Eine Bemerkung zum Axiomensystem des Morgenstern/Thompson-Außenhandelsmodells

Zusammenfassung Es kann gezeigt werden, daß sich im Außenhandelsmodell vonMorgenstern/ Thompson gewisse Aussagen nicht unbedingt als Resultate aus dem vorgeschlagenen Axiomensystem ergeben. Werden diese Aussagen in das Axiomensystem aufgenommen, so bleibt das System unabhängig.

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Summary In the Open Expanding Economy Model ofMorgenstern/Thompson it can be shown that some of the statements do not follow from the axioms. Adding these statements to the given system of axioms the new system is still independent.

     

Save — A general approach for calculating the spectral properties of solids

A new scheme is proposed for computation of the real and imaginary parts of the spectral functions of solids, including the density of states and wavenumber dependent susceptibility. Improvements over previous schemes result from analytic integration over small spherical cells with quadratic expansion of energy denominators.     

Understanding Refractive Index Changes in Homologous Series of Unbranched Organic Compounds Based on Beer's Law

Changes of the refractive index for homologous series of hydrocarbons are usually plotted versus the density. While there is a clear linear dependence for alkanes and alkenes, the linearity deteriorates for homologous series with functional groups involving heteroatoms. The slope can even become negative, e. g., for carboxylic acids. For gaining a deeper understanding and to establish a more general correlation, we reinvestigate the corresponding theories starting with the Newton-Laplace, Gladstone-Dale and the Lorentz-Lorenz rules. We revisit the concept of molar refractivity pioneered by Landolt and Brühl and show that it is closely connected with a twin of Beer's law. We conclude that the refractive index of homologues series should better be plotted versus the molar concentration of the main UV-chromophore, the C−H bond, which actually causes the refractive index changes. This new approach is not limited to alkanes and alkenes but holds for homologous series with functional groups including heteroatoms.     

Preparation,Crystal Structures,and Thermal Studies of Alkaline Earth Nitrocarboxylates

The preparation, crystal structures, and thermal properties of [Ca(pyr)₂(4‐nba)₂]_n ( 1 ) (pyr = pyrazole; 4‐nba = 4‐nitrobenzoate) {[Ca(H₂O)₂(3‐npth)] · H₂O}_n ( 2 ) (3‐npth = 3‐nitrophthalate), [Mg(H₂O)₅(3‐npth)] · 2H₂O ( 3 ), and [Mg(H₂O)₄(2‐nba)₂] ( 4 ) (2‐nba = 2‐nitrobenzoate) are reported. The anhydrous Ca^II compound 1 and the diaqua Ca^II‐3‐nitrophthalate monohydrate 2 are one‐dimensional coordination polymers containing a hexacoordinate Ca^II ion located on a center of inversion in 1 and a heptacoordinated Ca^II ion in 2 . In 1 , the 4‐nitrobenzoate moiety acts as a μ₂‐bridging bidentate ligand, whereas the 3‐nitrophthalate anion exhibits a μ₃‐bridging pentadentate coordination mode in 2 . The hexacoordinate Mg^II‐containing compounds 3 and 4 do not contain a [Mg(H₂O)₆]²⁺ unit and the central Mg^II ion is coordinated to at least one monodentate carboxylate unit namely the monodentate 3‐npth molecule in 3 and two trans monodentate 2‐nba molecules in 4 . Hydrogen bonding between the lattice water molecules results in the formation of a water dimer in 3 . A comparative study of 17 alkaline earth nitrocarboxylates is described.     

Synthesis and Crystal Structure of Tellurium(II) bis(2‐methoxycarbonylethanethiolate): A Novel Coordination Mode of Tellurium

The tellurium(II) dithiolates Te[SCH₂CH₂C(O)OCH₃]₂, ( 1 ), Te[SCH₂CH₂CH₂SC(O)CH₃]₂, ( 2 ), and Te[SCH₂CH₂CH₂CH₂SC(O)CH₃]₂, ( 3 ) were synthesized from Te(S^tBu)₂ and the corresponding thiol. All compounds are sensitive toward higher temperatures and light and decompose to elemental tellurium and the disulfide. In the solid state, the Te atom of 1 exhibits the novel Te(S₂Te₂) coordination mode. Additionally to the two Te—S bonds, each Te atom forms two long Te···Te contacts to neighboring molecules, leading to a coordination number of four and a distorted sawhorse configuration. No intramolecular Te···O interactions are present in the solid state, in accordance with ab initio calculations (MP2/ecp‐basis) for the isolated molecule. ¹²⁵Te NMR shifts of all compounds lay within a narrow range and close to the respective shift of other Te(SCH₂R)₂ compounds. VT ¹²⁵Te NMR spectra gave no hint to donor acceptor interactions in solution for any of the compounds and thus corroborate results from IR‐spectroscopy, ab initio geometry optimizations, and thermochemical calculations.     

Monitoring the Reversibility of GPCR Signaling by Combining Photochromic Ligands with Label-free Impedance Analysis

G protein-coupled cell surface receptors (GPCR) trigger complex intracellular signaling cascades upon agonist binding. Classic pharmacological assays provide information about binding affinities, activation or blockade at different stages of the signaling cascade, but real time dynamics and reversibility of these processes remain often disguised. We show that combining photochromic NPY receptor ligands, which can be toggled in their receptor activation ability by irradiation with light of different wavelengths, with whole cell label-free impedance assays allows observing the cell response to receptor activation and its reversibility over time. The concept demonstrated on NPY receptors may be well applicable to many other GPCRs providing a deeper insight into the time course of intracellular signaling processes.