Convex polytopes whose projection bodies and difference sets are polars

In a paper by the author and B. Weissbach it was proved that the projection body and the difference set of ad-simplex (d≥2) are polars. Obviously, ford=2 a convex domain has this property if and only if its difference set is bounded by a so-called Radon curve. A natural question emerges about further classes of convex bodies inR ^d (d≥3) inducing the mentioned polarity. The aim of this paper is to show that a convexd-polytope (d≥3) is a simplex if and only if its projection body and its difference set are polars.     

Symmetric plasmas and their decay

Spherically symmetric global solutions are shown to exist for the relativistic Vlasov-Maxwell system of plasma physics. In view of a conjectured perturbation result concerning in particular nearly symmetric global solutions, we investigate the asymptotic properties of the symmetric solutions. In the case of only one particle species (say ions but no electrons) we get satisfactory decay estimates; in the general case (ions and electrons) we have preliminary results.Parts of this paper were written during a stay at Indiana University, Bloomington. The author gratefully acknowledges many pleasant conversations with R. Glassey     

On consistency of bounding operations in deterministic global optimization

This technical comment refers to the discussion of strong consistency of several bounding procedures in Lemma 2.1 and Proposition 2.1 of Ref. 1. A necessary clarification is given of the notion of convergence _q in Lemma 2.1, and a derivation of Proposition 2.1 is presented that includes a new and simple consistency proof of the classical bounding by convex envelopes used in many branch-and-bound procedures.     

Analysis and evolution of basic strategies in investment planning for modern flexible technologies

Investment decisions for new technologies still contain a comparatively high degree of uncertainty. For reducing this uncertainty, the author proposes a process of strategic-investment-planning that is divided into four steps. First, the technologies under consideration are classified according to their degree of novelty, their position in the life cycle und their technological characteristics. Secondly, the impact of the new technologies on the enterprise's competitive position is determined. From the technology-portfolio, introduction strategies can be derived. Finally, the calendar of technologies demonstrates how to plan for future structural changes in manufacturing technology. The presented instruments are based on empirical research conducted by the author.     

CHLORINATION OF ISOLATED CHLOROPHYLLS in vitro

Abstract— It was shown that chlorophyll a and its epimer chlorophyll a' are chlorinated and hydroxyl-ated during thin layer chromatography with silica gel plates. Hydroxylated chlorophyll a could not be chlorinated. Chlorinated and non chlorinated chlorophylls could be separated and determined by high performance liquid chromatography, because chlorophylls do not alter during this procedure. These findings support the assumption that Chi RC I is a preparation artifact. The extent of chlorination depends on chloride availability on the thin layer and on time. Chlorination and hydroyxlation do not take place under nitrogen atmosphere. The mechanism of chlorination during the thin layer chromatography procedure is discussed.     

MO-LCAO Calculations of Polymethines

Idealized polymethines are defined as conjugated chain molecules with complete bond equilization and charge alternation. A constant π-bond order along the chain with N atoms has been derived for three types of polymethines which differ by the nature of the heteroatomic end groups. Corresponding to the number of π-electrons they are termined (N + 1)π-, Nπ- or (N ? 1)π-polymethines. This classification embraces closed shell as well as open shell systems. The relations for the energy eigenvalues, coefficients and derived quantities have been obtained in closed form. The results for the different classes of polymethines are strongly related. Their molecular properties should be similar.     

Nitro- and fluoropolyformals. III. Copolyformals from mixtures of fluoro- and nitro-α,ω-diols

Polyformals of fluoro-, nitramine-, and C-nitrodiols show widely differing properties with respect to glass transition temperature, melting transition, and solubility. Polymers with desirable combinations of these properties, e.g., low T_g, high nitro content, and good solubility in polar solvents, were expected to result from acid-promoted copolycondensation of appropriate mixtures of diols with formaldehyde. A series of such condensations were carried out and the polymers obtained from binary mixtures of fluoro- and nitrodiols, different nitrodiols, and fluoro- or nitrodiols and carboranediols, were characterized by GPC, ¹H-NMR, and DSC analysis.