Ordinary differential equations and their exponentials

In the context of Synthetic Differential Geometry, we discuss vector fields/ordinary differential equations as actions; in particular, we exploit function space formation (exponential spaces) in the category of actions.     

Synthesis of 2,3-Dihydrothiazolo[3,2-a]pyrimidin-5-ones by a Michael-type Tandem Reaction

Although various thiazoles are known in literature for their biological and pharmacological properties only a few multi-step synthesis pathways for the preparation of thiazolo[3,2-a]pyrimidinones have been reported, which are tedious and time-consuming. An alternative synthesis pathway is described, which allows the preparation of 2,3-dihydrothiazolo[3,2-a]pyrimidin-5-ones in a one-step process based on a Michael-type tandem reaction. By heating of 2-thiobarbituric acid with ethyl 4-bromocrotonate in ethanol at 60°C for 2 h, a 2,3-dihydrothiazolo[3,2-a]pyrimidin-5-one was obtained in 73% yield, whereas carrying out the reaction at room temperature results in the formation of an unstable unsaturated ester. The structures of both, the α,β-unsaturated ester as well as the 2,3-dihydrothiazolo[3,2-a]pyrimidin-5-one were confirmed by NMR spectroscopy. Additionally, the structure of the 2,3-dihydrothiazolo[3,2-a]pyrimidin-5-one was investigated by single-crystal X-ray analysis. The described approach offers a significant improvement over previously reported synthesis pathways because it allows the simple preparation of 2,3-dihydrothiazolo[3,2-a]pyrimidin-5-ones with good yields in a one-step reaction.     

Three-dimensional woodpile photonic crystal templates for the infrared spectral range

High-quality templates of three-dimensional woodpile photonic crystals are fabricated in photoresist SU-8 by use of femtosecond laser lithography. The samples have smooth surfaces, are mechanically stable, and are resistant to degradation under environmental and chemical influences. Fundamental and higher-order photonic stopgaps are identified in the wavelength range 2.0-8.0 microm. These templates can be used for subsequent infiltration by optically active or high-refractive-index materials.     

Multi-Mix Feedstock Problems on Microcomputers

The solution of the large linear-programming problems encountered by feed-mix companies and cooperatives when they use optimization to formulate their different blends from common stocks of raw materials poses a big problem for these organizations. The present approach of using mainframe computers to solve these problems proves to be either expensive or, in some cases, very time-consuming. This paper describes a solution approach based on the decomposition of the large problems, and its implementation on microcomputers.     

The calculation of logft values and spectroscopic factors for nuclei in the mass range 10–15

Wave functions obtained in previous shell-model calculations [1, 2] for states of nuclei with massesA=10–15 are used to calculate logft values and spectroscopic factors. These wave functions, which were based on a modified surface delta two-body interaction, comprise the following active shell-model spaces: the 1p _3/2 and 1p _1/2 orbitals for mass 10–14 nuclei and restricted combinations of the 1p _1/2, 2s _1/2, 1d _5/2 and 1d _3/2 orbitals for mass 15 nuclei, leading to four different calculations in the latter case. The calculated results support evidence that the modified surface delta interaction is a valid approximation to the effective interaction in light nuclei.     

Parallel and time sequential optical multiplex systems for pattern recognition

Two optical multiplex arrangements for pattern recognition are compared. In the first system the Fourier spectrum of an object transparency is optically multiplied for parallel processing with a matrix of different holographic Fourier filters. In the other arrangement the spectrum of the object transparency is switched time sequentially by means of a light beam deflector onto different filters in the Fourier plane. In comparison the time sequential method appears better adapted for high information content.     

Notiz über den Chloraufschluß niobhaltiger Substanzen

In an investigation on the decomposition of oxide minerals containing Ti, Nb, Fe, U and Y mixtures of TiO₂, Nb₂O₅, Fe₂O₃, U₃O₈ and Y₂O₃ have been heated in streaming Cl₂ containing SOCl₂. In order to avoid the formation of NbOCl₃, which is highly disturbing the distribution pattern of the chlorides, the reaction boat was covered with carbon powder. TiCl₄ was absorbed in sulphuric acid; NbCl₅, FeCl₃ and UCl₄ were condensed in the reaction tube and were separated by usual methods; YCl₃ remained in the reaction boat.