A 13-membered crown ether with an azoxy subunit in the macrocycle: Synthesis and X-ray structure

The presented azoxy compound is an example of a new crown ether analogue. It has been synthesized by the reduction of an open chain dinitro compound with stannite under strongly alkaline conditions. A method for the separation of the azo and azoxy compounds formed simultaneously has been proposed. The structures of two crystallographically independent molecules of compound2 have been determined. In spite of the small size of the macroring in compound2, the phenyl residues around the azoxy group have atrans orientation. Supplementary Data relating to this article have been deposited with the British Library as Supplementary Publication No. 82157 (11 pages).     

Structural and physical properties of Mg3−xZnxSb2 (x=0-1.34)

The Mg_3−xZn_xSb₂ phases with x=0-1.34 were prepared by direct reactions of the elements in tantalum tubes. According to the X-ray single crystal and powder diffraction, the Mg_3−xZn_xSb₂ phases crystallize in the same P3¯m1 space group as the parent Mg₃Sb₂ phase. The Mg_3−xZn_xSb₂ structure is different from the other substituted structures of Mg₃Sb₂, such as (Ca, Sr, Ba) Mg₂Sb₂ or Mg_5.23Sm_0.77Sb₄, in a way that in Mg_3−xZn_xSb₂ the Mg atoms on the tetrahedral sites are replaced, while in the other structures Mg on the octahedral sites is replaced. Thermoelectric performance for the two members of the series, Mg₃Sb₂ and Mg_2.36Zn_0.64Sb₂, was evaluated from low to room temperatures through resistivity, Seebeck coefficient and thermal conductivity measurements. In contrast to Mg₃Sb₂ which is a semiconductor, Mg_2.36Zn_0.64Sb₂ is metallic and exhibits an 18-times larger dimensionless figure-of-merit, ZT, at room temperature. However, thermoelectric performance of Mg_2.36Zn_0.64Sb₂ is still poor and it is mostly due to its large electrical resistivity.     

Hubble Law: Measure and Interpretation

We have had the chance to live through a fascinating revolution in measuring the fundamental empirical cosmological Hubble law. The key progress is analysed: (1) improvement of observational means (ground-based radio and optical observations, space missions); (2) understanding of the biases that affect both distant and local determinations of the Hubble constant; (3) new theoretical and observational results. These circumstances encourage us to take a critical look at some facts and ideas related to the cosmological red-shift. This is important because we are probably on the eve of a new understanding of our Universe, heralded by the need to interpret some cosmological key observations in terms of unknown processes and substances.     

Some generalizations of the classical moment problem

The article is devoted to two generalizations of the classical power moment problem, namely: 1) instead of representing the moment sequence by ⁿ , a representation by polynomialsP _n (), ¹, connected with a Jacobi matrix, appears; 2) in the representation, instead of ⁿ , the expression ⁿ figures, where is a real generalized function (i.e., we investigate some infinite-dimensional moment problem).The work is partially supported by the DFG, Project 436 UKR 113/39/0 and by the CRDF, Project UM1-2090.     

$\Phi $-functions for complex 2D-objects

Within two-dimensional cutting and packing problems with irregular shaped objects, the concept of -functions has been proven to be very helpful for several solution approaches. In order to construct such -functions a previous work, in which so-called primary objects are considered, is continued. Now -functions are constructed for pairs of objects which can be represented as a finite combination (union, intersection, complement) of primary objects which allows the handling of arbitrary shaped objects by appropriate approximations of sufficient accuracy.Received: October 2002, Revised: October 2003, AMS classification: 65K05, 90C26, 90B06All correspondence to: Guntram Scheithauer     

Image of the Spectral Measure of a Jacobi Field and the Corresponding Operators

By definition, a Jacobi field is a family of commuting selfadjoint three-diagonal operators in the Fock space The operators J(ϕ) are indexed by the vectors of a real Hilbert space H₊. The spectral measure ρ of the field J is defined on the space H₋ of functionals over H₊. The image of the measure ρ under a mapping is a probability measure ρ_K on T₋. We obtain a family J_K of operators whose spectral measure is equal to ρ_K. We also obtain the chaotic decomposition for the space L²(T₋, d_{ρ K}).     

Synthesis and biological evaluation of some new class of benzothiazole–pyrazole ligands containing arene ruthenium,rhodium and iridium complexes

Transition Metal Chemistry - Metal complexes 1–9 have been synthesized by reacting the benzothiazole–pyrazole derivative ligands (L1, L2 and L3) with the metal precursors of ruthenium...