The representation dimension of domestic weakly symmetric algebras

Auslander’s representation dimension measures how far a finite dimensional algebra is away from being of finite representation type. In [1], M. Auslander proved that a finite dimensional algebra A is of finite representation type if and only if the representation dimension of A is at most 2. Recently, R. Rouquier proved that there are finite dimensional algebras of an arbitrarily large finite representation dimension. One of the exciting open problems is to show that all finite dimensional algebras of tame representation type have representation dimension at most 3. We prove that this is true for all domestic weakly symmetric algebras over algebraically closed fields having simply connected Galois coverings.     

Optimal control problems with applications to the elimination of substrate diffusing and convecting through immobilized enzyme

Some optimization problems concerning a substrate in a fluid are considered. The concentration of the substrate is affected by diffusion, convection, and elimination by enzymes, and the problem is to find the optimal distribution of enzymes. In this paper, the rate of elimination and the transmission coefficient are optimized. Mathematically, these problems are optimal control problems, and they are analyzed by means of Pontryagin's maximum principle.     

TEM investigations on PECVD-titanium carbide layers

TiC_x-PECVD-layers were characterized by TEM. EDX analysis and electron diffraction. TiC_x-layers deposited using benzene showed a columnar structure, at which the column size decreases with rising excess carbon content. TiC_x-layers deposited using n-heptane presented a lamellar structure, at which the lamellar thickness diminishes with an increasing excess carbon content. In dependence on the layer thickness a periodic progress of the element contents was observed, at which a maximum for Ti and Cl correlates with a minimum for C. It was found that the incorporated chlorine is bonded to titanium. The lattice parameter depends on the chlorine content. Using TiCl₄/H₂/Ar-gas mixtures without any hydrocarbon, layers containing TiH₂ are formed.     

Structure and Magnetic Properties of Ce3Ge0.66In4.34 and Ce11Ge4.74In5.26

New indides Ce₃Ge_0.66In_4.34 and Ce₁₁Ge_4.74In_5.26 were synthesized from the elements by arc‐melting and subsequent annealing at 870 K. Single crystals were grown through special annealing procedures in sealed tantalum tubes in a high‐frequency furnace. Both compounds were investigated on the basis of X‐ray powder and single crystal data: I4/mcm, La₃GeIn₄ type, a = 848.8(1), c = 1192.0(2) pm, Z = 4, wR2 = 0.0453, 499 F² values, 17 variables for Ce₃Ge_0.66In_4.34 and I4/mmm, Sm₁₁Ge₄In₆ type (ordered version of the Ho₁₁Ge₁₀ type), a = 1199.3(2), c = 1662.0(3) pm, wR2 = 0.0507, 1217 F² values, 41 variables for Ce₁₁Ge_4.74In_5.26. The Ce₃Ge_0.66In_4.34 structure shows a mixed Ge/In occupancy on the 4c Wyckoff position. This site is octahedrally coordinated by cerium atoms. These octahedra share all edges, leading to a three‐dimensional network. The latter is penetrated by a two‐dimensional indium substructure which consists of flattened tetrahedra at In–In distances of 291 and 300 pm. The Ce₁₁Ge_4.74In_5.26 structure contains three crystallographically independent germanium sites. The latter are coordinated by eight or nine cerium neighbors. These CN8 and CN9 polyhedra are condensed to a complex network which is penetrated by a three‐dimensional indium network with In–In distances of 301–314 pm. The 16m site shows a mixed In/Ge occupancy. Chemical bonding in both compounds is dominated by the p elements. Both ternaries studied exhibit localized magnetism due to the presence of Ce³⁺ ions. The compound Ce₃GeIn₄ remains paramagnetic down to 1.72 K, whereas Ce₁₁Ge₄In₆ orders ferromagnetically at T_C = 7.5 K.     

Curium isotopes in Chernobyl fallout

In nuclear reactors plutonium and transplutonium isotopes are produced by multiple neutron capture of uranium and plutonium and are important for the energy production and their composition reflects the core burnout. Under normal operation these elements are not released to the environment in significant amounts. There are accordingly very few areas or source terms where exotic transplutonium elements, such as curium isotopes, can be studied in the environment. The Chernobyl accident provided a complex spectrum of fission and activation products in fallout while the relative amounts, compared to the core inventory, of refractory elements such as transuranium and transplutonium elements were small. The major alpha-activity consisted of ²⁴²Cm (T _1/2 = 163 d) that would have decayed after a few years. In this study we have demonstrated the presence of so called supported ²⁴²Cm from the long-lived ²⁴²Am^m (T _1/2 = 141 a) in environmental samples, following fallout from the Chernobyl accident. It has also been possible to assess the core burn up by using the data obtained for the Cm isotopes. The curium isotopes ²⁴³Cm (T _1/2 = 29.1 a) and ²⁴⁴Cm (T _1/2 = 18.1 a) cannot be resolved by conventional alpha-spectrometry. The assessment of these isotopes in environmental samples contaminated from the Chernobyl accident has been made by studying the effective half-life of the mixture of the isotopes. The data are compared with those previously obtained by high-resolution alpha-spectrometry and spectral deconvolution.     

PHYTOCHROME EVOLUTION: A PHYLOGENETIC TREE WITH THE FIRST COMPLETE SEQUENCE OF PHYTOCHROME FROM A CRYPTOGAMIC PLANT: (Selaginella martensii SPRING)

We have sequenced cDNA and genomic clones coding for phytochrome of the fern Selaginella. On the amino acid level, this phytochrome shares sequence homologies with phytochromes of higher plants which range between 62 (phytochrome B of Arabidopsis) and 55 (56)% [phytochrome C of Arabidopsis (Avena)]. Introns in the Selaginella gene are short and occupy positions known from phytochrome sequences of higher plants. A rooted phylogenetic tree based on mutation distances puts Selaginella phytochrome closest to the hypothetical ancestor. A similar tree arises if the tree is constructed with partial sequences (about 200 amino acids) around the chromophore attachment site. An extension of this tree by sequences of other cryptogamic plants (Mougeotia, Ceratodon, Psilotum) shows all these sequences including those of the phytochromes B and C of Arabidopsis on a branch, well separated from the branch formed by phytochromes known to accumulate in etiolated plants. The rooted phytochrome phylogenetic tree, however, is difficult to reconcile with the fossil record.     

ESCA: Eine Methode zur Bestimmung von Elementen und ihren Bindungszust?nden in der Oberfl?che von Festk?rpern

Zusammenfassung ESCA (nach Siegbahn: Electron Spectroscopy for Chemical Analysis) beruht auf dem Photoeffekt an inneren Atomorbitalen und ist auf alle Substanzen anwendbar. Die Routineuntersuchungen werden überwiegend an Festkörpern durchgeführt. Informationsträger sind Photo- und Augerelektronen, die verlustfrei von der Festkörperoberfläche emittiert werden. Auf Grund der Oberflächenempfindlichkeit gehört ESCA zu den mikrochemischen Verfahren. Die erfaßte Schichtdicke ist gegeben durch die Austrittstiefe der Photo- und Augerelektronen. Sie beträgt einige Monolagen, maximal 100 Å. Man kann davon ausgehen, daß bei einer untersuchten Fläche von 0,5 cm² und homogener Verteilung eines Elementes in den obersten 100 Å eine Konzentration von 1 % noch sicher nachgewiesen wird. Die Empfindlichkeitsunterschiede von Element zu Element liegen innerhalb eines Faktors 10. Matrixeffekte sind noch wesentlich geringer. Deshalb sind gute Voraussetzungen für eine quantitative Analyse gegeben. ESCA ist zwar nicht direkt ein Verfahren zur Spurenanalyse, wohl aber nach geeigneter Anreicherung. Der besondere Vorteil von ESCA liegt darin, daß man nicht nur Elemente nachweist, sondern an Hand von chemischen Verschiebungen, Linienaufspaltungen und Shake-up-Satelliten zuverlässige Aussagen über ihren Bindungszustand erhält. Weiterhin kann innerhalb des Bereiches der Austrittstiefe der Photoelektronen differenziert werden; dadurch ergeben sich Möglichkeiten zur zerstörungsfreien Aufnahme von Tiefenverteilungen von Elementen und Verbindungen. Zum Vordringen in tiefere Schichten kann ESCA mit abbauenden Verfahren gekoppelt werden. Nach Ionenbeschußabbau ist wegen ioneninduzierter Reaktionen in der Regel jedoch kein Verbindungsnachweis mehr möglich.

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ESCA: A method for the determination of elements and their valence states in the surfaces of solids

Summary ESCA — or Electron Spectroscopy for Chemical Analysis (the term used by its inventor, Siegbahn)-is based on the effects of X-rays on the inner orbitals of atoms and is applicable to all substances. Routine ESCA investigations are carried out chiefly on solids. The information is provided by photo- and Auger electrons, which are emitted from the surfaces of solids without energy losses. Because of its surface sensitivity ESCA may be regarded as a microchemical method. The comprehended layer thickness is given by the escape depths of the photo- and Auger electrons. The range is from a few monolayers to 100 Å. As a rule, an element that is distributed homogeneously in the uppermost 100 Å of an area of 0.5 cm² can still be detected reliably at a concentration of 1%. The differences in sensitivity from element to element are within a factor of ten. Matrix effects are considerably smaller still. ESCA is therefore well suited for quantitative analysis. Though not directly suitable for trace analysis, ESCA can be used for that purpose after appropriate enrichment techniques have been applied. The special advantage of ESCA is that, in addition to detecting elements, it provides reliable information on their valence states by means of chemical shifts, line splitting and shake-up satellites. Apart from this, ESCA permits in-depth discrimination within the range of the escape depths of the photo electrons; it therefore provides opportunities for the non-destructive recording of the depth distributions of elements and compounds. For investigation of lower layers, ESCA can be combined with methods which involve the removal of outer layers. After removal of layers by ion bombardment, however, ion-induced reactions generally prevent the detection of compounds.

Hauptvortrag auf dem Internationalen Symposium für mikrochemische Arbeitsmethoden (ISM) Davos, Mai 1977     

Biocatalytic asymmetric hydrogen transfer employing Rhodococcus ruber DSM 44541

Nonracemic sec-alcohols of opposite absolute configuration were obtained either by asymmetric reduction of the corresponding ketone using 2-propanol as hydrogen donor or by enantioselective oxidation through kinetic resolution of the rac-alcohol using acetone as hydrogen acceptor employing whole lyophilized cells of Rhodococcus ruber DSM 44541. The microbial oxidation/reduction system exhibits not only excellent stereo- and enantioselectivity but also a broad substrate spectrum. Due to the exceptional tolerance of the biocatalyst toward elevated concentrations of organic materials (solvents, substrates and cosubstrates), the process is highly efficient. The simple preparation of the biocatalyst and its ease of handling turns this system into a versatile tool for organic synthesis.