Interval groups related to finite Coxeter groups I

We elaborate presentations of the interval groups related to all quasi-Coxeter elements in the Coxeter group of type $D_n$. This is the only case of the infinite families of finite Coxeter groups that admits proper quasi-Coxeter elements. The presentations we obtain are over a set of generators in bijection with what we call Carter generating set, and the relations are those defined by the related Carter diagram along with a twisted or a cycle commutator relator, depending on whether the quasi-Coxeter element is a Coxeter element or not. In a subsequent work, we complete our analysis to cover all the exceptional cases of finite Coxeter groups, and establish that almost all the interval groups related to proper quasi-Coxeter elements are not isomorphic to the related Artin groups, hence establishing a new family of interval groups with nice presentations. Alongside the proof of the main results of this paper, we establish important properties related to the dual approach to Coxeter and Artin groups

Nanoparticules et colloïdes multifonctionnels à base de clusters d’éléments de transition et complexes de lanthanides

The first part of this work involves the development and characterization ofnovel nanoparticles (NPs) of multifunctional silica with complex architectures.The challenge is to meet the increasing demand for development of newnon-toxic colloidal systems, magnetic and/or luminescent in the NIR regionfor potential applications in biotechnology. This objective was achievedby closely associating molybdenum clusters compounds with maghemitenanocrystals and/or gold in 50 nm silica NPs. An evaluation of thecytotoxicity of NPs containing clusters of transition elements of Cs2Mo6Br14and a time-gated fluorescence microscopy of Cs2Mo6I8(C2F5COO)6@SiO2NPs incorporated in cancer cells are presented.In the second part, microcrystalline powders of heteronuclear lanthanidebasedcoordination polymers with general chemical formula [Ln2-2xLn’2x(bdc)3,4H2O] ∞ 0 ≤ x ≤ 1 were dissolved in glycerol . These NPsexhibit luminescent properties identical to that of the bulk material.A detailed study of this new green synthetic route and a study of thestability over time and a dilution of the obtained colloids were performed.La première partie de ce travail porte sur l’élaboration et la caractérisation de nouvelles nanoparticules (NPs) multifonctionnelles de silice à architectures complexes. L’enjeu est de répondre à la demande croissante d’élaboration de nouveaux systèmes colloïdaux non toxiques, magnétiques et/ou luminescents dans la région NIR pour des applications potentielles en biotechnologie. Cet objectif a été atteint en associant intimement des composés à clusters de molybdène avec des nanocristaux de maghémite et/ou d’or dans une NPs de silice de 50 nm. Une évaluation de la cytotoxicité des NPs contenant des clusters d’éléments de transition Cs2Mo6Br14 ainsi qu’un suivi par microscopie de fluorescence en temps retardé des NPs Cs2Mo6I8(C2F5COO)6@SiO2 incorporées dans des cellules cancéreuses sont présentés. Dans la deuxième partie, des poudres microcristallines de composés hétéronucléaires de polymères de coordination à base de terres rares de formule chimique générale [Ln2-2xLn’2x(bdc)3,4H2O]∞ avec 0 ≤ x ≤ 1 ont été nanométrisées dans du glycérol. Ces NPs présentent des propriétés luminescentes identiques à celles du matériau massif. Une étude détaillée de cette nouvelle voie de synthèse répondant aux principes de la chimie verte ainsi qu’une étude de la stabilité en fonction du temps et de la dilution des colloïdes obtenus ont été réalisées

Interval groups related to finite Coxeter groups, Part II

We provide a complete description of the presentations of the interval groups related to quasi-Coxeter elements in finite Coxeter groups. In the simply laced cases, we show that each interval group is the quotient of the Artin group associated with the corresponding Carter diagram by the normal closure of a set of twisted cycle commutators, one for each 4-cycle of the diagram. Our techniques also reprove an analogous result for the Artin groups of finite Coxeter groups, which are interval groups corresponding to Coxeter elements. We also analyse the situation in the non-simply laced cases, where a new Garside structure is discovered. Furthermore, we obtain a complete classification of whether the interval group we consider is isomorphic or not to the related Artin group. Indeed, using methods of Tits, we prove that the interval groups of proper quasi-Coxeter elements are not isomorphic to the Artin groups of the same type, in the case of $D_n$ when $n$ is even or in any of the exceptional cases. In [BHNR22], we show using different methods that this result holds for type $D_n$ for all $n \geq 4$

Multifunctional hybrid silica nanoparticles based on [Mo₆Br₁₄]²⁻ phosphorescent nanosized clusters, magnetic γ-Fe₂O₃ and plasmonic gold nanoparticles

International audienceWe report on the synthesis, characterization and photophysical study of new luminescent and magnetic hybrid silica nanoparticles. Our method is based on the co-encapsulation of single maghemite γ-Fe2O3 nanoparticles and luminescent molybdenum cluster units [Mo6Br(i)8Br(a)6](2-) through a water-in-oil (W/O) microemulsion technique. The as-prepared core-shell [Cs2Mo6Br14-γFe2O3]@SiO2 nanoparticles (45-53 nm) possess a single magnetic core (6, 10.5 or 15 nm) and the cluster units are dispersed in the entire volume of the silica sphere. The [Cs2Mo6Br14-γFe2O3]@SiO2 nanoparticles have a perfect spherical shape with a good monodispersity and they display red and near-infrared (NIR) emission in water under UV excitation, whose intensity depends on the magnetic core size. The hybrid nanoparticles have been characterized by transmission electron microscopy (TEM), high annular angular dark field scanning transmission electron microscopy (HAADF-STEM), energy-dispersive X-ray spectroscopy (EDX), UV-Vis-NIR spectroscopy and magnetometer SQUID analysis. Small gold nanoparticles were successfully nucleated at the surface of the hybrid silica nanoparticles in order to add plasmonic properties

Statistical Models for Predicting the Optimum Gypsum Content in Cement Mortar

One of the most important problems in concrete industry in Iraq is deterioration due to internal sulfate attack that causes damage of concrete and hence reduces its compressive strength, increases its expansion and may be lead to its cracking and destruction. Linear regression analysis is used to predict the optimum SO3 content (O.G.C) on the basis of cement chemical composition, Blaine fineness and age. Three models are presented, the first one is an early age model (less than or equal to 7- days). Then a late age (greater than 7-days) model was developed based on the predicted optimum SO3 content of early age and late age. The third model was an all ages model and it is a general model specially for OPC. The important results obtained are the positive effect of C3S, C3A and C4AF on optimum SO3 content in cement mortar. The effect of C3A on optimum SO3 content is about twice that of C4AF. The study also showed a trend of positive and important effect of the fineness of cement

Statistical Model for Predicting the Optimum Gypsum Content in Concrete

The problem of internal sulfate attack in concrete is widespread in Iraq and neighboring countries.This is because of the high sulfate content usually present in sand and gravel used in it. In the present study the total effective sulfate in concrete was used to calculate the optimum SO3 content. Regression models were developed based on linear regression analysis to predict the optimum SO3 content usually referred as (O.G.C) in concrete. The data is separated to 155 for the development of the models and 37 for checking the models. Eight models were built for 28-days age. Then a late age (greater than 28-days) model was developed based on the predicted optimum SO3 content of 28-days and late age. Eight developed models were built for all ages. The important results obtained from the developed models are the positive effect of C3S, C3A and C4AF on optimum SO3 content. The effect of C3A on optimum SO3 content is about twice that of C4AF. The study also showed a trend of positive and important effect of the fineness of cement except in some models and this is due to statistical overla