Constraint algorithm for k-presymplectic Hamiltonian systems. Application to singular field theories

The k-symplectic formulation of field theories is especially simple, since only tangent and cotangent bundles are needed in its description. Its defining elements show a close relationship with those in the symplectic formulation of mechanics. It will be shown that this relationship also stands in the presymplectic case. In a natural way,one can mimick the presymplectic constraint algorithm to obtain a constraint algorithmthat can be applied to k-presymplectic field theory, and more particularly to the Lagrangian and Hamiltonian formulations offield theories defined by a singular Lagrangian, as well as to the unified Lagrangian-Hamiltonian formalism (Skinner--Rusk formalism) for k-presymplectic field theory. Two examples of application of the algorithm are also analyzed.

Unified formalism for non-autonomous mechanical systems

We present a unified geometric framework for describing both the Lagrangian and Hamiltonian formalisms of regular and non-regular time-dependent mechanical systems, which is based on the approach of Skinner and Rusk (1983). The dynamical equations of motion and their compatibility and consistency are carefully studied, making clear that all the characteristics of the Lagrangian and the Hamiltonian formalisms are recovered in this formulation. As an example, it is studied a semidiscretization of the nonlinear wave equation proving the applicability of the proposed formalism.

La teoría de Morales-Ramis y el algoritmo de Kovacic

La teor\'\ı a de Morales–Ramis es la teor\'\ı a de Galois en el contextode los sistemas din\'amicos y relaciona dos tipos diferentes de integrabilidad:integrabilidad en el sentido de Liouville de un sistema hamiltonianoe integrabilidad en el sentido de la teor\'\ı a de Galois diferencial deuna ecuaci\'on diferencial. En este art\'\i culo se presentan algunas aplicacionesde la teor\'\i a de Morales–Ramis en problemas de no integrabilidadde sistemas hamiltonianos cuya ecuaci\'on variacional normal a lo largode una curva integral particular es una ecuaci\'on diferencial lineal desegundo orden con coeficientes funciones racionales. La integrabilidadde la ecuaci\'on variacional normal es analizada mediante el algoritmode Kovacic.

Incorporating features of distribution and progression for automatic Makam classification

Automatic classification of makams from symbolic data is a rarely studied topic. In this paper, first a review of an n-gram based approach is presented using various representations of the symbolic data. While a high degree of precision can be obtained, confusion happens mainly for makams using (almost) the same scale and pitch hierarchy but differ in overall melodic progression, seyir. To further improve the system, first n-gram based classification is tested for various sections of the piece to take into account a feature of the seyir that melodic progression starts in a certain region of the scale. In a second test, a hierarchical classification structure is designed which uses n-grams and seyir features in different levels to further improve the system.

Interaccion among systems of finite size in predictive relativistic mechanics -II. Electromagnetic and gravitational interactions

We explicitly construct a closed system of differential equations describing the electromagnetic and gravitational interactions among bodies to first order in the coupling constants, retaining terms up to order c-2. The Breit and Barker and O'Connell Hamiltonians are recovered by means of a coordinate transformation. The method used throws light on the meaning of these coordinates.

Average ground-state energy of finite Fermi systems

Semiclassical theories such as the Thomas-Fermi and Wigner-Kirkwood methods give a good description of the smooth average part of the total energy of a Fermi gas in some external potential when the chemical potential is varied. However, in systems with a fixed number of particles N, these methods overbind the actual average of the quantum energy as N is varied. We describe a theory that accounts for this effect. Numerical illustrations are discussed for fermions trapped in a harmonic oscillator potential and in a hard-wall cavity, and for self-consistent calculations of atomic nuclei. In the latter case, the influence of deformations on the average behavior of the energy is also considered.

Separability and distillability of multiparticle quantum systems

We present a family of 3-qubit states to which any arbitrary state can be depolarized. We fully classify those states with respect to their separability and distillability properties. This provides a sufficient condition for nonseparability and distillability for arbitrary states. We generalize our results to N-particle states.

Lattice-gas model of particles with orientational and positional degrees of freedom: Mean-field treatment

We consider a lattice-gas model of particles with internal orientational degrees of freedom. In addition to antiferromagnetic nearest-neighbor (NN) and next-nearest-neighbor (NNN) positional interactions we also consider NN and NNN interactions arising from the internal state of the particles. The system then shows positional and orientational ordering modes with associated phase transitions at Tp and To temperatures at which long-range positional and orientational ordering are, respectively, lost. We use mean-field techniques to obtain a general approach to the study of these systems. By considering particular forms of the orientational interaction function we study coupling effects between both phase transitions arising from the interplay between orientational and positional degrees of freedom. In mean-field approximation coupling effects appear only for the phase transition taking place at lower temperatures. The strength of the coupling depends on the value of the long-range order parameter that remains finite at that temperature.

Global eriodicity and complete integrability of discrete dynamical systems

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

Knowledge, networks of cities and growth in regional urban systems

The objective of this paper is to measure the impact of different kinds of knowledge and external economies on urban growth in an intraregional context. The main hypothesis is that knowledge leads to growth, and that this knowledge is related to the existence of agglomeration and network externalities in cities. We develop a three-tage methodology: first, we measure the amount and growth of knowledge in cities using the OCDE (2003) classification and employment data; second, we identify the spatial structure of the area of analysis (networks of cities); third, we combine the Glaeser - Henderson - De Lucio models with spatial econometric specifications in order to contrast the existence of spatially static (agglomeration) and spatially dynamic (network) external economies in an urban growth model. Results suggest that higher growth rates are associated to higher levels of technology and knowledge. The growth of the different kinds of knowledge is related to local and spatial factors (agglomeration and network externalities) and each knowledge intensity shows a particular response to these factors. These results have implications for policy design, since we can forecast and intervene on local knowledge development paths.

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

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

Hard instances of algorithms and proof systems

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

Biophysical requirements of power-supply systems: nuclear energy and fossil energy

The report presents a grammar capable of analyzing the process of production of electricity in modular elements for different power-supply systems, defined using semantic and formal categories. In this way it becomes possible to individuate similarities and differences in the process of production of electricity, and then measure and compare “apples” with “apples” and “oranges” with “oranges”. For instance, when comparing the various unit operations of the process of production of electricity with nuclear energy to the analogous unit operations of the process of production of fossil energy, we see that the various phases of the process are the same. The only difference is related to characteristics of the process associated with the generation of heat which are completely different in the two systems. As a matter of facts, the performance of the production of electricity from nuclear energy can be studied, by comparing the biophysical costs associated with the different unit operations taking place in nuclear and fossil power plants when generating process heat or net electricity. By adopting this approach, it becomes possible to compare the performance of the two power-supply systems by comparing their relative biophysical requirements for the phases that both nuclear energy power plants and fossil energy power plants have in common: (i) mining; (ii) refining/enriching; (iii) generating heat/electricity; (iv) handling the pollution/radioactive wastes. This report presents the evaluation of the biophysical requirements for the two powersupply systems: nuclear energy and fossil energy. In particular, the report focuses on the following requirements: (i) electricity; (ii) fossil-fuels, (iii) labor; and (iv) materials.

Moderating effects of management control systems and innovation on performance. Simple methods for correcting the effects of measurement error for interaction effects in small samples

In the accounting literature, interaction or moderating effects are usually assessed by means of OLS regression and summated rating scales are constructed to reduce measurement error bias. Structural equation models and two-stage least squares regression could be used to completely eliminate this bias, but large samples are needed. Partial Least Squares are appropriate for small samples but do not correct measurement error bias. In this article, disattenuated regression is discussed as a small sample alternative and is illustrated on data of Bisbe and Otley (in press) that examine the interaction effect of innovation and style of use of budgets on performance. Sizeable differences emerge between OLS and disattenuated regression

Hereditary completeness for systems of exponentials and reproducing kernels

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