Parabolic subgroups in FC-type Artin groups

Parabolic subgroups are the building blocks of Artin groups. This paper extends previous results of Cumplido, Gebhardt, Gonzales-Meneses and Wiest, known only for parabolic subgroups of finite type Artin groups, to parabolic subgroups of FC-type Artin groups. We show that the class of finite type parabolic subgroups is closed under intersection. We also study an analog of the curve complex for mapping class group constructed by Cumplido et al. using parabolic subgroups. We extend the construction of this complex, called the complex of parabolic subgroups, to FC-type Artin groups. We show that this simplicial complex is, in most cases, infinite diameter and conjecture that it is δ-hyperbolic.     

Collective Strategy Condensation: When Envy Splits Societies

Human societies are characterized by three constituent features, besides others. (A) Options, as for jobs and societal positions, differ with respect to their associated monetary and non-monetary payoffs. (B) Competition leads to reduced payoffs when individuals compete for the same option as others. (C) People care about how they are doing relatively to others. The latter trait—the propensity to compare one’s own success with that of others—expresses itself as envy. It is shown that the combination of (A)–(C) leads to spontaneous class stratification. Societies of agents split endogenously into two social classes, an upper and a lower class, when envy becomes relevant. A comprehensive analysis of the Nash equilibria characterizing a basic reference game is presented. Class separation is due to the condensation of the strategies of lower-class agents, which play an identical mixed strategy. Upper-class agents do not condense, following individualist pure strategies. The model and results are size-consistent, holding for arbitrary large numbers of agents and options. Analytic results are confirmed by extensive numerical simulations. An analogy to interacting confined classical particles is discussed.     

Subset representations and eigenvalues of the universal intertwining matrix

We solve a combinatorial question concerning eigenvalues of the universal intertwining endomorphism of a subset representation.     

Synthesis and characterization of VO–vanillin complex immobilized on MCM-41 and its facile catalytic application in the sulfoxidation reaction,and synthesis of 2,3-dihydroquinazolin-4(1H)-ones and disulfides in green media

In this work, a vanillin complex is immobilized onto MCM-41 and characterized by FT-IR, X-ray diffraction, scanning electron microscopy, energy dispersive spectroscopy, thermogravimetric analysis, and BET techniques. This supported Schiff base complex was found to be an efficient and recoverable catalyst for the chemoselective oxidation of sulfides into sulfoxides and thiols into their corresponding disulfides (using hydrogen peroxide as a green oxidant) and also a suitable catalyst for the preparation of 2,3-dihydroquinazolin-4(1H)-one derivatives in water at 90°C. Using this protocol, we show that a variety of disulfides, sulfoxides, and 2,3-dihydroquinazolin-4(1H)-one derivatives can be synthesized in green conditions. The catalyst can be recovered and recycled for further reactions without appreciable loss of catalytic performance.     

Functional zinc(II) phthalocyanines bearing Schiff base complexes as oxidation catalysts for bleaching systems

Oxidation catalysis is used to increase the performance of hydrogen peroxide in laundry bleach applications. Bleach catalysts provide cost‐effective, energy‐saving and environmentally friendly bleach systems yielding perfect stain removal at lower temperatures. This comparative study is based on the synthesis of bis[bis(salicylhydrazonephenoxy)manganese(III)] phthalocyaninatozinc(II) ( 2 ), bis[bis(salicylhydrazonephenoxy)cobalt(III)] phthalocyaninatozinc(II) ( 3 ) and bis[bis(salicylhydrazonephenoxy)iron(III)] phthalocyaninatozinc(II) ( 4 ) as tri‐nuclear complexes consisting of two Schiff base complexes substituting a zinc phthalocyanine. Complexion on the periphery to obtain complexes 2 , 3 , 4 was performed through the reaction of a Schiff base‐substituted phthalocyanine using MnCl₂?4H₂O, CoCl₂?6H₂O or FeCl₃?6H₂O salts in basic condition in dimethylformamide. Fourier transform infrared, ¹H NMR, ¹³C NMR, UV–visible, inductively coupled plasma optical emission and mass spectra were applied to characterize the prepared compounds. The bleach performances of the three phthalocyanine compounds 2 , 3 , 4 were examined by the degradation of morin as hydrophilic dye. The degradation progress in the presence of catalysts 2 , 3 , 4 /H₂O₂ combination in aqueous solution was investigated using an online spectrophotometric method. It was found that the catalysts 2 , 3 , 4 exhibited better bleaching performance at 25 °C than tetraactylethylethylenediamine as bleach activator used in powder detergent formulations for stain removal. Copyright © 2015 John Wiley & Sons, Ltd.