Steric Modulation of the Porphycene System by Alkyl Substituents: 9,10,19,20-Tetraalkylporphycenes

Porphycene ( 2 ), a planar structural isomer of porphyrin ( 1 ) recognized and synthesized only recently, exhibits short N … N distances allowing exceptionally strong N-H … N hydrogen bonds to be formed. Although the N₄-coordination hole of 2 is smaller than that of 1 , the new tetrapyrrolic macrocycle is capable of complexation with a broad spectrum of metal ions to give the respective metalloporphycenes. In accord with model considerations, both N-H … N hydrogen bonding and complexation of 2 may be modulated by peripheral alkyl groups through changes in the geometry of the porphycene skeleton arising from non-bonded repulsions between the substituents. In this publication are delineated some of the consequences of structural variation of 2 by introduction of alkyl groups at the 9,10,19,20-positions.     

On the stability of some high-resolution beamforming methods

Orthogonal beamforming is the name of certain high-resolution methods for estimating the spectra of a wave field received by an array of sensors. The methods use the eigenvalues and eigenvectors of the spectral matrix of the sensor outputs. The problem is to predict the behavior of such methods when only an estimate of the matrix is known. The sensor outputs may consist of sensor noise, ambient noise and noise from a finite set of discrete sources. The properties of the eigensystem of the spectral matrix in the case of weak ambient noise motivate the methods of orthogonal beamforming, for example Pisarenko's nonlinear peak estimates and the projection estimates of Owsley. If the spectral matrix is estimated by one of the classical methods, some asymptotic distributional properties of the matrix estimate and its eigensystem are well known. They can be used to determine asymptotic expressions, e.g. for the first and second moments of the peak estimators and to approximate the distributions. The parameters, however, cannot be calculated in applications, since the eigensystem of the exact spectral matrix is required. Therefore, we have developed bounds for the deviation of the peak estimates which only use weak knowledge about the matrix. We have applied some results on perturbations of hermitian operators. The asymptotic behavior of the bounds for the projection estimator is investigated and possibilities for their estimation are indicated. Finally, we report on extensive simulations with random matrices to evaluate the new bounds. As a result, we have found that the projection estimator behaves stably and there are tight bounds if the eigenvalues of interest are sufficiently separated from the rest.     

Note on the motion of surface films in a rotating cylinder

Summary The motion of an insoluble and incompressible surface film at the gas-liquid interface of a fluid system in a finite revolving cylinder is dealt with experimentally. It is shown that the film motion induced by the side-walls affects the film motion at the plane gas-liquid interface considerably. Measurements show a difference of 20 to 30% for small speeds of rotation.With 5 Figures     

Thermal hysteresis at the cubic/tetragonal phase transition in melt-grown BaTiO3 single crystals

Thermal hysteresis at the cubic/tetragonal phase transition in BaTiO₃ single crystals can be extended from the usually observed 2-4 K to about 15 K if the influence of mechanical preparation is reduced as much as possible. The effect is discussed using the mean-field theory, supposing clamping of the clusters of the new phase by the surrounding matrix of the parent phase.