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.     

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.     

Historical Aspects of the Chemical Bond. Chemical Relationality versus Physical Objectivity

Chemists have always defined the properties of materials on the basis of the changes observed when they reacted with other substances. Whereas this approach led chemists to relational concepts such as affinity, acid, and oxidant, physicists made measurements of objects they considered unchanged, determining their mass, charge, dipole moment, etc. In the middle of the 18th century, the Jesuit Josip Ruder Bocovi started thinking about the way in which atoms might be present in crystals, introducing a new concept according to which atoms in condensed phases represented punctual centres of attracting and repelling forces. Josef Loschmidt became aware of these ideas through the philosopher J. F. Herbart, and it is to Loschmidt that we owe the first representation of bonds as atomic spheres penetrating one another. The term quantum chemistry was first used by the physicist Arthur Erich Haas, who was born in Brno. However, Hans Hellmann (1903–1938) was the true founder of quantum chemistry. Hellmann, who was shot in Moscow in 1938, was the first person to realize the quantum-physical effect that leads to the chemical bond. In the 1960s K. Ruedenberg and others took theory a stage further when – thanks to the concept of the localized electron pair – they realized that the different approaches to the phenomenon of the chemical bond taken by chemists and physicists were largely comparable. This made it possible to bring the differing standpoints largely into line with one another.     

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.     

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.     

Pharmacokinetics of ICG and HPPH-car for the detection of normal and tumor tissue using fluorescence, near-infrared reflectance imaging: a case study

We present in vivo fluorescent, near-infrared (NIR), reflectance images of indocyanine green (ICG) and carotene-conjugated 2-devinyl-2-(1-hexyloxyethyl) pyropheophorbide (HPPH-car) to discriminate spontaneous canine adenocarcinoma from normal mammary tissue. Following intravenous administration of 1.0 mg kg-1 ICG or 0.3 mg kg-1 HPPH-car into the canine, a 25 mW, 778 nm or 70 mW, 660 nm laser diode beam, expanded by a diverging lens to approximately 4 cm in diameter, illuminated the surface of the mammary tissue. Successfully propagating to the tissue surface, ICG or HPPH-car fluorescence generated from within the tissue was collected by an image-intensified, charge-coupled device camera fitted with an 830 or 710 nm bandpass interference filter. Upon collecting time-dependent fluorescence images at the tissue surface overlying both normal and diseased tissue volumes, and fitting these images to a pharmacokinetic model describing the uptake (wash-in) and release (wash-out) of fluorescent dye, the pharmacokinetics of fluorescent dye was spatially determined. Mapping the fluorescence intensity owing to ICG indicates that the dye acts as a blood pool or blood persistent agent, for the model parameters show no difference in the ICG uptake rates between normal and diseased tissue regions. The wash-out of ICG was delayed for up to 72 h after intravenous injection in tissue volumes associated with disease, because ICG fluorescence was still detected in the diseased tissue 72 h after injection. In contrast, HPPH-car pharmacokinetics illustrated active uptake into diseased tissues, perhaps owing to the overexpression of LDL receptors associated with the malignant cells. HPPH-car fluorescence was not discernable after 24 h. This work illustrates the ability to monitor the pharmacokinetic delivery of NIR fluorescent dyes within tissue volumes as great as 0.5-1 cm from the tissue surface in order to differentiate normal from diseased tissue volumes on the basis of parameters obtained from the pharmacokinetic models.     

Technical Procedures for the Syntheses of Carotenoids and Related Compounds from 6-Oxo-isophorone: Syntheses of (3R,3′R)-Zeaxanthin. Part I

Starting from the readily available, optically active (4R)-4-hydroxy-2,2,6-trimethylcyclohexanone ( 1 ), a new technical synthesis of (3R,3′R)-zeaxanthin is described. According to a 2(C₉ + C₆) + C₁₀ = C₄₀ construction scheme, the ketone 1 was first transformed with (E)-3-methylpent-2-en-4-yn-1-ol ( 5 ) into a C₁₅-intermediate which, by a three-step sequence, could be converted into the known olefinic C₁₅-Wittig salt 4 . Optimized conditions for the final Wittig reaction of 4 with the C₁₀-dialdehyde 3 are discussed. Based on 1 , the overall yield of the entire technical process is ca. 40%.