An approximation method using approximate approximations

The aim of this paper is to extend the method of approximate approximations to boundary value problems. This method was introduced by V. Maz'ya in 1991 and has been used until now for the approximation of smooth functions defined on the whole space and for the approximation of volume potentials. In the present paper we develop an approximation procedure for the solution of the interior Dirichlet problem for the Laplace equation in two dimensions using approximate approximations. The procedure is based on potential theoretical considerations in connection with a boundary integral equations method and consists of three approximation steps as follows. In a first step the unknown source density in the potential representation of the solution is replaced by approximate approximations. In a second step the decay behavior of the generating functions is used to gain a suitable approximation for the potential kernel, and in a third step Nyström's method leads to a linear algebraic system for the approximate source density. For every step a convergence analysis is established and corresponding error estimates are given.

Ground state correlation energy of the Be-sequence for Z = 4-20 in MCDF approximation

The ground state (J = 0) electronic correlation energy of the 4-electron Be-sequence is calculated in the Multi-Configuration Dirac-Fock approximation for Z = 4-20. The 4 electrons were distributed over the configurations arising from the 1s, 2s, 2p, 3s, 3p and 3d orbitals. Theoretical values obtained here are in good agreement with experimental correlation energies.

Zur Approximation der Gleichungen von Navier-Stokes

In der vorliegenden Arbeit betrachten wir die Strömung einer zähen, inkompressiblen, instationären Flüssigkeit in einem dreidimensionalen beschränkten Gebiet, deren Verhalten wird mit den instationären Gleichungen von Navier-Stokes beschrieben. Diese Gleichungen gelten für viele wichtige Strömungsprobleme, beispielsweise für Luftströmungen weit unterhalb der Schallgeschwindigkeit, für Wasserströmungen, sowie für flüssige Metalle. Im zweidimensionalen Fall konnten für die Navier-Stokes-Gleichungen bereits weitreichende Existenz-, Eindeutigkeits- und Regularitätsaussagen bewiesen werden. Im allgemeinen dreidimensionalen Fall, falls also die Daten keinen Kleinheitsannahmen unterliegen, hat man bisher lediglich Existenz und Eindeutigkeit zeitlich lokaler starker Lösungen nachgewiesen. Außerdem existieren zeitlich global so genannte schwache Lösungen, deren Regularität für den Nachweis der Eindeutigkeit im dreidimensionalen Fall allerdings nicht ausreicht. Somit bleibt die Lücke zwischen der zeitlich lokalen, eindeutigen starken Lösung und den zeitlich globalen, nicht eindeutigen schwachen Lösungen der Navier-Stokes-Gleichungen im dreidimensionalen Fall weiterhin offen. Das renommierte Clay Mathematics Institute hat dieses Problem zu einem von sieben Millenniumsproblemen erklärt und für seine Lösung eine Million US-Dollar ausgelobt. In der vorliegenden Arbeit wird ein neues Approximationsverfahren für die Navier-Stokes-Gleichungen entwickelt, das auf einer Kopplung der Eulerschen und Lagrangeschen Beschreibung zäher Strömungen beruht.

Varying the dietary supply of C and N to manipulate the manure composition of water buffalo heifers in Oman

Optimizing the composition of manure has the potential to reduce nutrient losses to the environment and to increase crop yields. In this study the effect of dietary ratios of carbon (C) to nitrogen (N) and neutral detergent fibre (NDF) to soluble carbohydrates (SC) on faeces composition of water buffalo heifers was assessed. Two digestibility trials were conducted with 12 animals each, fed one control and four test diets composed to achieve (1) high C/N and high NDF/SC ratios (HH), (2) low C/N and low NDF/SC ratios (LL), (3) high C/N and low NDF/SC ratios (HL) and (4) low C/N and high NDF/SC (LH) ratios. Faecal C/N ratios were generally lower than dietary C/N ratios, but the reduction was especially large for high C/N ratio diets (HH=55 %, HL=51 %). Faecal N concentration was positively correlated (r^2 = 0.6; P < 0.001) with N intake, but the increase in faecal N was more pronounced for diets that supplied low amounts of N. Faecal NDF concentration was positively related to NDF intake (r^2 = 0.42; P < 0.001), as well as the faecal C/N ratio (r^2 = 0.3; P < 0.001). Results demonstrate that C/N ratio and NDF concentration of buffalo manure were affected by diet composition. Diets with high C/N ratio and low NDF/SC ratio are preferable with regard to manure quality, but may not satisfy the nutritional requirements of producing animals, since N concentration in these diets was low and fibre concentration simultaneously high.

Causes of legume rotation induced yield increases in cereals grown on West African soils

This study was conducted to investigate soil biological and chemical factors that give rise to cereal yield enhancing effects of legume rotations on sandy, nutrient poor West African soils. The aim was not only to gain more information on the role of legume residues and microorganisms in the soil nutrient cycle. But the study aimed at evaluating if differences in substrate qualities (e.g. root residues) cause changes in the microbial community structure due to specific and highly complex microbe-root-soil interactions. Site and system specific reactions of microorganisms towards rewetting, simulating the onset of rainy season, were observed. Higher respiration rates, higher amounts of microbial biomass carbon (Cmic) and nitrogen (Nmic) as well as higher ergosterol, muramic acid, glucosamine and adenylate concentrations were measured in CL soils of Koukombo and in both soils from Fada. The immediate increase in ATP concentrations after rewetting was likely caused by rehydration of microbial cells where N was not immobilized and, thus, available for plants facilitating their rapid development. Legume root residues led only to slightly better plant performances compared to the control, while the application of cereal roots reduced seedling growth. In contrast to sorghum seedlings, the microbial community did not react to the mineral treatment. Thus the energy supply in form of organic amendments increased microbial indices compared to mineral P application and the control. The results of basal respiration rates, Cmic and Corg levels indicate that the microbial community in the soil from Koukombo is less efficient in substrate use compared to microorganisms in the soil from Fada. However, the continuous carbon input by legume root residues might have contributed to these differences in soil fertility. With the 33P isotopic exchange method a low buffering capacity was detected in both soils irrespective of treatments. Calculated E values (E1min to E1min-1d and E1d-3m) indicated a slowly release of P due to root turnover while applied mineral P is taken up by plants or fixed to the soil. Due to the fact that sorghum growth reacted mainly to the application of mineral P and the microorganisms solely to the organic inputs, the combination of both amendments seems to be the best approach to a sustainable increase of crop production on many nutrient-poor, sandy West African soils. In a pot experiment, were CC and CL soils from Fada and Koukombo were adjusted to the same level of P and N concentrations, crop growth was significantly higher on CL soils, compared to the respective treatments on CC soils. Mycorrhizal infection of roots was increased and the number of nematodes, predominantly free living nematodes, was almost halfed on rotation soils. In conclusion, increased nutrient availability (especially P and N) through the introduction of legumes is not the only reason for the observed yield increasing effects. Soil biological factors seem to also play an important role. In a root chamber experiment the pH gradient along the root-soil-interface was measured at three times using an antimony microelectrode. For Fada soils, pH values were higher on CL than CC soils while the opposite was true for the Koukombo soils. Site-specific differences between Fada and Koukombo soils in N content and microbial community structures might have created varying crop performances leading to the contrasting pH findings. However, the mechanisms involved in this highly complex microbe-root-soil interaction remain unclear.

Enlarging a training set for genomic selction by imputation of un-genotyped animals in populations of varying genetic architecture

Background: The most common application of imputation is to infer genotypes of a high-density panel of markers on animals that are genotyped for a low-density panel. However, the increase in accuracy of genomic predictions resulting from an increase in the number of markers tends to reach a plateau beyond a certain density. Another application of imputation is to increase the size of the training set with un-genotyped animals. This strategy can be particularly successful when a set of closely related individuals are genotyped. ----- Methods: Imputation on completely un-genotyped dams was performed using known genotypes from the sire of each dam, one offspring and the offspring’s sire. Two methods were applied based on either allele or haplotype frequencies to infer genotypes at ambiguous loci. Results of these methods and of two available software packages were compared. Quality of imputation under different population structures was assessed. The impact of using imputed dams to enlarge training sets on the accuracy of genomic predictions was evaluated for different populations, heritabilities and sizes of training sets. ----- Results: Imputation accuracy ranged from 0.52 to 0.93 depending on the population structure and the method used. The method that used allele frequencies performed better than the method based on haplotype frequencies. Accuracy of imputation was higher for populations with higher levels of linkage disequilibrium and with larger proportions of markers with more extreme allele frequencies. Inclusion of imputed dams in the training set increased the accuracy of genomic predictions. Gains in accuracy ranged from close to zero to 37.14%, depending on the simulated scenario. Generally, the larger the accuracy already obtained with the genotyped training set, the lower the increase in accuracy achieved by adding imputed dams. ----- Conclusions: Whenever a reference population resembling the family configuration considered here is available, imputation can be used to achieve an extra increase in accuracy of genomic predictions by enlarging the training set with completely un-genotyped dams. This strategy was shown to be particularly useful for populations with lower levels of linkage disequilibrium, for genomic selection on traits with low heritability, and for species or breeds for which the size of the reference population is limited.

Methods of generating carrier-envelope-phase stabilized, intense, few-cycle laser pulses

Ultrafast laser pulses have become an integral part of the toolbox of countless laboratories doing physics, chemistry, and biological research. The work presented here is motivated by a section in the ever-growing, interdisciplinary research towards understanding the fundamental workings of light-matter interactions. Specifically, attosecond pulses can be useful tools to obtain the desired insight. However access to, and the utility of, such pulses is dependent on the generation of intense, few-cycle, carrier-envelope-phase stabilized laser pulses. The presented work can be thought of as a sort of roadmap towards the latter. From the oscillator which provides the broadband seed to amplification methods, the integral pieces necessary for the generation of attosecond pulses are discussed. A range of topics from the fundamentals to design challenges is presented, outfitting the way towards the practical implementation of an intense few-cycle carrier-envelope-phase stabilized laser source.

Asymptotic model for shape resonance control of diatomics by intense non-resonant light: universality in the single-channel approximation

Non-resonant light interacting with diatomics via the polarizability anisotropy couples different rotational states and may lead to strong hybridization of the motion. The modification of shape resonances and low-energy scattering states due to this interaction can be fully captured by an asymptotic model, based on the long-range properties of the scattering (Crubellier et al 2015 New J. Phys. 17 045020). Remarkably, the properties of the field-dressed shape resonances in this asymptotic multi-channel description are found to be approximately linear in the field intensity up to fairly large intensity. This suggests a perturbative single-channel approach to be sufficient to study the control of such resonances by the non-resonant field. The multi-channel results furthermore indicate the dependence on field intensity to present, at least approximately, universal characteristics. Here we combine the nodal line technique to solve the asymptotic Schrödinger equation with perturbation theory. Comparing our single channel results to those obtained with the full interaction potential, we find nodal lines depending only on the field-free scattering length of the diatom to yield an approximate but universal description of the field-dressed molecule, confirming universal behavior.

An analysis of household farm investment decisions under varying land tenure arrangements in Ghana

Land tenure insecurity is widely perceived as a disincentive for long-term land improvement investment hence the objective of this paper is to evaluate how tenure (in)security associated with different land use arrangements in Ghana influenced households’ plot level investment decisions and choices. The paper uses data from the Farmer-Based Organisations (FBO) survey. The FBO survey collected information from 2,928 households across three ecological zones of Ghana using multistaged cluster sampling. Probit and Tobit models tested the effects of land tenancy and ownership arrangements on households’ investment behaviour while controlling other factors. It was found that marginal farm size was inversely related to tenure insecurity while tenure insecurity correlate positively with value of farm land and not farm size. Individual ownership and documentation of land significantly reduced the probability of households losing uncultivated lands. Individual land ownership increased both the probability of investing and level of investments made in land improvement and irrigation probably due to increasing importance households place on land ownership. Two possible explanations for this finding are: First, that land markets and land relations have changed significantly over the last two decades with increasing money transaction and fixed agreements propelled by population growth and increasing value of land. Secondly, inclusion of irrigation investment as a long term investment in land raises the value of household investment and the time period required to reap the returns on the investments. Households take land ownership and duration of tenancy into consideration if the resource implications of land investments are relatively huge and the time dimension for harvesting returns to investments is relatively long.