Nachweis und Bestimmung des Wismuts

Ohne Zusammenfassung     

Tantal und Niob

Ohne Zusammenfassung     

Millimetre-wave fibre–wireless transmission systems with reduced effects of fibre chromatic dispersion

This paper describes two techniques for the implementation of millimetre-wave (mm-wave) wireless communication systems incorporating optical fibre distribution networks. Fibre chromatic dispersion can exhibit severe effects on the transportation of mm-wave frequencies over fibre, resulting in greatly reduced post-detection rf powers. Each mm-wave fibre–wireless system demonstrated here incorporates a method for the generation and modulation of an optical mm-wave carrier, which enables the effect of fibre dispersion to be significantly reduced. One set-up is a direct-detection scheme where optical single-sideband (SSB) with carrier modulation is used to overcome fibre dispersion effects. The other system employs a self-heterodyne arrangement in which a dual-frequency optical source generates a low phase-noise mm-wave beat signal. Data transmission is achieved by externally modulating the dual-mode signal and reduced effects of fibre dispersion are observed.     

A Photochemical Route towards Metal Sulfide Nanosheets from Layered Metal Thiolate Complexes

Synthesizing nanomaterials with anisotropic architectures, especially two‐dimensional (2D) nanosheets (NSs), is a key focus of materials science research. Metal sulfide nanosheets (MSNSs) are typically obtained involving exfoliation of bulk metal sulfides with layered structures. The synthesis of NSs of intrinsically non‐layered metal sulfides has received relatively less attention. Metal alkanethiolates with lamellar structures are now shown to serve as effective scaffolds for constructing NSs. A novel photochemical step was employed to transform 2D metal thiolates into MSNSs. By this strategy the 2D nature of metal thiolate precursors was preserved in the final products, resulting in the successful synthesis of NSs of binary PbS, CdS, and Cu₉S₅, as well as ternary wurtzite CuInS₂, Cu₂SnS₃. Results encourage the wider utilization of photochemical strategies in the synthesis of anisotropic MSNSs.     

On linear transformations preserving rank one matrices over commutative rings

We show that over any cummutative ring R,the combinations, of 2 × 2 minors are the only quadratic forms vanishing on the matrices of rank 1. Hence any invertible linear transformation on matrices that preserves the rank-1 set over R will automatically do the same over all extensions of R. Similarly, the linear combinations of 4 × 4 Paffians are the only quadratic forms vanishing on the alternating matrices of rank 2. Hence again any invertible transformation preserving that set over R will do so formally. This fact allows us to determine the collection of such transformations     

Real classification of complex quadrics

Canonical forms are given for complex quadric surfaces (and conics) under real changes of variable. The basic idea is to use known results on pairs of real quadratic forms.     

Notes toward higher differential algebra

This paper is a self-contained introduction to a theory of higher differential algebra. The results were originally accumulated in sporadic attempts to forge a link between differential algebra and the study of formal groups, and one trace of that goal is included here as motivation. Primarily, however, the theory is of interest because it preserves for arbitrary rings much of the formal structure of ordinary differential algebra for Ritt algebras. Some of the results have appeared in weaker form in the literature, so it seems worthwhile to put the theory on record.