Combed 3-Manifolds with Concave Boundary, Framed Links, and Pseudo-Legendrian Links

We provide combinatorial realizations, according to the usual objects/moves scheme, of the following three topological categories: (1) pairs (M,v) where M is a 3-manifold (up to diffeomorphism) and v is a (non-singular vector) field, up to homotopy; here possibly the boundary of M is non-empty and v may be tangent to the boundary, but only in a concave fashion, and homotopy should preserve tangency type; (2) framed links L in M, up to framed isotopy; (3) triples (M,v,L), with (M,v) as above and L transversal to v, up to pseudo-Legendrian isotopy (transversality-preserving simultaneous homotopy of v and isotopy of L). All realizations are based on the notion of branched standard spine, and build on results previously obtained. Links are encoded by means of diagrams on branched spines, where the diagram is smooth with respect to the branching. Several motivations for being interested in combinatorial realizations of the topological categories considered in this paper are given in the introduction. The encoding of links is suitable for the comparison of the framed and the pseudo-Legendrian categories, and some applications are given in connection with contact structures, torsion and finite-order invariants. An estension of Trace's notion of winding number of a knot diagram is introduced and discussed.Comment: 38 pages, 33 figure

Volume and homology of one-cusped hyperbolic 3-manifolds

Let M be a complete, finite-volume, orientable hyperbolic manifold having exactly one cusp. If we assume that pi_1(M) has no subgroup isomorphic to a genus-2 surface group, and that either (a) H_1(M;Z_p) has dimension at least 5 for some prime p, or (b) H_1(M;Z_2) has dimension at least 4, and the subspace of H^2(M;Z_2) spanned by the image of the cup product has dimension at most 1, then vol M > 5.06 If we assume that H_1(M;Z_2) has dimension at least 7, and that the compact core of M does not contain a genus-2 closed incompressible surface, then vol M > 5.06.Comment: 31 pages. This version agrees with the published version of the paper, except that an error in the published abstract has been corrected. In particular, the result which applies to manifolds with mod 2 homology of dimension at least 7 is stronger and has a shorter proof than the corresponding result in version

Real-time monitoring of proton exchange membrane fuel cell stack failure

Uneven pressure drops in a 75-cell 9.5-kWe proton exchange membrane fuel cell stack with a U-shaped flow configuration have been shown to cause localised flooding. Condensed water then leads to localised cell heating, resulting in reduced membrane durability. Upon purging of the anode manifold, the resulting mechanical strain on the membrane can lead to the formation of a pin-hole/membrane crack and a rapid decrease in open circuit voltage due to gas crossover. This failure has the potential to cascade to neighbouring cells due to the bipolar plate coupling and the current density heterogeneities arising from the pin-hole/membrane crack. Reintroduction of hydrogen after failure results in cell voltage loss propagating from the pin-hole/membrane crack location due to reactant crossover from the anode to the cathode, given that the anode pressure is higher than the cathode pressure. Through these observations, it is recommended that purging is avoided when the onset of flooding is observed to prevent irreparable damage to the stack

Combinatorial Hopf algebra of superclass functions of type DD

We provide a Hopf algebra structure on the space of superclass functions on the unipotent upper triangular group of type D over a finite field based on a supercharacter theory constructed by Andr\'e and Neto. Also, we make further comments with respect to types B and C. Type A was explores by M. Aguiar et. al (2010), thus this paper is a contribution to understand combinatorially the supercharacter theory of the other classical Lie types.Comment: Last section modified. Recent development added and correction with respect to previous version state

Spectral geometry as a probe of quantum spacetime

Employing standard results from spectral geometry, we provide strong evidence that in the classical limit the ground state of three-dimensional causal dynamical triangulations is de Sitter spacetime. This result is obtained by measuring the expectation value of the spectral dimension on the ensemble of geometries defined by these models, and comparing its large scale behaviour to that of a sphere (Euclidean de Sitter). From the same measurement we are also able to confirm the phenomenon of dynamical dimensional reduction observed in this and other approaches to quantum gravity -- the first time this has been done for three-dimensional causal dynamical triangulations. In this case, the value for the short-scale limit of the spectral dimension that we find is approximately 2. We comment on the relevance of these results for the comparison to asymptotic safety and Horava-Lifshitz gravity, among other approaches to quantum gravity.Comment: 25 pages, 6 figures. Version 2: references to figures added, acknowledgment added

Existence for Competitive Equilibrium by Means of Generalized Quasivariational Inequalities

A competitive economic equilibrium model integrated with exchange, consumption, and production is considered. Our goal is to give an existence result when the utility functions are concave, proper, and upper semicontinuous. To this aim we are able to characterize the equilibrium by means of a suitable generalized quasi-variational inequality; then we give the existence of equilibrium by using the variational approach

Cosmological measurements, time and observables in (2+1)-dimensional gravity

We investigate the relation between measurements and the physical observables for vacuum spacetimes with compact spatial surfaces in (2+1)-gravity with vanishing cosmological constant. By considering an observer who emits lightrays that return to him at a later time, we obtain explicit expressions for several measurable quantities as functions on the physical phase space of the theory: the eigentime elapsed between the emission of a lightray and its return to the observer, the angles between the directions into which the light has to be emitted to return to the observer and the relative frequencies of the lightrays at their emission and return. This provides a framework in which conceptual questions about time, observables and measurements can be addressed. We analyse the properties of these measurements and their geometrical interpretation and show how they allow an observer to determine the values of the Wilson loop observables that parametrise the physical phase space of (2+1)-gravity. We discuss the role of time in the theory and demonstrate that the specification of an observer with respect to the spacetime's geometry amounts to a gauge fixing procedure yielding Dirac observables.Comment: 38 pages, 11 eps figures, typos corrected, references update

Slave-boson approach to the infinite-U Anderson-Holstein impurity model

The infinite-$U$ Anderson-Holstein impurity model is studied with a focus on the interplay between the strong electron correlation and the weak electron-phonon interaction. The slave boson method has been employed in combination with the large degeneracy expansion (1/N) technique. The charge and spin susceptibilities and the phonon propagator are obtained in the approximation scheme where the saddle point configuration and the Gaussian 1/N fluctuations are taken into account. The spin susceptibility is found not to be renormalized by electron-phonon interaction, while the charge susceptibility is renormalized. From the renormalized charge susceptibility the Kondo temperature is found to increase by the electron-phonon interaction. It turns out that the bosonic 1/N Gaussian fluctuations play a very crucial role, in particular, for the phonon propagator.Comment: 12pages, 3 figures. Published in Physical Review

Construction, Management and Visualization of 3D Models of Large Archeological and Architectural Sites for E-Heritage GIS Systems

In this paper we present an integrated system developed in order to record, construct, pre-process, manage, visualize and visually navigate 3D models reality based of large archeological and architectural sites for eHeritage GIS systems. The framework integrates structured geometrical and documentary information resulting from multiple sources with the aim to enhance the knowledge of those sites within the frame of its historical evolution and its institutional management in a 3D GIS/DB. The developed applications were designed for different types of users, with a largely scalable interface, able to support different output devices and to work at different levels of iconicity. The system allows a full comprehension of the buildings in their own context, permitting to discover unknown relationships, to evaluate their architectural occupancy and to quickly access a complex system of information. The framework has been tested in two different systems - designed and developed to satisfy both internal (cataloguing, documentation, preservation, management of archaeological heritage) and external (communication through the web portal) purposes: the first, in Pompeii, developed in order to have a web-based system that uses Open Source software and complies with national and international standards; the second one, a prototype designed to make available on the Google Earth platform the complete Palladian corpus documentation implemented by the CISAAP