Computing Generators of Free Modules over Orders in Group Algebras

Let E be a number field and G be a finite group. Let A be any O_E-order of full rank in the group algebra E[G] and X be a (left) A-lattice. We give a necessary and sufficient condition for X to be free of given rank d over A. In the case that the Wedderburn decomposition E[G] \cong \oplus_xM_x is explicitly computable and each M_x is in fact a matrix ring over a field, this leads to an algorithm that either gives elements \alpha_1,...,\alpha_d \in X such that X = A\alpha_1 \oplus ... \oplusA\alpha_d or determines that no such elements exist. Let L/K be a finite Galois extension of number fields with Galois group G such that E is a subfield of K and put d = [K : E]. The algorithm can be applied to certain Galois modules that arise naturally in this situation. For example, one can take X to be O_L, the ring of algebraic integers of L, and A to be the associated order A(E[G];O_L) \subseteq E[G]. The application of the algorithm to this special situation is implemented in Magma under certain extra hypotheses when K = E = \IQ.

Effects of Different Feeding Regimes on the Digestibility and Faecal Excretion of Nitrogen, Soluble Carbohydrates and Fibre Fractions in Water Buffaloes kept under Subtropical Conditions

In the course of the ‘Livestock Revolution’, extension and intensification of, among others, ruminant livestock production systems are current phenomena, with all their positive and negative side effects. Manure, one of the inevitable secondary products of livestock rearing, is a valuable source of plant nutrients and its skillful recycling to the soil-plant interface is essential for soil fertility, nutrient - and especially phosphorus - uses efficiency and the preservation or re-establishment of environmentally sustainable farming systems, for which organic farming systems are exemplarily. Against this background, the PhD research project presented here, which was embedded in the DFG-funded Research Training Group 1397 ‘Regulation of soil organic matter and nutrient turnover in organic agriculture ’ investigated possibilities to manipulate the diets of water buffalo (Bubalus bubalis L.) so as to produce manure of desired quality for organic vegetable production, without affecting the productivity of the animals used. Consisting of two major parts, the first study (chapter 2) tested the effects of diets differing in their ratios of carbon (C) to nitrogen (N) and of structural to non-structural carbohydrates on the quality of buffalo manure under subtropical conditions in Sohar, Sultanate of Oman. To this end, two trials were conducted with twelve water buffalo heifers each, using a full Latin Square design. One control and four tests diets were examined during three subsequent 7 day experimental periods preceded each by 21 days adaptation. Diets consisted of varying proportions of Rhodes grass hay, soybean meal, wheat bran, maize, dates, and a commercial concentrate to achieve a (1) high C/N and high NDF (neutral detergent fibre)/SC (soluble carbohydrate) ratio (HH), (2) low C/N and low NDF/SC ratio (LL); (3) high C/N and low NDF/SC ratio (HL) and (4) low C/N and high NDF/SC (LH) ratio. Effects of these diets, which were offered at 1.45 times maintenance requirements of metabolizable energy, and of individual diet characteristics, respectively, on the amount and quality of faeces excreted were determined and statistically analysed. The faeces produced from diets HH and LL were further tested in a companion PhD study (Mr. K. Siegfried) concerning their nutrient release in field experiments with radish and cabbage. The second study (chapter 3) focused on the effects of the above-described experimental diets on the rate of passage of feed particles through the gastrointestinal tract of four randomly chosen animals per treatment. To this end, an oral pulse dose of 683 mg fibre particles per kg live weight marked with Ytterbium (Yb; 14.5 mg Yb g-1 organic matter) was dosed at the start of the 7 day experimental period which followed 21 days of adaptation. During the first two days a sample for Yb determination was kept from each faecal excretion, during days 3 – 7 faecal samples were kept from the first morning and the first evening defecation only. Particle passage was modelled using a one-compartment age-dependent Gamma-2 model. In both studies individual feed intake and faecal excretion were quantified throughout the experimental periods and representative samples of feeds and faeces were subjected to proximate analysis following standard protocols. In the first study the organic matter (OM) intake and excretion of LL and LH buffaloes were significantly lower than of HH and HL animals, respectively. Digestibility of N was highest in LH (88%) and lowest in HH (74%). While NDF digestibility was also highest in LH (85%) it was lowest in LL (78%). Faecal N concentration was positively correlated (P≤0.001) with N intake, and was significantly higher in faeces excreted by LL than by HH animals. Concentrations of fibre and starch in faecal OM were positively affected by the respective dietary concentrations, with NDF being highest in HH (77%) and lowest in LL (63%). The faecal C/N ratio was positively related (P≤0.001) to NDF intake; C/N ratios were 12 and 7 for HH and LL (P≤0.001), while values for HL and LH were 11.5 and 10.6 (P>0.05). The results from the second study showed that dietary N concentration was positively affecting faecal N concentration (P≤0.001), while there was a negative correlation with the faecal concentration of NDF (P≤0.05) and the faecal ratios of NDF/N and C/N (P≤0.001). Particle passage through the mixing compartment was lower (P≤0.05) for HL (0.033 h-1) than for LL (0.043 h-1) animals, while values of 0.034 h-1 and 0.038 h-1 were obtained for groups LH and HH. At 55.4 h, total tract mean retention time was significantly (P≤0.05) lower in group LL that in all other groups where these values varied between 71 h (HH) and 79 h (HL); this was probably due to the high dietary N concentration of diet LL which was negatively correlated with time of first marker appearance in faeces (r= 0.84, P≤0.001), while the dietary C concentration was negatively correlated with particle passage through the mixing compartment (r= 0.57, P≤0.05). The results suggest that manure quality of river buffalo heifers can be considerably influenced by diet composition. Despite the reportedly high fibre digestion capacity of buffalo, digestive processes did not suppress the expression of diet characteristics in the faeces. This is important when aiming at producing a specific manure quality for fertilization purposes in (organic) crop cultivation. Although there was a strong correlation between the ingestion and the faecal excretion of nitrogen, the correlation between diet and faecal C/N ratio was weak. To impact on manure mineralization, the dietary NDF and N concentrations seem to be the key control points, but modulating effects are achieved by the inclusion of starch into the diet. Within the boundaries defined by the animals’ metabolic and (re)productive requirements for energy and nutrients, diet formulation may thus take into account the abiotically and biotically determined manure turnover processes in the soil and the nutrient requirements of the crops to which the manure is applied, so as to increase nutrient use efficiency along the continuum of the feed, the animal, the soil and the crop in (organic) farming systems.

Increasing scepticism toward potential liars: effects of existential threat on veracity judgments and the moderating role of honesty norm activation

With the present research, we investigated effects of existential threat on veracity judgments. According to several meta-analyses, people judge potentially deceptive messages of other people as true rather than as false (so-called truth bias). This judgmental bias has been shown to depend on how people weigh the error of judging a true message as a lie (error 1) and the error of judging a lie as a true message (error 2). The weight of these errors has been further shown to be affected by situational variables. Given that research on terror management theory has found evidence that mortality salience (MS) increases the sensitivity toward the compliance of cultural norms, especially when they are of focal attention, we assumed that when the honesty norm is activated, MS affects judgmental error weighing and, consequently, judgmental biases. Specifically, activating the norm of honesty should decrease the weight of error 1 (the error of judging a true message as a lie) and increase the weight of error 2 (the error of judging a lie as a true message) when mortality is salient. In a first study, we found initial evidence for this assumption. Furthermore, the change in error weighing should reduce the truth bias, automatically resulting in better detection accuracy of actual lies and worse accuracy of actual true statements. In two further studies, we manipulated MS and honesty norm activation before participants judged several videos containing actual truths or lies. Results revealed evidence for our prediction. Moreover, in Study 3, the truth bias was increased after MS when group solidarity was previously emphasized.

Immunologisches Reaktionsvermögen als Indikator für Belastungen bei der Milchkuh

Mit ansteigenden Jahresmilchleistungen werden die Kühe einer hohen metabolischen Belastung ausgesetzt, die bei einer suboptimalen Gestaltung der Lebensbedingungen mit einer Erhöhung der Inzidenzrate von Faktorenkrankheiten einhergehen kann. Im Vordergrund der Untersuchungen stand die Frage, inwieweit metabolische Belastungszustände von Milchkühen in der Phase des Puerperiums und in Abhängigkeit von der Milchleistung sowie Belastungen durch eine klinische Erkrankung zu Beginn der Laktation mit Hilfe von Parametern der immunologischen Abwehr und der Reaktion des Immunsystems auf eine Challenge dargestellt werden können. In die Untersuchung wurden insgesamt 68 klinisch gesunde sowie 20 klinisch erkrankte Milchkühe der Rasse Holstein Friesian einbezogen. Die Untersuchungen erfolgten in den Zeiträumen 10-21 Tage sowie 14-15 Wochen nach der Kalbung. Dazu wurden an jeweils drei Untersuchungstagen (Tag 0, 2, 7) Blutproben aus der Vena jugularis entnommen. Zur Stimulierung des unspezifischen Immunsystems wurde in beiden Versuchszeiträumen an den Untersuchungstagen 0 und 2 der Paramunitätsinducer Zylexis® appliziert. Ferner wurde den Kühen zu Beginn der Laktation der Tollwutimpfstoff Rabisin® verabreicht. Für die Auswertung wurden die untersuchten Milchkühe in Gruppen unterteilt. Die klinisch gesunden Kühe wurden anhand der nach Fett und Eiweiß korrigierten 305-Tage-Leistung in die Gruppe M = mittleres Leistungsniveau (Milchmengenleistung 6.500-8.990 kg) und die Gruppe H = hohes Leistungsniveau (Milchmengenleistung 9.000-12.500 kg) aufgeteilt. Die klinisch erkrankten Kühe wurden in der Gruppe K zusammengefasst. Zur Beurteilung der Immunabwehr wurden die Parameter Phagozytoseaktivität der isolierten Neutrophilen Granulozyten, die Vollblutbakterizidie, die Lymphozytenproliferation mit den Mitogenen ConA, PHA und PWM sowie die spezifische Antikörperbildung gegen Tollwut untersucht. Anhand der Parameter Phagozytoseaktivität, Vollblutbakterizidie und Lymphozytenproliferation wurde zusätzlich die Reaktion auf die Challenge mit dem Paramunitätsinducer Zylexis® überprüft. Zur Erfassung der metabolischen Belastungszustände wurden verschiedene Stoffwechselparameter und hämatologische Parameter erfasst. Zu Beginn der Laktation konnten bei den Kühen in der mittleren und hohen Leistungsgruppe signifikant höhere Konzentrationen an ß-Hydroxybuttersäure und Freien Fettsäuren im Vergleich zu der Laktationsmitte festgestellt werden. Die Kühe mit einem hohen Leistungsniveau zeigten darüber hinaus eine signifikant höhere Bilirubinkonzentration am Laktationsanfang gegenüber der Laktationsmitte. Die mittlere Konzentration der freien Fettsäuren lag bei den Kühen in beiden Leistungsgruppen oberhalb des Referenzbereiches und wies auf eine negative Energiebilanz zu Laktationsbeginn hin. Die mittleren Konzentrationen bzw. Enzymaktivitäten der Parameter Cholesterol, Harnstoff, AST, GLDH, γ-GT, Gesamtprotein, Kalzium und Phosphor wiesen in der Laktationsmitte signifikant höhere Werte als am Laktationsanfang auf. Dabei lagen die mittleren Enzymaktivitäten von AST und GLDH sowie die Konzentrationen von Harnstoff und Gesamtprotein in der Laktationsmitte oberhalb des Referenzbereiches. Die untersuchten Stoffwechselparameter wurden durch die Challenge mit einem Paramunitätsinducer nicht signifikant beeinflusst. Hinsichtlich der Immunparameter zeigten die Milchkühe mit einem mittleren Leistungsniveau in Abhängigkeit vom Laktationszeitpunkt zu Beginn der Laktation eine signifikant höhere Phagozytoseaktivität gegenüber der Laktationsmitte (p < 0,05). Die Gruppe mit einem hohen Leistungsniveau wies dagegen keine signifikanten Unterschiede in der Phagozytoseaktivität zwischen den beiden Untersuchungszeiträumen auf. Bei den Immunparametern Vollblutbakterizidie und Lymphozytenproliferation konnten bei den Kühen beider Gruppen keine signifikanten Unterschiede in Abhängigkeit vom Laktationszeitpunkt festgestellt werden. Im Hinblick auf die Milchleistung wiesen die Kühe in den beiden Leistungsgruppen am Untersuchungstag 0 weder zu Beginn noch in der Mitte der Laktation signifikante Unterschiede bezüglich der untersuchten Immunparameter auf. Nach der Challenge durch den Paramunitätsinducer reagierten einzig die Kühe mit einer mittleren Leistung zu Beginn der Laktation auf die Challenge mit einer signifikanten Reduzierung der mittleren Phagozytoseaktivität von Tag 0 zu Tag 2 (p < 0,05). Bei den weiteren untersuchten Immunparametern konnten weder bei den Kühen mit einer mittleren noch mit einer hohen Leistung eine signifikante Reaktion auf die Challenge nachgewiesen werden. Die klinisch erkrankten Kühe zeigten im Vergleich zu den klinisch gesunden Kühen keine unterschiedlichen Konzentrationen bzw. Aktivitäten der untersuchten Stoffwechselparameter. Auch konnten anhand der immunologischen Parameter und der Reaktion auf die Challenge keine Unterschiede zwischen den klinisch gesunden Kühen festgestellt werden. Die in der vorliegenden Untersuchung geprüften metabolischen Belastungen konnten weder anhand der Immunparameter noch durch die Reaktion der Immunparameter auf eine Challenge dargestellt werden. Es wird geschlussfolgert, dass das immunologische Reaktionsvermögen nicht geeignet ist, um als Indikator für Belastungszustände bei der Milchkuh herangezogen zu werden.

Predicted properties of the superheavy elements. III. Element 115, Eka-Bismuth

Element 115 is expected to be in group V-a of the periodic table and have most stable oxidation states of I and III. The oxidation state of I, which plays a minor role in bismuth chemistry, should be a major factor in 115 chemistry. This change will arise because of the large relativistic splitting of the spherically symmetric 7p_l/2 shell from the 7P_3/2 shell. Element 115 will therefore have a single 7p_3/2 electron outside a 7p^2_1/2 closed shell. The magnitude of the first ionization energy and ionic radius suggest a chemistry similar to Tl^+. Similar considerations suggest that 115^3+ will have a chemistry similar to Bi^3+. Hydrolysis will therefore be easy and relatively strongly complexing anions of strong acids will be needed in general to effect studies of complexation chemistry. Some other properties of 115 predicted are as follows: ionization potentials I 5.2 eV, II 18.1 eV, III 27.4 eV, IV 48.5 eV, 0 \rightarrow 5^+ 159 eV; heat of sublimation, 34 kcal (g-atom)^-1; atomic radius, 2.0 A; ionic radius, 115^+ 1.5 A, 115^3+ 1.0 A; entropy, 16 cal deg^-1 (g-atom)^-l (25°); standard electrode potential 115^+ |115, -1.5 V; melting and boiling points are similar to element 113.

Relativistic LCAO with Minimax Principle and New Balanced Basis Sets

Relativistic density functional theory is widely applied in molecular calculations with heavy atoms, where relativistic and correlation effects are on the same footing. Variational stability of the Dirac Hamiltonian is a very important field of research from the beginning of relativistic molecular calculations on, among efforts for accuracy, efficiency, and density functional formulation, etc. Approximations of one- or two-component methods and searching for suitable basis sets are two major means for good projection power against the negative continuum. The minimax two-component spinor linear combination of atomic orbitals (LCAO) is applied in the present work for both light and super-heavy one-electron systems, providing good approximations in the whole energy spectrum, being close to the benchmark minimax finite element method (FEM) values and without spurious and contaminated states, in contrast to the presence of these artifacts in the traditional four-component spinor LCAO. The variational stability assures that minimax LCAO is bounded from below. New balanced basis sets, kinetic and potential defect balanced (TVDB), following the minimax idea, are applied with the Dirac Hamiltonian. Its performance in the same super-heavy one-electron quasi-molecules shows also very good projection capability against variational collapse, as the minimax LCAO is taken as the best projection to compare with. The TVDB method has twice as many basis coefficients as four-component spinor LCAO, which becomes now linear and overcomes the disadvantage of great time-consumption in the minimax method. The calculation with both the TVDB method and the traditional LCAO method for the dimers with elements in group 11 of the periodic table investigates their difference. New bigger basis sets are constructed than in previous research, achieving high accuracy within the functionals involved. Their difference in total energy is much smaller than the basis incompleteness error, showing that the traditional four-spinor LCAO keeps enough projection power from the numerical atomic orbitals and is suitable in research on relativistic quantum chemistry. In scattering investigations for the same comparison purpose, the failure of the traditional LCAO method of providing a stable spectrum with increasing size of basis sets is contrasted to the TVDB method, which contains no spurious states already without pre-orthogonalization of basis sets. Keeping the same conditions including the accuracy of matrix elements shows that the variational instability prevails over the linear dependence of the basis sets. The success of the TVDB method manifests its capability not only in relativistic quantum chemistry but also for scattering and under the influence of strong external electronic and magnetic fields. The good accuracy in total energy with large basis sets and the good projection property encourage wider research on different molecules, with better functionals, and on small effects.