On the rate of convergence of sequential quadratic programming with nondifferentiable exact penalty function in the presence of constraint degeneracy

We analyze the convergence of a sequential quadratic programming (SQP) method for nonlinear programming for the case in which the Jacobian of the active constraints is rank deficient at the solution and/or strict complementarity does not hold for some or any feasible Lagrange multipliers. We use a nondifferentiable exact penalty function, and we prove that the sequence generated by an SQP using a line search is locally R-linearly convergent if the matrix of the quadratic program is positive definite and constant over iterations, provided that the Mangasarian-Fromovitz constraint qualification and some second-order sufficiency conditions hold. Received: April 28, 1998 / Accepted: June 28, 2001?Published online April 12, 2002     

Vanishing cycles of pencils of hypersurfaces

We prove an extended Lefschetz principle for a large class of pencils of hypersurfaces having isolated singularities, possibly in the axis, and show that the module of vanishing cycles is generated by the images of certain variation maps.     

A remark on sets having the Steinhaus property

A point set satisfies the Steinhaus property if no matter how it is placed on a plane, it covers exactly one integer lattice point. Whether or not such a set exists, is an open problem. Beck has proved [1] that any bounded set satisfying the Steinhaus property is not Lebesgue measurable. We show that any such set (bounded or not) must have empty interior. As a corollary, we deduce that closed sets do not have the Steinhaus property, fact noted by Sierpinski [3] under the additional assumption of boundedness.     

Classical and statistical analysis of40Ar(300 MeV)+197Au deep inelastic interaction

We examine the way in which local field effects in the neutron refractive index affect the values of coherent scattering lengths determined by various kinds of neutron optical measurements. We find that under typical experimental conditions these effects are negligible for interferometry measurements but that they are significant for gravity refractometry measurements, producing changes in the effective scattering length of as much as two or three standard deviations in some cases. Refined values of the scattering lengths are obtained for the thirteen elements for which data are presently available. The special role of local field effects in neutron transmission is also discussed.     

Irreducible representations of infinite-dimensional Lie algebras

Some results concerning the operatorially irreducible, topologically irreducible, operatorially and topologically irreducible representations of a class of infinite-dimensional Lie algebras by bounded operators in a complex Banach space are obtained.     

Stereochemie und1H-NMR-Spektren einiger vom Pentaerythrit abgeleiteten Spiro-1,3-dioxane

Summary Mono- and trispiro-1,3-dioxanes with mobile, fixed and semimobile structures were obtained by the condensation reaction of pentaerythritol with aldehydes and symmetrical or unsymmetrical ketones. The conformational analysis of the obtained compounds was undertaken by means of¹H-NMR spectroscopy. The spiro-1,3-dioxanes obtained with aldehydes or nonsymmetrical ketones represent fixed (anancomeric) structures. Ketalisation with 4-t-butyl-cyclohexanone leads to a semimobile structure of a trispiro-1,3-dioxane in which the two marginal cyclohexanic rings are fixed, while the two middle ones are mobile, continuously flipping at room temperature. The solvent effect on the NMR spectra is also discussed. Utilisation of benzene-d ₆ makes it possible to interpret some of the complex spectra with superposed signals on the basis of the aromatic solvent induced shift (ASIS).

     

Theoretical determination of the ablation rate of metals in multiple-nanosecond laser pulses irradiation regime

A detailed understanding of the physical determinants of the ablation rate in multiple nanosecond laser pulses regime is of key importance for technological applications such as patterning and pulsed-laser deposition. Here, theoretical modeling is employed to investigate the ablation of thick metallic plates by intense, multiple nanosecond laser pulses. A new photo-thermal model is proposed, in which the complex phenomena associated to the ablation process are accounted for as supplementary terms of the classical heat equation. The pulsed laser ablation in the nanosecond regime is considered as a competition between thermal vapourization and melt ejection under the action of the plasma recoil pressure. Computer simulations using the photo-thermal model presented here and the comparison of the theoretical results with experiment indicate two different mechanisms that contribute to the decrease of the ablation efficiency. First, during the ablation process the vapour/plasma plume expanding above the irradiated target attenuates the laser beam that reaches the sample, leading to a marked decrease of the ablation efficiency. Additional attenuation of the laser beam incident on the sample is produced due to the heating of the plasma by the absorption of the laser beam into the plasma plume. The second mechanism by which the ablation efficiency decreases consists of the reduction of the incident laser intensity with the lateral area, and of the melt ejection velocity with the depth of the hole.