Lusternik-Schnirelmann category of simplicial complexes and finite spaces

In this paper we establish a natural definition of Lusternik-Schnirelmann category for simplicial complexes via the well known notion of contiguity. This category has the property of being homotopy invariant under strong equivalences, and only depends on the simplicial structure rather than its geometric realization. In a similar way to the classical case, we also develop a notion of geometric category for simplicial complexes. We prove that the maximum value over the homotopy class of a given complex is attained in the core of the complex. Finally, by means of well known relations between simplicial complexes and posets, specific new results for the topological notion of category are obtained in the setting of finite topological spaces.Comment: 18 pages, 10 figures, this is a new version with some minor changes and a new exampl

A monolithic (Si) massively broadband non-reverberant monopole

Accepted versio

A Method to Determine the In-Air Spatial Spread of Clinical Electron Beams

We propose and analyze in detail a method to measure the in-air spatial spread parameter of clinical electron beams. Measurements are performed at the center of the beam and below the adjustable collimators sited in asymmetrical configuration in order to avoid the distortions due to the presence of the applicator. The main advantage of our procedure lies in the fact that the dose profiles are fitted by means of a function which includes, additionally to the Gaussian step usually considered, a background which takes care of the dose produced by different mechanisms that the Gaussian model does not account for. As a result, the spatial spread is obtained directly from the fitting procedure and the accuracy permits a good determination of the angular spread. The way the analysis is done is alternative to that followed by the usual methods based on the evaluation of the penumbra width. Besides, the spatial spread found shows the quadratic-cubic dependence with the distance to the source predicted by the Fermi-Eyges theory. However, the corresponding values obtained for the scattering power are differing from those quoted by ICRU nr. 35 by a factor ~2 or larger, what requires of a more detailed investigation.Comment: 11 pages, 5 Postscript figures, to be published in Medical Physic

Use of nanofiltration membrane technology for ceramic industry wastewater treatment

A study has been undertaken of an advanced wastewater treatment approach using polymer nanofiltration membranes, in an attempt to obtain water of sufficient quality to allow it to be reused in the same production process or, alternatively, to be discharged without any problems. The study has initially focused on the removal of organic matter (reduction of COD) and the most representative ions present in the wastewater, such as Na+ , Mg2+, Cl- , and SO4 2- . In a first part of the study, with a view to optimising the experimental phase, a simulation has been performed of the nanofiltration process using the NanoFlux software. Among other things, the simulation allows the most suitable membranes to be selected as a function of the permeate flow rate and desired level of retention in the substances to be removed. The subsequent experimentation was carried out in a laboratory tangential filtration system that works with flat membranes. It was found that retention values of about 90% were obtained for the studied substances, with a good permeate flow rate, using low operating pressures. These results demonstrate the feasibility of the studied technology and its potential as a treatment for improving ceramic industry wastewater qualit

Polishing of Porcelain Tiles in Industrial- and Laboratory-scale

This work reports the design and use of a laboratory-scale tribometer and a new developed tool-holder to reproduce the industrial polishing process for ceramic tiles in laboratory-scale. The mechanical conditions in a typical industrial polishing process were used to execute the tests in industrial-scale on a single polishing head test- rig. The results of spatial glossiness and roughness distribution from the industrial-scale test were taken as reference. After adaption of parameters the tests were repeated on a tribometer in laboratory-scale. The custom-made CNC- tribometer allows all parameters and kinematics used in the industry to be controlled and provides additionally a very high position accuracy of the tool. The new developed tool-holder provides similar contact conditions as known from the industrial process. The results of the evolution of glossiness and roughness from laboratory-scale test are compared with the data obtained from the test in industrial-scale and show that the tribometer and the new tool- holder accurately reproduce the polishing process from industrial-scale in laboratory