Multivector Field Formulation of Hamiltonian Field Theories: Equations and Symmetries

We state the intrinsic form of the Hamiltonian equations of first-order Classical Field theories in three equivalent geometrical ways: using multivector fields, jet fields and connections. Thus, these equations are given in a form similar to that in which the Hamiltonian equations of mechanics are usually given. Then, using multivector fields, we study several aspects of these equations, such as the existence and non-uniqueness of solutions, and the integrability problem. In particular, these problems are analyzed for the case of Hamiltonian systems defined in a submanifold of the multimomentum bundle. Furthermore, the existence of first integrals of these Hamiltonian equations is considered, and the relation between {\sl Cartan-Noether symmetries} and {\sl general symmetries} of the system is discussed. Noether's theorem is also stated in this context, both the ``classical'' version and its generalization to include higher-order Cartan-Noether symmetries. Finally, the equivalence between the Lagrangian and Hamiltonian formalisms is also discussed.Comment: Some minor mistakes are corrected. Bibliography is updated. To be published in J. Phys. A: Mathematical and Genera

Non-standard connections in classical mechanics

In the jet-bundle description of first-order classical field theories there are some elements, such as the lagrangian energy and the construction of the hamiltonian formalism, which require the prior choice of a connection. Bearing these facts in mind, we analyze the situation in the jet-bundle description of time-dependent classical mechanics. So we prove that this connection-dependence also occurs in this case, although it is usually hidden by the use of the ``natural'' connection given by the trivial bundle structure of the phase spaces in consideration. However, we also prove that this dependence is dynamically irrelevant, except where the dynamical variation of the energy is concerned. In addition, the relationship between first integrals and connections is shown for a large enough class of lagrangians.Comment: 17 pages, Latex fil

Higher-order Mechanics: Variational Principles and other topics

After reviewing the Lagrangian-Hamiltonian unified formalism (i.e, the Skinner-Rusk formalism) for higher-order (non-autonomous) dynamical systems, we state a unified geometrical version of the Variational Principles which allows us to derive the Lagrangian and Hamiltonian equations for these kinds of systems. Then, the standard Lagrangian and Hamiltonian formulations of these principles and the corresponding dynamical equations are recovered from this unified framework.Comment: New version of the paper "Variational principles for higher-order dynamical systems", which was presented in the "III Iberoamerican Meeting on Geometry, Mechanics and Control" (Salamanca, 2012). The title is changed. A detailed review is added. Sections containing results about variational principles are enlarged with additional comments, diagrams and summarizing results. Bibliography is update

Properties of Multisymplectic Manifolds

This lecture is devoted to review some of the main properties of multisymplectic geometry. In particular, after reminding the standard definition of multisymplectic manifold, we introduce its characteristic submanifolds, the canonical models, and other relevant kinds of multisymplectic manifolds, such as those where the existence of Darboux-type coordinates is assured. The Hamiltonian structures that can be defined in these manifolds are also studied, as well as other important properties, such as their invariant forms and the characterization by automorphisms.Comment: 10 pp. Changes in Sections 5 and 7 (where brief guides to the proofs of theorems have been added). Lecture given at the workshop on {\sl Classical and Quantum Physics: Geometry, Dynamics and Control. (60 Years Alberto Ibort Fest), Instituto de Ciencias Matem\'aticas (ICMAT)}, Madrid (Spain), 5--9 March 201

Classical field theory on Lie algebroids: Variational aspects

The variational formalism for classical field theories is extended to the setting of Lie algebroids. Given a Lagrangian function we study the problem of finding critical points of the action functional when we restrict the fields to be morphisms of Lie algebroids. In addition to the standard case, our formalism includes as particular examples the case of systems with symmetry (covariant Euler-Poincare and Lagrange Poincare cases), Sigma models or Chern-Simons theories.Comment: Talk deliverd at the 9th International Conference on Differential Geometry and its Applications, Prague, September 2004. References adde

Universidad de Ciencias Médicas de La Habana. Facultad de Estomatología de La Habana

Introducción: la masticación constituye un proceso fundamental en la función digestiva, considerándose como su fase inicial.Objetivo: determinar factores de riesgo del desdentamiento y la asociación de trastornos del tracto digestivo superior con desdentamiento no rehabilitado con prótesis oportunamenteMétodo: cien pacientes entre 40 y 65 años, 50 desdentados y 50 dentados, fueron interrogados y examinados con una encuesta en la Facultad de Estomatología entre 2007-2009.Resultados: las odontopatías, poca educación en salud dental, escolaridad, higiene oral, acceso a servicios dentales y ancianidad, mostraron alto riesgo del desdentamiento significativo, p = 0.05. Se encontraron diferencias porcentuales elevadas a favor de los desdentados con significación clínica y estadística, p = 0.05, en tener síntomas digestivos, más de 3 síntomas, regurgitación, disfagia, dolor retro-esternal, pirosis, plenitud gástrica y síntomas post-desdentamiento. Los desdentados fueron 7.2 años más añosos, tuvieron 2.3 más síntomas digestivos en medias, y estuvieron 12 meses más sin rehabilitación protésica en mediana, que los íntegros dentarios, con significación estadística, p = 0.05. Los desdentados mostraron asociación entre demora de rehabilitación protésica de 25 a 144 meses, tener 3 síntomas o más (p=0.051), y padecer disfagia, pirosis y acidez estadísticamente significativa, p = 0.05.Conclusiones: se confirmaron factores de riesgo y se halló asociación estadística entre desdentamiento, tiempo sin prótesis y síntomas del tracto digestivo superior</p

Diversidad genética y conservación de pinos nativos de la cuenca del río Cupatitzio, en Michoacán

La conservación de los hábitats terrestres asociados a cuencas hidrográficas tiene como componente intrínseco la conservación de los recursos genéticos de las especies que conforman la cubierta vegetal de estos sistemas. El objetivo del presente estudio fue evaluar los niveles de variación y estructura genética de las poblaciones de pino distribuidas en la cuenca del río Cupatitzio, en Michoacán, con el uso de cuatro microsatélites de núcleo. El estudio incluye ocho poblaciones de cuatro especies de pino distribuidas en las zonas altas, media y baja de la cuenca. Los resultados indican que las poblaciones SL3 de P. pseudostrobus y RB6 de P. douglasiana contienen los valores más altos de variación genética (HE =0.674 y HE= 0.615, respectivamente). Las poblaciones presentan importantes niveles de endogamia (FIS entre 0.057-0.544) y una diferenciación genética significativa (FST entre 0.094-0.152), la cual se asocia de manera moderada con la distribución geográfica de las poblaciones (r= 0.443) y se agrupa de acuerdo con las especies. La parte alta de la Reserva, en Quinceo y la Tzaráracua, presenta los niveles más bajos de variación genética y los mayores niveles de endogamia, por lo que se recomienda hacer actividades de restauración en estas localidades. Así mismo, se sugieren actividades de conservación in situ en San Lorenzo y la parte baja de la Reserva, ya que ambas poblaciones presentan los tamaños efectivos más grandes y son representativas del acervo genético de los bosques de pino en la cuenca del Cupatitzio

Symmetries in Classical Field Theory

The multisymplectic description of Classical Field Theories is revisited, including its relation with the presymplectic formalism on the space of Cauchy data. Both descriptions allow us to give a complete scheme of classification of infinitesimal symmetries, and to obtain the corresponding conservation laws.Comment: 70S05; 70H33; 55R10; 58A2

Nivel de conocimientos y autocuidado de adultos con asma de la consulta de neumología. Monterrey-México.

El asma es una enfermedad crónica, su tratamiento es complejo y su adecuado manejo depende en gran parte del nivel conocimientos, destrezas y capacidad de autocuidado del paciente. Objetivos: evaluar la relación entre el nivel de conocimientos y las capacidades de autocuidado de pacientes con asma. Material y Métodos: estudio descriptivo transversal dentro de los meses de septiembre a noviembre en pacientes con diagnóstico de asma que acudieron a la consulta externa del servicio de Neumología en el Hospital General de Zona No. 33 de Monterrey Nuevo León. México. La muestra estuvo constituida por 174 pacientes. Se firmó consentimiento informado y se aplicaron el Cuestionario de conocimientos acerca de Asma y la Escala de Valoración de la Capacidad de Agencia de Autocuidado. Los datos se analizaron mediante estadística descriptiva, se utilizaron pruebas de correlación de Spearman considerando un nivel de significancia de .05. Resultados: los participantes tuvieron 40.2 años (DE=16,04) con escolaridad de 11.49 años (DE=3,72) en promedio. A medida que se incrementó la edad, disminuyeron el nivel de conocimientos y el de autocuidado (valores de r=-0,338 y -0,218 respectivamente, p<,05

Effect of environmental conditions on the concentration of tear inflammatory mediators during contact lens wear

Purpose: To analyze the influence of environmental conditions on the concentrations of tear inflammatory mediators during contact lens (CL) wear. Methods: Fifty-four CL wearers completed 4 visits combining the bilateral use of omafilcon A or comfilcon A CL and a 90-minute exposure to 2 environmental conditions: standard [50% relative humidity (RH), 23°C, 930 mb] or adverse (5% RH, localized air flow, 23°C, 750 mb). Four microliters of tears was collected by capillarity from each subject. Changes in concentration of epidermal growth factor (EGF); interleukin (IL)-1 receptor antagonist, IL-1b, IL-2, IL-4, IL-6, and IL-8; tumor necrosis factor (TNF) a; monocyte chemoattractant protein-1; and matrix metalloproteinase (MMP)-9 were analyzed. The effects of the environment, CL type, and symptoms were evaluated using a 3-way mixed analysis of variance with repeated measures. Results: Under the standard condition, EGF significantly increased [0.36; 95% confidence interval (CI), 0.08 to 0.64], and IL-1b (20.48; 95% CI, 20.84 to 20.12) and IL-2 (20.48; 95% CI, 20.87 to 20.09) significantly decreased. Under the adverse condition, IL-6 significantly increased (0.35; 95% CI, 0.09 to 0.62). Comparing conditions, EGF change was significantly lower (P = 0.02) and IL-1b, IL-2, IL-6, and TNF-a changes were significantly higher (P # 0.04) under the adverse condition. Additionally, IL-1b significantly decreased with comfilcon A (20.51; 95% CI, 20.88 to 20.15), being significantly lower (P = 0.01) than the change with omafilcon A (0.06; 95% CI, 20.23 to 0.35). Conclusions: The secretion of several tear inflammatory mediators during CL wear differs depending on the environmental conditions and the CL type used. These outcomes might help to understand the effect of the environment and CL materials on the ocular surface of CL wearersPartially supported by the Junta de Castilla y Leon and the European Social Fund through Project VA317-11 (scholarship)