Microbial use of organic substrates and maize growth, especially in saline and alkaline soils of Pakistani Punjab

This thesis consists of 4 main parts: (1) impact of growing maize on the decomposition of incorporated fresh alfalfa residues, (2) relationships between soil biological and other soil properties in saline and alkaline arable soils from the Pakistani Punjab, (3) decomposition of compost and plant residues in Pakistani soils along a gradient in salinity, and (4) interactions of compost and triple superphosphate on the growth of maize in a saline Pakistani soil. These 4 chapters are framed by a General Introduction and a Conclusions section. (1) In the first study, the effects of growing maize plants on the microbial decomposition of freshly chopped alfalfa residues was investigated in a 90-day pot experiment using a sandy arable soil. Assuming that the addition of alfalfa residues did not affect the decomposition of native soil organic matter, only 27% of the alfalfa residues were found as CO2. This suggests that a considerable part of alfalfa-C remained undecomposed in the soil. However, only 6% of the alfalfa residues could be recovered as plant remains in treatment with solely alfalfa residues. Based on d13C values, it was calculated that plant remains in treatment maize + alfalfa residues contained 14.7% alfalfa residues and 85.3% maize root remains. This means 60% more alfalfa-C was recovered in this treatment. (2) In the second study, the interactions between soil physical, soil chemical and soil biological properties were analysed in 30 Pakistani soils from alkaline and saline arable sites differing strongly in salinisation and in soil pH. The soil biological properties were differentiated into indices for microbial activity, microbial biomass, and community structure with the aim of assessing their potential as soil fertility indices. (3) In the third study, 3 organic amendments (compost, maize straw and pea straw) were added to 5 Pakistani soils from a gradient in salinity. Although salinity has depressive effects on microbial biomass C, biomass N, biomass P, and ergosterol, the clear gradient according to the soil salt concentration was not reflected by the soil microbial properties. The addition of the 3 organic amendments always increased the contents of the microbial indices analysed. The amendment-induced increase was especially strong for microbial biomass P and reflected the total P content of the added substrates. (4) The fourth study was greenhouse pot experiment with different combinations of compost and triple superphosphate amendments to investigate the interactions between plant growth, microbial biomass formation and compost decomposition in a strongly saline Pakistani arable soil in comparison to a non-saline German arable soil. The Pakistani soil had a 2 times lower content of ergosterol, a 4 times lower contents of microbial biomass C, biomass N and biomass P, but nearly a 20 times lower content of NaHCO3 extractable P. The addition of 1% compost always had positive effects on the microbial properties and also on the content of NaHCO3 extractable P. The addition of superphosphate induced a strong and similar absolute increase in microbial biomass P in both soils.

Lagrangian approximations and weak solutions of the Navier-Stokes equations

The motion of a viscous incompressible fluid flow in bounded domains with a smooth boundary can be described by the nonlinear Navier-Stokes equations. This description corresponds to the so-called Eulerian approach. We develop a new approximation method for the Navier-Stokes equations in both the stationary and the non-stationary case by a suitable coupling of the Eulerian and the Lagrangian representation of the flow, where the latter is defined by the trajectories of the particles of the fluid. The method leads to a sequence of uniquely determined approximate solutions with a high degree of regularity containing a convergent subsequence with limit function v such that v is a weak solution of the Navier-Stokes equations.

Redox reactions of group 5 elements, including element 105, in aqueous solutions

Standard redox potentials E^0(M^z+x/M^z+) in acidic solutions for group 5 elements including element 105 (Ha) and the actinide, Pa, have been estimated on the basis of the ionization potentials calculated via the multiconfiguration Dirac-Fock method. Stability of the pentavalent state was shown to increase along the group from V to Ha, while that of the tetra- and trivalent states decreases in this direction. Our estimates have shown no extra stability of the trivalent state of hahnium. Element 105 should form mixed-valence complexes by analogy with Nb due to the similar values of their potentials E^0(M^3+/M^2+). The stability of the maximumoxidation state of the elements decreases in the direction 103 > 104 > 105.

The electronic structure of anionic halide complexes of element 105 in aqueous solutions and their extraction by aliphatic amines

To study the complex formation of group 5 elements (Nb, Ta, Ha, and pseudoanalog Pa) in aqueous HCI solutions of medium and high concentrations the electronic structures of anionic complexes of these elements [MCl_6]^-, [MOCl_4]^-, [M(OH)-2 Cl_4]^-, and [MOCl_5]^2- have been calculated using the relativistic Dirac-Slater Discrete-Variational Method. The charge density distribution analysis has shown that tantalum occupies a specific position in the group and has the highest tendency to form the pure halide complex, [TaCl_6-. This fact along with a high covalency of this complex explains its good extractability into aliphatic amines. Niobium has equal trends to form pure halide [NbCl_6]^- and oxyhalide [NbOCl_5]^2- species at medium and high acid concentrations. Protactinium has a slight preference for the [PaOCl_5]^2- form or for the pure halide complexes with coordination number higher than 6 under these conditions. Element 105 at high HCl concentrations will have a preference to form oxyhalide anionic complex [HaOCl_5]^2- rather than [HaCl_6]^-. For the same sort of anionic oxychloride complexes an estimate has been done of their partition between the organic and aqueous phases in the extraction by aliphatic amines, which shows the following succession of the partition coefficients: P_Nb < P_Ha < P_Pa.

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.

On Solutions of Holonomic Divided-Difference Equations on Non-Uniform Lattices

The main aim of this paper is the development of suitable bases (replacing the power basis x^n (n\in\IN_\le 0) which enable the direct series representation of orthogonal polynomial systems on non-uniform lattices (quadratic lattices of a discrete or a q-discrete variable). We present two bases of this type, the first of which allows to write solutions of arbitrary divided-difference equations in terms of series representations extending results given in [16] for the q-case. Furthermore it enables the representation of the Stieltjes function which can be used to prove the equivalence between the Pearson equation for a given linear functional and the Riccati equation for the formal Stieltjes function. If the Askey-Wilson polynomials are written in terms of this basis, however, the coefficients turn out to be not q-hypergeometric. Therefore, we present a second basis, which shares several relevant properties with the first one. This basis enables to generate the defining representation of the Askey-Wilson polynomials directly from their divided-difference equation. For this purpose the divided-difference equation must be rewritten in terms of suitable divided-difference operators developed in [5], see also [6].

Controlling the transport of an ion: classical and quantum mechanical solutions

The accurate transport of an ion over macroscopic distances represents a challenging control problem due to the different length and time scales that enter and the experimental limitations on the controls that need to be accounted for. Here, we investigate the performance of different control techniques for ion transport in state-of-the-art segmented miniaturized ion traps. We employ numerical optimization of classical trajectories and quantum wavepacket propagation as well as analytical solutions derived from invariant based inverse engineering and geometric optimal control. The applicability of each of the control methods depends on the length and time scales of the transport. Our comprehensive set of tools allows us make a number of observations. We find that accurate shuttling can be performed with operation times below the trap oscillation period. The maximum speed is limited by the maximum acceleration that can be exerted on the ion. When using controls obtained from classical dynamics for wavepacket propagation, wavepacket squeezing is the only quantum effect that comes into play for a large range of trapping parameters. We show that this can be corrected by a compensating force derived from invariant based inverse engineering, without a significant increase in the operation time.