A model of fads,fashions, and group formation

I develop a model of consumer behavior where agents purchase goods in order to signify personal characteristics. Agents purchase goods in order to imitate agents similar to them and agents they want to emulate. Depending on parameter values of consumer preferences the model generates stable groups, fads, and fashion cycles, or a mixture of both. The model is unique to the economic literature on fads in that the extinction of fads occurs endogenously in the model. © 2004 Wiley Periodicals, Inc. Complexity 9: 51–61, 2004     

On divisibility properties of certain multinomial coefficients—II

A recent conjecture of Myerson and Sander concerns divisibility properties of certain multinomial coefficients. We obtain results in this direction by further pursuing a line of attack developed earlier by the first author.     

An ab initio molecular orbital study of the grignard reagents CH3MgCl and [CH3MgCl]2: The Schlenk equilibrium

Ab initio molecular orbital calculations are used to study the modified Schlenk equilibrium: 2RMgCl (RMgCl)² MgR₂ + MgCl₂ Mg(Cl₂)MgR₂ with R=H and CH₃. In the absence of any solvents, calculations indicate that the formation of the various possible bridged dimers (RMgCl)₂ is substantially exothermic. However, using dimethylether as a model solvent, we show that the formation of the dimer (Me₂O)(CH₃)Mg(Cl₂)Mg(CH₃)(OMe₂) is exothermic only when entropic effects are included.     

Photocatalytic Water Oxidation by a Pyrochlore Oxide upon Irradiation with Visible Light: Rhodium Substitution Into Yttrium Titanate

A stable visible‐light‐driven photocatalyst (λ≥450 nm) for water oxidation is reported. Rhodium substitution into the pyrochlore Y₂Ti₂O₇ is demonstrated by monitoring Vegard′s law evolution of the unit‐cell parameters with changing rhodium content, to a maximum content of 3 % dopant. Substitution renders the solid solutions visible‐light active. The overall rate of oxygen evolution is comparable to WO₃ but with superior light‐harvesting and surface‐area‐normalized turnover rates, making Y₂Ti_1.94Rh_0.06O₇ an excellent candidate for use in a Z‐scheme water‐splitting system.     

Photoswitchable Sol–Gel Transitions and Catalysis Mediated by Polymer Networks with Coumarin-Decorated Cu24L24 Metal–Organic Cages as Junctions

Photoresponsive materials that change in response to light have been studied for a range of applications. These materials are often metastable during irradiation, returning to their pre-irradiated state after removal of the light source. Herein, we report a polymer gel comprising poly(ethylene glycol) star polymers linked by Cu₂₄L₂₄ metal–organic cages/polyhedra (MOCs) with coumarin ligands. In the presence of UV light, a photosensitizer, and a hydrogen donor, this “polyMOC” material can be reversibly switched between Cu^II, Cu^I, and Cu⁰. The instability of the MOC junctions in the Cu^I and Cu⁰ states leads to network disassembly, forming Cu^I/Cu⁰ solutions, respectively, that are stable until re-oxidation to Cu^II and supramolecular gelation. This reversible disassembly of the polyMOC network can occur in the presence of a fixed covalent second network generated in situ by copper-catalyzed azide-alkyne cycloaddition (CuAAC), providing interpenetrating supramolecular and covalent networks.