Numerical semigroups of maximal and almost maximal length

Communicated by R. B. McFadden     

A general procedure for obtaining wave functions obeying the virial theorem

The virial theorem for molecules is shown to have two different forms, one employing the energy gradient the other involving the Hellmann–Feynman force. While the former VT can be fulfilled by a uniform scaling of the basis set, the latter cannot be satisfied in certain basis sets, and can give unrealistic results in others. The scaling procedure is applied to molecules at nonstationary points on the potential energy surface and it is found that energy components can change substantially, especially at short bondlengths, while the change in total energy is small. The effects on molecular properties are also small.     

Pressure and temperature dependence of the electric field gradient (EFG) in CdS

Using the time differential perturbed angular correlation technique (TDPAC), the electric hyperfine interaction of¹¹¹Cd in the II-VI-semiconductor CdS was investigated. The results of the temperature and pressure dependence of the electric field gradient (EFG) are discussed. The binding energyE _b for¹¹¹In at a Cd lattice site and a Cd vacancy (¹¹¹In_Cd–V_Cd–pair) could be estimated to 340 meV±80 meV by means of an Arrhenius-Plot. The disappearance of the 79 MHz and 73 MHz frequencies under a pressure of about 30 kbar could be due to their vacancy character or to the beginning of the phase transition to rocksalt structure.     

Auger electron microscopy: An overview

The aim of Auger electron imaging is to obtain quantitative surface elemental distribution maps at high spatial resolution. The realization of this goal is complicated by many instrumental effects and by spurious data processing contributions giving rise to an image contrast unrelated to the specimen surface composition. The critical properties of scanning Auger microscopy that may cause such a false information or imaging artefacts are reviewed. Instrumental or data processing related effects appear in the case of the beam current variation, of the background slope effect, and of the use of a combined peak to background ratio. The second set of artefacts are mainly due to the significant differences between the penetration depth of the exciting primary electrons and the escape depth of the Auger electron signal. In this case the net effect is a surface elemental contrast which is dominated by the substrate or by the overlayer rather than by the surface under investigation. In addition, there are also topographical effects of the specimen under test which normally affect the Auger yield and hence the contrast in the image. Methods for the successful suppression of some of these artefacts are outlined. They are based on the creation of reference images from complementary signals acquired by additional detection channels in parallel with the Auger signal of interest.Invited lecture presented at the Seminar on Secondary Electrons in Electron Spectroscopy, Microscopy, and Microanalysis, Chlum (The Czech Republic), 21–24 September 1993.     

Industrial Applications of Mössbauer Spectroscopy

Hyperfine Interactions - The historical development of the use of Mössbauer spectroscopy in industrial applications is briefly outlined. The power of the technique for the study of...     

Size of the Detection Area of a Phase-Doppler Anemometer for reflecting and refracting particles

Measurements of particle size distributions in multi-phase flows with a phase-Doppler anemometer yield incorrect results if polydisperse particles are investigated. For weighting biased size distributions, different in situ methods, requiring the size of the detection area, are known, but all of these weighting procedures are restricted to very small measuring volumes if off-axis instrument configurations are considered. Moreover, the weighting functions have some disadvantages in the case of poor statistics in single size classes or the results are not suitable for determining the size of the detection area for particles which are larger than the beam waist. Therefore, the intention in this work was to measure the size of the detection area for different kinds of monodisperse particles, different instrument configurations and varied instrument sensitivities experimentally and to develop an improved weighting procedure that copes with the above difficulties. The application of the results obtained from the investigations with monodisperse particles to measured particle size distributions and volume flux densities of polydisperse water droplets in a spray cone of an atomizer confirms the applicability of this weighting procedure. It is still restricted to directed flows, perpendicular to the fringes.     

Dominant strategy mechanisms for contract auctions with risk aversion and moral hazard

Within the class dominant strategy incentive compatible mechanisms, we show that there exists an optimal contracting mechanism for the principal for a version of the incomplete information principal-agent problem in which several agents compete for a contract and the principal selects an agent via a contract auction. In our auction model, we assume that the principal and the agents are risk averse, and we allow for uncountably many agent types. We also assume that the principal's probability measure over type profiles in such that correlation between agent's types is possible. Thus, we do not require that agents' types be independently distributed. Finally, we impose limited liability constraints upon the set of contracts. Due to the nature of the individual rationality and incentive compatibility constraints, the existence problem is nonstandard and novel existence arguments are required. We prove existence using a measurable selection result and a new notion of compactness called K-compactness.