Geometria integral i convexitat en espais de curvatura holomorfa constant

En aquest treball es tracten qüestions de la geometria integral clàssica a l'espai hiperbòlic i projectiu complex i a l'espai hermític estàndard, els anomenats espais de curvatura holomorfa constant. La geometria integral clàssica estudia, entre d'altres, l'expressió en termes geomètrics de la mesura de plans que tallen un domini convex fixat de l'espai euclidià. Aquesta expressió es dóna en termes de les integrals de curvatura mitja. Un dels resultats principals d'aquest treball expressa la mesura de plans complexos que tallen un domini fixat a l'espai hiperbòlic complex, en termes del que definim com volums intrínsecs hermítics, que generalitzen les integrals de curvatura mitja. Una altra de les preguntes que tracta la geometria integral clàssica és: donat un domini convex i l'espai de plans, com s'expressa la integral de la s-èssima integral de curvatura mitja del convex intersecció entre un pla i el convex fixat? A l'espai euclidià, a l'espai projectiu i hiperbòlic reals, aquesta integral correspon amb la s-èssima integral de curvatura mitja del convex inicial: se satisfà una propietat de reproductibitat, que no es té en els espais de curvatura holomorfa constant. En el treball donem l'expressió explícita de la integral de la curvatura mitja quan integrem sobre l'espai de plans complexos. L'expressem en termes de la integral de curvatura mitja del domini inicial i de la integral de la curvatura normal en una direcció especial: l'obtinguda en aplicar l'estructura complexa al vector normal. La motivació per estudiar els espais de curvatura holomorfa constant i, en particular, l'espai hiperbòlic complex, es troba en l'estudi del següent problema clàssic en geometria. Quin valor pren el quocient entre l'àrea i el perímetre per a successions de figures convexes del pla que creixen tendint a omplir-lo? Fins ara es coneixia el comportament d'aquest quocient en els espais de curvatura seccional negativa i que a l'espai hiperbòlic real les fites obtingudes són òptimes. Aquí provem que a l'espai hiperbòlic complex, les cotes generals no són òptimes i optimitzem la superior.

Integral formulae for a Riemannian manifold with a distribution

We obtain a new series of integral formulae for symmetric functions of curvature of a distribution of arbitrary codimension (an its orthogonal complement) given on a compact Riemannian manifold, which start from known formula by P.Walczak (1990) and generalize ones for foliations by several authors: Asimov (1978), Brito, Langevin and Rosenberg (1981), Brito and Naveira (2000), Andrzejewski and Walczak (2010), etc. Our integral formulae involve the co-nullity tensor, certain component of the curvature tensor and their products. The formulae also deal with a number of arbitrary functions depending on the scalar invariants of the co-nullity tensor. For foliated manifolds of constant curvature the obtained formulae give us the classical type formulae. For a special choice of functions our formulae reduce to ones with Newton transformations of the co-nullity tensor.

On the impact of leverage constraints on asset prices and trading volume

Researchers have used stylized facts on asset prices and trading volumein stock markets (in particular, the mean reversion of asset returnsand the correlations between trading volume, price changes and pricelevels) to support theories where agents are not rational expected utilitymaximizers. This paper shows that this empirical evidence is in factconsistent with a standard infite horizon perfect information expectedutility economy where some agents face leverage constraints similar tothose found in todays financial markets. In addition, and in sharpcontrast to the theories above, we explain some qualitative differencesthat are observed in the price-volume relation on stock and on futuresmarkets. We consider a continuous-time economy where agents maximize theintegral of their discounted utility from consumption under both budgetand leverage con-straints. Building on the work by Vila and Zariphopoulou(1997), we find a closed form solution, up to a negative constant, for theequilibrium prices and demands in the region of the state space where theconstraint is non-binding. We show that, at the equilibrium, stock holdingsvolatility as well as its ratio to stock price volatility are increasingfunctions of the stock price and interpret this finding in terms of theprice-volume relation.

Soluble models in two-dimensional dilaton gravity

A one-parameter class of simple models of two-dimensional dilaton gravity, which can be exactly solved including back-reaction effects, is investigated at both classical and quantum levels. This family contains the RST model as a special case, and it continuously interpolates between models having a flat (Rindler) geometry and a constant curvature metric with a nontrivial dilaton field. The processes of formation of black hole singularities from collapsing matter and Hawking evaporation are considered in detail. Various physical aspects of these geometries are discussed, including the cosmological interpretation.

Linear stochastic differential algebraic equations with constant coefficients

We consider linear stochastic differential-algebraic equations with constant coefficients and additive white noise. Due to the nature of this class of equations, the solution must be defined as a generalised process (in the sense of Dawson and Fernique). We provide sufficient conditions for the law of the variables of the solution process to be absolutely continuous with respect to Lebesgue measure.

Equilibrium play and best response to (Stated) beliefs in constant sum games

We report experimental results on one-shot two person 3x3 constant sum games played by non-economists without previous experience in the laboratory. Although strategically our games are very similar to previous experiments in which game theory predictions fail dramatically, 80% of actions taken in our experiment coincided with the prediction of the unique Nash equilibrium in pure strategies and 73% of actions were best responses to elicited beliefs. We argue how social preferences, presentation effects and belief elicitation procedures may influence how subjects play in simple but non trivial games and explain the diferences we observe with respect to previous work.

The Impact of prevention measures and organisational factors on occupational injuries

This paper analyses the impact of a series of managerial and organisational factors on occupational injuries. These consist of occupational safety measures, as regards both the intensity and the orientation of risk prevention in companies, and the adoption of certain work organisation practices, quality management and the use of flexible production technologies. We estimate a negative binomial regression based on a sample of 213 Spanish industrial establishments, defining a constant random parameter to take account of non-observable heterogeneity. Our results show that occupational safety measures, the intensive use of quality management tools and the empowerment of workers all help to reduce the number of injuries. We have also confirmed the presence of synergies between the organisational factors analysed and the development of an occupational safety strategy featuring participation and the extension of prevention to all levels of the organisation.

Improving the risk concept: a revision of Arrow-Pratt theory in the context of controlled dynamic stochastic environments

In the literature on risk, one generally assume that uncertainty is uniformly distributed over the entire working horizon, when the absolute risk-aversion index is negative and constant. From this perspective, the risk is totally exogenous, and thus independent of endogenous risks. The classic procedure is "myopic" with regard to potential changes in the future behavior of the agent due to inherent random fluctuations of the system. The agent's attitude to risk is rigid. Although often criticized, the most widely used hypothesis for the analysis of economic behavior is risk-neutrality. This borderline case must be envisaged with prudence in a dynamic stochastic context. The traditional measures of risk-aversion are generally too weak for making comparisons between risky situations, given the dynamic �complexity of the environment. This can be highlighted in concrete problems in finance and insurance, context for which the Arrow-Pratt measures (in the small) give ambiguous.

The non-linear Dirichlet problem in Hadamard manifolds

We prove existence theorems for the Dirichlet problem for hypersurfaces of constant special Lagrangian curvature in Hadamard manifolds. The first results are obtained using the continuity method and approximation and then refined using two iterations of the Perron method. The a-priori estimates used in the continuity method are valid in any ambient manifold.

Expectativas del paciente y su correlación con la escala de Constant y el cuestionario de calidad de vida SF-36

El objetivo del estudio es la evaluación subjetiva del hombro a través del análisis de expectativas en el dolor, la funcionalidad, las actividades de la vida diaria y la fuerza que el paciente espera obtener tras el tratamiento de la patología del hombro, y posteriormente, evaluar la correlación de estos datos obtenidos con los resultados en la escala de Constant y en el SF- 36. La hipótesis que nos planteamos fue que las expectativas del paciente son independientes del estado funcional del hombro y de la percepción de la calidad de vida.

Els marges del pensament polític contemporani

La crisi i esfondrament del pensament metafísic heretat de la modernitat deixa la filosofia contemporània davant d'un nou paradigma on el coneixement s’ha de construir prescindint de tota identitat i fonamentació. El meu projecte s’estableix com un recorregut descendent que parteix d’un àmbit concret, com és el del problema de la manca de fonamentació en la filosofia política contemporània, per arribar a la veritable arrel del problema general que no és altre que la mateixa naturalesa del llenguatge filosòfic. El punt de partida és la pregunta sobre la possibilitat d’una filosofia política en termes postmetafísics. La filosofia política, atrapada entre les forces de la tirania unitària del concepte metafísic i la dissolució pràctica en pro de la realitat instrumental, traça ponts cap a l’estètica i la deconstrucció, que tenen com a corol•lari final qüestionar-nos els propis límits del pensament polític. El concepte d’impolític és una sortida deconstructiva a aquest atzucac. Des d’Esposito, Rancière, Nancy, però sobretot Massimo Cacciari, he aprofundit en el paradigma postmetafísic que origina aquesta negació política de la pròpia política, política com els seus límits, relació com a distància i identitat com a silenci. És evident que la clau de volta és l’herència i recepció contemporània de Nietzsche i la seva crítica a la transcendentalitat moderna en el sí de l’elaboració d’un coneixement en un naufragi constant pel fracàs de la síntesi que anhela. És aquesta herència la que ha possibilitat aquest pensament negatiu contemporani, el del joc wittgensteinià, la deconstrucció del valor que queda convertit en el seu propi marge (Derrida). Definim així no només una comunitat política basada en la incommensurabilitat dels seus membres alhora buits de contingut (Musil), sinó un model de llenguatge que és el seu propi silenci, un llenguatge en contínua lluita contra sí mateix. El meu projecte és una relectura d’aquesta veritat no identitària on el concepte de diàleg pren una importància cabdal. La filosofia de la música aquí es presenta com un terreny fèrtil d’eines conceptuals a l’hora de desenvolupar-ho. La música és el llenguatge negatiu que només troba possibilitat en la seva pròpia impossibilitat de contingut sintètic. Més enllà de les referències obligatòries a chönberg i Adorno entre altres, el camí iniciat per Bergson amb la introducció de la temporalitat a la discussió obra la porta al paper de l’esdveniment en aquest discurs sobre la impossibilitat. Tornant a la filosofia, on el propi llenguatge filosòfic es defineix ja com a impossible, l’esdeveniment reobre l’antiga tensió entre l’escriptura i la paraula viva, veritable fonament del problema, i vèrtex de la possibilitat d’aquesta filosofia impossible.

Variació segons edat i sexe del component força de l'escala de Constant de valoració de la funció de l’espatlla

Un dels instruments més utilitzats per a mesurar la funció de l’espatlla és el conegut com a Constant Score on una quarta part del valor total de la valoració funcional de l’espatlla correspon a la força d’aquesta regió anatòmica. En el disseny original del Constant Score no es tingueren en compte les possibles variacions dels valors normals de força en funció de l’edat o del sexe. Aquesta variació no ha estat mai correctament establerta. Aquest treball pretén establir l’existència de diferències en la força de l’espatlla entre diferents grups d’edat i entre sexes.

Negative Fukui functions: new insights based on electronegativity equalization

The occurrence of negative values for Fukui functions was studied through the electronegativity equalization method. Using algebraic relations between Fukui functions and different other conceptual DFT quantities on the one hand and the hardness matrix on the other hand, expressions were obtained for Fukui functions for several archetypical small molecules. Based on EEM calculations for large molecular sets, no negative Fukui functions were found

Simple finite field method for calculation of static and dynamic vibrational hyperpolarizabilities: curvature contributions

In the static field limit, the vibrational hyperpolarizability consists of two contributions due to: (1) the shift in the equilibrium geometry (known as nuclear relaxation), and (2) the change in the shape of the potential energy surface (known as curvature). Simple finite field methods have previously been developed for evaluating these static field contributions and also for determining the effect of nuclear relaxation on dynamic vibrational hyperpolarizabilities in the infinite frequency approximation. In this paper the finite field approach is extended to include, within the infinite frequency approximation, the effect of curvature on the major dynamic nonlinear optical processes

The curvature of the conical intersection seam: an approximate second-order analysis

We present a method for analyzing the curvature (second derivatives) of the conical intersection hyperline at an optimized critical point. Our method uses the projected Hessians of the degenerate states after elimination of the two branching space coordinates, and is equivalent to a frequency calculation on a single Born-Oppenheimer potential-energy surface. Based on the projected Hessians, we develop an equation for the energy as a function of a set of curvilinear coordinates where the degeneracy is preserved to second order (i.e., the conical intersection hyperline). The curvature of the potential-energy surface in these coordinates is the curvature of the conical intersection hyperline itself, and thus determines whether one has a minimum or saddle point on the hyperline. The equation used to classify optimized conical intersection points depends in a simple way on the first- and second-order degeneracy splittings calculated at these points. As an example, for fulvene, we show that the two optimized conical intersection points of C2v symmetry are saddle points on the intersection hyperline. Accordingly, there are further intersection points of lower energy, and one of C2 symmetry - presented here for the first time - is found to be the global minimum in the intersection space