A generic polynomial solution for the differential equation of hypergeometric type and six sequences of orthogonal polynomials related to it

In this work, we present a generic formula for the polynomial solution families of the well-known differential equation of hypergeometric type s(x)y"n(x) + t(x)y'n(x) - lnyn(x) = 0 and show that all the three classical orthogonal polynomial families as well as three finite orthogonal polynomial families, extracted from this equation, can be identified as special cases of this derived polynomial sequence. Some general properties of this sequence are also given.

Solution properties of the de Branges differential recurrence equation

In this 1984 proof of the Bieberbach and Milin conjectures de Branges used a positivity result of special functions which follows from an identity about Jacobi polynomial sums thas was published by Askey and Gasper in 1976. The de Branges functions Tn/k(t) are defined as the solutions of a system of differential recurrence equations with suitably given initial values. The essential fact used in the proof of the Bieberbach and Milin conjectures is the statement Tn/k(t)<=0. In 1991 Weinstein presented another proof of the Bieberbach and Milin conjectures, also using a special function system Λn/k(t) which (by Todorov and Wilf) was realized to be directly connected with de Branges', Tn/k(t)=-kΛn/k(t), and the positivity results in both proofs Tn/k(t)<=0 are essentially the same. In this paper we study differential recurrence equations equivalent to de Branges' original ones and show that many solutions of these differential recurrence equations don't change sign so that the above inequality is not as surprising as expected. Furthermore, we present a multiparameterized hypergeometric family of solutions of the de Branges differential recurrence equations showing that solutions are not rare at all.

A semi-phenomenological approach to the structure and transport properties of macromolecules in solution

Motiviert durch die Lebenswissenschaften (Life sciences) haben sich Untersuchungen zur Dynamik von Makromolekülen in Lösungen in den vergangenen Jahren zu einem zukunftsweisenden Forschungsgebiet etabliert, dessen Anwendungen von der Biophysik über die physikalische Chemie bis hin zu den Materialwissenschaften reichen. Neben zahlreichen experimentellen Forschungsprogrammen zur räumlichen Struktur und den Transporteigenschaften grosser MolekÄule, wie sie heute praktisch an allen (Synchrotron-) Strahlungsquellen und den Laboren der Biophysik anzutreffen sind, werden gegenwärtig daher auch umfangreiche theoretische Anstrengungen unternommen, um das Diffusionsverhalten von Makromolekülen besser zu erklären. Um neue Wege für eine quantitative Vorhersagen des Translations- und Rotationsverhaltens grosser Moleküle zu erkunden, wurde in dieser Arbeit ein semiphänomenologischer Ansatz verfolgt. Dieser Ansatz erlaubte es, ausgehend von der Hamiltonschen Mechanik des Gesamtsystems 'Molekül + Lösung', eine Mastergleichung für die Phasenraumdichte der Makromoleküle herzuleiten, die den Einfluss der Lösung mittels effektiver Reibungstensoren erfasst. Im Rahmen dieses Ansatzes gelingt es z.B. (i) sowohl den Einfluss der Wechselwirkung zwischen den makromolekularen Gruppen (den sogenannten molekularen beads) und den Lösungsteilchen zu analysieren als auch (ii) die Diffusionseigen schaften für veschiedene thermodynamische Umgebungen zu untersuchen. Ferner gelang es auf der Basis dieser Näherung, die Rotationsbewegung von grossen Molekülen zu beschreiben, die einseitig auf einer Oberfläche festgeheftet sind. Im Vergleich zu den aufwendigen molekulardynamischen (MD) Simulationen grosser Moleküle zeichnet sich die hier dargestellte Methode vor allem durch ihren hohen `Effizienzgewinn' aus, der für komplexe Systeme leicht mehr als fünf Grössenordnungen betragen kann. Dieser Gewinn an Rechenzeit erlaubt bspw. Anwendungen, wie sie mit MD Simulationen wohl auch zukünftig nicht oder nur sehr zögerlich aufgegriffen werden können. Denkbare Anwendungsgebiete dieser Näherung betreffen dabei nicht nur dichte Lösungen, in denen auch die Wechselwirkungen der molekularen beads zu benachbarten Makromolekülen eine Rolle spielt, sondern auch Untersuchungen zu ionischen Flüssigkeiten oder zur Topologie grosser Moleküle.

Drainage, salt leaching and physico-chemical properties of irrigated man-made terrace soils in a mountain oasis of northern Oman

Little is known about the sustainability of irrigated oasis agriculture in northern Oman. The objective of this study therefore was to examine which factors allowed agricultural productivity to be apparently maintained during the two millenia of a mountain oasis’ existence. Soil moisture and physico-chemical properties were measured in a typical flood-irrigated field sown to alfalfa (Medicago sativa L.). Particle size, organic (C_org) and inorganic carbon content, pH and electrical conductivity (EC)of the soil profile were analyzed at 0.15, 0.45 and 1.00 m. Saturated hydraulic conductivity and the soil’s apparent bulk density and water potential were determined from undisturbed samples at 0.05, 0.25 and 0.60 m. During irrigation cycles of 6–9 days, volumetric water contents ranged from 30% to 13%. A tracer experiment with potassium bromide revealed that 52–56% of the irrigation water was stored in the upper 0.4 m of the soil. The rest of the water moved further down the profile, thus providing the necessary drainage to avoid the build-up of toxic salt concentrations. Due to differences in pore size, plant-available water in the topsoil amounted to 18.7% compared to 13% and 13.5% at 0.25- and 0.60-m depth, respectively. The aggregate structure in the upper 1.0 m of the profile is likely preserved by concentrations of calcium carbonate (CaCO3) from 379 to 434 mg kg^-1 and C_org from 157 to 368 mg kg^-1 soil. The data indicate that the sustainability of this irrigated landuse system is due to high water quality with low sodium but high CaCO3 concentration, the elaborate terrace structure and water management which allows adequate drainage.

Bacterial ecology of ancient Saharan salt-enrichment ponds at Teguidda-n-Tessoumt

Little is known about the bacterial ecology of evaporative salt-mining sites (salterns) of which Teguidda-n-Tessoumt at the fringe of the West-African Saharan desert in Niger is a spectacular example with its many-centuries-old and very colorful evaporation ponds. During the different enrichment steps of the salt produced as a widely traded feed supplement for cattle, animal manure is added to the crude brine, which is then desiccated and repeatedly crystallized. This study describes the dominant Bacteria and Archaea communites in the brine from the evaporation ponds and the soil from the mine, which were determined by PCR-DGGE of 16S rDNA. Correspondence analysis of the DGGE-community fingerprints revealed a change in community structure of the brine samples during the sequential evaporation steps which was, however, unaffected by the brine's pH and electric conductivity (EC). The Archaea community was dominated by a phylogenetically diverse group of methanogens, while the Bacteria community was dominated by gamma proteobacteria. Microorganisms contained in the purified salt product have the potential to be broadly disseminated and are fed to livestock across the region. In this manner, the salt mines represent an intriguing example of long-term human activity that has contributed to the continual selection, cultivation, and dissemination of cosmopolitan microorganisms.

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.

Finite element method for the accurate solution of diatomic molecules

We present the Finite-Element-Method (FEM) in its application to quantum mechanical problems solving for diatomic molecules. Results for Hartree-Fock calculations of H_2 and Hartree-Fock-Slater calculations of molecules like N_2 and C0 have been obtained. The accuracy achieved with less then 5000 grid points for the total energies of these systems is 10_-8 a.u., which is demonstrated for N_2.

Solution of the Hartree-Fock-Slater equations for diatomic molecules by the finite-element method

We present the finite-element method in its application to solving quantum-mechanical problems for diatomic molecules. Results for Hartree-Fock calculations of H_2 and Hartree-Fock-Slater calculations for molecules like N_2 and CO are presented. The accuracy achieved with fewer than 5000 grid points for the total energies of these systems is 10^-8 a.u., which is about two orders of magnitude better than the accuracy of any other available method.

Ions of the superheavy elements in vacuum and in solution

The extension of the Periodic Table into the range of unknown atomic numbers of above one hundred requires relativistic calculations. The results of the latter are used to indicate probable values for X-ray transition lines which will be useful for identification of the atomic species formed during collision between accelerated ions and the target. If the half-lives of the isotopes are long, then the chemistry of these new species becomes an important question which is reviewed for E110, E 111 and E112. The possible structural chemistry of the elements E108 to E112 is suggested. Finally the effects of solvation on ions of the actinide and superheavy elements have been studied.

Solution of the time dependent Dirac-Fock-Slater equation for many-electron collisions systems using a time window method

We present a new scheme to solve the time dependent Dirac-Fock-Slater equation (TDDFS) for heavy many electron ion-atom collision systems. Up to now time independent self consistent molecular orbitals have been used to expand the time dependent wavefunction and rather complicated potential coupling matrix elements have been neglected. Our idea is to minimize the potential coupling by using the time dependent electronic density to generate molecular basis functions. We present the first results for 16 MeV S{^16+} on Ar.

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)

Constructing a ‘moment of crisis’ and its adequate solution

The rejection of the European Constitution marks an important crystallization point for debate about the European Union (EU) and the integration process. The European Constitution was envisaged as the founding document of a renewed and enlarged European Union and thus it was rather assumed to find wide public support. Its rejection was not anticipated. The negative referenda in France and the Netherlands therefore led to a controversial debate about the more fundamental meaning and the consequences of the rejection both for the immediate state of affairs as well as for the further integration process. The rejection of the Constitution and the controversy about its correct interpretation therefore present an intriguing puzzle for political analysis. Although the treaty rejection was taken up widely in the field of European Studies, the focus of existing analyses has predominantly been on explaining why the current situation occurred. Underlying these approaches is the premise that by establishing the reasons for the rejection it is possible to derive the ‘true’ meaning of the event for the EU integration process. In my paper I rely on an alternative, discourse theoretical approach which aims to overcome the positivist perspective dominating the existing analyses. I argue that the meaning of the event ‘treaty rejection’ is not fixed or inherent to it but discursively constructed. The critical assessment of this concrete meaning-production is of high relevance as the specific meaning attributed to the treaty rejection effectively constrains the scope for supposedly ‘reasonable’ options for action, both in the concrete situation and in the further European integration process more generally. I will argue that the overall framing suggests a fundamental technocratic approach to governance from part of the Commission. Political struggle and public deliberation is no longer foreseen as the concrete solutions to the citizens’ general concerns are designed by supposedly apolitical experts. Through the communicative diffusion and the active implementation of this particular model of governance the Commission shapes the future integration process in a more substantial way than is obvious from its seemingly limited immediate problem-solving orientation of overcoming the ‘constitutional crisis’. As the European Commission is a central actor in the discourse production my analysis focuses on the specific interpretation of the situation put forward by the Commission. In order to work out the Commission’s particular take on the event I conducted a frame analysis (according to Benford/Snow) on a body of key sources produced in the context of coping with the treaty rejection.

On Solution Sets of Information Inequalities

We investigate solution sets of a special kind of linear inequality systems. In particular, we derive characterizations of these sets in terms of minimal solution sets. The studied inequalities emerge as information inequalities in the context of Bayesian networks. This allows to deduce important properties of Bayesian networks, which is important within causal inference.

Biofuel as the solution of alternative energy production?

There have being increasing debate on the prospects of biofuel becoming the next best alternative to solving the problem of CO2 emission and the escalating fuel prices, but the question is whether this assertion is true and also if it comes without any cost to pay. This paper seeks to find out whether this much praised alternative to solving these problems is a better option or another way for the developed countries to find more areas where they could get cheap land, labour and raw materials for the production of biofuel. This will focus mainly on some effects the growing biofuel production has on food security, livelihood of people, the environment and some land conflicts developing as a result of land grabbing for biofuel production in the developing countries.

Die Carbonylierung acyclischer Diaminocarbene

Das Dissertationsprojekt befasst sich mit dem synthetischen Potential acyclischer Diaminocarbene (aDACs; Verbindungen des Typs (R2N)2C:) und prüft dabei insbesondere deren Reaktivität gegenüber Kohlenmonoxid (CO). Grundlage des Vorhabens ist eine Aufsehen erregende Beobachtung von SIEMELING et al. (Chem. Sci., 2010, 1, 697): Der Prototyp der aDACs, das Bis(diisopropylamino)carben, ist in der Lage CO zu aktivieren. Dabei wird zunächst ein intermediäres Keten des Typs (R2N)2C=C=O generiert, das in Folge einer intramolekularen Reaktion ein stabiles β-Lactamderivat ausbildet. Eine Sensation, schließlich ging man in der Fachwelt bis dato davon aus, dass cyclische und acyclische Diaminocarbene für derartige Reaktionen nicht elektrophil genug seien. Ziel der vorliegenden Arbeit war eine systematische Auslotung der aDAC-Reaktivität gegenüber CO. Im Rahmen der durchgeführten Untersuchungen ist es gelungen, das Feld der literaturbekannten aDACs von 12 auf 19 zu erweitern. Die Carbene, ihre Formamidiniumsalz-Vorstufen, sowie die korrespondierenden Carben–Metallkomplexe konnten in den meisten Fällen vollständig charakterisiert werden. Es konnte gezeigt werden, dass manche Isopropyl-substituierten aDACs in inertem Lösemittel einer β-Umlagerung unterliegen sowie, dass eine solche intramolekulare Reaktivität innerhalb dieser Substanzklasse nicht trivial ist: Zum Teil ganz ähnlich substituierte aDACs sind in Lösung unbegrenzt haltbar. Die Reaktivität gegenüber CO konnte an etwa einem Dutzend aDACs studiert werden. Lediglich in einem Fall zeigte sich das Carben inert. In einem sterisch überfrachteten Fall entstand in einer regio- und stereoselektiven Folgereaktion ein biologisch aktives bicyclisches β-Lactamderivat. In den meisten Fällen ergaben sich betainische Oxyallylspezies des Typs [(R2N)2C]2CO als intermolekulare Folgeprodukte. Die mechanistische Scheidelinie zwischen intra- und intermolekularer Keten-Folgereaktion konnte anhand der Carbonylierung sterisch ganz ähnlich substituierter aDACs aufgezeigt werden. Die gewonnenen Erkenntnisse liefern deutliche Hinweise darauf, dass das chemische Verhalten der aDACs gegenüber CO eher durch feinste elektronische Unterschiede als durch den sterischen Anspruch der Carben-Substituenten beeinflusst wird. Mit Hilfe von In-Situ-IR-Spektroskopie gelang es in manchen Fällen, bei denen eine Isolierung der Carbonylierungsprodukte nicht glückte, die Generierung hochreaktiver Oxyallylspezies zu belegen. Weiterhin konnte im Zuge der In-Situ-IR-Studien das zuvor nur postulierte Diaminoketen als primäres Carbonylierungsprodukt dingfest gemacht werden (ν(C=C=O) = 2085 1/cm): Es handelt sich hierbei um den ersten experimentellen Nachweis eines Diaminoketens überhaupt.