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.     

Single-crystal esr study of x-irradiated 2-chloro-2,2'-spirobis (1,3,2-benzodioxaphosphole): phosphorus in an octahedral geometry with the unpaired electron and chlorine in axial positions

X-irradiation of a single crystal of 2-chloro-2,2'-spirobis(1,3,2-benzodioxaphosphole) yields the oriented P^VI radical anion formed by electron capture. Directions of maximum values of the magnetic hyperfine tensors of ³¹P, ³⁵Cl, and ³⁷Cl are coincident and oriented along the P—Cl linkage, indicating an octahedral structure with the unpaired electron and chlorine in axial positions.     

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.     

Effect of temperature and molecular weight on the rate of spreading of polystyrene melts on plane soda lime glass surfaces

The effect of temperature T and weight-average molecular weight M?_w on the rate of spreading of polystyrene melts on plane solid surfaces has been examined. The activation energy E of spreading was estimated to be 25.2 ± 3 kcal/mole, which is of the same magnitude as the activation energy for flow of polystyrene melts. The rate of spreading was found to be inversely proportional to M?_w raised to the 1.5 power. This rate of spreading, measured as the time rate of increase in the liquid–solid contact area, dA/dt, could be expressed as where γ_1v is the melt surface tension and θ_d and θ_s are the dynamic and static contact angles, respectively. The numerical value of K has been calculated to be (6.025 ± 3.693) × 10^?14 in the temperature range of 110–260°C and for the values of M?_w from 2000 to 37000.     

Self-Sensitized Photo-Oxygenation of 1-Benzyl-3, 4-dihydroisoquinolines

The air oxidation of 1-benzyl-3, 4-dihydroisoquinolines is shown to be a self-sensitized photo-oxidation proceeding via singlet oxygen.     

An unusual stereospecific epoxidation with “per-amberlyst 15®”

4-Methyl-4-naphthoquinol and its 5-methyl derivative on treatment with per-Amberlyst 15 are converted to the corresponding cis-2,3-epoxides in high yields. The latter structure was determined by X-ray crystallography.     

Light scattering from nonequilibrium electron-hole plasma excited by picosecond laser pulses in GaAs

A picosecond dye laser is used to excite electron-hole plasma of density between 10¹⁸ to 10¹⁹ cm^-3 in GaAs. The plasma density and distribution function within ? 20 psec of excitation is probed by Raman scattering. The lineshape of the single particle excitation spectra of the plasma can be explained only by assuming that the electron distribution function is in nonthermal equilibrium.