Cycloaddition of Carbodiimides with a Heteroaromatic Substituent to Allenic Acids

Cycloaddition of the allenic acid 3 with the N -cyclohexyl-N′ -heteroaromatic carbodiimides 2a and 2b gave the isomeric pyrido[1,2-a]pyrimidinones 4 and 5 and thiazolo[3,2-a]pyrimidinones 6 and 7 , respectively, instead of the expected Diels-Alder adducts analogous to 1 . The compounds of the latter type, i.e. 8 and 9 , were formed from 3 and carbodiimides 2c and 2d , respectively, containing an N′-(pyrazin-2-yl) or N′-(pyrimidin-2-yl) substituent.     

A general Hungarian method for the algebraic transportation problem

In this paper the algebraic transportation problem is introduced which covers besides the Hitchcock and the time transportation problem several other types of transportation problems of practical relevance. To solve this algebraic transportation problem admissible transformations are considered and characterized. Thereupon a transformation algorithm is described which is a generalization of the Hungarian method for the classical transportation problem as well as of a threshold method for time transportation problems.     

Efficiency and Optimality in Minisum,Minimax 0-1 Programming Problems

Inspired by an increasing interest in multicriteria 0-1 programming problems in general and by a recent result on the reducibility of minimax to minisum problems in particular, we consider properties of efficient and optimal solutions to two-criteria (minisum and minimax) 0-1 programming problems with any constraint set.A solution procedure is suggested for solving problems whose objective functions are a convex combination of these criteria. The solution properties are illustrated with examples mainly within the context of locational decision problems.     

Elementary constructions of locally compact affine planes

In this paper we describe several elementary constructions of 4-, 8- and 16-dimensional locally compact affine planes. The new planes share many properties with the classical ones and are very easy to handle. Among the new planes we find translation planes, planes that are constructed by gluing together two halves of different translation planes, 4-dimensional shift planes, etc. We discuss various applications of our constructions, e.g. the construction of 8- and 16-dimensional affine planes with a point-transitive collineation group which are neither translation planes nor dual translation planes, the proof that a 2-dimensional affine plane that can be coordinatized by a linear ternary field with continuous ternary operation can be embedded in 4-, 8- and 16-dimensional planes, the construction of 4-dimensional non-classical planes that admit at the same time orthogonal and non-orthogonal polarities. We also consider which of our planes have tangent translation planes in all their points. In a final section we generalize the Knarr-Weigand criterion for topological ternary fields.This research was supported by a Feodor Lynen fellowship.     

Comparison of bacterial and phage display peptide libraries in search of target-binding motif

Genetic engineering allows modification of bacterial and bacteriophage genes, which code for surface proteins, enabling display of random peptides on the surface of these microbial vectors. Biologic peptide libraries thus formed are used for high-throughput screening of clones bearing peptides with high affinity for target proteins. There are reports of many successful affinity selections performed with phage display libraries and substantially fewer cases describing the use of bacterial display systems. In theory, bacterial display has some advantages over phage display, but the two systems have never been experimentally compared. We tested both techniques in selecting streptavidin-binding peptides from two commercially available libraries. Under similar conditions, selection of phage-displayed peptides to model protein streptavidin proved convincingly better.     

Shape coexistence and other aspects of nuclear structure in40Ar

Theγ-decay of⁴⁰Ar has been studied by particle-γ-ray coincidence measurements in the³⁷Cl(α, pγ) reaction at 12 and 13 MeV bombarding energy. Particle-γ-ray angular correlations and linear polarizations ofγ-rays were measured at 12 MeV. A lifetime measurement using the Doppler-shift attenuation method was performed at 11 MeV. The coexistence of spherical and deformed states in⁴⁰Ar could be concluded from the observation of aK ^π=0⁺ rotational band which has itsI ^π=0⁺ through 6⁺ members at 2,121, 2,524, 3,515 and 4,959 KeV excitation energy. The intrinsic quadrupole moment derived fromB(E2) values is ∥Q ₀∥=1,320 _?120 ⁺⁶⁰ mb. Negative-parity states with high spin were observed at 4,858(5^?), 4,494(5^?), 4,226(4^?) and 4,991 KeV(4^?) excitation energy. A complete account of all levels below 5 MeV excitation energy is obtained by a model in which twod _3/2 proton holes couple weakly to the⁴²Ca levels below 4.75 MeV excitation energy.     

Synthesis of Aristotelia-type alkaloids. Part V. Biomimetic synthesis of (±)-aristomakine and (±)-aristomakinine

Biomimetic syntheses of racemic aristomakinine ((±)- 3 ) and aristomakine ((±)- 4 ), an unusual indole alkaloid bearing an N-isopropyl group, are described. The key step is a Grob-type fragmentation of anti-15-aristotelinyl methanesulfonate ((±)- 2 ) to the intermediate iminium ion I which, upon subsequent hydrolysis, furnished aristomakinine ((±)- 3 ). On the other hand, the same intermediate could be reduced in situ to aristomakine ((±)- 4 ). The controversial relative configurations of the two alkaloids have been firmly established by means of NOE difference experiments.     

The vibrations of formaldehyde

A new six-dimensional variational code is presented for the determination of the vibrational energy levels of four-atom molecules which are either linearly connected or centrally connected. Internal (displacement) coordinates are used. It is demonstrated for the CCSD(T) surface of formaldehyde, due to Martin, Lee and Taylor, and it is shown that a small scaling of the force constants leads to a high-accuracy surface.     

On n‐dependent groups and fields

First, an example of a 2‐dependent group without a minimal subgroup of bounded index is given. Second, all infinite n‐dependent fields are shown to be Artin‐Schreier closed. Furthermore, the theory of any non separably closed PAC field has the IP_n property for all natural numbers n and certain properties of dependent (NIP) valued fields extend to the n‐dependent context.