Structural reliability and stochastic structural optimization

Mathematical Methods of Operations Research -     

Quantum confinement in layer-by-layer deposited colloidal HgTe nanocrystals determined by spectroscopic ellipsometry

We report spectroscopic ellipsometry studies in the energy range of 0.5-5 eV on samples of 1-10 bilayers of polymer and HgTe nanocrystals, which exhibit strong transitions at higher critical points in the dispersion relation. We show that the dispersion relation for nanocrystals can be modelled with the same concepts for critical points as used in semiconductor bulk optics. We find an energy shift of up to 0.4 eV of the critical points to higher energies compared to the HgTe bulk properties, caused by quantum confinement in the nanocrystals, which increases with decreasing nanocrystal size.     

Eine ErweiterungT(V′) des Ordinalzahlensystems 58-0158-0158-01(Λ0) von G. Jäger

Summary This paper gives a recursive generalization of a strong notation system of ordinals, which was devellopped by Jäger [3]. The generalized systemT(V) is based on a hierarchy of Veblen-functions for inaccessible ordinals. The definition ofT(V) assumes the existence of a weak Mahlo-ordinal. The wellordering ofT(V) is provable in a formal system of second order arithmetic with the axiom schema of ₂ ¹ -comprehension in a similar way, as it is proved in [6] for the weaker notation systemT(V).     

A Highly Stereoselective Synthesis of C(11)-Functionalized Aromatic Steroids by an Intramolecular Benzocyclobutene-Olefin -Cycloaddition. Preliminary Communication

The racemic cis-anti-trans-steroids 9 to 11 have been synthesized in a highly stereoselective manner starting from 4-methoxybenzocyclobutene carboxylic acid via the key step 8 → 9 . (cf. Scheme 2).     

Ein v. Staudt-Clausenscher Satz für periodische Bernoullizahlen

Letk, n be relatively prime integers, 1k<n. The numbersB _k ^m =m(i/2) ^m cot^(m–1)(k/n),m2, belong to then-th cyclotomic field. They occur as values of certain simple Dirichlet series at integral arguments and have a natural interpretation as generalized Bernoulli numbers. Therefore the arithmetic properties of these numbers arouse some interest. Ifn is not a prime power,B _k ^m /m is an algebraic integer. In the other case, i.e.n=p ^e ,p prime, the fractional part ofB _k ^m /m resp.B _k ^m is determined in this paper. It is periodic modulop–1 and exhibits a connection between these Bernoulli numbers and the Stirling numbers of the second kind.     

Arbeiten über Phosphorsäure und Thiophosphorsäureester mit einem heterocyclischen Substituenten 9. Mitteilung 1. Aza-Analogie I: Aza-Analoge von Phthalimid-, Benztriazol- und 1,2,3-Benztriazin-4(3H)-on-Derivaten

Aza-analogues of the known pesticidal dithiophosphates 2, 4 and 5 have been prepared by replacing the phthalimide, benzotriazole and 1,2,3-benzotriazin-4(3H)-one moieties resp. in 2 by those of quinolinic acid imide (6), cinchomeronic acid imide (7) and pyrazine-2,3-dicarboxylic acid imide (12), in 4 by 1H-v-triazolo[4,5-b]pyridine (15) and in 5 by pyrido[2,3-e]1,2,3-triazin-4(3H)-one (21). Compared to the known compounds the new esters are less or at best equally pesticidal with an equal or even higher mammalian toxicity.     

α,ω-Diisocyanatocarbodiimides, -Polycarbodiimides,and Their Derivatives

Research in the field of low-molecular weight, oligomeric and polymeric α,ω-diisocyanatocarbodiimides and -polycarbodiimides has been fruitful, not only in connection with these compounds themselves, but also—as so often happens in chemistry—with quite different problems. Novel synthetic methods, discoveries concerning the properties of low-molecular weight carbodiimides and phosphane imide derivatives, as well as results on the fragmentation reactions of four-membered heterocyclic compounds containing oxygen, phosphorus, and nitrogen, and a better understanding of the diisocyanate polyaddition process are among the many by-products of this research. The “high- and low-temperature formation” of polycarbodiimides and the homogeneous and heterogeneous catalysis of this process are described, and the fundamental importance of four-membered ring fragmentation mechanisms resulting in the formation of phosphane imide derivatives is outlined. Interesting building blocks for the diisocyanate polyaddition and polycondensation processes can be synthesized by many derivatization reactions of oligomeric and high-molecular weight polycarbodiimides and polyuretonimines. The in situ production of polycarbodiimides via matrix reactions in flexible polyurethane foams leads to a cellular arrangement of the material due to the pronounced symmetrical growth processes. Combination-foams with increased carbonation tendencies are formed in this way. Attention is drawn to several industrial applications of α,ω-diisocyanatopolycarbodiimides, of high-molecular weight cross-linked polyuretonimines, and of polycarbodiimide foams.     

Fluordiazadiphosphetidine, 11. Mitt.: Eine neue Methode zur Herstellung der doppelt zwitterionischen Verbindung (CH3N)6P4F8

A new synthetic route for the preparation of the betain-like compound (CH₃N)₆P₄F₈ from (CH₃NPF₃)₂,N-methyl-hexamethyldisilazane andN,N-dimethyl-urea has been found. The steps of this multi-stage reaction could be rationalized to a far extent.

10. Mitteilung:Kubjacek M., Utvary K., Mh. Chem.112, 305 (1981).     

The Synthesis of 4b, 5, 12, 12a-Tetrahydro-5, 12-ethano-13H-indeno[2,3-b]anthracenes, 4b, 5, 10, 10a - tetrahydro-5,10-ethano-11H-indeno[2,3-b]naphtalenes and 1,2,3,4,4a, 9a-Hexahydro-1,4-(peri-naphthaleno)-fluorenes

The synthesis of endo- and exo-13-oxo-4b, 5, 12, 12a-tetrahydro-5, 12-ethanoindeno[2,3-b]anthracene ( 23 ; Schemes 1 and 2), exo- and endo-11-oxo-4b, 5, 10, 10a-tetrahydro-5, 10-ethano-indeno[2,3-b]naphthalene ( 31 ; Scheme 3), 1,2,3,4,4a,9a-hexahydro?1,4-(peri-naphthaleno)-fluoren-9-one (36; Scheme 4), and the corresponding hydrocarbons of the stereoisomeric ketone pairs 23 and 36 , is described.