Hamiltonisation, measure preservation and first integrals of the multi-dimensional rubber Routh sphere

We consider the multi-dimensional generalisation of the problem of a sphere, with axi-symmetric mass distribution, that rolls without slipping or spinning over a plane. Using recent results from Garc\'ia-Naranjo (arXiv: 1805:06393) and Garc\'ia-Naranjo and Marrero (arXiv: 1812.01422), we show that the reduced equations of motion possess an invariant measure and may be represented in Hamiltonian form by Chaplygin's reducing multiplier method. We also prove a general result on the existence of first integrals for certain Hamiltonisable Chaplygin systems with internal symmetries that is used to determine conserved quantities of the problem.Comment: 23 pages, 1 figure. Submitted to the special issue of Theor. Appl. Mech. in honour of Chaplygin's 150th anniversar

Conversión hidrotermal de biomasa en bioproductos valiosos

Los procesos hidrotérmicos son una excelente alternativa para convertir desechos de biomasa en productos de alto valor energético. El alcance de este proyecto ofrece el estudio de 5 tipos de biomasa distintos: café, madera blanca, arroz, lignina y madera negra (Zilkha). La reacción se llevó a cabo en un reactor continúo cambiando las condiciones de presión y temperatura. El café demostró ser la materia primar de mayor rendimiento, alcanzando valores de hasta el 70% y, por el contrario, la lignina alcanzó muy bajos rendimientos, no sobrepasando el 13%. Para analizar el bioproducto solido obtenido se realizó un análisis termogravimétrico. A partir de estos datos, se propuso un nuevo método denominado ‘desplazamiento’ que refleja las diferencias entre los perfiles del producto sólido logrado y la biomasa no tratada. También se utilizaron técnicas de HPLC y MALDI-TOF-MS que demostraron mayores concentraciones en los bioproductos líquidos obtenidos según aumentaba la temperatura de reacción.University of NottinghamGrado en Ingeniería Químic

Measuring dispersion in the context of ordered qualitative scales

Producción CientíficaThe main purpose of this contribution is to measure the dispersion associated with the different results of a variable when they form a set of linguistic terms obtained after examining different qualities of people, services, etc, ordered, but with a non-homogeneous and non-quantifiable distance between the linguistic terms.Ministerio de Economía, Industria y Competitividad (project ECO2016-77900-P

Gauge Transformations, Twisted Poisson Brackets and Hamiltonization of Nonholonomic Systems

In this paper we study the problem of Hamiltonization of nonholonomic systems from a geometric point of view. We use gauge transformations by 2-forms (in the sense of Severa and Weinstein [29]) to construct different almost Poisson structures describing the same nonholonomic system. In the presence of symmetries, we observe that these almost Poisson structures, although gauge related, may have fundamentally different properties after reduction, and that brackets that Hamiltonize the problem may be found within this family. We illustrate this framework with the example of rigid bodies with generalized rolling constraints, including the Chaplygin sphere rolling problem. We also see how twisted Poisson brackets appear naturally in nonholonomic mechanics through these examples

Past observable dynamics of a continuously monitored qubit

Monitoring a quantum observable continuously in time produces a stochastic measurement record that noisily tracks the observable. For a classical process such noise may be reduced to recover an average signal by minimizing the mean squared error between the noisy record and a smooth dynamical estimate. We show that for a monitored qubit this usual procedure returns unusual results. While the record seems centered on the expectation value of the observable during causal generation, examining the collected past record reveals that it better approximates a moving-mean Gaussian stochastic process centered at a distinct (smoothed) observable estimate. We show that this shifted mean converges to the real part of a generalized weak value in the time-continuous limit without additional postselection. We verify that this smoothed estimate minimizes the mean squared error even for individual measurement realizations. We go on to show that if a second observable is weakly monitored concurrently, then that second record is consistent with the smoothed estimate of the second observable based solely on the information contained in the first observable record. Moreover, we show that such a smoothed estimate made from incomplete information can still outperform estimates made using full knowledge of the causal quantum state.Comment: 11 pages, 4 figure

Hitchin-Kobayashi correspondence, quivers, and vortices

A twisted quiver bundle is a set of holomorphic vector bundles over a complex manifold, labelled by the vertices of a quiver, linked by a set of morphisms twisted by a fixed collection of holomorphic vector bundles, labelled by the arrows. When the manifold is Kaelher, quiver bundles admit natural gauge-theoretic equations, which unify many known equations for bundles with extra structure. In this paper we prove a Hitchin--Kobayashi correspondence for twisted quiver bundles over a compact Kaehler manifold, relating the existence of solutions to the gauge equations to a stability criterion, and consider its application to a number of situations related to Higgs bundles and dimensional reductions of the Hermitian--Einstein equations.Comment: 28 pages; larger introduction, added references for the introduction, added a short comment in Section 1, typos corrected, accepted in Comm. Math. Phy

Teaching-innovation experience in competitiveness and innovation in business

The aim of this paper is to contrast the students’ opinions about the teaching innovation experience carried out in the subject “Competitividad en Innovación en la Empresa” (Competitiveness and Innovation in Business). The procedure will start with the subject’s profile, going through the main objectives and teaching methodology, to finish with evaluation and assessment, as suggested in the subject’s syllabus for the academic year 2007/08. Taking this as a starting point and, due to the fact that the number of students in the control group is not very high, we suggest changing both the teaching methodology and the evaluation. These changes will be contrasted with the students’ acceptance and involvement.PROCEEDINGS C