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1.
Clemens G. Raab Georg Regensburger Jamal Hossein Poor 《Journal of Pure and Applied Algebra》2021,225(5):106564
A formal computation proving a new operator identity from known ones is, in principle, restricted by domains and codomains of linear operators involved, since not any two operators can be added or composed. Algebraically, identities can be modelled by noncommutative polynomials and such a formal computation proves that the polynomial corresponding to the new identity lies in the ideal generated by the polynomials corresponding to the known identities. In order to prove an operator identity, however, just proving membership of the polynomial in the ideal is not enough, since the ring of noncommutative polynomials ignores domains and codomains. We show that it suffices to additionally verify compatibility of this polynomial and of the generators of the ideal with the labelled quiver that encodes which polynomials can be realized as linear operators. Then, for every consistent representation of such a quiver in a linear category, there exists a computation in the category that proves the corresponding instance of the identity. Moreover, by assigning the same label to several edges of the quiver, the algebraic framework developed allows to model different versions of an operator by the same indeterminate in the noncommutative polynomials. 相似文献
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Robin F. Weitkamp Beate Neumann Hans‐Georg Stammler Berthold Hoge 《Angewandte Chemie (International ed. in English)》2020,59(14):5494-5499
We report on the first examples of isolated silanol–silanolate anions, obtained by utilizing weakly coordinating phosphazenium counterions. The silanolate anions were synthesized from the recently published phosphazenium hydroxide hydrate salt with siloxanes. The silanol–silanolate anions are postulated intermediates in the hydroxide‐mediated polymerization of aryl and alkyl siloxanes. The silanolate anions are strong nucleophiles because of the weakly coordinating character of the phosphazenium cation, which is perceptible in their activity in polysiloxane depolymerization. 相似文献
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Tricyclic skeletons have been generated from acyclic enyne precursors by using an intramolecular Pauson-Khand reaction in combination with aldol, Michael and alkylation reactions. 相似文献
6.
Let R be a discrete nonsingular equivalence relation on a standard probability space , and let V be an ergodic strongly asymptotically central automorphism of R. We prove that every V-invariant cocycle with values in a Polish group G takes values in an abelian subgroup of G.
The hypotheses of this result are satisfied, for example, if A is a finite set, a closed, shift-invariant subset, V is the shift, μ a shift-invariant and ergodic probability measure on X, the two-sided tail-equivalence relation on X, a shift-invariant subrelation which is μ-nonsingular, and a shift-invariant cocycle. 相似文献
7.
Thin Ca films were evaporated on Si(1 1 1) under UHV conditions and subsequently annealed in the temperature range 200–650 °C. The interdiffusion of Ca and Si was examined by ex situ Auger depth profiling. In situ monitoring of the Si 2p core-level shift by X-ray photoemission spectroscopy (XPS) was employed to study the silicide formation process. The formation temperature of CaSi2 films on Si(1 1 1) was found to be about 350 °C. Epitaxial growth takes place at T≥400 °C. The morphology of the films, measured by atomic force microscopy (AFM), was correlated with their crystallinity as analyzed by X-ray diffraction (XRD). According to measurements of temperature-dependent I–V characteristics and internal photoemission the Schottky-barrier height of CaSi2 on Si(1 1 1) amounts to qΦBn=0.25 eV on n-type and to qΦBp=0.82 eV on p-type silicon. 相似文献
8.
Johannes Elschner Rainer Hinder Gunther Schmidt 《Advances in Computational Mathematics》2002,16(2-3):139-156
This paper is devoted to the numerical study of diffraction by periodic structures of plane waves under oblique incidence. For this situation Maxwell's equations can be reduced to a system of two Helmholtz equations in R
2 coupled via quasiperiodic transmission conditions on the piecewise smooth interfaces between different materials. The numerical analysis is based on a strongly elliptic variational formulation of the differential problem in a bounded periodic cell involving nonlocal boundary operators. We obtain existence and uniqueness results for discrete solutions and provide the corresponding error analysis. 相似文献
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The high-temperature cubic phase of non-stoichiometric strontium ferrite SrFeOx (2.5≤x≤3.0) has been studied by in situ neutron powder diffraction in air over the temperature range 300-1273 K. The composition of SrFeOx changes within the range 2.56≤x≤2.81 from 1273 to 673 K, respectively.Rietveld refinements of the diffraction patterns show that the high-temperature cubic phase of SrFeOx is consistent with a face-centred Fm3c structure. This structure leads to agreement with previous density measurements. This cell allows the high-temperature structure of SrFeOx to be described in terms of a solid solution of the composition end members. Cubic SrFeOx at high temperature is found to closely obey Vegard's law. The density of cubic SrFeOx is also found to exhibit a linear relationship with composition. 相似文献