Computation of relativistic symmetry orbitals for finite double point groups

A program is presented for the construction of relativistic symmetry-adapted molecular basis functions. It is applicable to 36 finite double point groups. The algorithm, based on the projection operator method, automatically generates linearly independent basis sets. Time reversal invariance is included in the program, leading to additional selection rules in the non-relativistic limit.

On the equivariant Tamagawa number conjecture for abelian extensions of a quadratic imaginary field

Let k be a quadratic imaginary field, p a prime which splits in k/Q and does not divide the class number hk of k. Let L denote a finite abelian extention of k and let K be a subextention of L/k. In this article we prove the p-part of the Equivariant Tamagawa Number Conjecture for the pair (h0(Spec(L)),Z[Gal(L/K)]).

Computations in Relative Algebraic K-Groups

Let G be finite group and K a number field or a p-adic field with ring of integers O_K. In the first part of the manuscript we present an algorithm that computes the relative algebraic K-group K_0(O_K[G],K) as an abstract abelian group. We solve the discrete logarithm problem, both in K_0(O_K[G],K) and the locally free class group cl(O_K[G]). All algorithms have been implemented in MAGMA for the case K = \IQ. In the second part of the manuscript we prove formulae for the torsion subgroup of K_0(\IZ[G],\IQ) for large classes of dihedral and quaternion groups.

Fourier-Matrizen und Ringe mit Basis

Bei der Bestimmung der irreduziblen Charaktere einer Gruppe vom Lie-Typ entwickelte Lusztig eine Theorie, in der eine sogenannte Fourier-Transformation auftaucht. Dies ist eine Matrix, die nur von der Weylgruppe der Gruppe vom Lie-Typ abhängt. Anhand der Eigenschaften, die eine solche Fourier- Matrix erfüllen muß, haben Geck und Malle ein Axiomensystem aufgestellt. Dieses ermöglichte es Broue, Malle und Michel füur die Spetses, über die noch vieles unbekannt ist, Fourier-Matrizen zu bestimmen. Das Ziel dieser Arbeit ist eine Untersuchung und neue Interpretation dieser Fourier-Matrizen, die hoffentlich weitere Informationen zu den Spetses liefert. Die Werkzeuge, die dabei entstehen, sind sehr vielseitig verwendbar, denn diese Matrizen entsprechen gewissen Z-Algebren, die im Wesentlichen die Eigenschaften von Tafelalgebren besitzen. Diese spielen in der Darstellungstheorie eine wichtige Rolle, weil z.B. Darstellungsringe Tafelalgebren sind. In der Theorie der Kac-Moody-Algebren gibt es die sogenannte Kac-Peterson-Matrix, die auch die Eigenschaften unserer Fourier-Matrizen besitzt. Ein wichtiges Resultat dieser Arbeit ist, daß die Fourier-Matrizen, die G. Malle zu den imprimitiven komplexen Spiegelungsgruppen definiert, die Eigenschaft besitzen, daß die Strukturkonstanten der zugehörigen Algebren ganze Zahlen sind. Dazu müssen äußere Produkte von Gruppenringen von zyklischen Gruppen untersucht werden. Außerdem gibt es einen Zusammenhang zu den Kac-Peterson-Matrizen: Wir beweisen, daß wir durch Bildung äußerer Produkte von den Matrizen vom Typ A(1)1 zu denen vom Typ C(1) l gelangen. Lusztig erkannte, daß manche seiner Fourier-Matrizen zum Darstellungsring des Quantendoppels einer endlichen Gruppe gehören. Deswegen ist es naheliegend zu versuchen, die noch ungeklärten Matrizen als solche zu identifizieren. Coste, Gannon und Ruelle untersuchen diesen Darstellungsring. Sie stellen eine Reihe von wichtigen Fragen. Eine dieser Fragen beantworten wir, nämlich inwieweit rekonstruiert werden kann, zu welcher endlichen Gruppe gegebene Matrizen gehören. Den Darstellungsring des getwisteten Quantendoppels berechnen wir für viele Beispiele am Computer. Dazu müssen unter anderem Elemente aus der dritten Kohomologie-Gruppe H3(G,C×) explizit berechnet werden, was bisher anscheinend in noch keinem Computeralgebra-System implementiert wurde. Leider ergibt sich hierbei kein Zusammenhang zu den von Spetses herrührenden Matrizen. Die Werkzeuge, die in der Arbeit entwickelt werden, ermöglichen eine strukturelle Zerlegung der Z-Ringe mit Basis in bekannte Anteile. So können wir für die meisten Matrizen der Spetses Konstruktionen angeben: Die zugehörigen Z-Algebren sind Faktorringe von Tensorprodukten von affinen Ringe Charakterringen und von Darstellungsringen von Quantendoppeln.

Church-Rosser groups and growing context-sensitive groups

A finitely generated group is called a Church-Rosser group (growing context-sensitive group) if it admits a finitely generated presentation for which the word problem is a Church-Rosser (growing context-sensitive) language. Although the Church-Rosser languages are incomparable to the context-free languages under set inclusion, they strictly contain the class of deterministic context-free languages. As each context-free group language is actually deterministic context-free, it follows that all context-free groups are Church-Rosser groups. As the free abelian group of rank 2 is a non-context-free Church-Rosser group, this inclusion is proper. On the other hand, we show that there are co-context-free groups that are not growing context-sensitive. Also some closure and non-closure properties are established for the classes of Church-Rosser and growing context-sensitive groups. More generally, we also establish some new characterizations and closure properties for the classes of Church-Rosser and growing context-sensitive languages.

Synthese und Charakterisierung neuer symmetrischer und unsymmetrischer Spiro-p-oligophenyle

In der vorliegenden Arbeit wurden neue symmetrische Spiro-p-oligophenyle der allgemeinen Form Spiro-o-Φ[n,n] mit der Gesamtkettenlänge o=2n+2 Phenylringen (o > 10) und der Zahl n der Phenylringe in den p-Oligophenylsubstituenten am Spirobifluorenkern, dargestellt. Neben den symmetrischen Verbindungen wurden erstmals auch unsymmetrische Spiro-p-oligophenyle der allgemeinen Form Spiro-o-Φ[n,m] mit o=n+m+2 (o = 3-7) und n ≠ m synthetisiert. Aufgrund der sehr geringen Löslichkeit der größeren Verbindungen wurden löslichkeitssteigernde Substituenten an den endständigen Phenylringen angebracht. Bei den Verbindungen, die mit Trimethylsilyl-Gruppen (TMS-) in den endständigen meta-Positionen „3“ und „5“ substituiert wurden, konnte die Löslichkeit um mehrere Größenordnungen gesteigert werden, sodass die Darstellung der symmetrischen Verbindungen bis zu einer Kettenlänge von 16 Phenylringen möglich wurde. Nach erfolgreicher Synthese und Aufreinigung wurden die TMS-Gruppen wieder entfernt und die erhaltenen, unsubstituierten Verbindungen charakterisiert. Zusätzlich wurden auch die TMS-Derivate untersucht. Zur Charakterisierung zählten neben der Reinheits- und Strukturanalytik unter anderem auch spektroskopische (UV/Vis-Absorption, Fluoreszenz, Fluoreszenzquantenausbeute), elektrochemische (Cyclovoltammetrie) und thermische (Thermogravimetrie, Dynamische Differenzkalorimetrie) Untersuchungen. Hier wurde unter anderem der Einfluss der Kettenlänge und der Position der Spiroverknüpfung auf isomere Verbindungen gleicher Kettenlänge untersucht. Bei den spektroskopischen Messungen konnte eine Konvergenz der längstwelligen Absorptionsbanden, bzw. kürzestwelligen Fluoreszenzbanden mit zunehmender Kettenlänge beobachtet werden. Die effektive Konjugationslänge konnte so aus experimentellen Daten bestimmt werden zu 12 Phenylringen in der Absorption und 14 Phenylringen in der Fluoreszenz. Bei den Isomeren gleicher Kettenlänge zeigte sich in der Absorption eine hypsochrome Verschiebung der Absorptionsmaxima mit zunehmender Verschiebung der Spiroverknüpfung zum Kettenende hin, während die Position der Spiroverknüpfung keinen messbaren Einfluss auf die Verschiebung der Fluoreszenzbanden hatte. Die Substitution mit TMS in den meta-Positionen zeigte keinen messbaren Einfluss auf die Absorptions- bzw. Fluoreszenzbanden. Die elektrochemischen Untersuchungen zeigten mit zunehmender Kettenlänge eine erleichterte Oxidation und Reduktion, während bei Isomeren gleicher Kettenlänge die Oxidation mit Verschiebung der Spiroverknüpfung zum Kettenende hin erschwert und die Reduktion erleichtert war. Die thermogravimetrischen Analysen (TGA) zeigten eine außerordentlich hohe thermische Stabilität (5% Massenabnahme unter Schutzgas) der Spiro-p-oligophenyle von Td,5% = 474°C bei Spiro-5Φ[1,2] bis 570°C bei Spiro 8Φ[3,3]. Ebenso blieben hohe Rückstandsmassen unter Schutzgas bei 850°C zurück, wie das Beispiel Spiro 8Φ[3,3] mit 68% zeigt. Die Verbindungen zeigten hohe Schmelzpunkte (max. 496°C bei Spiro-6Φ[0,4]) und Glasübergangstemperaturen (max. 434°C bei p-TMS-Spiro-8Φ[3,3]). Viele der Verbindungen, besonders die in den meta-Positionen TMS-substituierten Verbindungen, bildeten stabile amorphe Gläser.

Status and Potential of Smallholder Livestock Production Systems in Xishuangbanna, southern P.R. China

With Chinas rapid economic development during the last decades, the national demand for livestock products has quadrupled within the last 20 years. Most of that increase in demand has been answered by subsidized industrialized production systems, while million of smallholders, which still provide the larger share of livestock products in the country, have been neglected. Fostering those systems would help China to lower its strong urban migration streams, enhance the livelihood of poorer rural population and provide environmentally save livestock products which have a good chance to satisfy customers demand for ecological food. Despite their importance, China’s smallholder livestock keepers have not yet gained appropriate attention from governmental authorities and researchers. However, profound analysis of those systems is required so that adequate support can lead to a better resource utilization and productivity in the sector. To this aim, this pilot study analyzes smallholder livestock production systems in Xishuangbanna, located in southern China. The area is bordered by Lao and Myanmar and geographically counts as tropical region. Its climate is characterized by dry and temperate winters and hot summers with monsoon rains from May to October. While the regionis plain, at about 500 m asl above sea level in the south, outliers of the Himalaya mountains reach out into the north of Xishuangbanna, where the highest peak reaches 2400 m asl. Except of one larger city, Jinghong, Xishuangbanna mainly is covered by tropical rainforest, areas under agricultural cultivation and villages. The major income is generated through inner-Chinese tourism and agricultural production. Intensive rubber plantations are distinctive for the lowland plains while small-scaled traditional farms are scattered in the mountane regions. In order to determine the current state and possible future chances of smallholder livestock production in that region, this study analyzed the current status of the smallholder livestock sector in the Naban River National Nature Reserve (NRNNR), an area which is largely representative for the whole prefecture. It covers an area of about 50square kilometer and reaches from 470 up to 2400 m asl. About 5500 habitants of different ethnic origin are situated in 24 villages. All data have been collected between October 2007 and May 2010. Three major objectives have been addressed in the study: 1. Classifying existing pig production systems and exploring respective pathways for development 2. Quantifying the performance of pig breeding systemsto identify bottlenecks for production 3. Analyzing past and current buffalo utilization to determine the chances and opportunities of buffalo keeping in the future In order to classify the different pig production s ystems, a baseline survey (n=204, stratified cluster sampling) was carried out to gain data about livestock species, numbers, management practices, cultivated plant species and field sizes as well associo-economic characteristics. Sampling included two clusters at village level (altitude, ethnic affiliation), resulting in 13 clusters of which 13-17 farms were interviewed respectively. Categorical Principal Component Analysis (CatPCA) and a two-step clustering algorithm have been applied to identify determining farm characteristics and assort recorded households into classes of livestock production types. The variables keep_sow_yes/no, TLU_pig, TLU_buffalo, size_of_corn_fields, altitude_class, size_of_tea_plantationand size_of_rubber_fieldhave been found to be major determinants for the characterization of the recorded farms. All farms have extensive or semi-intensive livestock production, pigs and buffaloes are predominant livestock species while chicken and aquaculture are available but play subordinate roles for livelihoods. All pig raisers rely on a single local breed, which is known as Small Ear Pig (SMEP) in the region. Three major production systemshave been identified: Livestock-corn based LB; 41%), rubber based (RB; 39%) and pig based (PB;20%) systems. RB farms earn high income from rubber and fatten 1.9 ±1.80 pigs per household (HH), often using purchased pig feed at markets. PB farms own similar sized rubber plantations and raise 4.7 ±2.77 pigs per HH, with fodder mainly being cultivated and collected in theforest. LB farms grow corn, rice and tea and keep 4.6 ±3.32 pigs per HH, also fed with collected and cultivated fodder. Only 29% of all pigs were marketed (LB: 20%; RB: 42%; PB: 25%), average annual mortality was 4.0 ±4.52 pigs per farm (LB: 4.6 ±3.68; RB: 1.9 ±2.14; PB: 7.1 ±10.82). Pig feed mainly consists of banana pseudo stem, corn and rice hives and is prepared in batches about two to three times per week. Such fodder might be sufficient in energy content but lacks appropriate content of protein. Pigs therefore suffer from malnutrition, which becomes most critical in the time before harvest season around October. Farmers reported high occurrences of gastrointestinal parasites in carcasses and often pig stables were wet and filled with manure. Deficits in nutritional and hygienic management are major limits for development and should be the first issues addressed to improve productivity. SME pork was found to be known and referred by local customers in town and by richer lowland farmers. However, high prices and lacking availability of SME pork at local wet-markets were the reasons which limited purchase. If major management constraints are overcome, pig breeders (PB and LB farms) could increase the share of marketed pigs for town markets and provide fatteners to richer RB farmers. RB farmers are interested in fattening pigs for home consumption but do not show any motivation for commercial pig raising. To determine the productivity of input factors in pig production, eproductive performance, feed quality and quantity as well as weight development of pigs under current management were recorded. The data collection included a progeny history survey covering 184 sows and 437 farrows, bi-weekly weighing of 114 pigs during a 16-months time-span on 21 farms (10 LB and 11 PB) as well as the daily recording of feed quality and quantity given to a defined number of pigs on the same 21 farms. Feed samples of all recorded ingredients were analyzed for their respective nutrient content. Since no literature values on thedigestibility of banana pseudo stem – which is a major ingredient of traditional pig feed in NRNNR – were found, a cross-sectional digestibility trial with 2x4 pigs has been conducted on a station in the research area. With the aid of PRY Herd Life Model, all data have been utilized to determine thesystems’ current (Status Quo = SQ) output and the productivity of the input factor “feed” in terms of saleable life weight per kg DM feed intake and monetary value of output per kg DM feed intake.Two improvement scenarios were simulated, assuming 1) that farmers adopt a culling managementthat generates the highest output per unit input (Scenario 1; SC I) and 2) that through improved feeding, selected parameters of reproduction are improved by 30% (SC II). Daily weight gain averaged 55 ± 56 g per day between day 200 and 600. The average feed energy content of traditional feed mix was 14.92 MJ ME. Age at first farrowing averaged 14.5 ± 4.34 months, subsequent inter-farrowing interval was 11.4 ± 2.73 months. Littersize was 5.8 piglets and weaning age was 4.3 ± 0.99 months. 18% of piglets died before weaning. Simulating pig production at actualstatus, it has been show that monetary returns on inputs (ROI) is negative (1:0.67), but improved (1:1.2) when culling management was optimized so that highest output is gained per unit feed input. If in addition better feeding, controlled mating and better resale prices at fixed dates were simulated, ROI further increased to 1:2.45, 1:2.69, 1:2.7 and 1:3.15 for four respective grower groups. Those findings show the potential of pork production, if basic measures of improvement are applied. Futureexploration of the environment, including climate, market-season and culture is required before implementing the recommended measures to ensure a sustainable development of a more effective and resource conserving pork production in the future. The two studies have shown that the production of local SME pigs plays an important role in traditional farms in NRNNR but basic constraints are limiting their productivity. However, relatively easy approaches are sufficient for reaching a notable improvement. Also there is a demand for more SME pork on local markets and, if basic constraints have been overcome, pig farmers could turn into more commercial producers and provide pork to local markets. By that, environmentally safe meat can be offered to sensitive consumers while farmers increase their income and lower the risk of external shocks through a more diverse income generating strategy. Buffaloes have been found to be the second important livestock species on NRNNR farms. While they have been a core resource of mixed smallholderfarms in the past, the expansion of rubber tree plantations and agricultural mechanization are reasons for decreased swamp buffalo numbers today. The third study seeks to predict future utilization of buffaloes on different farm types in NRNNR by analyzing the dynamics of its buffalo population and land use changes over time and calculating labor which is required for keeping buffaloes in view of the traction power which can be utilized for field preparation. The use of buffaloes for field work and the recent development of the egional buffalo population were analyzed through interviews with 184 farmers in 2007/2008 and discussions with 62 buffalo keepers in 2009. While pig based farms (PB; n=37) have abandoned buffalo keeping, 11% of the rubber based farms (RB; n=71) and 100% of the livestock-corn based farms (LB; n=76) kept buffaloes in 2008. Herd size was 2.5 ±1.80 (n=84) buffaloes in early 2008 and 2.2 ±1.69 (n=62) in 2009. Field work on own land was the main reason forkeeping buffaloes (87.3%), but lending work buffaloes to neighbors (79.0%) was also important. Other purposes were transport of goods (16.1%), buffalo trade (11.3%) and meat consumption(6.4%). Buffalo care required 6.2 ±3.00 working hours daily, while annual working time of abuffalo was 294 ±216.6 hours. The area ploughed with buffaloes remained constant during the past 10 years despite an expansion of land cropped per farm. Further rapid replacement of buffaloes by tractors is expected in the near future. While the work economy is drastically improved by the use of tractors, buffaloes still can provide cheap work force and serve as buffer for economic shocks on poorer farms. Especially poor farms, which lack alternative assets that could quickly be liquidizedin times of urgent need for cash, should not abandon buffalo keeping. Livestock has been found to be a major part of small mixed farms in NRNNR. The general productivity was low in both analyzed species, buffaloes and pigs. Productivity of pigs can be improved through basic adjustments in feeding, reproductive and hygienic management, and with external support pig production could further be commercialized to provide pork and weaners to local markets and fattening farms. Buffalo production is relatively time intensive, and only will be of importance in the future to very poor farms and such farms that cultivate very small terraces on steep slopes. These should be encouraged to further keep buffaloes. With such measures, livestock production in NRNNR has good chances to stay competitive in the future.