Asymptotic expansion of the logistic midrange

Using the symbolic computation program MAPLE, we compute several terms of an asymptotic expansion for the distribution function of the logistic midrange.     

Isotrope Unterräume rationaler quadratischer Formen

Ohne ZusammenfassungDiese Arbeit wurde während eines Aufenthaltes von Schmidt in der Bundesrepublik Deutschland als Preisträger der Alexander von Humboldt-Stiftung geschrieben.     

Synthesis of cationic molybdenum and cobalt diene complexes from neutral allyl compounds by ligand exchange in a strong protic acid

Conclusions The allyl ligand in neutral molybdenum and cobalt complexes is readily exchanged by dienes in the presence of a strong protic acid with the formation of cationic complexes. This exchange is facilitated by an increase in the basicity of the starting compounds.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 7, pp. 1655–1657, July, 1987.     

Dual Characterizations of Set Containments with Strict Convex Inequalities

Characterizations of the containment of a convex set either in an arbitrary convex set or in the complement of a finite union of convex sets (i.e., the set, described by reverse-convex inequalities) are given. These characterizations provide ways of verifying the containments either by comparing their corresponding dual cones or by checking the consistency of suitable associated systems. The convex sets considered in this paper are the solution sets of an arbitrary number of convex inequalities, which can be either weak or strict inequalities. Particular cases of dual characterizations of set containments have played key roles in solving large scale knowledge-based data classification problems where they are used to describe the containments as inequality constraints in optimization problems. The idea of evenly convex set (intersection of open half spaces), which was introduced by W. Fenchel in 1952, is used to derive the dual conditions, characterizing the set containments.     

Morphological and electronic properties of the thin film phase of pentacene investigated by AFM and STM/STS

We investigated the morphological, structural and electronic properties of Pentacene thin films grown by vacuum thermal evaporation on different inert substrates at room temperature. The results of our AFM and STM analysis give an interplanar spacing of 1.54 nm corresponding to the (0 0 1) distance of the so-called “thin film phase”. The STS measurements show an HOMO-LUMO gap of 2.2 eV.     

Study on the possibilities of controlling the laser output beam properties by an intracavity deformable mirror

The possibilities of controlling the laser beam properties by a deformable mirror introduced into the laser optical cavity were studied theoretically and experimentally. The experiments were performed under conditions of an industrial high power transverse flow cw CO₂ laser operating with a stable resonator of a folded configuration. A deformable bimorph mirror of a surface profile controlled by the voltage applied to the mirror electrodes is implemented to the laser system as a back cavity mirror or as a one of the inner folding mirrors. The near-and far-field characteristics of the laser beam versus the resonator configuration controlled by the changes of the focal length of the deformable mirror are discussed in the paper. The analysis reveals that the resonator with an inner deformable mirror is much more sensitive to the mirror curvature variations than the resonator in which the deformable mirror is used as a back cavity mirror. The presented results show that dynamic and controllable changes in the resonator properties result in the controlled modification and optimisation of the laser output power and spatial parameters of the laser radiation.