A stereoselective 3-endo-alkyl-5,6-dehydroisoquinuclidine synthesis.

Cycloaddition of N-carbethoxy-2-alkyl-1,2-dihydropyridines $\text{4}$ with phenylvinylsulfone $\text{5}$ provides adducts $\text{6}$, which upon desulfonylation afford stereoselectively N-carbethoxy-3-$\text{endo}$- alkyl-5,6-dehydroisoquinuclidines $\text{1}$.     

Synthesis of N-alkyl derivatives of 4-(2′-aminoethyl)indole

N-Substituted 4-(2′-aminoethyl)indoles are attainable in good yields from indole-4-acetic acid ( 2 ). Several methods of preparation for 2 were tried or considered. A new sequence involving Arndt-Eistert homologation of indole-4-carboxylic acid has been devised, which is no more laborious than a literature homologation sequence involving indole-4-acetonitrile, and which provides somewhat better overall yields than the literature method.     

N-Alkyl derivatives of trans-6,7-dihydroxy-1,2,3,4,4a,5,10,10b-octahyrobenzo[g]quinoline A congener of apomorphine lacking the non-oxygenated aromatic ring

A synthetic sequence leading to the title compounds began with methyl 5,6-dimethoxy-2-tetralone-3-carboxylate and involved a multi-step construction of the heterocyclic ring. The trans-fused isomer was isolated from the cyclization step. However, the possibility of formation of some cis-fused isomer cannot be precluded.     

A new laser concept for isotopically selective analysis of noble gases

A new laser approach for the isotopically selective analysis of noble gases is presented. This approach uses noble gas atoms prepared in the 1s ⁵ metastable state. Hyperfine levels in the 1s ⁵ and 2p ⁹ states form two-level systems in Ne, Ar, Kr, and Xe which can be excited by a commercially available single-frequency laser system. Absorption of photons from such a laser, and the resulting momentum transfer, can be used to selectively deflect the desired isotope from a supersonic atomic beam into a detection area. Light from the same laser can then be used to selectively count atoms of the desired isotope using the photon-burst technique. Thus, enrichment and selective detection are accomplished with a single laser in a single pass through the apparatus.The problem of analyzing for⁸⁵Kr in a sample of noble gases extracted from the air is examined in detail. This is a stringent test of the selectivity of this approach because⁸⁵Kr has the same nuclear spin, and thus similar hyperfine splittings, as naturally occurring⁸³Kr. Calculations indicate that isotopic selectivity of the new approach is easily adequate to resolve⁸⁵Kr in a 10¹⁰ excess of⁸³Kr.     

Numerical solutions of some parabolic inverse problems

In this article we transform a large class of parabolic inverse problems into a nonclassical parabolic equation whose coefficients consist of trace type functionals of the solution and its derivatives subject to some initial and boundary conditions. For this nonclassical problem, we introduce a variational form by defining a new function. Both continuous and discrete Galerkin procedures are illustrated in this paper. The error estimates are also derived.     

Nonlinear convection at a porous flat plate with application to heat transfer from a dike

Solutions for a class of coupled nonlinear differential equations, arising in free convection flow at a vertical flat plate embedded in a saturated porous medium at high Reynolds numbers in the presence of heat sources (or sinks) and with nonlinear density temperature variation, are obtained. Further, using the Schauder theory and numerical results, existence and analyticity results are established.     

On Hyperbolic Once-Punctured-Torus Bundles

For a hyperbolic once-punctured-torus bundle over a circle, a choice of normalization determines a family of arcs in the Riemann sphere. We show that, in each arc in the family, the set of cusps is dense and forms a single orbit of a finitely generated semigroup of Möbius transformations. This was previously known for the case of the complement of the figure-eight knot.     

Anomalous linewidths and peak-height ratios in137Ba hyperfine lines

We have investigated several effects of optical pumping in the hyperfine spectrum of the6s6p ¹ P ₁6s ^{2 1} S ₀ transition in¹³⁷Ba. Most of these effects are explained by absorption strength changes which occur because of redistribution of population among magnetic substates. At very low laser intensities, no redistribution effects are observed. At higher intensities, it is possible to either empty the magnetic substates that are accessible to optical excitation, or to redistribute the population among these states until a steady-state condition is achieved. The first case results in the familiar disappearance of a hyperfine line. The less familiar second case can result in peak-height ratios in the Ba¹ P ₁¹ S ₀ hyperfine spectrum that differ by almost a factor of three from the low-intensity case. In this second case, the observed linewidth can either broaden or narrow, depending on whether redistribution decreases or increases absorption strength. At high intensities, saturation effects dominate and branching to intermediateD states becomes apparent. We report here the result of a numerically integrated rate equation model which shows good agreement with our experiments.     

A micromechanical basis for partitioning the evolution of grain bridging in brittle materials

A micromechanical model is developed for grain bridging in monolithic ceramics. Specifically, bridge formation of a single, non-equiaxed grain spanning adjacent grains is addressed. A cohesive zone framework enables crack initiation and propagation along grain boundaries. The evolution of the bridge is investigated through a variance in both grain angle and aspect ratio. We propose that the bridging process can be partitioned into five distinct regimes of resistance: propagate, kink, arrest, stall, and bridge. Although crack propagation and kinking are well understood, crack arrest and subsequent “stall” have been largely overlooked. Resistance during the stall regime exposes large volumes of microstructure to stresses well in excess of the grain boundary strength. Bridging can occur through continued propagation or reinitiation ahead of the stalled crack tip. The driving force required to reinitiate is substantially greater than the driving force required to kink. In addition, the critical driving force to reinitiate is sensitive to grain aspect ratio but relatively insensitive to grain angle. The marked increase in crack resistance occurs prior to bridge formation and provides an interpretation for the rapidly rising resistance curves which govern the strength of many brittle materials at realistically small flaw sizes.