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.

Gauge transformations in the Lagrangian and Hamilton formalisms of generally covariant theories

We study spacetime diffeomorphisms in the Hamiltonian and Lagrangian formalisms of generally covariant systems. We show that the gauge group for such a system is characterized by having generators which are projectable under the Legendre map. The gauge group is found to be much larger than the original group of spacetime diffeomorphisms, since its generators must depend on the lapse function and shift vector of the spacetime metric in a given coordinate patch. Our results are generalizations of earlier results by Salisbury and Sundermeyer. They arise in a natural way from using the requirement of equivalence between Lagrangian and Hamiltonian formulations of the system, and they are new in that the symmetries are realized on the full set of phase space variables. The generators are displayed explicitly and are applied to the relativistic string and to general relativity.

Hamilton Jacobi theory for constrained systems

We extend the HamiltonJacobi formulation to constrained dynamical systems. The discussion covers both the case of first-class constraints alone and that of first- and second-class constraints combined. The HamiltonDirac equations are recovered as characteristic of the system of partial differential equations satisfied by the HamiltonJacobi function.

Hamilton-Jacobi theory for constrained systems

We extend the HamiltonJacobi formulation to constrained dynamical systems. The discussion covers both the case of first-class constraints alone and that of first- and second-class constraints combined. The HamiltonDirac equations are recovered as characteristic of the system of partial differential equations satisfied by the HamiltonJacobi function.

Periodic orbits near a heteroclinic loop formed by one dimensional orbit and a 2-dimensional manifold: application to the charged collinear 3-body problem

The paper is devoted to the study of a type of differential systems which appear usually in the study of some Hamiltonian systems with 2 degrees of freedom. We prove the existence of infinitely many periodic orbits on each negative energy level. All these periodic orbits pass near the total collision. Finally we apply these results to study the existence of periodic orbits in the charged collinear 3–body problem.

Bienestar del lechón en la fase de cebo

Los cerdos necesitan espacio para desarrollar actividades como descansar, comer, explorar o interaccionar con otros individuos del corral. En los cerdos de engorde, por tanto, el espacio disponible por individuo es un factor relevante y densidades excesivamente altas llevan a diversos problemas desde un punto de vista del bienestar. Al mismo tiempo, es importante considerar las relaciones sociales que se establecen entre los animales y el grado en que estas se ven alteradas por cuestiones de manejo como la mezcla de animales. En ocasiones, los cerdos desarrollan problemas de conducta muy importantes derivados de estos y otros factores, como la mordedura de colas. Así, los tres problemas principales de los cerdos durante la fase de cebo están relacionados con densidades demasiado altas en los corrales, mezcla de animales y conductas redirigidas como la caudofagia.

Bienestar del lechón en la fase de lactación, destete y transición

Tanto el momento del nacimiento como del destete implican para el lechón un conjunto de cambios importantes a los cuales debe responder el lechón para restablecer su equilibrio fisiológico interno (homeostasis). La capacidad de adaptación del lechón a estos cambios va a influir no sólo su bienestar en estas fases, sino otros parámetros productivos durante el engorde. A continuación se describen los fenómenos más destacables en relación al bienestar del lechón durante estas fases productivas: la mortalidad neonatal, el estrés del destete y de la formación de grupos durante la transición.

Bienestar durante el transporte

El transporte y sacrificio son las dos fases de la producción porcina más críticas desde el punto de vista del bienestar animal (Moss, 1992). Durante estas fases los animales son sometidos en un periodo de tiempo relativamente corto a un elevado número de factores estresantes. Estos factores incluyen la falta de agua y alimento, el proceso de carga y descarga, la mezcla con animales desconocidos, los movimientos del vehículo, los cambios de temperatura y humedad relativa, y la interacción con personal desconocido asociado a un manejo diferente, y a veces más brusco, que el recibido previamente (SCAHAW, 2002). Si bien cada uno de estos factores por separado tendría poco o ningún efecto negativo sobre el bienestar del animal, la combinación de varios de ellos tiene efectos aditivos, potenciando la respuesta de estrés del animal. La respuesta de estrés no solo tiene efectos sobre el bienestar animal, también puede tener efectos negativos sobre la calidad de la canal y de la carne, de forma que, en general, cuanto más intensa o duradera es dicha respuesta –y, por lo tanto, cuanto peor es el bienestar de los animales-, mayores son las repercusiones negativas sobre la calidad de la canal y de la carne. Por lo tanto, mejorar el bienestar de los animales durante su transporte y sacrificio permite responder simultáneamente a dos requisitos de mercado cada vez más importantes.

Heteroclinic orbits for a class of Hamiltonian systems on Riemannian manifolds

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Preparació d'òxids mesoporosos mitjançant nanocasting

S’ha sintetitzat pel mètode de nanocasting pols nanomètrica d’In2O3, NiO i Co3O4 utilitzant diferents mesoestructures de sílice (SBA-16, SBA-15 i KIT-6) com a motlle rígid. Les rèpliques obtingudes s’han caracteritzat amb les tècniques de difracció de raigs X, microscòpia electrònica de rastreig, microscòpia electrònica de transmissió d’alta resolució i BET. L’òxid d’indi, l’òxid de níquel i l’òxid de cobalt obtinguts a partir de la sílice SBA-15 i KIT-6 conserven perfectament l’estructura mesopòrica del motlle, amb valors del diàmetre de porus al voltant dels 7-8 nm. Les rèpliques del motlle SBA-15 estan formades per nanofilaments llargs, mentre que les rèpliques de KIT-6 presenten una estructura hexagonal. A partir del motlle de tipus gàbia (SBA-16), si bé el Co3O4 obtingut és mesopòric, en els altres dos casos (In2O3 i NiO) no s’ha observat ordenament. Per a les rèpliques In2O3 KIT-6 i NiO SBA-15, la caracterització mitjançant BET ha permès corroborar el caràcter mesoestructurat de les mostres.

Geography of resonances and Arnold diffusion in a priori unstable Hamiltonian systems

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A computational and geometric approach to phase resetting curves and surfaces

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Fast numerical algorithms for the computation of invariant tori in Hamiltonian systems

In this paper, we develop numerical algorithms that use small requirements of storage and operations for the computation of invariant tori in Hamiltonian systems (exact symplectic maps and Hamiltonian vector fields). The algorithms are based on the parameterization method and follow closely the proof of the KAM theorem given in [LGJV05] and [FLS07]. They essentially consist in solving a functional equation satisfied by the invariant tori by using a Newton method. Using some geometric identities, it is possible to perform a Newton step using little storage and few operations. In this paper we focus on the numerical issues of the algorithms (speed, storage and stability) and we refer to the mentioned papers for the rigorous results. We show how to compute efficiently both maximal invariant tori and whiskered tori, together with the associated invariant stable and unstable manifolds of whiskered tori. Moreover, we present fast algorithms for the iteration of the quasi-periodic cocycles and the computation of the invariant bundles, which is a preliminary step for the computation of invariant whiskered tori. Since quasi-periodic cocycles appear in other contexts, this section may be of independent interest. The numerical methods presented here allow to compute in a unified way primary and secondary invariant KAM tori. Secondary tori are invariant tori which can be contracted to a periodic orbit. We present some preliminary results that ensure that the methods are indeed implementable and fast. We postpone to a future paper optimized implementations and results on the breakdown of invariant tori.

Resultados de diversas alternativas a la castración quirúrgica de cerdos

El objetivo de este estudio fue evaluar el efecto de la castración quirúrgica (MC), la inmunocastración (MI), la producción de hembras (HE) y machos enteros (ME) sobre la productividad, el comportamiento y el bienestar animal. La castración quirúrgica se realizó a los siete días de edad y la inmunocastración mediante la administración a los 77 y 146 días de edad de un producto compuesto por una forma modifi cada del GnRF conjugado a una proteína capaz de inducir la formación de anticuerpos frente al GnRF. Durante el engorde, se evaluó el consumo individual, peso, espesor de grasa y lomo de 120 cerdos (36 ME, 36 MI, 24 MC y 24 hembras HE). Asimismo, se registró el comportamiento de los animales durante dos días consecutivos en las semanas 9, 11, 20, 21, 23 y 25. Los MI presentaron un crecimiento e ingestión diarias superior a los ME y un mejor índice de conversión que los MC. El espesor de lomo de los MI fue superior al de los MC, pero inferior al de los ME. La actividad se vio reducida en los MI en comparación con los ME, especialmente después de la segunda administración. Estos resultados sugieren que la inmunocastración es una alternativa a la castración quirúrgica. Result of differet alternatives to surgical castration of pigs The objective of this study was to evaluate the effect of surgical castration (MC), immunocastration (MI), keeping females (HE) and entire males (ME) on performance, behaviour and welfare. The surgical castration was carried out at 7 days of age, and the immunocastration through the administration at 77 and 146 days of age of a modifi ed form of GnRF conjugated to protein to induce the formation of antibodies against GnRF. Individual consumption, weight and fat and loin depth of 120 pigs (36 ME, 36 MI, 24MC and 24 HE) was measured. Moreover, behaviour was recorded during two consecutive days in weeks 9, 11, 20, 21, 23 and 25. MI presented a higher growth and feed intake compared to ME and a better conversion ratio than MC. Loin depth was higher for MI than for MC, but lower than for ME. Activity was reduced in MI compared to ME, especially after the second administration. These results suggest that immunocastration is an alternative to surgical castration.

Effect of magnesium sulphate and L-tryptophan and genotype on the feed intake, behaviour and meat quality of pigs

Sixty-nine entire male pigs with different halothane genotype (homozygous halothane positive – nn –, n=36; and homozygous halothane negative – NN-, n=33) were fed with a supplementation of magnesium sulphate (Mg) and/or L-tryptophan (Trp) in the diet for 5 days before slaughter. Animals were housed individually and were submitted to stressful ante mortem conditions (mixed in the lorry according to treatments and transported 1 hour on rough roads). Individual feed intake was recorded during the 5-d treatment. At the abattoir, pig behaviour was assessed in the raceway to the stunning system and during the stunning period by exposure to CO2. Muscle pH, colour, water holding capacity, texture and cathepsin activities were determined to assess meat quality. The number of pigs with an individual feed intake lower than 2 kg/d was significantly different among diets (P&0.05; Control: 8.7 %; Mg&Trp: 43.5 %; Trp: 17.4 %) and they were considered to have inadequate supplement intake. During the ante mortem period, 15.2 % of pigs included in the experiment died, and this percentage decreased to 8.7 % in those pigs with a feed intake & 2kg/day, all of them from the stress-sensitive pigs (nn). In general, no differences were observed in the behaviour of pigs along the corridor leading to the stunning system and inside the CO2 stunning system. During the stunning procedure, Trp diet showed shorter periods of muscular excitation than control and Mg&Trp diets. The combination of a stressful ante mortem treatment and Mg&Trp supplementation led to carcasses with high incidence of severe skin lesions. Different meat quality results were found when considering all pigs or considering only those with adequate supplement intake. In this later case, Trp increased pH45 (6.15) vs Control diet (5.96) in the Longissimus thoracis (LT) muscle (P&0.05) and pH at 24h (Trp: 5.59 vs C: 5.47) led to a higher incidence of dark, firm and exudative (DFD) traits in SM muscle (P&0.05). Genotype affected negatively all the meat quality traits. Seventy-five percent of LT and 60.0 % of the SM muscles from nn pigs were classified as pale, soft and exudative (PSE), while none of the NN pigs showed these traits (P&0.0001). No significant differences were found between genotypes on the incidence of DFD meat. Due to the negative effects observed in the Mg&Trp group in feed intake and carcass quality, the utilization of a mixture of magnesium sulphate and tryptophan is not recommended.