The bidmensional stefan problem with convection: the time dependent case

This paper considers the time dependent stefan problem with convection in the fluid phase governed by the Stokes equation, and with adherence of the fluid on the lateral boundaries: The existence of a weak solution is obtained via the introduction of a temperature dependent penalty term in the fluid flow equation, together with the application of various compactness arguments.     

Zur Bestimmung des Adrenalins

Ohne Zusammenfassung     

Mechanism of the cobalt oxazoline palladacycle (COP)-catalyzed asymmetric synthesis of allylic esters

The catalytic enantioselective S(N)2' displacement of (Z)-allylic trichloroacetimidates catalyzed by the palladium(II) complex [COP-OAc](2) is a broadly useful method for the asymmetric synthesis of chiral branched allylic esters. A variety of experiments aimed at elucidating the nature of the catalytic mechanism and its rate- and enantiodetermining steps are reported. Key findings include the following: (a) the demonstration that a variety of bridged-dipalladium complexes are present and constitute resting states of the COP catalyst (however, monomeric palladium(II) complexes are likely involved in the catalytic cycle); (b) labeling experiments establishing that the reaction proceeds in an overall antarafacial fashion; (c) secondary deuterium kinetic isotope effects that suggest substantial rehybridization at both C1 and C3 in the rate-limiting step; and (d) DFT computational studies (B3-LYP/def2-TZVP) that provide evidence for bidentate substrate-bound intermediates and an anti-oxypalladation/syn-deoxypalladation pathway. These results are consistent with a novel mechanism in which chelation of the imidate nitrogen to form a cationic palladium(II) intermediate activates the alkene for attack by external carboxylate in the enantiodetermining step. Computational modeling of the transition-state structure for the acyloxy palladation step provides a model for enantioinduction.     

External cavity quantum cascade laser for quartz tuning fork photoacoustic spectroscopy of broad absorption features

We demonstrate mid-infrared spectroscopy of large molecules with broad absorption features using a tunable external cavity quantum cascade laser. Absorption spectra for two different Freons are measured over the range 1130-1185 cm(-1) with 0.2 cm(-1) resolution via laser photoacoustic spectroscopy with quartz tuning forks as acoustic transducers. The measured spectra are in excellent agreement with published reference absorption spectra.     

On hyperbolic once-punctured-torus bundles II: fractal tessellations of the plane

We describe fractal tessellations of the complex plane that arise naturally from Cannon–Thurston maps associated to complete, hyperbolic, once-punctured-torus bundles. We determine the symmetry groups of these tessellations. To our wives, Ardyth and Elena.     

A nonlinear parabolic free boundary problem

Summary When two immiscible fluids in a porous medium are in contact with one another, an interface is formed and the movement of the fluids results in a free boundary problem for determining the location of the interface along with the pressure distribution throughout the medium. The pressure satisfies a nonlinear parabolic partial differential equation on each side of the interface while the pressure and the volumetric velocity are continuous across the interface. The movement of the interface is related to the pressure through Darcy’s law. Two kinds of boundary conditions are considered. In Part I the pressure is prescribed on the known boundary. A weak formulation of the classical problem is obtained and the existence of a weak solution is demonstrated as a limit of a sequence of classical solutions to certain parabolic boundary value problems. In Part II the same analysis is carried out when the flux is specified on the known boundary, employing special techniques to obtain the uniform parabolicity of the sequence of approximating problems. Entrata in Redazione il 29 novembre 1975. This research was supported in part by the National Science Foundation, the Senior Fellowship Program of the North Atlantic Treaty Organization, the Italian Consiglio Nazionale delle Ricerche, and the Texas Tech. University.     

A priori estimate for continuation of the solution of the heat equation in the space variable

Summary Let u(x, t) satisfy the heat equation in a region D in the x−t plane and vanish initially. Let |u|<M₀ in D and |u _i ² |<∈ in D* ⊂ D. Then, in D−D*, |u|< , where B=B(x, t) satisfies O<B<1 and B(x, t) and M₁ are given explicity by simple formulas. The a priori bound is applied to an error analysis of a numerical procedure for continuing solutions of the heat equation in the space variable. Work was performed under the auspices of the U. S. Atomic Energy Commission.