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Peter Fleischmann / Georg Seiderer (Hg.), Archive und Archivare in Franken im Nationalsozialismus (Franconia 10), Neustadt an der Aisch: Verlagsdruckerei Schmidt 2019. XIII, 567 S., 53 teils farb. Abb. ISBN 978-3-940049-25-4. € 28,–

Peter Fleischmann (Bearb.), Die handgezeichneten Karten des Staatsarchivs Nürnberg bis 1806 (Bayerische Archivinventare, Bd. 49), München (Generaldirektion der Archive Bayerns) 1998. 566 S.

Festschrift Rudolf Endres: Zum 65. Geburtstag gewidmet von Kollegen, Freunden und Schülern. Hg. von Charlotte Bühl und Peter Fleischmann, Neustadt/Aisch (Degener) 2000, 855 S.

Stefan Fuchs, Herrschaftswissen und Raumerfassung im 16. Jahrhundert. Kartengebrauch im Dienste des Nürnberger Stadtstaates (Veröffentlichungen des Nationalen Forschungsschwerpunkts Medienwandel – Medienwechsel – Medienwissen, Historische Perspektiven 35), Zürich: Chronos Verlag 2018. 312 S., 31 Farbabb. ISBN 978-3-0340-1346-8. € 48,–/CHF 48,–

Let k be a field of characteristic p and V a finite-dimensional k-vector space. An element g ∈ GL ⁢ ( V ) {g\in{\rm GL}(V)} is called a bireflection if it centralizes a subspace of codimension less than or equal to 2. It is known by a result of Kemper that if for a finite p-group G ≤ GL ⁢ ( V ) {G\leq{\rm GL}(V)} the ring of invariants Sym ⁢ ( V * ) G {{\rm Sym}(V^{*})^{G}} is Cohen–Macaulay, G is generated by bireflections. Although the converse is false in general, it holds in special cases e.g. for particular families of groups consisting of bireflections. In this paper we give, for p > 2 {p>2} , a classification of all finite unipotent subgroups of GL ⁢ ( V ) {{\rm GL}(V)} consisting of bireflections. Our description of the groups is given explicitly in terms useful for exploring the corresponding rings of invariants. This further analysis will be the topic of a forthcoming paper.

Let f(x) be a formal power series with coefficients in the field k and let n ? 1. We define the notion of n-transcendence of f(x) over k and, more generally, the stable transcendence function dk(f(x), n). It is shown that, if k has prime characteristic p, this function determines the minimal Krull dimension dk(G) of the universal modular Galois-algebras of an elementary Abelian p-group G, introduced in [2, 3, 4, 5]. Since the concept of n-transcendence is of independent interest in all characteristics, a number of fundamental theorems are proved where the generalized Artin-Schreier polynomials surprisingly play a central role. We make a plausible conjecture in the case when k = Fp, the truth of which would imply a conjectural result concerning dFp (G) previously investigated by the authors.

LetKbe an algebraically closed field and$\mathbb{A}$n≅Knaffinen-space. It is known that a finite group$\frak{G}$can only act freely on$\mathbb{A}$nifKhas characteristicp> 0 and$\frak{G}$is ap-group. In that case the group action is “non-linear” and the ring of regular functionsK[$\mathbb{A}$n] must be atrace-surjectiveK−$\frak{G}$-algebra.Now letkbe an arbitrary field of characteristicp> 0 and letGbe a finitep-group. In this paper we study the category$\mathfrak{Ts}$of all finitely generated trace-surjectivek−Galgebras. It has been shown in [13] that the objects in$\mathfrak{Ts}$are precisely those finitely generatedk−GalgebrasAsuch thatAG≤Ais a Galois-extension in the sense of [7], with faithful action ofGonA. Although$\mathfrak{Ts}$is not an abelian category it has “s-projective objects”, which are analogues of projective modules, and it has (s-projective) categorical generators, which we will describe explicitly. We will show thats-projective objects and their rings of invariants are retracts of polynomial rings and therefore regular UFDs. The category$\mathfrak{Ts}$also has “weakly initial objects”, which are closely related to the essential dimension ofGoverk. Our results yield a geometric structure theorem for free actions of finitep-groups on affinek-varieties. There are also close connections to open questions on retracts of polynomial rings, to embedding problems in standard modular Galois-theory ofp-groups and, potentially, to a new constructive approach to homogeneous invariant theory.

Let G be a Sylow p -subgroup of the unitary groups GU(3,q2)GU(3,q2), GU(4,q2)GU(4,q2), the symplectic group Sp(4,q)Sp(4,q) and, for q odd, the orthogonal group O+(4,q)O+(4,q). In this paper we construct a presentation for the invariant ring of G acting on the natural module. In particular we prove that these rings are generated by orbit products of variables and certain invariant polynomials which are images under Steenrod operations, applied to the respective invariant form defining the corresponding classical group. We also show that these generators form a SAGBI basis and the invariant ring for G is a complete intersection.

Human papillomavirus 6b L1 virus-like particles (VLPs) were successfully expressed using Bombyx mori nucleopolyhedrovirus (BmNPV) bacmid expression system and rapidly purified using size exclusion chromatography after ultracentrifugation procedure and characterized by capillary zone electrophoresis (CZE). The average capillary electrophoresis migration time was 11 min with the relative standard deviation (RSD) of 0.3% of human papillomavirus 6b L1 VLPs. After this threefold fractionation, the CZE samples were still further investigated by dynamic light scattering and immuno blotting. The versatile technique, CZE not only proved to be a valuable tool for VLP characterization, but was also found to be reliable and precise. Thus CZE will also be an important option for the quality control of VLPs in pharmaceutical research level.

A previous study found that 1-phenylethanol (1PE) was a major endogenous volatile compound in tea (Camellia sinensis) flowers and can be transformed to glycosically conjugated 1PE (1PE-Gly). However, occurrences of 1PE-Gly in plants remain unknown. In this study, four 1PE-Glys have been isolated from tea flowers. Three of them were determined as (R)-1PE β-d-glucopyranoside ((R)-1PE-Glu), (S)-1PE-Glu, and (S)-1PE β-primeveroside ((S)-1PE-Pri), respectively, on the basis of NMR, MS, LC-MS, and GC-MS evidence. The other one was identified as (R)-1PE-Pri on the basis of LC-MS and GC-MS data. Moreover, these 1PE-Glys were chemically synthesized as the authentic standards to further confirm their occurrences in tea flowers. 1PE-Glu had a higher molar concentration than 1PE-Pri in each floral stage and organ. The ratio of (R) to (S) differed between 1PE-Glu and 1PE-Pri. In addition, a 1PE-Gly hydrolase β-primeverosidase recombinant protein produced in Escherichia coli exhibited high hydrolysis activity toward (R)-1PE-Pri. However, β-primeverosidase transcript level was not highly expressed in the anther part, which accumulated the highest contents of 1PE-Gly and 1PE. This suggests that 1PE-Gly may not be easily hydrolyzed to liberate 1PE in tea flowers. This study provides evidence of occurrences of 1PE-Glys in plants for the first time.

A method for carbon isotope ratio (δ(13)C) analysis was developed for compound-specific isotope analysis of tea volatiles, and the values were compared with the δ(13)C value from bulk isotope analyses. The δ(13)C value of 2-phenylethanol liberated via enzymatic hydrolysis of the 2-phenylethyl β-primeveroside standard was examined first. Isotope fractionations for 2-phenylethyl β-primeveroside from preparative high-performance liquid chromatography (HPLC) were also analyzed. The enzymatic treatment and the preparative HPLC process did not cause carbon isotope fractionations, substantiating the strategies available for δ(13)C analysis of volatile compounds. On the basis of the gas chromatography-combustion-isotope ratio mass spectrometry data from 2-phenylethanol, it was possible to derive the conditions for enzyme treatment and preparative HPLC of the glycoconjugates of 2-phenylethanol, (Z)-3-hexenol, and benzyl alcohol isolated from green tea leaves. Larger variations in δ(13)C were found for individual volatile compounds compared with bulk analytical data from the leaves, indicating the potential to utilize this strategy in assigning the geographical origin of green tea.

We apply recent results on Galois-ring extensions and trace surjective algebras to analyze dehomogenized modular invariant rings of finite p-groups, as well as related localizations. We describe criteria for the dehomogenized invariant ring to be polynomial or at least regular and we show that for regular affine algebras with possibly non-linear action by a p-group, the singular locus of the invariant ring is contained in the variety of the transfer ideal. If V is the regular module of an arbitrary finite p-group, or V is any faithful representation of a cyclic p-group, we show that there is a suitable invariant linear form, inverting which renders the ring of invariants into a “localized polynomial ring” with dehomogenization being a polynomial ring. This is in surprising contrast to the fact that for a faithful representation of a cyclic group of order larger than p, the ring of invariants itself cannot be a polynomial ring by a result of Serre. Our results here generalize observations made by Richman [R] and by Campbell and Chuai [CCH].

BACKGROUND Carotenoids are a major class of plant pigments and fulfill many functions in different organisms that either produce or consume them. Although the color of the stamina of tea (Camellia sinensis) flowers is clearly due to the presence of carotenoids, the carotenoid profile and content remain to be discovered. RESULTS We investigated the carotenoid profile of tea flowers and determined changes in concentrations over the floral development. The flowers contained oxygenated xanthophylls such as neoxanthin, lutein and zeaxanthin, as well as the hydrocarbons β-carotene and α-carotene. Flowers of the tea plant contain to vegetables comparable amounts of carotenoids. The content of 9′-cis-epoxycarotenoids, which serve as abscisic acid precursors, as well as changes in concentration of abscisic acid were studied. The concentrations of carotenoids decreased whereas the abscisic acid content increased over the floral development. Exogenously applied S-abscisic acid affected water uptake, flower opening and carotenoid accumulation. CONCLUSION In summary, this paper reports, for the first time, the carotenoid profile and content of tea flowers. The study revealed that carotenoids in tea flowers are an interesting target in respect of possible applications of tea flower extracts as well as biological functions of abscisic acid during floral development. © 2012 Society of Chemical Industry

We describe "quasi canonical modules" for modular invariant rings $R$ of finite group actions on factorial Gorenstein domains. From this we derive a general "quasi Gorenstein criterion" in terms of certain 1-cocycles. This generalizes a recent result of A. Braun for linear group actions on polynomial rings, which itself generalizes a classical result of Watanabe for non-modular invariant rings. We use an explicit classification of all reflexive rank one $R$-modules, which is given in terms of the class group of $R$, or in terms of $R$-semi-invariants. This result is implicitly contained in a paper of Nakajima (\cite{Nakajima:rel_inv})., Comment: 16 pages

Tubers of the closely related species Solanum tuberosum (potatoes) and Solanum phureja belong to the staff of life for humans. The coloration of the often very colorful tubers is caused by carotenoids (especially xanthophylls) and anthocyanins. The new S. phureja cultivars Mayan Gold and Mayan Twilight, the new S. tuberosum cultivar Red Laura and the traditional S. tuberosum variety Shetland Black were analyzed for their pigment content. The dominant anthocyanin in the red-skinned cultivars Red Laura and Mayan Twilight was characterized as pelargonidin-3-coumarylrutinoside-5-glucoside by LC-ESI-MS. The blue pigment of the Shetland Black cultivar was petunidin-3-coumaroylrutinoside-5-glucoside. Red Laura contained 10 mg anthocyanins g −1 dry weight and Shetland Black 31 mg anthocyanins g −1 dry weight. The main carotenoids in raw tubers are 9- cis -violaxanthin, lutein and one unidentified carotenoid in all S. tuberosum and S. phureja cultivars. Minor compounds were identified as neoxanthin and neochrome. Additionally, zeaxanthin and one further unidentified carotenoid could be found in Red Laura and Mayan Gold. No differences in the carotenoid composition between peel and parenchyma could be found. Total carotenoid content ranged from 2.57 ± 0.53 μg g −1 dry weight in Shetland Black to 14.77 ± 2.22 μg g −1 dry weight in Red Laura (calculated as β-carotene-equivalents). In heat processed tubers, high amounts of carotenoids either changed from all-trans to 9- cis and 13- cis -isomeric form or was degraded. The total pigment content was decreased by heat processing in all cultivars. 8.23 ± 2.98 μg g −1 dry weight could be found in Mayan Twilight and 1.51 ± 0.31 μg carotenoids g −1 dry weight in Shetland Black.

Let $G$ be a finite $p$-group and $k$ a field of characteristic $p>0$. We show that $G$ has a \emph{non-linear} faithful action on a polynomial ring $U$ of dimension $n=\mathrm{log}_p(|G|)$ such that the invariant ring $U^G$ is also polynomial. This contrasts with the case of \emph{linear and graded} group actions with polynomial rings of invariants, where the classical theorem of Chevalley-Shephard-Todd and Serre requires $G$ to be generated by pseudo-reflections. Our result is part of a general theory of "trace surjective $G$-algebras", which, in the case of $p$-groups, coincide with the Galois ring-extensions in the sense of \cite{chr}. We consider the \emph{dehomogenized symmetric algebra} $D_k$, a polynomial ring with non-linear $G$-action, containing $U$ as a retract and we show that $D_k^G$ is a polynomial ring. Thus $U$ turns out to be \emph{universal} in the sense that every trace surjective $G$-algebra can be constructed from $U$ by "forming quotients and extending invariants". As a consequence we obtain a general structure theorem for Galois-extensions with given $p$-group as Galois group and any prescribed commutative $k$-algebra $R$ as invariant ring. This is a generalization of the Artin-Schreier-Witt theory of modular Galois field extensions of degree $p^s$., 20 pages

Damascenone is well-known for its potent flavour with an extremely low odour threshold. Several glycosidically bound precursors of damascenone have been isolated from several plants, but little is known about their occurrences in green tea infusions. In this work, three major glycosidic precursors of damascenone, 9-O-β- d -glucopyranosyl-megastigma-6,7-dien-3,5,9-triol (1a), 9-O-β- d -glucopyranosyl-3-hydroxy-7,8-didehydro-β-ionol (2a), and 3-O-β- d -glucopyranosyl-3-hydroxy-7,8-didehydro-β-ionol (2b) were isolated and identified in green tea infusions, and the stereochemistries at C-3 and C-9 positions of aglycone parts of the three glycosidic precursors were determined as (3S, 9R)-1a, (3R, 9R)-2a, and (3R, 9R)-2b, respectively. Compounds 1a, 2a, and 2b as well as 3-O-β- d -glucopyranosyl-megastigma-6,7-dien-3,5,9-triol (1b) were hydrolysed to form damascenone in a model system with strong acidic conditions (pH 2.0) and at high temperature (90 °C). In contrast to hydrolysis of 2a and 2b, more damascenone was transformed from 1a and 1b. Furthermore, the β- d -glucosyl moiety at the C-3 position gave a higher dehydration rate from megastigma-6,7-dien-3,5,9-triol to 3-hydroxy-7,8-didehydro-β-ionol than compound 1a carrying the sugar residue at C-9 position. Interestingly, the four glycosidic precursors of damascenone were not hydrolysed to give damascenone under slightly acidic conditions (pH 5.4 and 120 °C for 10 min), but they could be transformed to damascenone in the presence of green tea infusions even under the equal conditions.

Let f:=p/q∈K(x) be a rational function in one variable. By Lüroth’s theorem, the collection of intermediate fields K(f)⊊L⊊K(x) is in bijection with inequivalent proper decompositions f=g∘h, with g,h∈K(x) of degrees ≥2. In [Alonso, Cesar, Gutierrez, Jaime, Recio, Tomas, 1995. A rational function decomposition algorithm by near-separated polynomials. J. Symbolic Comput. 19, 527–544] an algorithm is presented to calculate such a function decomposition. In this paper we describe a simplification of this algorithm, avoiding expensive solutions of linear equations. A MAGMA implementation shows the efficiency of our method. We also prove some indecomposability criteria for rational functions, which were motivated by computational experiments.

Preparative HSCCC (high-speed counter-current chromatography) could be applied for the isolation of 9'-cis-neoxanthin from a crude carotenoid extract of fresh spinach leaves. The separation was performed on a Pharma-Tech Research Corp. CCC 1000 with a solvent system composed of hexane:ethanol:water at a volume ratio of 5:5:4.5 at a flow rate of 3 mL/min and at 850 rpm, using the lower phase as mobile phase. 9'-cis-neoxanthin with a purity of up to 94% could be obtained with a single HSCCC purification step of the crude carotenoid extract.

Let G be a finite group acting on a polynomial ring A over the field K and let A G denote the corresponding ring of invariants. Let B be the subalgebra of A G generated by all homogeneous elements of degree less than or equal to the group order | G | . Then in general B is not equal to A G if the characteristic of K divides | G | . However we prove that the field of fractions Quot ( B ) coincides with the field of invariants Quot ( A G ) = Quot ( A ) G . We also study various localizations and homomorphisms of modular invariant rings as tools to construct generators for A G . We prove that there is always a nonzero transfer c ∈ A G of degree | G | , such that the localization ( A G ) c can be generated by fractions of homogeneous invariants of degrees less than 2 ⋅ | G | − 1 . If A = Sym ( V ⊕ F G ) with finite-dimensional F G -module V, then c can be chosen in degree one and 2 ⋅ | G | − 1 can be replaced by | G | . Let N denote the image of the classical Noether-homomorphism (see the definition in the paper). We prove that N contains the transfer ideal and thus can be used to calculate generators for A G by standard elimination techniques using Grobner-bases. This provides a new construction algorithm for A G .

Let k be a field of positive characteristic p and let G be a finite group. In this paper we study the category TsG of finitely generated commutative k-algebras A on which G acts by algebra automorphisms with surjective trace. If A = k[X], the ring of regular functions of a variety X, then trace-surjective group actions on A are characterized geometrically by the fact that all point stabilizers on X are p'-subgroups or, equivalently, that A is a Galois extension of the ring of P invariants for every Sylow p-group P of G. We investigate categorical properties, using a version of Frobenius-reciprocity for group actions on k-algebras, which is based on tensor induction for modules. We also describe projective generators in TsG , extending and generalizing the investigations started in [8], [7] and [9] in the case of p-groups. As an application we show that for an abelian or p-elementary group G and k large enough, there is always a faithful (possibly nonlinear) action on a polynomial ring such that the ring of invariants is also a polynomial ring. This would be false for linear group actions by a result of Serre. For p-solvable groups we obtain a structure theorem on trace-surjective algebras, generalizing the corresponding result for p-groups in [8]., 23 pages, accepted by J. of Algebra

C-13 norisoprenoids such as β-ionone, 3 hydroxy-β-ionone, and 3 hydroxy-5,6-epoxy-β-ionone are important carotenoid related aroma compounds in fruits. Apart from chemical degradation (photo-oxygenation, (auto)oxidation, thermal degradation), enzymatic cleavage is an important flavor formation pathway [ Enzell, C. (1985) . Biodegradation of carotenoids – an important route to aroma compounds. Pure and Applied Chemistry, 57(5), 693–700; Winterhalter, P., & Rouseff, R. (Eds.). (2001) . Carotenoid-derived aroma compounds. ACS symposium series 802, Washington, DC: American Chemical Society (ISBN 0-8412-3729-8)]. In nectarines, the content of carotenoid degradation products depends on the degree of maturity. In fully ripened fruit up to 40% of the aglycons are C-13 norisoprenoids [Aubert, C., Gunata, Z., Ambid, C., & Baumes, R. (2003). Changes in physicochemical characteristics and volatile constituents of yellow- and white-fleshed nectarines during maturation and artificial ripening. Journal of Agriculture and Food Chemistry, 51(10), 3083–3091]. Regiospecific carotenoid cleavage enzymes have been shown to be involved in aroma formation in different plants and fruits [Bouvier, F., Suire, C., Mutterer, J., & Camara, B. (2003). Oxidative remodeling of chromoplast carotenoids: identification of the carotenoid dioxygenase CsCCD and CsZCD genes involved in crocus secondary metabolite biogenesis. Plant Cell, 15(1), 47–62; Fleischmann, P., Studer, K., & Winterhalter, P., (2002). Partial purification and kinetic characterization of a carotenoid cleavage enzyme from quince fruit (Cydonia oblonga). Journal of Agriculture and Food Chemistry, 50(6), 1677–1680; Fleischmann, P., Watanabe, N., & Winterhalter, P., (2003). Enzymatic carotenoid cleavage in star fruit (Averrhoa carambola). Phytochemistry, 63(2), 131–137; Schwartz, Qin & Zeevaart, 2001 ]. This paper describes the isolation and partial characterization of carotenoid cleavage enzymes in nectarines, isolated from ripe skin of commercially available fruit. The enzyme is characterized by its kinetic parameters (vmax, Km, time constant, temperature dependence, activation energy).

the cohomological connectivity of the symmetric algebra S(V ) to be the smallest positive integer m such that H m (G;S(V ))6 0. We show that min dimK(V P ) +m + 1; dimK(V ) is a lower bound for the depth of S(V ) G . We characterize those representations for which the lower bound is sharp and give several examples of representations satisfying the criterion. In particular, we show that if G is p-nilpotent and P is cyclic then, for any modular representation, the depth of S(V ) G is min dimK(V P ) + 2; dimK(V ) .

We study the cohomology modules H i (G;R) of a p-group G acting on a ring R of characteristic p, for i > 0. In particular, we are interested in the Cohen-Macaulay property and the depth of H i (G;R) regarded as an R G -module. We rst determine the support of H i (G;R), which turns out to be independent of i. Then we study the Cohen-Macaulay property for H 1 (G;R). Further results are restricted to the special case that G is cyclic and R is the symmetric algebra of a vector space on which G acts. We determine the depth of H i (G;R) for i odd and obtain results in certain cases for i even. Along the way, we determine the degrees in which the transfer map Tr G :R! R G has non-zero image.

We prove that for a modular representation, the depth of the ring of invariants is the sum of the dimension of the fixed point space of the p-Sylow subgroup and the grade of the relative trace ideal. We also determine which of the Dickson invariants lie in the radical of the relative trace ideal and we describe how to use the Dickson invariants to compute the grade of the relative trace ideal.

This paper presents the first description of an enzyme fraction exhibiting carotenoid cleavage activity isolated from fruit skin of Averrhoa carambola. Partial purification of the enzyme could be achieved by acetone precipitation, ultrafiltration (300 kDa, 50 kDa), isoelectric focusing (pH 3-10) and sodium dodecyl sulfate polyacrylamide gel electrophoresis (7.5%). In this way, an enzymatically active protein fraction was obtained, consisting of four proteins in the molecular weight range of between 12 and 90 kDa. Using beta-carotene as substrate, the enzyme activity was detected spectrophotometrically at 505 nm. The main reaction product, detected by GC analysis, was beta-ionone. This proves that the isolated enzymes are closely related to aroma metabolism and release of star fruit. The time constant of the reaction was 16.6 min, the Michaelis Constant K(m)=3.6 micromol 1(-1) and the maximum velocity V(max)=10.5 x 10(-3) micromol l(-1) s(-1) mg((Protein))(-1). The optimum temperature was 45 degrees C.

The most time-consuming part of the Niederreiter algorithm for factoring univariate polynomials over finite fields is the computation of elements of the nullspace of a certain matrix. This paper describes the so-called ``black-box'' Niederreiter algorithm, in which these elements are found by using a method developed by Wiedemann. The main advantages over an approach based on Gaussian elimination are that the matrix does not have to be stored in memory and that the computational complexity of this approach is lower. The black-box Niederreiter algorithm for factoring polynomials over the binary field was implemented in the C programming language, and benchmarks for factoring high-degree polynomials over this field are presented. These benchmarks include timings for both a sequential implementation and a parallel implementation running on a small cluster of workstations. In addition, the Wan algorithm, which was recently introduced, is described, and connections between (implementation aspects of) Wan's and Niederreiter's algorithm are given.

We present a new method, called reversed double ordering, for reordering arbitrary matrices prior to LU factorization. This reordering creates a variable-band matrix. We compare the fill-in of the LU factorization for sparse matrices with respect to reversed double ordering, column minimum degree ordering, and the reversed Cuthill--McKee algorithm. Moreover, we combine the first two reorderings with good success.

The progenitors of damascenone (1), the most intensive C13-norisoprenoid volatile aroma constituent of rose essential oil, were surveyed in the flowers of Rosa damascena Mill. Besides 9-O-β-D-glucopyranosyl-3-hydroxy-7,8-didehydro-β-ionol (4b), a stable progenitor already isolated from the residual water after steam distillation of flowers of R. damascena Mill., two labile progenitors were identified to be (3S, 9R)- and (3S, 9S)-megastigma-6,7-dien-3,5,9-triol 9-O-β-D-glucopyranosides (2b) based on their synthesis and HPLC-MS analytical data. Compound 2b gave damascenone (1), 3-hydroxy-β-damascone (3) and 4b upon heating under acidic conditions.

Mit der multitronic vereint Audi den Komfort heutiger Automatikgetriebe mit der Dynamik und der Wirtschaftlichkeit manueller Schaltgetriebe. Teil 1 befasste sich mit dem Getriebekonzept, der vorliegende Teil 2 beschreibt die Steuerung und Regelung des Getriebes.

LetGbePSLn(q),PSUn(q),Sp2n(q) orPSp2n(q), whereqis a power of the primep. Using results on the numbers of special squarefree polynomials over finite fields, we describe and count the conjugacy classes ofp′-elements with abelian centralizers inG. Similar results are obtained for the semisimple orbits ofGon the corresponding finite Lie algebras.

Let R R be a commutative ring, V V a finitely generated free R R -module and G ≤ G L R ( V ) G\le GL_R(V) a finite group acting naturally on the graded symmetric algebra A = S ( V ) A=S(V) . Let β ( V , G ) \beta (V,G) denote the minimal number m m , such that the ring A G A^G of invariants can be generated by finitely many elements of degree at most m m . For G = Σ n G=\Sigma _n and V ( n , k ) V(n,k) , the k k -fold direct sum of the natural permutation module, one knows that β ( V ( n , k ) , Σ n ) ≤ n \beta (V(n,k),\Sigma _n) \le n , provided that n ! n! is invertible in R R . This was used by E. Noether to prove β ( V , G ) ≤ | G | \beta (V,G) \le |G| if | G | ! ∈ R ∗ |G|! \in R^* . In this paper we prove β ( V ( n , k ) , Σ n ) ≤ m a x { n , k ( n − 1 ) } \beta (V(n,k),\Sigma _n) \le max\{n,k(n-1)\} for arbitrary commutative rings R R and show equality for n = p s n=p^s a prime power and R = Z R = \mathbb {Z} or any ring with n ⋅ 1 R = 0 n\cdot 1_R=0 . Our results imply β ( V , G ) ≤ m a x { | G | , rank ⁡ ( V ) ( | G | − 1 ) } \begin{equation*} \beta (V,G)\le max\{|G|, \operatorname {rank}(V)(|G|-1)\}\end{equation*} for any ring with | G | ∈ R ∗ |G| \in R^* .

Let p(n) be the set of all partitions of n ϵ N and denote an element c = 1c12c2 … ncn ϵ p(n) by the sequence (c1, c2, … cn) ϵ Nn0 with ∑i = 1,…nci · i = n. For n ϵ N and ∈ ϵ {0, ± 1} we define F n, ϵ (X)≔ Σ (c k )ϵP(n) Π (k=1,…,c k > 0) X c k −1 ·(X−ϵ) . Then fn, ∈(q) equals the number of conjugacy classes in GLn(q) or Un(q2) for ∈ = 1 or −1 respectively or the number of adjoint GLn(q)- or Un(q2)-orbits on their finite Lie algebras, if ∈ = 0. In this paper we give a unified proof of this together with a polynomial identity for fn, ∈(X), involving partitions and ‘multipartitions’ of n.

In this paper an algorithm is presented to determine the number of semisimple conjugacy classes for a given centralizertype for the Chevalley groupsSLn(q) andSUn(q). Moreover we give the exact number of regular semisimple classes of this groups and a summary of results on the generic classnumber of exceptional Chevalley groups of adjoint type.

Carotenoids are a major class of plant pigments and fulfill many functions in different organisms that either produce or consume them. Although the color of the stamina of tea (Camellia sinensis) flowers is clearly due to the presence of carotenoids, the carotenoid profile and content remain to be discovered.We investigated the carotenoid profile of tea flowers and determined changes in concentrations over the floral development. The flowers contained oxygenated xanthophylls such as neoxanthin, lutein and zeaxanthin, as well as the hydrocarbons β-carotene and α-carotene. Flowers of the tea plant contain to vegetables comparable amounts of carotenoids. The content of 9'-cis-epoxycarotenoids, which serve as abscisic acid precursors, as well as changes in concentration of abscisic acid were studied. The concentrations of carotenoids decreased whereas the abscisic acid content increased over the floral development. Exogenously applied S-abscisic acid affected water uptake, flower opening and carotenoid accumulation.In summary, this paper reports, for the first time, the carotenoid profile and content of tea flowers. The study revealed that carotenoids in tea flowers are an interesting target in respect of possible applications of tea flower extracts as well as biological functions of abscisic acid during floral development.

Carotenoid derived volatiles are important fragrance compounds, which contribute to the scents of flowers from diverse taxa. A famous example is represented by the flowers of Osmanthus fragrans where apocarotenoids account for more than 20% of all volatiles. In the recent years, bio-degradation of carotenoids has been shown to be an important route for apocarotenoids formation. Here, we report on the contribution the O. fragrans carotenoid cleavage dioxygenase 1 to the synthesis of the two predominant C(13)-apocarotenoids, α- and β-ionone, derived from α-and β-carotene, respectively.