Many-electron relativistic calculation and interpretation of atomic processes in time dependent heavy-ion scattering

The time dependence of a heavy-ion-atom collision system is solved via a set of coupled channel equations using energy eigenvalues and matrix elements from a self-consistent field relativistic molecular many-electron Dirac-Fock-Slater calculation. Within this independent particle model we give a full many-particle interpretation by performing a small number of single-particle calculations. First results for the P(b) curves for the Ne K-hole excitation for the systems F{^8+} - Ne and F{^6+} - Ne as examples are discussed.

Quality Governance based on Enterprise Engineering Method and Six Sigma Approach

Enterprise Modeling (EM) is currently in operation either as a technique to represent and understand the structure and behavior of the enterprise, or as a technique to analyze business processes, and in many cases as support technique for business process reengineering. However, EM architectures and methods for Enterprise Engineering can also used to support new management techniques like SIX SIGMA, because these new techniques need a clear, transparent and integrated definition and description of the business activities of the enterprise to be able to build up, optimize and operate an successful enterprise. The main goal of SIX SIGMA is to optimize the performance of processes. A still open question is: "What are the adequate Quality criteria and methods to ensure such performance? What must we do to get Quality governance?" This paper describes a method including an Enterprise Engineering method and SIX SIGMA strategy to reach Quality Governance

Solution of the Hartree-Fock equations for atoms and diatomic molecules with the finite element method

The finite element method (FEM) is now developed to solve two-dimensional Hartree-Fock (HF) equations for atoms and diatomic molecules. The method and its implementation is described and results are presented for the atoms Be, Ne and Ar as well as the diatomic molecules LiH, BH, N_2 and CO as examples. Total energies and eigenvalues calculated with the FEM on the HF-level are compared with results obtained with the numerical standard methods used for the solution of the one dimensional HF equations for atoms and for diatomic molecules with the traditional LCAO quantum chemical methods and the newly developed finite difference method on the HF-level. In general the accuracy increases from the LCAO - to the finite difference - to the finite element method.

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.

A computer-algebraic approach to the study of the symmetry properties of molecules and clusters

This thesis work is dedicated to use the computer-algebraic approach for dealing with the group symmetries and studying the symmetry properties of molecules and clusters. The Maple package Bethe, created to extract and manipulate the group-theoretical data and to simplify some of the symmetry applications, is introduced. First of all the advantages of using Bethe to generate the group theoretical data are demonstrated. In the current version, the data of 72 frequently applied point groups can be used, together with the data for all of the corresponding double groups. The emphasize of this work is placed to the applications of this package in physics of molecules and clusters. Apart from the analysis of the spectral activity of molecules with point-group symmetry, it is demonstrated how Bethe can be used to understand the field splitting in crystals or to construct the corresponding wave functions. Several examples are worked out to display (some of) the present features of the Bethe program. While we cannot show all the details explicitly, these examples certainly demonstrate the great potential in applying computer algebraic techniques to study the symmetry properties of molecules and clusters. A special attention is placed in this thesis work on the flexibility of the Bethe package, which makes it possible to implement another applications of symmetry. This implementation is very reasonable, because some of the most complicated steps of the possible future applications are already realized within the Bethe. For instance, the vibrational coordinates in terms of the internal displacement vectors for the Wilson's method and the same coordinates in terms of cartesian displacement vectors as well as the Clebsch-Gordan coefficients for the Jahn-Teller problem are generated in the present version of the program. For the Jahn-Teller problem, moreover, use of the computer-algebraic tool seems to be even inevitable, because this problem demands an analytical access to the adiabatic potential and, therefore, can not be realized by the numerical algorithm. However, the ability of the Bethe package is not exhausted by applications, mentioned in this thesis work. There are various directions in which the Bethe program could be developed in the future. Apart from (i) studying of the magnetic properties of materials and (ii) optical transitions, interest can be pointed out for (iii) the vibronic spectroscopy, and many others. Implementation of these applications into the package can make Bethe a much more powerful tool.

Approximate approximations for the Poisson and the Stokes equations

The method of approximate approximations is based on generating functions representing an approximate partition of the unity, only. In the present paper this method is used for the numerical solution of the Poisson equation and the Stokes system in R^n (n = 2, 3). The corresponding approximate volume potentials will be computed explicitly in these cases, containing a one-dimensional integral, only. Numerical simulations show the efficiency of the method and confirm the expected convergence of essentially second order, depending on the smoothness of the data.

Approximate solutions and error estimates for a Stokes boundary value problem

The aim of this paper is the numerical treatment of a boundary value problem for the system of Stokes' equations. For this we 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 system of Stokes' equations in two dimensions. 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.

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.

Ermittlung geeigneter Methoden zur Differenzierung und Qualitätsbeurteilung unterschiedlicher Milchqualitäten aus verschiedenen on-farm-Experimenten

Zusammenfassung: Ziel der Arbeit war ein Methodenvergleich zur Beurteilung der Milchqualität unterschiedlicher Herkünfte. Am Beispiel von Milchproben aus unterschiedlicher Fütterung sowie an Milchproben von enthornten bzw. horntragenden Kühen wurde geprüft, welche der angewendeten Methoden geeignet ist, die Vergleichsproben zu unterscheiden (Differenzierungsfähigkeit der Methoden) und inwieweit eine Qualitätsbeurteilung möglich ist (hinsichtlich Milchleistung, Fett-, Eiweiß-, Lactose- (=F,E,L), Harnstoff-gehalt und Zellzahl (=SCC), Säuerungseigenschaften (=SE), Fettsäuremuster (=FS-Muster), Protein- und Metabolit-Zusammensetzung (=Pr&M), Fluoreszenz-Anregungs-Spektroskopie-Eigenschaften (=FAS) und Steigbild-Merkmalen). Zusätzlich wurde vorab die Steigbildmethode (=SB-M) für das Produkt Rohmilch standardisiert und charakterisiert, um die Reproduzierbarkei der Ergebnisse sicherzustellen. Die Untersuchungen zur SB-M zeigten, dass es Faktoren gibt, die einen deutlichen Einfluß auf die Bildmerkmals-Ausprägung aufweisen. Dazu gehören laborseitig die Klimabedingungen in der Kammer, die Verdünnungsstufe der Probe, die Standzeiten der Vorverdünnung (Reaktionen mit der Luft, Alterung usw.), und tagesspezifisch auftretende Effekte, deren Ursache unbekannt ist. Probenseitig sind sehr starke tierindividuelle Effekte auf die Bildmerkmals-Ausprägung festzustellen, die unabhängig von Fütterung, Alter, Laktationsstadium und Genetik auftreten, aber auch Fütterungsbedingungen der Kühe lassen sich in der Bildmerkmals-Ausprägung wiederfinden. Die Art der Bildauswertung und die dabei berücksichtigten Bildmerkmale ist von großer Bedeutung für das Ergebnis. Die im Rahmen dieser Arbeit untersuchten 46 Probenpaare (aus den Fütterungsvergleichen (=FV) und zur Thematik der Hörner) konnten in 91% der Fälle korrekt gruppiert werden. Die Unterschiede konnten benannt werden. Drei FV wurden auf drei biologisch-dynamischen Höfen unter Praxis-Bedingungen durchgeführt (on-farm-Experimente). Es wurden jeweils zwei vergleichbare Gruppen à mindestens 11 Kühen gebildet, die im Cross-Over-Design gefüttert wurden, mit Probennahme am 14. und 21. Tag je Periode. Es wurden folgende FV untersucht: A: Wiesenheu vs. Kleegrasheu (=KG-Heu), B: Futterrüben (=FuR) vs. Weizen (Ergänzung zu Luzernegrasheu ad lib.), C: Grassilage vs. Grasheu. Bei Versuch A sind die Futtereffekte am deutlichsten, Gruppeneffekte sind gering. Die Milch der Wiesenheu-Variante hat weniger CLA’s und n3- FS und mehr mittellangkettige FS (MCT-FS), das Pr&M-Muster weist auf „Gewebereifung und Ausdifferenzierung“ vs. bei KG-Heu „Nährstoff-fülle, Wachstum und Substanz-Einlagerung und die SB zeigen fein ausdifferenzierte Bildmerkmale. Bei Versuch B sind die Futtereffekte ähnlich groß wie die Gruppeneffekte. Bei vergleichbarer Milchleistung weist die Milch der FuR-Variante höhere F- und E-Gehalte auf, sie säuert schneller und mehr, das FS-Muster weist auf eine „intensive“ Fütterung mit vermehrt MCT- FS, und die Pr&M-Untersuchungen charakterisieren sie mit „Eisentransport und Fetttröpfchenbildung“ vs. bei Weizen „mehr Abwehr-, Regulations- und Transportfunktion“ /. „mehr Lipidsynthese“. Die SB charakterisieren mit „große, kräftige Formen, verwaschen“ vs. „kleine, ausdifferenzierte Bildmerkmal“ für FuR vs. Weizen. Die FAS charakterisiert sie mit „Saftfutter-typisch“ vs. „Samentypisch“. Versuch C weist die geringsten Futtereffekt auf, und deutliche Gruppen- und Zeiteffekte. Milchleistung und F,E,L-Gehalte zeigen keinen Futtereffekt. Die Milch der Heu-Variante säuert schneller, und sie weist mehr SCT und MCT- FS auf. Pr&M-Untersuchungen wurden nicht durchgeführt. Die SB charakterisieren bei Heumilch mit „fein, zart, durchgestaltet, hell“, bei Silagemilch mit „kräftig, wäßrig-verwaschen, dunkler“. Die FAS kann keine konsistenten Unterschiede ermitteln. Der Horn-Einfluß auf die Milchprobe wurde an 34 Probenpaaren untersucht. Von 11 Höfen wurden je zwei möglichst vergleichbare Gruppen zusammengestellt, die sich nur im Faktor „Horn“ unterscheiden, und im wöchentlichen Abstand drei mal beprobt. F,E,L, SCC und SE der Proben sowie die FAS-Messungen weisen keine konsistenten signifikanten Unterschiede zwischen den Horn-Varianten auf. Pr&M weisen bei den untersuchten Proben (von zwei Höfen) auf Horneffekte hin: bei Eh eine Erhöhung von Immun-Abwehr-Funktionen, sowie einer Abnahme phosphorylierter C3- und C6-Metabolite und Beta-Lactoglobulin. Mit den SB ließen sich für die gewählten Merkmale (S-Größe und g.B.-Intensität) keine Horneffekte feststellen. FS, Pr&M-Muster sowie Harnstoffgehalt und SB (und z.T. Milchleistung) zeigten je FV ähnliche Effekt-Intensitäten für Futter-, Gruppen- und Zeiteffekte, und konnten die Cross-Over-Effekte gut wiedergeben. F- und E-Gehalte konnten neben tierindividuellen Effekten nur in FV B auch Futtereffekte aufzeigen. In FV C zeigten die SE der Proben den deutlichsten Futtereffekt, die anderen Methoden zeigten hier vorrangig Gruppen-Effekte, gefolgt von Futter- und Zeiteffekten. Die FAS zeigte den SB vergleichbare Ergebnisse, jedoch weniger sensibel reagierend. Die Interpretation von Qualitätsaspekten war bei konsistent differenzierbaren Proben (FV A, B, C) am fundiertesten mit Hilfe der FS möglich, da über die Synthese von FS und beeinflussende Faktoren schon vielfältige Erkenntnisse vorliegen. Das Pr&M-Muster war nach einer weiteren Methodenentwicklung bei der Deutung von Stoffwechselprozessen sehr hilfreich. Die FAS konnte z.T. eine zu der Fütterungsvariante passende Charakterisierung liefern. Für die SB-M fehlt es noch an Referenzmaterial, um Angaben zu Qualitätsaspekten zu machen, wenngleich Probenunterschiede aufgezeigt und Proben-Eigenschaften charakterisiert werden konnten.

Effects of Organic and Inorganic Fertilizers on Growth and Yield of Banana (Musa AAA cv. Malindi) in Oman

The Sultanate of Oman is located on the south-eastern coast of the Arabian Peninsula, which lies on the south-western tip of the Asian continent. The strategic geographical locations of the Sultanate with its many maritime ports distributed on the Indian Ocean have historically made it one of the Arabian Peninsula leaders in the international maritime trade sector. Intensive trading relationships over long time periods have contributed to the high plant diversity seen in Oman where agricultural production depends entirely on irrigation from groundwater sources. As a consequence of the expansion of the irrigated area, groundwater depletion has increased, leading to the intrusion of seawater into freshwater aquifers. This phenomenon has caused water and soil salinity problems in large parts of the Al-Batinah governorate of Oman and threatens cultivated crops, including banana (Musa spp.). According to the Ministry of Agriculture and Fisheries, the majority of South Al-Batinah farms are affected by salinity (ECe > 4 dS m-1). As no alternative farmland is available, the reclamation of salt-affected soils using simple cultural practices is of paramount importance, but in Oman little scientific research has been conducted to develop such methods of reclamation. This doctoral study was initiated to help filling this research gap, particularly for bananas. A literature review of the banana cultivation history revealed that the banana germplasm on the Arabian Peninsula is probably introduced from Indonesia and India via maritime routes across the Indian Ocean and the Red Sea. In a second part of this dissertation, two experiments are described. A laboratory trial conducted at the University of Kassel, in Witzenhausen, Germany from June to July 2010. This incubation experiment was done to explore how C and N mineralization of composted dairy manure and date palm straw differed in alkaline non-saline and saline soils. Each soil was amended with four organic fertilizers: 1) composted dairy manure, 2) manure + 10% date palm straw, 3) manure + 30% date palm straw or 4) date palm straw alone, in addition to un-amended soils as control. The results showed that the saline soil had a lower soil organic C content and microbial biomass C than the non-saline soil. This led to lower mineralization rates of manure and date palm straw in the saline soil. In the non-saline soil, the application of manure and straw resulted in significant increases of CO2 emissions, equivalent to 2.5 and 30% of the added C, respectively. In the non-amended control treatment of the saline soil, the sum of CO2-C reached only 55% of the soil organic C in comparison with the non-saline soil. In which 66% of the added manure and 75% of the added straw were emitted, assuming that no interactions occurred between soil organic C, manure C and straw C during microbial decomposition. The application of straw always led to a net N immobilization compared to the control. Salinity had no specific effect on N mineralization as indicated by the CO2-C to Nmin ratio of soil organic matter and manure. However, N immobilization was markedly stronger in the saline soil. Date palm straw strongly promoted saprotrophic fungi in contrast to manure and the combined application of manure and date palm straw had synergistic positive effects on soil microorganisms. In the last week of incubation, net-N mineralization was observed in nearly all treatments. The strongest increase in microbial biomass C was observed in the manure + straw treatment. In both soils, manure had no effect on the fungi-specific membrane component ergosterol. In contrast, the application of straw resulted in strong increases of the ergosterol content. A field experiment was conducted on two adjacent fields at the Agricultural Research Station, Rumais (23°41’15” N, 57°59’1” E) in the South of Al-Batinah Plain in Oman from October 2007 to July 2009. In this experiment, the effects of 24 soil and fertilizer treatments on the growth and productivity of Musa AAA cv. 'Malindi' were evaluated. The treatments consisted of two soil types (saline and amended non-saline), two fertilizer application methods (mixed and ring applied), six fertilizer amendments (1: fresh dairy manure, 2: composted dairy manure, 3: composted dairy manure and 10% date palm straw, 4: composted dairy manure and 30% date palm straw, 5: only NPK, and 6: NPK and micronutrients). Sandy loam soil was imported from another part of Oman to amended the soil in the planting holes and create non-saline conditions in the root-zone. The results indicate that replacing the saline soil in the root zone by non-saline soil improved plant growth and yield more than fertilizer amendments or application methods. Particularly those plants on amended soil where NPK was applied using the ring method and which received micronutrients grew significantly faster to harvest (339 days), had a higher average bunch weight (9.5 kg/bunch) and were consequently more productive (10.6 tonnes/hectare/cycle) compared to the other treatments.

Socio-economic characterization of integrated cropping systems in urban and peri-urban agriculture of Faisalabad, Pakistan

Faisalabad city is surrounded by agricultural lands, where farmers are growing vegetables, grain crops, and fodder for auto-consumption and local marketing. To study the socioeconomic impact and resource use in these urban and peri-urban agricultural production (UPA) systems, a baseline survey was conducted during 2009–2010. A total of 140 households were selected using a stratified sampling method and interviewed with a structured questionnaire. The results revealed that 96 % of the households rely on agriculture as their main occupation. Thirty percent of the households were owners of the land and the rest cultivated either rented or sharecropped land. Most of the families (70 %) were headed by a member with primary education, and only 10 % of the household head had a secondary school certificate. Irrigationwater was obtained from waste water (37 %), canals (27 %), and mixed alternative sources (36 %). A total of 35 species were cultivated in the UPA systems of which were 65% vegetables, 15% grain and fodder crops, and 5% medicinal plants. Fifty-nine percent of the households cultivated wheat, mostly for auto-consumption. The 51 % of the respondents grew cauliflower (Brassica oleracea L.) and gourds (Cucurbitaceae) in the winter and summer seasons, respectively. Group marketing was uncommon and most of the farmers sold their produce at the farm gate (45 %) and on local markets (43 %). Seeds and fertilizers were available from commission agents and dealers on a credit basis with the obligation to pay by harvested produce. A major problem reported by the UPA farmers of Faisalabad was the scarcity of high quality irrigation water, especially during the hot dry summer months, in addition to lacking adequate quantities of mineral fertilizers and other inputs during sowing time. Half of the respondents estimated their daily income to be less than 1.25 US$ and spent almost half of it on food. Monthly average household income and expenses were 334 and 237 US$, respectively.