On the upper bound of the number of limit cycles obtained by the second order averaging method I

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On the upper bound of the number of limit cycles obtained by the second order averaging method II

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On the number of higher order Delaunay triangulations

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Avalanches in a fluctuationless first-order phase transition in a random-bond Ising model

We study the behavior of the random-bond Ising model at zero temperature by numerical simulations for a variable amount of disorder. The model is an example of systems exhibiting a fluctuationless first-order phase transition similar to some field-induced phase transitions in ferromagnetic systems and the martensitic phase transition appearing in a number of metallic alloys. We focus on the study of the hysteresis cycles appearing when the external field is swept from positive to negative values. By using a finite-size scaling hypothesis, we analyze the disorder-induced phase transition between the phase exhibiting a discontinuity in the hysteresis cycle and the phase with the continuous hysteresis cycle. Critical exponents characterizing the transition are obtained. We also analyze the size and duration distributions of the magnetization jumps (avalanches).

Edge excitations and topological order in rotating Bose gas

The edge excitations and related topological orders of correlated states of a fast rotating Bose gas are studied. Using exact diagonalization of small systems, we compute the energies and number of edge excitations, as well as the boson occupancy near the edge for various states. The chiral Luttinger-liquid theory of Wen is found to be a good description of the edges of the bosonic Laughlin and other states identified as members of the principal Jain sequence for bosons. However, we find that in a harmonic trap the edge of the state identified as the Moore-Read (Pfaffian) state shows a number of anomalies. An experimental way of detecting these correlated states is also discussed.

Higher order Lagrangian systems: Geometric structures, Dynamics, and Constraints

In order to study the connections between Lagrangian and Hamiltonian formalisms constructed from aperhaps singularhigher-order Lagrangian, some geometric structures are constructed. Intermediate spaces between those of Lagrangian and Hamiltonian formalisms, partial Ostrogradskiis transformations and unambiguous evolution operators connecting these spaces are intrinsically defined, and some of their properties studied. Equations of motion, constraints, and arbitrary functions of Lagrangian and Hamiltonian formalisms are thoroughly studied. In particular, all the Lagrangian constraints are obtained from the Hamiltonian ones. Once the gauge transformations are taken into account, the true number of degrees of freedom is obtained, both in the Lagrangian and Hamiltonian formalisms, and also in all the intermediate formalisms herein defined.

A Case-based reasoning approach to validate grammatical gender and number agreement in Spanish language

Across Latin America 420 indigenous languages are spoken. Spanish is considered a second language in indigenous communities and is progressively introduced in education. However, most of the tools to support teaching processes of a second language have been developed for the most common languages such as English, French, German, Italian, etc. As a result, only a small amount of learning objects and authoring tools have been developed for indigenous people considering the specific needs of their population. This paper introduces Multilingual–Tiny as a web authoring tool to support the virtual experience of indigenous students and teachers when they are creating learning objects in indigenous languages or in Spanish language, in particular, when they have to deal with the grammatical structures of Spanish. Multilingual–Tiny has a module based on the Case-based Reasoning technique to provide recommendations in real time when teachers and students write texts in Spanish. An experiment was performed in order to compare some local similarity functions to retrieve cases from the case library taking into account the grammatical structures. As a result we found the similarity function with the best performance