Thermodynamic functions of element 105 in neutral and ionized states

The basic thermodynamic functions, the entropy, free energy, and enthalpy, for element 105 (hahnium) in electronic configurations d^3 s^2, d^3 sp, and d^4s^1 and for its +5 ionized state (5f^14) have been calculated as a function of temperature. The data are based on the results of the calculations of the corresponding electronic states of element 105 using the multiconfiguration Dirac-Fock method.

Bayes quadratic unbiased estimator of spatial covariance parameters

This work presents Bayes invariant quadratic unbiased estimator, for short BAIQUE. Bayesian approach is used here to estimate the covariance functions of the regionalized variables which appear in the spatial covariance structure in mixed linear model. Firstly a brief review of spatial process, variance covariance components structure and Bayesian inference is given, since this project deals with these concepts. Then the linear equations model corresponding to BAIQUE in the general case is formulated. That Bayes estimator of variance components with too many unknown parameters is complicated to be solved analytically. Hence, in order to facilitate the handling with this system, BAIQUE of spatial covariance model with two parameters is considered. Bayesian estimation arises as a solution of a linear equations system which requires the linearity of the covariance functions in the parameters. Here the availability of prior information on the parameters is assumed. This information includes apriori distribution functions which enable to find the first and the second moments matrix. The Bayesian estimation suggested here depends only on the second moment of the prior distribution. The estimation appears as a quadratic form y'Ay , where y is the vector of filtered data observations. This quadratic estimator is used to estimate the linear function of unknown variance components. The matrix A of BAIQUE plays an important role. If such a symmetrical matrix exists, then Bayes risk becomes minimal and the unbiasedness conditions are fulfilled. Therefore, the symmetry of this matrix is elaborated in this work. Through dealing with the infinite series of matrices, a representation of the matrix A is obtained which shows the symmetry of A. In this context, the largest singular value of the decomposed matrix of the infinite series is considered to deal with the convergence condition and also it is connected with Gerschgorin Discs and Poincare theorem. Then the BAIQUE model for some experimental designs is computed and compared. The comparison deals with different aspects, such as the influence of the position of the design points in a fixed interval. The designs that are considered are those with their points distributed in the interval [0, 1]. These experimental structures are compared with respect to the Bayes risk and norms of the matrices corresponding to distances, covariance structures and matrices which have to satisfy the convergence condition. Also different types of the regression functions and distance measurements are handled. The influence of scaling on the design points is studied, moreover, the influence of the covariance structure on the best design is investigated and different covariance structures are considered. Finally, BAIQUE is applied for real data. The corresponding outcomes are compared with the results of other methods for the same data. Thereby, the special BAIQUE, which estimates the general variance of the data, achieves a very close result to the classical empirical variance.

Some New Classes of Orthogonal Polynomials and Special Functions

In dieser Dissertation präsentieren wir zunächst eine Verallgemeinerung der üblichen Sturm-Liouville-Probleme mit symmetrischen Lösungen und erklären eine umfassendere Klasse. Dann führen wir einige neue Klassen orthogonaler Polynome und spezieller Funktionen ein, welche sich aus dieser symmetrischen Verallgemeinerung ableiten lassen. Als eine spezielle Konsequenz dieser Verallgemeinerung führen wir ein Polynomsystem mit vier freien Parametern ein und zeigen, dass in diesem System fast alle klassischen symmetrischen orthogonalen Polynome wie die Legendrepolynome, die Chebyshevpolynome erster und zweiter Art, die Gegenbauerpolynome, die verallgemeinerten Gegenbauerpolynome, die Hermitepolynome, die verallgemeinerten Hermitepolynome und zwei weitere neue endliche Systeme orthogonaler Polynome enthalten sind. All diese Polynome können direkt durch das neu eingeführte System ausgedrückt werden. Ferner bestimmen wir alle Standardeigenschaften des neuen Systems, insbesondere eine explizite Darstellung, eine Differentialgleichung zweiter Ordnung, eine generische Orthogonalitätsbeziehung sowie eine generische Dreitermrekursion. Außerdem benutzen wir diese Erweiterung, um die assoziierten Legendrefunktionen, welche viele Anwendungen in Physik und Ingenieurwissenschaften haben, zu verallgemeinern, und wir zeigen, dass diese Verallgemeinerung Orthogonalitätseigenschaft und -intervall erhält. In einem weiteren Kapitel der Dissertation studieren wir detailliert die Standardeigenschaften endlicher orthogonaler Polynomsysteme, welche sich aus der üblichen Sturm-Liouville-Theorie ergeben und wir zeigen, dass sie orthogonal bezüglich der Fisherschen F-Verteilung, der inversen Gammaverteilung und der verallgemeinerten t-Verteilung sind. Im nächsten Abschnitt der Dissertation betrachten wir eine vierparametrige Verallgemeinerung der Studentschen t-Verteilung. Wir zeigen, dass diese Verteilung gegen die Normalverteilung konvergiert, wenn die Anzahl der Stichprobe gegen Unendlich strebt. Eine ähnliche Verallgemeinerung der Fisherschen F-Verteilung konvergiert gegen die chi-Quadrat-Verteilung. Ferner führen wir im letzten Abschnitt der Dissertation einige neue Folgen spezieller Funktionen ein, welche Anwendungen bei der Lösung in Kugelkoordinaten der klassischen Potentialgleichung, der Wärmeleitungsgleichung und der Wellengleichung haben. Schließlich erklären wir zwei neue Klassen rationaler orthogonaler hypergeometrischer Funktionen, und wir zeigen unter Benutzung der Fouriertransformation und der Parsevalschen Gleichung, dass es sich um endliche Orthogonalsysteme mit Gewichtsfunktionen vom Gammatyp handelt.

Bieberbach's Conjecture, the de Branges and Weinstein Functions and the Askey-Gasper Inequality

The Bieberbach conjecture about the coefficients of univalent functions of the unit disk was formulated by Ludwig Bieberbach in 1916 [Bieberbach1916]. The conjecture states that the coefficients of univalent functions are majorized by those of the Koebe function which maps the unit disk onto a radially slit plane. The Bieberbach conjecture was quite a difficult problem, and it was surprisingly proved by Louis de Branges in 1984 [deBranges1985] when some experts were rather trying to disprove it. It turned out that an inequality of Askey and Gasper [AskeyGasper1976] about certain hypergeometric functions played a crucial role in de Branges' proof. In this article I describe the historical development of the conjecture and the main ideas that led to the proof. The proof of Lenard Weinstein (1991) [Weinstein1991] follows, and it is shown how the two proofs are interrelated. Both proofs depend on polynomial systems that are directly related with the Koebe function. At this point algorithms of computer algebra come into the play, and computer demonstrations are given that show how important parts of the proofs can be automated.

Functions satisfying holonomic q-differential equations

In a similar manner as in some previous papers, where explicit algorithms for finding the differential equations satisfied by holonomic functions were given, in this paper we deal with the space of the q-holonomic functions which are the solutions of linear q-differential equations with polynomial coefficients. The sum, product and the composition with power functions of q-holonomic functions are also q-holonomic and the resulting q-differential equations can be computed algorithmically.

Characterization of DnmA, the Dnmt2 homolog in Dictyostelium discoideum

Eukaryotic DNA m5C methyltransferases (MTases) play a major role in many epigenetic regulatory processes like genomic imprinting, X-chromosome inactivation, silencing of transposons and gene expression. Members of the two DNA m5C MTase families, Dnmt1 and Dnmt3, are relatively well studied and many details of their biological functions, biochemical properties as well as interaction partners are known. In contrast, the biological functions of the highly conserved Dnmt2 family, which appear to have non-canonical dual substrate specificity, remain enigmatic despite the efforts of many researchers. The genome of the social amoeba Dictyostelium encodes Dnmt2-homolog, the DnmA, as the only DNA m5C MTase which allowed us to study Dnmt2 function in this organism without interference by the other enzymes. The dnmA gene can be easily disrupted but the knock-out clones did not show obvious phenotypes under normal lab conditions, suggesting that the function of DnmA is not vital for the organism. It appears that the dnmA gene has a low expression profile during vegetative growth and is only 5-fold upregulated during development. Fluorescence microscopy indicated that DnmA-GFP fusions were distributed between both the nucleus and cytoplasm with some enrichment in nuclei. Interestingly, the experiments showed specific dynamics of DnmA-GFP distribution during the cell cycle. The proteins colocalized with DNA in the interphase and were mainly removed from nuclei during mitosis. DnmA functions as an active DNA m5C MTase in vivo and is responsible for weak but detectable DNA methylation of several regions in the Dictyostelium genome. Nevertheless, gel retardation assays showed only slightly higher affinity of the enzyme to dsDNA compared to ssDNA and no specificity towards various sequence contexts, although weak but detectable specificity towards AT-rich sequences was observed. This could be due to intrinsic curvature of such sequences. Furthermore, DnmA did not show denaturant-resistant covalent complexes with dsDNA in vitro, although it could form covalent adducts with ssDNA. Low binding and methyltransfer activity in vitro suggest the necessity of additional factor in DnmA function. Nevertheless, no candidates could be identified in affinity purification experiments with different tagged DnmA fusions. In this respect, it should be noted that tagged DnmA fusion preparations from Dictyostelium showed somewhat higher activity in both covalent adduct formation and methylation assays than DnmA expressed in E.coli. Thus, the presence of co-purified factors cannot be excluded. The low efficiency of complex formation by the recombinant enzyme and the failure to define interacting proteins that could be required for DNA methylation in vivo, brought up the assumption that post-translational modifications could influence target recognition and enzymatic activity. Indeed, sites of phosphorylation, methylation and acetylation were identified within the target recognition domain (TRD) of DnmA by mass spectrometry. For phosphorylation, the combination of MS data and bioinformatic analysis revealed that some of the sites could well be targets for specific kinases in vivo. Preliminary 3D modeling of DnmA protein based on homology with hDNMT2 allowed us to show that several identified phosphorylation sites located on the surface of the molecule, where they would be available for kinases. The presence of modifications almost solely within the TRD domain of DnmA could potentially modulate the mode of its interaction with the target nucleic acids. DnmA was able to form denaturant-resistant covalent intermediates with several Dictyostelium tRNAs, using as a target C38 in the anticodon loop. The formation of complexes not always correlated with the data from methylation assays, and seemed to be dependent on both sequence and structure of the tRNA substrate. The pattern, previously suggested by the Helm group for optimal methyltransferase activity of hDNMT2, appeared to contribute significantly in the formation of covalent adducts but was not the only feature of the substrate required for DnmA and hDNMT2 functions. Both enzymes required Mg2+ to form covalent complexes, which indicated that the specific structure of the target tRNA was indispensable. The dynamics of covalent adduct accumulation was different for DnmA and different tRNAs. Interestingly, the profiles of covalent adduct accumulation for different tRNAs were somewhat similar for DnmA and hDNMT2 enzymes. According to the proposed catalytic mechanism for DNA m5C MTases, the observed denaturant-resistant complexes corresponded to covalent enamine intermediates. The apparent discrepancies in the data from covalent complex formation and methylation assays may be interpreted by the possibility of alternative pathways of the catalytic mechanism, leading not to methylation but to exchange or demethylation reactions. The reversibility of enamine intermediate formation should also be considered. Curiously, native gel retardation assays showed no or little difference in binding affinities of DnmA to different RNA substrates and thus the absence of specificity in the initial enzyme binding. The meaning of the tRNA methylation as well as identification of novel RNA substrates in vivo should be the aim of further experiments.

Assessing the users’ need for a spatial decision support system of smallholder farming in Kenya

Accurate data of the natural conditions and agricultural systems with a good spatial resolution are a key factor to tackle food insecurity in developing countries. A broad variety of approaches exists to achieve precise data and information about agriculture. One system, especially developed for smallholder agriculture in East Africa, is the Farm Management Handbook of Kenya. It was first published in 1982/83 and fully revised in 2012, now containing 7 volumes. The handbooks contain detailed information on climate, soils, suitable crops and soil care based on scientific research results of the last 30 years. The density of facts leads to time consuming extraction of all necessary information. In this study we analyse the user needs and necessary components of a system for decision support for smallholder farming in Kenya based on a geographical information system (GIS). Required data sources were identified, as well as essential functions of the system. We analysed the results of our survey conducted in 2012 and early 2013 among agricultural officers. The monitoring of user needs and the problem of non-adaptability of an agricultural information system on the level of extension officers in Kenya are the central objectives. The outcomes of the survey suggest the establishment of a decision support tool based on already available open source GIS components. The system should include functionalities to show general information for a specific location and should provide precise recommendations about suitable crops and management options to support agricultural guidance on farm level.

Moisture-dependent physical properties of locust bean (Parkia biglobosa) seeds

Seed moisture content is significant in the handling and processing of seeds. This work therefore determined the physical properties of Locust bean seeds as functions of seed moisture content in the moisture range of 5.9 – 28.2% dry basis. Mohsenin, Stepanoff and ASAE standard methods were used in determining the properties. Increases in seed dimensions vitz length = 10.2±1.0 – 11.3±0.9 mm; width = 8.5±0.8 – 9.1±0.6 mm; surface area = 191.2±24.6 – 208.3±26.3 mm2 ; geometric mean diameter = 7.78±0.49 – 8.12±0.03 and arithmetic mean diameter = 8.06±0.56 – 8.34±0.49 mm were recorded. Seed thickness = 5.49±0.43 – 5.26±0.62 mm; sphericity = 0.75±0.04 – 0.71±0.03; true density = 1251.96±55.5 - 1222±62.16 kgm-3 and porosity = 48.4±2.14 – 41.9±3.78 decreased. Static coefficient of friction increased on plywood (0.5±0.02 – 0.6±0.01), glass (0.4±0.05 – 0.5±0.01) and decreased on aluminium (0.5±0.02 – 0.5±0.04). A data of the physical properties of Locust bean; Parkia biglobosa was developed. This is useful for the design and development of equipment necessary for its handling and processing.