Minors of symmetric and exterior powers

We describe some of the determinantal ideals attached to symmetric, exterior and tensor powers of a matrix. The methods employed use elements of Zariski's theory of complete ideals and of representation theory.     

Correlation between mechanical and electrical properties on conductive SiC-fibre reinforced composites

Electrical and mechanical properties of ceramic composites are investigated to develop “smart materials” and establish a fracture prediction technique. The “smart materials” are based on silicon carbide fibre-reinforced composites. The SiC-fibres were checked to determine the changes in mechanical and electrical properties during the composites’ production. Samples were produced for the determination of the mechanical strength with in situ detection of the degree of damage by recording the electrical resistance.     

Characterization of the Composition of Solid Mixtures Using Particle Shape Distributions Obtained by Image Analysis

There are many applications of particle technology in which solid mixtures consisting of particles having the same chemical, mineralogical and physical properties are used. The particles are then distinguishable only by shape. The particle shape significantly influences the technological behaviour of the mixture and the properties of the materials produced. Therefore, mathematical procedures are necessary in order to determine the composition of such a mixture according to the proportions of certain particle shape classes. These classes are the respective components of the mixture. In this work, various statistical methods were tested to classify the particles by shape analysis. A two-component mixture of quartz and muscovite was used as a reference material. The results obtained by different theoretical methods were compared with each other. Alternative methods such as histogram fit and the EM algorithm provided better results than the conventional method of discriminant analysis, as expected. Because the statistical behaviour of the components can be estimated only using reference samples, a statistical error of about 5–10% depending on the respective sample size was met. However, this is a satisfactory result. It turned out that it is possible to conclude exclusively on the basis of the particle shape distribution about the composition of a mixture. The methodical knowledge obtained can be used in industrial applications such as the ceramic industry, the production of paints and the bulk solids technology.     

CHANGES IN TRANSMISSION CHARACTERISTICS OF POLYMETHYLMETHACRYLATE AND CELLULOSE (III) ACETATE DURING EXPOSURE TO ULTRAVIOLET LIGHT

Abstract— Ultraviolet-transparent polymethylmethacrylate (PMMA) and cellulose (III) acetate (CA) (often used as a cut-off filter in UVB [280–320 nm] biological effect studies) were exposed to a 20 W Philips TL 12 lamp to examine changes in transmission characteristics due to UVB exposure. Transmission of UVB and biologically weighted UVB (UV_BE(DNA)) through PMMA were similar, 88.3 and 83.5%, respectively. The absorption characteristics of PMMA did not change with time at any of the UV irradiance levels applied. However, transmission of UVB and UVB_BE(DNA)) through new CA differed considerably: 59% versus only 11%, respectively. Also, spectral absorption characteristics changed with time due to degradation of CA, at a rate that was dependent on the incident UVB irradiance. The decrease in transmission through CA of both UVB and UV_BE(DNA) can be described by exponential functions. The CA that was wrapped around the UV lamp showed dramatic changes in UV absorption over the first few hours of use. However, when CA was placed at a longer distance from the light source initial degradation was less. It is concluded that PMMA can be applied in UV effect studies as a reasonable alternative for quartz. The CA should, however, be used with care, because the large transmission decreases that were observed strongly hamper an accurate calculation of (biologically weighted) UVB dose rates.     

Cyclic ligands with fixed co-ordination geometry. Part 6(1). Chalcogenanthrenes as bridging ligands in dinuclear complexes of rhenium(I) and platinum(IV)-X-ray crystal structure of di(μ-chloro) (μ-2, 3, 7, 8-tetramethoxyselenanthrene) hexamethyl diplatinum(IV)

Summary The chalcogenanthrenes Vn₂EE; 2, 3, 7, 8-tetramethoxythianthrene (E=E=S), 2, 3, 7, 8-tetramethoxydibenzothiaselenin (E=S, E=Se), and 2, 3, 7, 8-tetramethoxyselenanthrene (E=E=Se), react with [{ReBr(CO)₃(THF)}₂] and [{PtXMe₃}₄] (X=Cl or Br) to give the dinuclear complexes [(fac-L₃M)₂(-X)₂ (-Vn₂EE)] (M=Re, L=CO, X=Br; M=Pt, L=Me, X=Cl or Br) in which the chalcogenanthrenes reveal a hitherto unknown co-ordination mode as bridging ligands. Telluranthrene (Pn₂ Te₂), however, forms mononuclear complexes of compositionfac-[L₃MX(Pn₂Te₂)] (M=Re, L=CO, X=Br; M=Pt, L=Me, X=Br) with a chelating chalcogenanthrene ligand. Whereas the rhenium compounds are not stable enough in solution to be studied by i.r. spectroscopy, the platinum compounds can be well characterised by their¹H n.m.r. spectra. Furthermore, the results of a single-crystal structure determination of [Pt₂Cl₂Me₆(Vn₂Se₂)] are reported. The Pt–Se distance of 259 pm indicates a relatively weak interaction between the chalcogenanthrene and the remaining dinuclear fragment of the molecule.     

Über eine Vermutung von S. Chowla und H. Walum

Ohne Zusammenfassung