Stochastic diffusion models with advertising and word-of-mouth effects

This paper presents a stochastic diffusion model which incorporates advertising word-of-mouth effects. The model defines a 3 variate stochastic process based on explicit assumptions regarding consumer behavior and consumers' response to advertising. The model generalizes a wide variety of advertising models and in addition includes several classes of consumers, interaction effects between these consumers and, of course, a stochastic framework that may be used for assessing the risk implications of advertising policies and for empirical analyses purposes.     

Low energy electron attenuation length studies in thin amorphous carbon films

The results of experiments on low energy electrons passing through thin amorphous carbon films are reported. For electron energies between 50 and 3000 eV, electron attenuation lengths were determined by electron transmission measurements through carbon films of thicknesses between 81 and 210 Å. The density of these amorphous carbon films was also obtained by a sink—float method and found to be 1.90 ± 0.05 g cm^?3. The electron attenuation length for inelastic scattering was found to increase monotonically from approximately 10 to 55 Å over the 50 to 3000 eV range. Over the 500–3000 eV energy region, the results are in good agreement with mean free paths calculated using optically measured dielectric functions.     

Solvent effects on radical homo- and copolymerizations of methacryloyl fluroride

The effect of solvent in homo- and copolymerizations of methacryloyl fluoride (MAF) was investigated in various aromatic solvents. In these solvents, there is a significant effect on the rate of polymerization, on the tacticity of the resulting poly(methacryloyl fluoride), and on the copolymerization of MAF with methyl methacrylate (MMA). The equilibrium constants between MAF and aromatic solvents were determined from NMR spectroscopic measurements. These results indicated that the solvent effect on the MAF polymerization stems from changes in reactivity of MAF induced by the strong MAF–solvent interaction as well as stabilization of the MAF radical by solvents. Copolymerization of MAF with both p-methoxystyrene (MSt) and p-nitrostyrene (NSt) was also studied.     

Liquid Drops on an Inclined Plane: The Relation between Contact Angles, Drop Shape, and Retentive Force

Contact angle hysteresis, drop shape, and drop retention were studied with a tiltable plane. Contact liquids were water and ethylene glycol. Four polymers and silicon wafers were used as substrates. When the plane was inclined, the shape of drops distorted, exhibiting advancing and receding contact angles. Drops remained stationary until a critical angle of tilt was exceeded, and then they began to move. The difference in the advancing and receding contact angles, or contact angle hysteresis, ranged from 9° to 66°, depending on the liquid and the substrate. Roughness did not seem to influence the hysteresis as much as the chemical nature of the surfaces. Elongation and back-to-front asymmetry were greater on surfaces with high hysteresis. We found a linear correlation between the aspect ratio of drops and their contact angle hysteresis. Also, the retentive force increased with elongation of the drops.     

Line parameter measurements and calculations of CO broadened by nitrogen at elevated temperatures

Measurements of the line strengths and collisional broadening widths of CO in a N₂ atmosphere were made from 300 to 600 K. The lines studied were the P(2), P(3), P(7), P(12), P(18), and P(22) lines of the fundamental band at 2100 cm^?1. The absorption spectra were parametrically fit to a Voigt lineshape model. The band strength was determined to be 250±8 cm^?2atm^?1. The broadening results are compared to Anderson-Tsao-Curnutte calculations and to other experimental studies. The possibility of using an equation of the form $\text{γ(T)=γ(T}{}_0\text{(}\text{T}{}_0\text{T}\text{)}{}^{\mathrm{n}}$ to extrapolate the temperature dependence of the half-widths to flame temperatures is discussed.     

Nearly perfect systems and effective generalizations of Shidlovski's Theorem

An effective proof of Shidlovski's Theorem is presented. The proof utilizes partial differential operators. A number of generalizations of Shidlovski's Theorem are proven, including results about approximation at more than one point. Additionally, partial differential equations are considered. The new methods give a particularly direct proof of Shidlovski's Theorem.     

Fiber architecture of the left ventricular wall: An asymptotic analysis

The goal of this paper is to derive the fiber architecture of the left ventricle from first principles. The principles used are (i) mechanical equilibrium, (ii) a stress tensor that is the sum of a hydrostatic pressure and a fiber stress, (iii) the assumption that fiber tubes have constant cross-sectional area along their length, (iv) axial symmetry, and (v) the approximation that the thickness of the ventricular wall is small in comparison with the other wall dimensions. From these hypotheses, it is deduced that the cardiac muscle fibers are approximate geodesics on a nested family of toroidal surfaces centered on a degenerate torus in the equatorial plane of the heart. (Exact geodesics are ruled out by the theory.) Formulae are derived for the fiber surfaces and the fiber-angle distribution through the wall, and a differential equation is derived for the shape of the middle surface of the left ventricle. The results are in substantial agreement with experimental observations.     

Cyloadditions of benzopyrones: Rapid access to bicyclic AB-ring analogues of anthracyclines

Cycloaddition of the benzopyrone 10b with 1,1-disubstituted alkenes 12, 14, and 16 produces fair yields of the lactones 13, 15, and 17, AB-ring analogues of the anthracyclines.