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1.
Divisible effect algebras and their relations to convex effect algebras and MV-algebras are studied. A categorical equivalence between divisible effect algebras and rational vector spaces is proved. Infinitesimal, sharp and extremal elements in divisible effect algebras are studied and their relations to properties of the state space are shown.  相似文献   
2.
Tensor products of quantum logics and effect algebras with some known problems are reviewed. It is noticed that although tensor products of effect algebras having at least one state exist, in the category of complex Hilbert space effect algebras similar problems as with tensor products of projection lattices occur. Nevertheless, if one of the two coupled physical systems is classical, tensor product exists and can be considered as a Boolean power. Some applications of tensor products (in the form of Boolean powers) to quantum measurements are reviewed.  相似文献   
3.
Application of graph-theoretic methods to new perimeter polynomials for connected clusters on a lattice yields extra data on the total number of clusters and for the coefficients in the series expansion for the mean size of clusters at low densities. The lattices studied are the square, the square with next nearest neighbors, the triangular, and the simple cubic.  相似文献   
4.
Ohne ZusammenfassungD 21.Die vorstehende Arbeit wurde auf Anregung und unter Leitung von Herrn Professor Dr. Wöhlisch ausgeführt.  相似文献   
5.
For any unit vector in an inner product space S, we define a mapping on the system of all -closed subspaces of S, F(S), whose restriction on the system of all splitting subspaces of S, E(S), is always a finitely additive state. We show that S is complete iff at least one such mapping is a finitely additive state on F(S). Moreover, we give a completeness criterion via the existence of a regular finitely additive state on appropriate systems of subspaces. Finally, the result will be generalized to general inner product spaces.  相似文献   
6.
The Lewis acid mediated cyclization of epoxides with 1,3-bis(trimethylsilyloxy)-1,3-butadienes, electroneutral equivalents of 1,3-dicarbonyl dianions, results in the formation of 2-alkylidenetetrahydrofurans with a great variety of substitution patterns and functional groups. This includes the synthesis of 2,3'-bifuranylidenes and 7-oxabicyclo[4.3.0]nonanes. The cyclization of dienes with functionalized epoxides containing base-labile groups proceeds with good chemoselectivity. In all reactions, good regio- and E diastereoselectivities are observed. Based on the stereoselectivities observed for reactions of 1,2-disubstituted epoxides, a working hypothesis for the mechanism of the reaction is suggested.  相似文献   
7.
Syntheses and Crystal Structures of the Phosphaneimine Complexes MCl2(Me3SiNPMe3)2 with M = Zn and Co, and CoCl2(HNPMe3)2 The molecular complexes MCl2(Me3SiNPMe3)2 (M = Zn, Co) have been prepared by the reaction of the dichlorides of zinc and cobalt with Me3SiNPMe3 in CH3CN and CH2Cl2, respectively, whereas the complex CoCl2(HNPMe3)2 has been prepared by the reaction of CoCl2 with NaF in boiling acetonitrile in the presence of Me3SiNPMe3. All complexes were characterized by IR spectroscopy and by crystal structure determinations. The complexes MCl2(Me3SiNPMe3)2 crystallize isotypically. ZnCl2(Me3SiNPMe3)2: Space group P212121, Z = 4, 2677 observed unique reflections, R = 0.024. Lattice dimensions at ?70°C: a = 1243.6; b = 1319.0; c = 1464.7 pm. CoCl2(Me3SiNPMe3)2: Space group P212121, Z = 4, 3963 observed unique reflections, R = 0,071. Lattice dimensions at ?80°C: a = 1236.3; b = 1317.4; c = 1457.6 pm. CoCl2(HNPMe3)2 · CH2Cl2: Space group Pbca, Z = 8, 1354 observed unique reflections, R = 0.055. Lattice dimensions at ?80°C: a = 1247.3; b = 998.4; c = 2882.4 pm. All complexes have monomeric molecular structures, in which the metal atoms are coordinated in a distorted tetrahedral fashion by the two chlorine atoms and by the nitrogen atoms of the phosphaneimine molecules.  相似文献   
8.
The reaction of beta-diketiminated aluminum(I) monomer LAl with a large bulky azide N3Ar' (L = HC(CMeNAr)2, Ar' = 2,6-Ar2C6H3, Ar = 2,6-iPr2C6H3) in the temperature range from -78 degrees C to room temperature affords two different isomers 2 and 3, which have been characterized by spectroscopic and X-ray structural analyses, as well as elemental analysis. The variable-temperature 1H NMR kinetic studies of this reaction indicate the existence of the monomer LAlNAr' (1) at low temperature and the thermal stability of the compounds increases in the order of 1 < 2 < 3.  相似文献   
9.
10.
Synthesis and Crystal Structure of [Ba(18-Crown-6)(DMF)4][Cd(Se4)2] The title compound has been prepared by the reaction of a DMF-solution of lithium polyselenide with BaSe2 and cadmium acetate in the presence of 18-crown-6, forming black crystals. The compound was characterized by IR spectroscopy and by an X-ray structure determination. Space group P2/a, Z = 4, 5392 observed unique reflections, R = 0.048. Lattice dimensions at ?90°C: a = 2021.9(12); b = 1019.8(6); c= 2270.8(14)pm, ß = 106.98(4)°. The structure consists of [Ba(18-crown-6)(DMF)4]2+ ions, in which the barium ions are coordinated by the six oxygen atoms of the crown ether molecule and by four oxygen atoms of the DMF molecules, and of [Cd(Se4)2]2? ions. The cadmium atoms are coordinated by two tetraselenide ions in a chelating fashion.  相似文献   
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