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

Empleo de materiales secundarios como materia prima de nuevos tipos de cementos

The present paper is a comparative study of some characteristics of new belite cements obtained from two kind of wastes, which were used as secondary raw materials: fly ash (FA), of low CaO content, from coal combustion, and ash from incineration of municipal solid waste (MSWIA). Cements were synthesised in a range of temperature between 700°C and 900°C from MSWIA and FA, which were previously activated by hydrothermal treatment at 200°C The evolution of cemented phases with the heating temperature was followed by X-ray diffraction (XRD). The results were compared with those obtained from heating the starting FA and MSWIA without the previous hydrothermal treatment. The degree of hydration was quantitatively evaluated by the combined water content, determined from thermogravimetric analyses, during a period of 28 days or 200 days from mixing depending of hydration kinetics of each cement.Este trabajo es un estudio comparativo de algunas de las características de nuevos cementos belíticos, obtenidos a partir de dos tipos de residuos, como materia prima secundaria: cenizas volantes (CV) de bajo contenido en cal, procedentes de la combustión del carbón y cenizas procedentes de la incineración de residuos sólidos urbanos (CIRSU). Los cementos fueron sintetizados en un rango de temperaturas comprendido entre 700°C y 900°C después de un tratamiento hidrotermal de la CV y CIRSU a 200°C La evolución de las fases cementicias, con la temperatura de calentamiento, fue estudiada por difracción de rayos X (DRX). Los resultados fueron comparados con aquellos obtenidos, directamente, por calentamiento de los residuos, sin un tratamiento hidrotermal previo de los mismos. El grado de hidratación fue cuantitativamente evaluado, por medio del análisis termogravimétrico, a partir del agua combinada de los cementos hidratados durante un período de 28 días o 200 días, dependiendo de la cinética de hidratación de cada cemento

Recubrimientos no cristalinos en rocas graníticas de Galicia: propiedades e hipótesis sobre su origen

[Resumen] La caracterización de nuevos recubrimientos de bajo grado de orden en macizos graníticos de Galicia y el estudio de algunas propiedades de éstos y de otros previamente descritos, confirma la hipótesis de la existencia de una serie continua de materiales cuya composición varía entre la de fosfatos de aluminio (variscita, evansita),aluminosilicatos poco ordenados (alofanos geológicos, haloisita) e hidróxidos de aluminio (gel de alúmina hidratado,gibbsita). Del análisis de sus características y de algunas de sus propiedades como superficie específica, reacción frente a los ani ones fluoruro y fosfato, solubilidad en diferentes extractantes, punto cero de carga,etc., se establecen y discuten diversas hipótesis sobre su origen. Se discuten además relaciones de equilibrio o en el sistema Si02-A1203-P20~,confrontándolas con los datos de aguas de escorrentla y solución del suelo.[Abstract] The characterization of low order coatings that appear on granitic rocks of Galicia and the study of some of their properties confirm the existence of a continuous series between Al-phosphates (variscite,evan site),aluminium silicates (allophane,halloysite) ano Al-hydroxides (criptogibbsite,gibbsite).Several hypothe sis about their origin are discussed on the basis OT properties like specific surface, reaction with fluoride and phosphate, pze, solubility in different extracttants, etc . Finally, the theoretical equilibrium relations in the system A1203-Si02-P205 are confronted with the composition of dralnage waters and soil solutio

Inmovilización/solidificación de residuos tóxicos y peligrosos en matrices de cemento

Immobilization and solidification of polluting waste, introduced into the industrial sector more than 20 years ago, and throughout last 10 years is being the object of a growing interest for engineers and environment scientists, has become a remarkable standardized process for treatment and management of toxic and hazardous liquid wastes, with special to those containing toxic metals. Experimental monitorization of the behaviour of immobilized waste by solidification and stabilisation in life time safe deposits is not possible, reason why it is essential to develop models predicting adequately the behaviour of structures that have to undergo a range of conditions simulating the environment where they are to be exposed. Such models can be developed only if the basic physical and chemical properties of the system matrix/solidifying-waste are known. In this work immobilization/solidification systems are analyzed stressing out the formulation systems based on Portland cement. Finally, some examples of the results obtained from the study of interaction of specific species of wastes and fixation systems are presented.La inmovilización y solidificación de residuos contaminantes, implantada en el sector comercial desde hace más de 20 años y que desde hace diez es objeto de creciente interés por parte de ingenieros y científicos medioambientales, se ha convertido en un proceso estandarizado único para el tratamiento y gestión de residuos tóxicos y peligrosos líquidos y, en especial, de los que contienen metales pesados. La monitorización experimental del comportamiento de un residuo inmovilizado por solidificación y estabilización en el tiempo de vida de un depósito de seguridad no es posible, por lo que es imprescindible desarrollar modelos que predigan satisfactoriamente el comportamiento del sistema bajo un rango representativo de condiciones del entorno de exposición. Tales modelos sólo pueden ser desarrollados si se conocen las propiedades básicas fisicoquímicas del sistema matriz solidificante-residuo. En el presente trabajo se analizan y discuten los sistemas de inmovilización/solidificación, profundizando en los sistemas de formulaciones basadas en cemento Portland. Por último, se presentan algunos ejemplos de los resultados obtenidos del estudio de las interacciones de especies concretas de residuos y sistemas de fijación

A Mixed Heterobimetallic Y/Eu-MOF for the Cyanosilylation and Hydroboration of Carbonyls

Supplementary Materials The following supporting information can be downloaded at: https://www.mdpi.com/article/10.3390/catal12030299/s1. Table S1: Elemental analysis of compounds Y/Eu-MOF. Table S2: ICP-AES results of compound Y/Eu-MOF. Table S3: Crystallographic data and structure refinement details of compound Y/Eu-MOF. Table S4: Selected bond lengths (Å) and angles (°) for compound Y/Eu-MOF. Table S5: Table of the continuous Shape Measurements for the MN3O6 coordination environment. Table S6: Table of the continuous Shape Measurements for the MO8 coordination environment. Table S7: Electrophoretic mobility and ζ-potential dependence, with the pH of the Y/Eu-MOFs particles dispersed in water. Conductivity fixed at 330 µS/cm. Table S8: Optimization of the reaction conditions in the hydroboration reaction. Table S9: Green metrics calculated for Y/Eu-MOF catalyst. Table S10: Catalytic cyanosilylation of benzaldehyde performances of Ln-MOFs, as reported in the literature. Figure S1: Figure of the pattern matching analysis and experimental PXRD for Y/Eu-MOF. Figure S2: Figure of the infrared spectra of the ligand and Y/Eu-MOF. Figure S3: SEM and EDS mapping of bulk material of Y/Eu-MOF. Figure S4: Images and particle size distribution (an overall of 250 particles) in the deposited fraction of Y/Eu-MOF catalyst non-suspended in water (about a 68% of the total amount), determined from optical microscope images. Figure S5: Images and particle size distribution (an overall of 250 particles) of Y/Eu-MOF crystals in the fraction steadily suspended in water (about a 32% of the total amount), determined from optical microscope images. Figure S6: Comparation of the particle size distribution of Y/Eu-MOF in the fraction steadily suspended in water and the non-suspended, determined from optical microscope images. Figure S7: Calibration line of conductivity (µS/cm) vs [NaCl] (mol/L). Figure S8: ζ-potential (mV) dependence with the pH of the Y/Eu-MOF. All the measurements were performed with constant conductivity of 330 µS/cm. Figure S9: Electrophoretic mobility (µm·cm/V·s) dependence with the pH of the Y/Eu-MOF. All the measurements were performed with constant conductivity of 330 µS/cm. Figure S10: Study of the recyclability of Y/Eu-MOF (0.5 mol%) catalyst on the cyanosilylation and hydroboration reaction of acetophenone as carbonyl substrate. Figure S11: Analysis of the TOF (h−1) obtained in the cyanosilylation reaction of acetophenone at different times of reaction with Y/Eu-MOF (0.5 mol%), with the optimized reaction conditions. Figure S12: Analysis of the TOF (h−1) obtained in the hydroboration reaction acetophenone at different times of reaction with Y/Eu-MOF (0.5 mol%), with the optimized reaction conditions. Scheme S1: Reaction conditions used for the study of recyclability of Y/Eu-MOF catalysts in the cyanosilylation reaction. Scheme S2: Reaction conditions used for the study of recyclability of Y/Eu-MOF catalysts in the hydroboration reaction. Scheme S3: Leaching test, carried out after the first and second cycles.Funding: This research has been funded by the State Research Agency (grants CTQ2017-84334-R and PGC2018-102052-B-C21) of the Spanish Ministry of Science, Innovation and Universities, the European Union (European Regional Development Fund—ERDF), Junta de Andalucía (P20_01041, UAL2020-AGR-B1781, B-FQM-734-UGR20 and FQM-394). E.E., S.R., and J.P. acknowledge the Government of the Basque Country, Juan de la Cierva Incorporación (grant no. IJC2019-038894-I) and University of Almeria (grant no. HIPATIA2021_04) for their respective fellowsHerein, to the best of our knowledge, the first heterobimetallic Y/Eu porous metal–organic framework (MOF), based on 3-amino-4-hydroxybenzoic acid (H2L) ligand, with the following formulae {[Y3.5Eu1.5L6(OH)3(H2O)3]·12DMF}n (in advance, namely Y/Eu-MOF), is described. The three-dimensional structure has been synthesized by solvothermal routes and thoroughly characterized, by means of single crystal X-ray diffraction, powder X-ray diffraction, electronic microscopy, ICP-AES, electrophoretic mobility, and FTIR spectra. Intriguingly, the porous nature allows for coordinated solvent molecules displacement, yielding unsaturated metal centers, which can act as a Lewis acid catalyst. This novel supramolecular entity has been tested in cyanosilylation and hydroboration reactions on carbonyl substrates of a diverse nature, exhibiting an extraordinary activity.Cierva Incorporación IJC2019-038894-IState Research Agency CTQ2017-84334-R, PGC2018-102052-B-C21University of Almeria HIPATIA2021_04Ministerio de Ciencia, Innovación y UniversidadesEuropean CommissionEuropean Regional Development FundJunta de Andalucía B-FQM-734-UGR20, FQM-394, IJC2019-038894-I, P20_01041, UAL2020-AGR-B178