$\Phi $-functions for complex 2D-objects

Within two-dimensional cutting and packing problems with irregular shaped objects, the concept of -functions has been proven to be very helpful for several solution approaches. In order to construct such -functions a previous work, in which so-called primary objects are considered, is continued. Now -functions are constructed for pairs of objects which can be represented as a finite combination (union, intersection, complement) of primary objects which allows the handling of arbitrary shaped objects by appropriate approximations of sufficient accuracy.Received: October 2002, Revised: October 2003, AMS classification: 65K05, 90C26, 90B06All correspondence to: Guntram Scheithauer     

On nonoscillating integrals for computing inhomogeneous Airy functions

Integral representations are considered of solutions of the inhomogeneous Airy differential equation . The solutions of these equations are also known as Scorer functions. Certain functional relations for these functions are used to confine the discussion to one function and to a certain sector in the complex plane. By using steepest descent methods from asymptotics, the standard integral representations of the Scorer functions are modified in order to obtain nonoscillating integrals for complex values of . In this way stable representations for numerical evaluations of the functions are obtained. The methods are illustrated with numerical results.

     

Spectral editing of 13C cp/MAS NMR spectra of complex systems: application to the structural characterisation of cork cell walls

A mathematical method of obtaining 13C CP/MAS subspectra of single components of a complex system is presented and applied to three- and four-component systems. The method is based on previously reported work that exploits different proton relaxation properties for different domains of an heterogeneous system. However, unlike the original method that obtained subspectra through a trial-and-error approach, the method here presented solves the problem mathematically, thus avoiding the time-consuming and non-rigorous trial-and-error step. The method is applied to mixtures of three and four polymers and to a more complex system: cork cell walls. As expected, as the number of components increases, the sharing of relaxation properties between different components is increasingly probable, either due to incidental coincidence of relaxation times or to specific interactions and intimate mixing of compounds. While this hinders the calculation of the subspectra of single chemical components, it may provide useful information about inter-component interactions. This possibility was demonstrated by the application of this method to cork cell walls. Both three-component and four-component approaches showed that three domains exist in cork cell walls: carbohydrate/lignin matrix, mobile suberin close to (probably bonded to) lignin groups (about 42% w/w) and hindered suberin close to (probably bonded to) carbohydrate-OCH2O groups (about 4% w/w).     

An evaluation of the growth of nitrides on semipolar substrates using two indicators

We evaluate the properties of nitride heterostructures on semipolar substrates using two indicators: the cancellation of the Quantum Confined Stark Effect and the volume density of elastic energy stored in the strained layers of GaN–GaInN heterostructures lattice‐matched to (hkl)‐oriented GaN semipolar substrates. These two parameters indicate that the growth on specific orientations is a plus when compared to growth on (0001) polar substrates. We will show that, unfortunately, one cannot simultaneously minimize the stored elastic energy and cancel the Quantum Confined Stark Effect, but it is possible to significantly reduce both of them. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Time-resolved spectroscopy of excitonic transitions in ZnO/(Zn, Mg)O quantum wells

We report on the optical spectroscopy of a series of ZnO/(Zn, Mg)O quantum wells of different widths, using time-resolved photoluminescence. The samples were grown by molecular beam epitaxy on ZnO templates, themselves deposited on sapphire substrates. The barriers consist of Zn_0.78Mg_0.22O layers. The presence of large internal electric fields in these quantum wells results in a competition between quantum confinement and the quantum confined Stark effect as the quantum well width is varied. A transition energy lying 0.5 eV below the ZnO excitonic gap was observed for the widest of our wells. The PL spectra of the wide quantum wells were obtained using time-integrated photoluminescence, taking a great care with screening effects induced by their very slow dynamics. The effect of the built-in electric field on the excitonic properties was investigated. The excitonic fine structure is shown to depend strongly on the enhancement or suppression of the exchange interaction as a function of the quantum well width.     

Short range order in the isotropic phase of antiferroelectric liquid crystals

Optical activity measurements in the isotropic phase of two antiferroelectric liquid crystal systems in which the chirality can be varied reveal unusual behaviour of the short range order. In one system the phase sequence as the chirality is increased is smectic A, smectic C^*_A, and smectic Q. In the other system the phase sequence is smectic C^*, smectic C^*_A, and smectic Q as the chirality is increased. The short range order of the isotropic phase behaves similarly for these systems, showing mean field behaviour at low chirality and far above the phase transition, but deviating from this behaviour significantly as the chirality is increased and the phase transition is approached. These optical activity results indicate how different is the short range order in the isotropic phase for these antiferroelectric liquid crystal systems and demonstrates the crucial role played by chirality. Past theoretical work that includes smecticlike fluctuations in the calculation of short range order in the isotropic phase is capable of qualitatively explaining these results.     

Vibrations of the phenoxyl radical.

Phenoxyl radical (C(6)H(5)O) was prepared photochemically in low-temperature argon matrices. The infrared absorption spectra were obtained for C(6)H(5)O and for the isotopically labeled species C(6)D(5)O and 1-(13)C(12)C(5)H(5)O. All but one IR-active fundamental vibrations were detected, most of them not previously observed. Combination of results from IR linear dichroism measurements on photooriented samples, determination of absolute IR intensities with the help of internal standards, analysis of isotopic shifts, and quantum chemical predictions (B3LYP/cc-pVTZ) led to a detailed assignment of phenoxyl radical vibrations. Significant frequency shifts are observed with respect to previously reported data based on resonance Raman studies in polar solutions. For some vibrations, these shifts reflect environment-induced structural changes, such as increase of the quinoid character of the phenoxyl radical in polar media. In particular, the frequency of the CO stretching vibration, readily observable in both IR and Raman experiments, is extremely sensitive to the environment and can thus be used to probe its polarity.     

An approach to the synthesis of furanoheliangolides through Diels-Alder reactions

The core structure of the natural sesquiterpene lactones furanoheliangolides, an 11-oxabicyclo[6.2.1]undecane system, was synthesized through a pathway involving two Diels-Alder reactions.     

Metabisulfite interference in biosensing and Folin-Ciocalteu analysis of polyphenols

Sodium metabisulfite is one of the forms of sulphurous compounds which are added as preservative in food and beverage processing industries. Its interference with different methods of analysis of polyphenols was investigated in the present work. Studies involved the reaction of metabisulfite at platinum electrodes either at a constant applied potential of +100 mV vs. Ag/AgCl electrode with amperometric detection, or at linear potential sweep in cyclic voltammetry experiments. In a second stage, its effect on the analysis of polyphenols that are oxidised by enzymes was examined by the inhibition that metabisulfite caused on caffeic acid oxidation in the presence of free and immobilized laccase. It was found that immobilized laccase was less inhibited than free laccase. A confirmation of the influence of metabisulfite on the Folin-Ciocalteu analysis was also done.     

Resolvents of cone pseudodifferential operators,asymptotic expansions and applications

We study the structure and asymptotic behavior of the resolvent of elliptic cone pseudodifferential operators acting on weighted Sobolev spaces over a compact manifold with boundary. We obtain an asymptotic expansion of the resolvent as the spectral parameter tends to infinity, and use it to derive corresponding heat trace and zeta function expansions as well as an analytic index formula.