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.     

Geometry of dislocated de Broglie waves

The geometrical structures implicit in the de Broglie waves associated with a relativistic charged scalar quantum mechanical particle in an external field are analyzed by employing the ray concept of the causal interpretation. It is shown how an osculating Finslerian metric tensor, a torsion tensor, and a tetrad field define respectively the strain, the dislocation density, and the Burgers vector in the natural state of the wave, which is a non-Riemannian space of distant parallelism. A quantum torque determined by the quantum potential is introduced and the example of a screw dislocated wave is discussed.     

Reaction titration: a convenient method for titering reactive hydride agents (Red-Al, LiAlH4, DIBALH, L-Selectride, NaH, and KH) by No-D NMR spectroscopy

The concentration of reactive metal hydride (Met-H) reducing agents can be determined (in < or = 20 min) using No-D NMR spectroscopy. The method involves (i) reacting Met-H with an excess of p-methoxybenzaldehyde, (ii) quenching with excess acetic acid, (iii) recording the No-D NMR spectrum of this homogeneous mixture, and (iv) deducing the concentration of Met-H from the % conversion (as measured by integration). By a conceptually related method, the titer of the basic alkali metal hydrides KH and NaH can also be determined.     

A one-pot synthesis of tertiary amines from amines,lactams and urethanes

A one-pot synthesis of unsymmetrical tertiary amines from amides, lactams and urethanes has been developed. The reaction is general for all cases examined with the exception of N-aryl containing examples, which are not accessible by this method.     

Patterned and controlled polyelectrolyte fractal growth and aggregations

Two-dimensional patterned and controlled polyelectrolyte aggregations (e.g., tree-like ramified structures) created by microcontact printing have been demonstrated and discussed. Polyelectrolyte-micropatterned aggregations on surfaces were controlled by the micropattern size and shape of PDMS stamps. The formation of aggregates was dependent on the ink and surface conditions, and the aggregates consisted of two distinct layers; strongly adsorbed, primary uniform layers and weakly adsorbed, secondary aggregation layers positioned on top of the primary layers. The adsorption of the primary layers was strong enough not to be washed away, while the aggregated secondary layers were easily removed by washing. The aggregation of secondary layers showed typical tree-like ramified structures of fractal growth and aggregation. Directional and confined stamping led to directing and confining the growth of the fractal polyelectrolyte clusters, respectively. The micropatterned primary uniform layers were not removed by extensive washing, and they were identified by selective nickel plating and charged particle selective adsorption in which the surface formed positive and negative micropatterns. These functional and patterned surfaces have great potentials for advanced devices and sensors.     

Effects of phosphine ligand chelation on the reactivity of monomeric parent amido ruthenium complexes: synthesis and reactivity of such a complex bearing monodentate ligands

The parent amido complex cis-(PMe(3))(4)Ru(H)(NH(2)) (2) has been prepared via the deprotonation of [cis-(PMe(3))(4)Ru(H)(NH(3))(+)][BPh(4)(-)]. The amido complex is a somewhat weaker base than the DMPE analogue trans-(DMPE)(2)Ru(H)(NH(2)) but is still basic enough to quantitatively deprotonate fluorene and reversibly deprotonate 1,3-cyclohexadiene and toluene. Complex 2 exhibits very labile phosphine ligands, two of which can be replaced by DMPE to yield the mixed complex cis-(PMe(3))(2)(DMPE)Ru(H)(NH(2)). Because of the ligand lability, 2 also undergoes hydrogenolysis and rapid exchange with labeled NH(3). The amide complex reacts with alkyl halides to yield E2 and S(N)2 products, along with ruthenium hydrido halide complexes including the ruthenium fluoride cis-(PMe(3))(4)Ru(H)(F). Ruthenium hydrido ammonia halide ion pair intermediates [cis-(PMe(3))(4)Ru(H)(NH(3))(+)][X(-)] are observed in some deprotonation and E2 reactions, and measurement of the equilibrium constants for NH(3) displacement from these complexes suggests that they benefit from significant hydrogen bonding between X(-) and NH(3) groups. Cumulenes also react with complex 2 to afford the products of insertion into an NH bond. The rates of neither these NH insertion reactions nor the reversible deprotonation reactions show any dependence on the concentration of PMe(3) present, suggesting that these reactions take place directly at the NH(2) group and do not involve precoordination of substrate to the metal center.     

Comparing the Atomic Structures of Binary MO2-SiO2 (M = Ti, Zr or Hf) Xerogels

The incorporation of transition-metal oxides into silica can give materials with useful optical, electronic or catalytic properties. For example, ZrO₂-SiO₂ and HfO₂-SiO₂ materials are of interest due to their high dielectric constants. Here we present a comparison of extended X-ray absorption fine structure and small-angle X-ray scattering results for acid-catalysed binary (MO₂) _x (SiO₂)_{1 – x} (M = Ti, Zr or Hf) xerogels, with x up to 0.4 and heat treatments up to 750°C. Detailed observations for TiO₂-SiO₂ and ZrO₂-SiO₂ xerogels provide a basis for interpretation of new results for HfO₂-SiO₂ xerogels. At low concentrations metal atoms are homogeneously incorporated into the silica network. Ti adopts coordinations of 4 or 6, and Zr and Hf both adopt higher coordination of 6 or 7 (the larger coordinations being due to ambient moisture). At higher concentrations, phase separation of metal oxide occurs. Such regions become clearly separated from the silica network for TiO₂, but remain very finely mixed with silica network for ZrO₂ and HfO₂.