Smoothing by mollifiers. Part I: semi-infinite optimization

We show that a compact feasible set of a standard semi-infinite optimization problem can be approximated arbitrarily well by a level set of a single smooth function with certain regularity properties. This function is constructed as the mollification of the lower level optimal value function. Moreover, we use correspondences between Karush–Kuhn–Tucker points of the original and the smoothed problem, and between their associated Morse indices, to prove the connectedness of the so-called min–max digraph for semi-infinite problems.      

A molecular mechanics study of methyl vinyl ether an related compounds

Utilizing the known structures of methyl vinyl ether and a few related compounds including anisol and phenol, the MM2 force field has been extended so that structures of these compounds may be calculated. The energy differences between conformations and configurations for many related molecules have been examined, and on the whole these are well calculated in cases where they are known. Dipole moments and heats of formation were also studied.     

On parametric nonlinear programming

In this tutorial survey we study finite dimensional optimization problems which depend on parameters. It is our aim to work out several basic connections with different mathematical areas. In particular, attention will be paid to unfolding and singularity theory, structural analysis of families of constraint sets, constrained optimization problems and semi-infinite optimization.     

High-Pressure Studies of Magnetism and Lattice Dynamics by Nuclear Resonant Scattering of Synchrotron Radiation

A review is given on recent high-pressure experiments using nuclear resonant scattering of synchrotron radiation. We shortly introduce the methodological aspects connected with high-pressure experiments applying nuclear forward scattering and nuclear inelastic scattering of synchrotron radiation. Selected examples for the study of magnetism are given for the Laves phases LuFe₂ and ScFe₂, where we studied the variation of the magnetic ordering temperature and of the Fe band moment as a function of pressure. An actual example for the study of lattice dynamics is a recent investigation of the phonon density-of-states in metallic iron with special emphasis on hcp ε-Fe, where the pressure-induced texture is used, in conjunction with theoretical calculations, to extract density of phonon states as seen parallel and perpendicular to the hexagonal c-axis. This revised version was published online in August 2006 with corrections to the Cover Date.     

Singular Perturbations of Elliptic Problems on Domains with Small Holes

Singular perturbation techniques are used to study the solutions of nonlinear second order elliptic boundary value problems defined on arbitrary plane domains from which a finite number of small holes of radius ρ_i(ε) have been removed, in the limit ε → 0. Asymptotic outer and inner expansions are constructed to describe the behavior of solutions at simple bifurcation and limit points. Since bifurcation usually occurs a eigenvalues of a linearized problem, we study in detail the dependence of the eigenvalues and eigenfunctions on ε, for ε → 0. These results are applied to the vibration of a rectangular membrane with one or two circular holes. The asymptotic analysis predicts a remarkably large sensitivity of eigenvalues and limit points to the ε-domain perturbation considered in this paper.     

The equivalence of strict convexity and injectivity of the gradient in bounded level sets

It is shown that Lipschitzian functions are strictly convex if and only if their generalized gradients are disjoint at distinct interior points of a given bounded level set.This work was supported by the Applied Mathematical Sciences subprogram of the Office of Energy Research, US Department of Energy, under Contract W-31-109-Eng-38.     

A memetic approach to construct transductive discrete support vector machines

Transductive learning involves the construction and application of prediction models to classify a fixed set of decision objects into discrete groups. It is a special case of classification analysis with important applications in web-mining, corporate planning and other areas. This paper proposes a novel transductive classifier that is based on the philosophy of discrete support vector machines. We formalize the task to estimate the class labels of decision objects as a mixed integer program. A memetic algorithm is developed to solve the mathematical program and to construct a transductive support vector machine classifier, respectively. Empirical experiments on synthetic and real-world data evidence the effectiveness of the new approach and demonstrate that it identifies high quality solutions in short time. Furthermore, the results suggest that the class predictions following from the memetic algorithm are significantly more accurate than the predictions of a CPLEX-based reference classifier. Comparisons to other transductive and inductive classifiers provide further support for our approach and suggest that it performs competitive with respect to several benchmarks.     

Chemical causes of the typical burnt smell after accidental fires

The components responsible for the typical burnt smell that occurs after accidental fires (e.g. in buildings) were identified. For this purpose, samples of odorous materials were taken from different real fire sites. Their volatile fractions were analysed by means of thermal desorption, headspace analysis and solid-phase microextraction (SPME) combined with gas chromatography–mass spectrometry (GC/MS). Measurements performed with SPME gave the highest number of analytes as well as the highest signal intensities. A divinylbenzene/carboxen/polydimethylsiloxane SPME fibre was found to be the most suitable for this task. To distinguish the odour-active compounds from the ca. 1,400 identified volatiles concentrated by SPME, an olfactory detection port was attached to the GC/MS and the column effluent was assessed by panellists. The results revealed that eleven odorous compounds were present in most of the investigated samples: acetophenone, benzyl alcohol, 4-ethyl-2-methoxyphenol, 2-hydroxybenzaldehyde, 2-hydroxy-5-methylbenzldehyde, 2-methoxyphenol, 2-methoxy-4-methylphenol, 2-methylphenol, 3-methylphenol, 4-methylphenol and naphthalene. Their odour activities were confirmed in additional olfactory experiments, and the relative ratios of these eleven compounds were determined. Based on these ratios, standard solutions that presented an intense odour with typical characteristics of the burnt smell were produced.     

Chiral homoenolate equivalents. I. Asymmetric synthesis of β-substituted aldehydes via metalated chiral allylamines

Metalated chiral allylamines of type 2 (M = Li, K) are used as chiral homoenolate equivalents and allow after alkylation and acidic hydrolysis asymmetric CC bond formations to β-substituted aldehydes in enantiomeric excesses up to 67%.