Our findings indicate that the use of engineering savings instead of general equilibrium potential savings downward biases economy-wide rebound effects and upward-biases backfire effects. The discrepancies between the traditional indicator and our proposed measure are analysed in the context of the Spanish economy.

Female stereotypes in household appliances advertising and their social role in Spain: the perpetuation of a no- longer-existing female condition

The following dissertation proposes a qualitative approach on the matter ofadvertising, society and construction of identity, based on the effect of householdappliances commercials in constructing female identity of Spanish women today.Conclusions will be drawn based on a juxtaposition of social background andadvertising content and on how Spanish women of today perceive the evolution offemale imagery depicted in advertisements. The aim is to demonstrate how muchcommercials mirrors society and how far it reinforces paradigms no longer existing

Assessing an intuitive condition for stability under a range of traffic conditions via a generalised Lu-Kumar network

We argue the importance both of developing simple sufficientconditions for the stability of general multiclass queueing networks and also of assessing such conditions under a range of assumptions on the weight of the traffic flowing between service stations. To achieve the former, we review a peak-rate stability condition and extend its range of application and for the latter, we introduce a generalisation of the Lu-Kumar network on which the stability condition may be tested for a range of traffic configurations. The peak-rate condition is close to exact when the between-station traffic is light, but degrades as this traffic increases.

Robustness of entanglement

In the quest to completely describe entanglement in the general case of a finite number of parties sharing a physical system of finite-dimensional Hilbert space an entanglement magnitude is introduced for its pure and mixed states: robustness. It corresponds to the minimal amount of mixing with locally prepared states which washes out all entanglement. It quantifies in a sense the endurance of entanglement against noise and jamming. Its properties are studied comprehensively. Analytical expressions for the robustness are given for pure states of two-party systems, and analytical bounds for mixed states of two-party systems. Specific results are obtained mainly for the qubit-qubit system (qubit denotes quantum bit). As by-products local pseudomixtures are generalized, a lower bound for the relative volume of separable states is deduced, and arguments for considering convexity a necessary condition of any entanglement measure are put forward.

World-line condition and the noninteraction theorem

A 6N-dimensional alternative formulation is proposed for constrained Hamiltonian systems. In this context the noninteraction theorem is derived from the world-line conditions. A model of two interacting particles is exhibited where physical coordinates are canonical.

On Ito's formula for elliptic diffusion processes

Bardina and Jolis [Stochastic process. Appl. 69 (1997) 83-109] prove an extension of Ito's formula for F(Xt, t), where F(x, t) has a locally square-integrable derivative in x that satisfies a mild continuity condition in t and X is a one-dimensional diffusion process such that the law of Xt has a density satisfying certain properties. This formula was expressed using quadratic covariation. Following the ideas of Eisenbaum [Potential Anal. 13 (2000) 303-328] concerning Brownian motion, we show that one can re-express this formula using integration over space and time with respect to local times in place of quadratic covariation. We also show that when the function F has a locally integrable derivative in t, we can avoid the mild continuity condition in t for the derivative of F in x.

Study of the effect of oral health on physical condition of professional soccer players of the Football Club Barcelona

Objectives: The objective of this study was to evaluate the oral health status of professional soccer players of F.C. Barcelona and its relation to the incidence of sport lesions. Methods: Thirty professional soccer players were consecutively evaluated in the seasons 2003/4, 2004/5 and 2005/6. A research protocol to assess their oral health was developed. DMFT, Quigley & Hein plaque index (PI), Löe & Silness gingival index (GI), World Health Organization malocclusion index, Ramfjord teeth probing pocket depth (PPD), TMJ examination and history of dental trauma were recorded. All physical injuries sustained by players during the season were documented from F.C. Barcelona medical services. Results: Mean DMFT score was 5.7 (SD 4.1), Quigley & Hein plaque index score was 2.3 (SD 1.1), Löe & Silness gingival index was 1.1 (SD 0.8), and periodontal pocket depth was 1.9 mm (SD 0.3). Pearson"s analysis showed a significant correlation between PI and GI (p<0.01). Nine players (30%) presented bruxism - the same proportion of those with severe malocclusion. Seven (23.3%) players had suffered uncomplicated crown fractures. The mean incidence of physical injuries was 8 (SD 3.4) per player. PI and PPD showed a statistically significant correlation to muscle injuries (p<0.05). Conclusions: Soccer players, despite intensive medical follow-up, have significant oral health problems such as untreated caries, gingivitis or malocclusion, and suffer dental trauma as a result of sports activities. Their physical condition could also be associated to oral health

Parental body condition does not correlate with offspring sex-ratio in Cory's shearwater

We analyzed offspring sex ratio variation in Mediterranean Cory's Shearwater (Calonectris d. diomedea) during two consecutive breeding seasons in two colonies. We test for differential breeding conditions between years and colonies looking at several breeding parameters and parental condition. We then explored the relationship between offspring sex ratio and parental condition and breeding parameters. This species is sexually dimorphic with males larger and heavier than females; consequently we expected differential parental cost in rearing sexes, or a greater sensitivity of male chicks to adverse conditions, which may lead to biased sex ratios. Chicks were sexed molecularly by the amplification of the CHD genes. Offspring sex ratio did not differ from parity, either at hatching or fledging, regardless of the colony or year. However, parental body condition and breeding parameters such as egg size and breeding success were different between years and colonies. Nevertheless, neither nestling mortality nor body condition at fledging varied between years or colonies, suggesting that male and female chicks were probably not differentially affected by variability in breeding conditions.

A Method for Sky-Condition Classification from Ground-Based Solar Radiation Measurements

Identification of clouds from satellite images is now a routine task. Observation of clouds from the ground, however, is still needed to acquire a complete description of cloud conditions. Among the standard meteorologicalvariables, solar radiation is the most affected by cloud cover. In this note, a method for using global and diffuse solar radiation data to classify sky conditions into several classes is suggested. A classical maximum-likelihood method is applied for clustering data. The method is applied to a series of four years of solar radiation data and human cloud observations at a site in Catalonia, Spain. With these data, the accuracy of the solar radiation method as compared with human observations is 45% when nine classes of sky conditions are to be distinguished, and it grows significantly to almost 60% when samples are classified in only five different classes. Most errors are explained by limitations in the database; therefore, further work is under way with a more suitable database