A Practical Procedure for the Solid-Phase Synthesis of Racemic 2,2′-Dihydroxy-1,1′-binaphthyl

Abstract: A high yielding solid-phase dimerisation of 2-naphthol by means of a ball-milling procedure is described.

     

Comparison of preconditioned Krylov subspace iteration methods for PDE-constrained optimization problems

The governing dynamics of fluid flow is stated as a system of partial differential equations referred to as the Navier-Stokes system. In industrial and scientific applications, fluid flow control becomes an optimization problem where the governing partial differential equations of the fluid flow are stated as constraints. When discretized, the optimal control of the Navier-Stokes equations leads to large sparse saddle point systems in two levels. In this paper, we consider distributed optimal control for the Stokes system and test the particular case when the arising linear system can be compressed after eliminating the control function. In that case, a system arises in a form which enables the application of an efficient block matrix preconditioner that previously has been applied to solve complex-valued systems in real arithmetic. Under certain conditions, the condition number of the so preconditioned matrix is bounded by 2. The numerical and computational efficiency of the method in terms of number of iterations and execution time is favorably compared with other published methods.     

Weighted maximal regularity estimates and solvability of non-smooth elliptic systems I

We develop new solvability methods for divergence form second order, real and complex, elliptic systems above Lipschitz graphs, with L ₂ boundary data. The coefficients A may depend on all variables, but are assumed to be close to coefficients A ₀ that are independent of the coordinate transversal to the boundary, in the Carleson sense ‖A−A ₀‖ _C defined by Dahlberg. We obtain a number of a priori estimates and boundary behaviour results under finiteness of ‖A−A ₀‖ _C . Our methods yield full characterization of weak solutions, whose gradients have L ₂ estimates of a non-tangential maximal function or of the square function, via an integral representation acting on the conormal gradient, with a singular operator-valued kernel. Also, the non-tangential maximal function of a weak solution is controlled in L ₂ by the square function of its gradient. This estimate is new for systems in such generality, and even for real non-symmetric equations in dimension 3 or higher. The existence of a proof a priori to well-posedness, is also a new fact.     

An improved palladium(II)-catalyzed method for the synthesis of aryl ketones from aryl carboxylic acids and organonitriles

A palladium(II)-catalyzed decarboxylative protocol for the synthesis of aryl ketones has been developed. The addition of TFA was shown to improve the reaction yield and employing THF as solvent enabled the use of solid nitriles and in only a small excess. Using this method, five different benzoic acids reacted with a wide range of nitriles to produce 29 diverse (hetero)aryl ketone derivatives in up to 94% yield.     

Dependence of Pressure,Combustion and Frequency Characteristics on Valved Pulsejet Combustor Geometries

An experimental analysis of valved pulsejets based on the Curtis-Dyna design and the concomitant results are discussed in the current paper. By altering the combustor length, the tail pipe length and by adding a flare at the aft-end, twelve different pulsejet configurations are tested. An axially-distributed array of piezoelectric pressure sensors and ion probes reveal the pressure and combustion dynamics inside these devices. Evidence is attained to support the claim that valved Curtis-Dyna pulsejets of the tested configurations behave like a Helmholtz resonator. Each cycle of a pulsejet is composed of temporally and spatially restrained combustion events. Altering the geometry induces an amplitude modulated low frequency instability inside the pulsejet that is characterized by sinusoidally-varying peak cycle pressures. The operating frequency, peak pressures and combustion activity of the pulsejets are characterized to reveal that reliable pulsejet operation requires proper amount of coupling — defined by low time lags — between the pressure peaks and combustion events.     

A generalized conjugate gradient,least square method

Summary A generalizeds-term truncated conjugate gradient method of least square type, proposed in [1a, b], is extended to a form more suitable for proving when the truncated version is identical to the full-term version. Advantages with keeping a control term in the truncated version is pointed out. A computationally efficient new algorithm, based on a special inner product with a small demand of storage is also presented.We also give simplified and slightly extended proofs of termination of the iterative sequence and of existence of ans-term recursion, identical to the full-term version. Important earlier results on this latter topic are found in [15, 16, 8 and 11].The research reported in this paper was partly supported by NATO Grant No. 648/83     

One-nucleon removal cross-sections for 17, 19C and 8, 10B

One-neutron removal cross-sections ( ) of ^{17, 19}C in various targets at about 900 MeV/nucleon, and one-proton removal cross-sections ( ) of ^{8, 10}B at about 1400 MeV/nucleon were measured using the fragment separator FRS at GSI. A significant increase of for ¹⁹C compared to its neighbors was observed. The same behavior was found for for the neutron-deficient nucleus ⁸B compared to the stable isotope ¹⁰B. These results support a one-neutron halo structure in ¹⁹C and a one-proton halo in ⁸B. Received: 26 July 2000 / Accepted: 11 January 2001