Asymptotics of number fields and the Cohen-Lenstra heuristics

We study the asymptotics conjecture of Malle for dihedral groups Dl of order 2l, where l is an odd prime. We prove the expected lower bound for those groups. For the upper bounds we show that there is a connection to class groups of quadratic number fields. The asymptotic behavior of those class groups is predicted by the Cohen-Lenstra heuristics. Under the assumption of this heuristic we are able to prove the expected upper bounds.

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)]).

The Parity of the Number of Irreducible Factors for Some Pentanomials

It is well known that Stickelberger-Swan theorem is very important for determining reducibility of polynomials over a binary field. Using this theorem it was determined the parity of the number of irreducible factors for some kinds of polynomials over a binary field, for instance, trinomials, tetranomials, self-reciprocal polynomials and so on. We discuss this problem for type II pentanomials namely x^m +x^{n+2} +x^{n+1} +x^n +1 \in\ IF_2 [x]. Such pentanomials can be used for efficient implementing multiplication in finite fields of characteristic two. Based on the computation of discriminant of these pentanomials with integer coefficients, it will be characterized the parity of the number of irreducible factors over IF_2 and be established the necessary conditions for the existence of this kind of irreducible pentanomials.

Parity of the Number of Irreducible Factors for Composite Polynomials

Various results on parity of the number of irreducible factors of given polynomials over finite fields have been obtained in the recent literature. Those are mainly based on Swan’s theorem in which discriminants of polynomials over a finite field or the integral ring Z play an important role. In this paper we consider discriminants of the composition of some polynomials over finite fields. The relation between the discriminants of composed polynomial and the original ones will be established. We apply this to obtain some results concerning the parity of the number of irreducible factors for several special polynomials over finite fields.

Influence of occupation number of single particle levels on K - K charge transfer in collisions of 90 keV - Ne{^9+} on Ne

The influence of the occupation of the single particle levels on the impact parameter dependent K - K charge transfer occuring in collisions of 90 keV Ne{^9+} on Ne was studied using coupled channel calculations. The energy eigenvalues and matrixelements for the single particle levels were taken from ab initio self consistent MO-LCAO-DIRAC-FOCK-SLATER calculations with occupation numbers corresponding to the single particle amplitudes given by the coupled channel calculations.

Management approaches in organic potato and tomato production

The presented thesis considered three different system approach topics to ensure yield and plant health in organically grown potatoes and tomatoes. The first topic describes interactions between late blight (Phytophthora infestans) incidence and soil nitrogen supply on yield in organic potato farming focussing in detail on the yield loss relationship of late blight based on results of several field trials. The interactive effects of soil N-supply, climatic conditions and late blight on the yield were studied in the presence and absence of copper fungicides from 2002-2004 for the potato cultivar Nicola. Under conditions of central Germany the use of copper significantly reduced late blight in almost all cases (15-30 %). However, the reductions in disease through copper application did not result in statistically significant yield increases (+0 – +10 %). Subsequently, only 30 % of the variation in yield could be attributed to disease reductions. A multiple regression model (R²Max), however, including disease reduction, growth duration and temperature sum from planting until 60 % disease severity was reached and soil mineral N contents 10 days after emergence could explain 75 % of the observed variations in yield. The second topic describes the effect of some selected organic fertilisers and biostimulant products on nitrogen-mineralization and efficiency, yield and diseases in organic potato and tomato trials. The organic fertilisers Biofeed Basis (BFB, plant derived, AgroBioProducts, Wageningen, Netherlands) and BioIlsa 12,5 Export (physically hydrolysed leather shavings, hair and skin of animals; ILSA, Arizignano, Italy) and two biostimulant products BioFeed Quality (BFQ, multi-compound seaweed extract, AgroBioProducts) and AUSMA (aqueous pine and spruce needle extract, A/S BIOLAT, Latvia), were tested. Both fertilisers supplied considerable amounts of nitrogen during the main uptake phases of the crops and reached yields as high or higher as compared to the control with horn meal fertilisation. The N-efficiency of the tested fertilisers in potatoes ranged from 90 to 159 kg yield*kg-1 N – input. Most effective with tomatoes were the combined treatments of fertiliser BFB and the biostimulants AUSMA and BFQ. Both biostimulants significantly increased the share of healthy fruit and/or the number of fruits. BFQ significantly increased potato yields (+6 %) in one out of two years and reduced R. solani-infestation in the potatoes. This suggests that the biostimulants had effects on plant metabolism and resistance properties. However, no effects of biostimulants on potato late blight could be observed in the fields. The third topic focused on the effect of suppressive composts and seed tuber health on the saprophytic pathogen Rhizoctonia solani in organic potato systems. In the present study 5t ha-1 DM of a yard and bio-waste (60/40) compost produced in a 5 month composting process and a 15 month old 100 % yard waste compost were used to assess the effects on potato infection with R. solani when applying composts within the limits allowed. Across the differences in initial seed tuber infestation and 12 cultivars 5t DM ha-1 of high quality composts, applied in the seed tuber area, reduced the infestation of harvested potatoes with black scurf, tuber malformations and dry core tubers by 20 to 84 %, 20 to 49 % and 38 to 54 %, respectively, while marketable yields were increased by 5 to 25 % due to lower rates of wastes after sorting (marketable yield is gross yield minus malformed tubers, tubers with dry core, tubers with black scurf > 15% infested skin). The rate of initial black scurf infection of the seed tubers also affected tuber number, health and quality significantly. Compared to healthy seed tubers initial black scurf sclerotia infestation of 2-5 and >10 % of tuber surface led in untreated plots to a decrease in marketable yields by 14-19 and 44-66 %, a increase of black scurf severity by 8-40 and 34-86 % and also increased the amount of malformed and dry core tubers by 32-57 and 109-214 %.

Ecophysiology of seed dormancy and salt tolerance of Grewia tenax (Forssk.) Fiori and Ziziphus spina-christi (L.) Willd.

Higher Education Commission (HEC) of Pakistan and German Academic Exchange Service (DAAD)

Algorithms for Tamagawa Number Conjectures

In dieser Arbeit werden Algorithmen zur Untersuchung der äquivarianten Tamagawazahlvermutung von Burns und Flach entwickelt. Zunächst werden Algorithmen angegeben mit denen die lokale Fundamentalklasse, die globale Fundamentalklasse und Tates kanonische Klasse berechnet werden können. Dies ermöglicht unter anderem Berechnungen in Brauergruppen von Zahlkörpererweiterungen. Anschließend werden diese Algorithmen auf die Tamagawazahlvermutung angewendet. Die Epsilonkonstantenvermutung kann dadurch für alle Galoiserweiterungen L|K bewiesen werden, bei denen L in einer Galoiserweiterung E|Q vom Grad kleiner gleich 15 eingebettet werden kann. Für die Tamagawazahlvermutung an der Stelle 1 wird ein Algorithmus angegeben, der die Vermutung für ein gegebenes Fallbeispiel L|Q numerischen verifizieren kann. Im Spezialfall, dass alle Charaktere rational oder abelsch sind, kann dieser Algorithmus die Vermutung für L|Q sogar beweisen.

The role of NGO in informal seed production and dissemination: The case of eastern Ethiopia

Seed is the basic input to crop production. Farmer-based seed production as an alternative agricultural technology transfer is increasingly given especial attention in developing countries where food insecurity is critical. This paper aims to assess the seed production and dissemination strategy among smallholder farmers in eastern Ethiopia that has been introduced by Hararghe Catholic Secretariat (a Non-GovernmentalOrganization). A survey of 160 households in four administrative districts and focus group discussions were used to collect data. While narratives helped understand the process, logistic regressionwas used to identify determinants of land allocation to seed production. Results indicate the crucial role of informal networks and social capital as facilitators of access to production inputs, information and knowledge. The informal seed supply system initiated by the NGO has a huge potential to benefit smallholder farmers by improving their access to higher-yielding varieties of various crops, thereby contributing to an increase in their wellbeing. However, the traditional practice of seed exchange, influenced by social relations, will remain uneconomical to seed producers. Thus, the paper suggests that this potential can be further exploited if some preconditions such as establishment of seed banks, investment in human capital, removal of the underlying constraints and creation of reliable seed markets are given emphasis.

Development and Integration of Biocontrol Products in Branched Broomrape (Phelipanche ramosa) management in Tomato

Parasitic weeds of the genera Striga, Orobanche, and Phelipanche pose a severe problem for agriculture because they are difficult to control and are highly destructive to several crops. The present work was carried out during the period October, 2009 to February, 2012 to evaluate the potential of arbuscular mycorrhizal fungi (AMF) to suppress P. ramosa on tomatoes and to investigate the effects of air-dried powder and aqueous extracts from Euphorbia hirta on germination and haustorium initiation in Phelipanche ramosa. The work was divided into three parts: a survey of the indigenous mycorrhizal flora in Sudan, second, laboratory and greenhouse experiments (conducted in Germany and Sudan) to construct a base for the third part, which was a field trial in Sudan. A survey was performed in 2009 in the White Nile state, Sudan to assess AMF spore densities and root colonization in nine fields planted with 13 different important agricultural crops. In addition, an attempt was made to study the relationship between soil physico-chemical properties and AMF spore density, colonization rate, species richness and other diversity indices. The mean percentage of AMF colonization was 34%, ranging from 19-50%. The spore densities (expressed as per 100 g dry soil) retrieved from the rhizosphere of different crops were relatively high, varying from 344 to 1222 with a mean of 798. There was no correlation between spore densities in soil and root colonization percentage. A total of 45 morphologically classifiable species representing ten genera of AMF were detected with no correlation between the number of species found in a soil sample and the spore density. The most abundant genus was Glomus (20 species). The AMF diversity expressed by the Shannon–Weaver index was highest in sorghum (H\= 2.27) and Jews mallow (H\= 2.13) and lowest in alfalfa (H\= 1.4). With respect to crop species, the genera Glomus and Entrophospora were encountered in almost all crops, except for Entrophospora in alfalfa. Kuklospora was found only in sugarcane and sorghum. The genus Ambispora was recovered only in mint and okra, while mint and onion were the only species on which no Acaulospora was found. The hierarchical cluster analysis based on the similarity among AMF communities with respect to crop species overall showed that species compositions were relatively similar with the highest dissimilarity of about 25% separating three of the mango samples and the four sorghum samples from all other samples. Laboratory experiments studied the influence of root and stem exudates of three tomato varieties infected by three different Glomus species on germination of P. ramosa. Root exudates were collected 21or 42 days after transplanting (DAT) and stem exudates 42 DAT and tested for their effects on germination of P. ramosa seeds in vitro. The tomato varieties studied did not have an effect on either mycorrhizal colonization or Phelipanche germination. Germination in response to exudates from 42 day old mycorrhizal plants was significantly reduced in comparison to non-mycorrhizal controls. Germination of P. ramosa in response to root exudates from 21 day old plants was consistently higher than for 42 day-old plants (F=121.6; P<.0001). Stem diffusates from non-mycorrhizal plants invariably elicited higher germination than diffusates from the corresponding mycorrhizal ones and differences were mostly statistically significant. A series of laboratory experiments was undertaken to investigate the effects of aqueous extracts from Euphorbia hirta on germination, radicle elongation, and haustorium initiation in P. ramosa. P. ramosa seeds conditioned in water and subsequently treated with diluted E. hirta extract (10-25% v/v) displayed considerable germination (47-62%). Increasing extract concentration to 50% or more reduced germination in response to the synthetic germination stimulants GR24 and Nijmegen-1 in a concentration dependent manner. P. ramosa germlings treated with diluted Euphorbia extract (10-75 % v/v) displayed haustorium initiation comparable to 2, 5-Dimethoxy-p-benzoquinon (DMBQ) at 20 µM. Euphorbia extract applied during conditioning reduced haustorium initiation in a concentration dependent manner. E. hirta extract or air-dried powder, applied to soil, induced considerable P. ramosa germination. Pot experiments were undertaken in a glasshouse at the University of Kassel, Germany, to investigate the effects of P. ramosa seed bank on tomato growth parameters. Different Phelipanche seed banks were established by mixing the parasite seeds (0 - 32 mg) with the potting medium in each pot. P. ramosa reduced all tomato growth parameters measured and the reduction progressively increased with seed bank. Root and total dry matter accumulation per tomato plant were most affected. P. ramosa emergence, number of tubercles, and tubercle dry weight increased with the seed bank and were, invariably, maximal with the highest seed bank. Another objective was to determine if different AM fungi differ in their effects on the colonization of tomatoes with P. ramosa and the performance of P. ramosa after colonization. Three AMF species viz. GIomus intraradices, Glomus mosseae and Glomus Sprint® were used in this study. For the infection, P. ramosa seeds (8 mg) were mixed with the top 5 cm soil in each pot. No mycorrhizal colonization was detected in un-inoculated control plants. P. ramosa infested, mycorrhiza inoculated tomato plants had significantly lower AMF colonization compared to plants not infested with P. ramosa. Inoculation with G. intraradices, G. mosseae and Glomus Sprint® reduced the number of emerged P. ramosa plants by 29.3, 45.3 and 62.7% and the number of tubercles by 22.2, 42 and 56.8%, respectively. Mycorrhizal root colonization was positively correlated with number of branches and total dry matter of tomatoes. Field experiments on tomato undertaken in 2010/12 were only partially successful because of insect infestations which resulted in the complete destruction of the second run of the experiment. The effects of the inoculation with AMF, the addition of 10 t ha-1 filter mud (FM), an organic residues from sugar processing and 36 or 72 kg N ha-1 on the infestation of tomatoes with P. ramosa were assessed. In un-inoculated control plants, AMF colonization ranged between 13.4 to 22.1% with no significant differences among FM and N treatments. Adding AMF or FM resulted in a significant increase of branching in the tomato plants with no additive effects. Dry weights were slightly increased through FM application when no N was applied and significantly at 36 kg N ha-1. There was no effect of FM on the time until the first Phelipanche emerged while AMF and N application interacted. Especially AMF inoculation resulted in a tendency to delayed P. ramosa emergence. The marketable yield was extremely low due to the strong fruit infestation with insects mainly whitefly Bemisia tabaci and tomato leaf miner (Tuta absoluta). Tomatoes inoculated with varied mycorrhiza species displayed different response to the insect infestation, as G. intraradices significantly reduced the infestation, while G. mosseae elicited higher insect infestation. The results of the present thesis indicate that there may be a potential of developing management strategies for P. ramosa targeting the pre-attachment stage namely germination and haustorial initiation using plant extracts. However, ways of practical use need to be developed. If such treatments can be combined with AMF inoculation also needs to be investigated. Overall, it will require a systematic approach to develop management tools that are easily applicable and affordable to Sudanese farmers. It is well-known that proper agronomical practices such as the design of an optimum crop rotation in cropping systems, reduced tillage, promotion of cover crops, the introduction of multi-microbial inoculants, and maintenance of proper phosphorus levels are advantageous if the mycorrhiza protection method is exploited against Phelipanche ramosa infestation. Without the knowledge about the biology of the parasitic weeds by the farmers and basic preventive measures such as hygiene and seed quality control no control strategy will be successful, however.

Prevalence of intestinal parasites in small ruminants and their senstivity to treatments with ethnobotanical remedies in Cholistan, Pakistan

Livestock production contributes substantially to the livelihoods of poor rural farmers in Pakistan; strengthening pastoral communities plays an imperative role in the country’s thrive for poverty alleviation. Intestinal helminths constitute a major threat for pastoral livestock keepers in the whole country because chronic infestation leads to distinct losses in livestock productivity, particularly the growth of young animals. Synthetic anthelmintics have long been considered the only effective way of controlling this problem but high prices, side effects and chemical residues/toxicity problems, or development of resistance, lead to their very limited use in many pastoral systems. Additionally, poor pastoralists in remote areas of Pakistan hardly have access to appropriate anthelmintic drugs, which are also relatively expensive due to the long routes of transportation. The search for new and more sustainable ways of supporting livestock keepers in remote areas has given rise to studies of ethno-botanicals or traditional plant-based remedies to be used in livestock health care. Plant-based remedies are cheap or free of cost, environmentally safe and generally create no problem of drug resistance; they thus might substitute allopathic drugs. Furthermore, these remedies are easily available in remote areas and simple to prepare and/or administer. Cholistan desert is a quite poor region of Pakistan and the majority of its inhabitants are practicing a nomadic life. The region’s total livestock population (1.29 million heads) is almost twice that of the human population. Livestock husbandry is the primordial occupation of the communities and traditionally wealth assessment was based on the number of animals, especially goats and sheep, owned by an individual. Fortunately, about 60% of this desert region is richly endowed with highly adapted grasses, shrubs and trees. This natural flora has a rich heritage of scientifically unexplored botanical pharmacopoeia. Against this background, the present research project that was conducted under the umbrella of the International Center for Development and Decent Work at Kassel University, focused on a development aspect: in the Cholistan desert region it was firstly examined how pastoralists manage their livestock, which major health problems they face for the different animal species, and which of the naturally occurring plants they use for the treatment of animal diseases (Chapter 2). For this purpose, a baseline survey was carried out across five locations in Cholistan, using a structured questionnaire to collect data from 100 livestock farmers (LF) and 20 local healers (LH). Most of LF and LH were illiterate (66%; 70%). On average, LH had larger herds (109 animals) than LF (85 animals) and were more experienced in livestock husbandry and management. On average LF spent about 163 Euro per year on the treatment of their livestock, with a huge variability in expenditures. Eighty-six traditional remedies based on 64 plants belonging to 43 families were used. Capparaceae was the botanical family with the largest number of species used (4), followed by Chenopodiaceae, Poaceae, Solanaceae and Zygophyllaceae (3). The plants Capparis decidua (n=55 mentions), Salsola foetida (n=52), Suaeda fruticosa (n=46), Haloxylon salicornicum (n=42) and Haloxylon recurvum (n=39) were said to be most effective against the infestations with gastrointestinal parasites. Aerial parts (43%), leaves (26%), fruits (9%), seeds and seed oils (9%) were the plant parts frequently used for preparation of remedies, while flowers, roots, bulbs and pods were less frequently used (<5%). Common preparations were decoction, jaggery and ball drench; oral drug administration was very common. There was some variation in the doses used for different animal species depending on age, size and physical condition of the animal and severity of the disease. In a second step the regionally most prevalent gastrointestinal parasites of sheep and goats were determined (Chapter 3) in 500 animals per species randomly chosen from pastoral herds across the previously studied five localities. Standard parasitological techniques were applied to identify the parasites in faecal samples manually collected at the rectum. Overall helminth prevalence was 78.1% across the 1000 animals; pure nematode infestations were most prevalent (37.5%), followed by pure trematode (7.9%), pure cestode (2.6%) and pure protozoa infestations (0.8%). Mixed infestations with nematodes and trematodes occurred in 6.4% of all animals, mixed nematode-cestode infestations in 3.8%, and all three groups were found in 19.1% of the sheep and goats. In goats more males (81.1%) than females (77.0%) were infested, the opposite was found in sheep (73.6% males, 79.5% females). Parasites were especially prevalent in suckling goats (85.2%) and sheep (88.5%) and to a lesser extent in young (goats 80.6%, sheep 79.3%) and adult animals (goats 72.8%, sheep 73.8%). Haemonchus contortus, Trichuris ovis and Paramphistomum cervi were the most prevalent helminths. In a third step the in vitro anthelmintic activity of C. decidua, S. foetida, S. fruticosa, H. salicornicum and H. recurvum (Chapter 2) was investigated against adult worms of H. contortus, T. ovis and P. cervi (Chapter 3) via adult motility assay (Chapter 4). Various concentrations ranging from 7.8 to 500 mg dry matter/ml of three types of extracts of each plant, i.e. aqueous, methanol, and aqueous-methanol (30:70), were used at different time intervals to access their anthelmintic activity. Levamisol (0.55 mg/ml) and oxyclozanide (30 mg/ml) served as positive and phosphate-buffered saline as negative control. All extracts exhibited minimum and maximum activity at 2 h and 12 h after parasite exposure; the 500 mg/ml extract concentrations were most effective. Plant species (P<0.05), extract type (P<0.01), parasite species (P<0.01), extract concentration (P<0.01), time of exposure (P<0.01) and their interactions (P<0.01) had significant effects on the number of immobile/dead helminths. From the comparison of LC50 values it appeared that the aqueous extract of C. decidua was more potent against H. contortus and T. ovis, while the aqueous extract of S. foetida was effective against P. cervi. The methanol extracts of H. recurvum were most potent against all three types of parasites, and its aqueous-methanol extract was also very effective against T. ovis and P. cervi. Based on these result it is concluded that the aqueous extract of C. decidua, as well as the methanol and aqueous-methanol extract of H. recurvum have the potential to be developed into plant-based drugs for treatment against H. contortus, T. ovis and P. cervi infestations. Further studies are now needed to investigate the in vivo anthelmintic activity of these plants and plant extracts, respectively, in order to develop effective, cheap and locally available anthelmintics for pastoralists in Cholistan and neighboring desert regions. This will allow developing tangible recommendations for plant-based anthelminthic treatment of sheep and goat herds, and by this enable pastoralists to maintain healthy and productive flocks at low costs and probably even manufacture herbal drugs for marketing on a regional scale.

Effects of row spacing on productivity and nodulation of two soybean varieties under hot sub-moist tropical conditions in south-western Ethiopia

The objective of this study was to determine the optimum row spacing to improve the productivity of two soybean (Glycine max L.) varieties under the tropical hot sub-moist agroecological conditions of Ethiopia. A two-year split-plot design experiment was conducted to determine the effect of variety (Awasa-95 [early-maturing], Afgat [medium-maturing]) and row spacing (RS: 20, 25, 30, 35, 40, 45, 50, 55, 60 cm) on the productivity, nodulation and weed infestation of soybean. Seed and total dry matter (TDM) yield per ha and per plant, and weed dry biomass per m^2 were significantly affected by RS. Soybean variety had a significant effect on plant density at harvest and some yield components (plant height, number of seeds/pod, and 1000 seed weight). Generally, seed and TDM yield per ha and per plant were high at 40 cm RS, and weed dry biomass per m^2 was higher for RS >= 40 cm than for narrower RS. However, the results did not demonstrate a consistent pattern along the RS gradient. The medium-maturing variety Afgat experienced higher mortality and ended up with lower final plant density at harvest, but higher plant height, number of seeds per pod and 1000 seed weight than the early-maturing variety Awasa-95. The results indicate that 40 cm RS with 5 cm plant spacing within a row can be used for high productivity and low weed infestation of both soybean varieties in the hot sub-moist tropical environment of south-western Ethiopia.