Implicit semi-direct methods based on root-free sparse factorization procedures

In this paper new extendable sparse symmetric factorisation procedures are presented for the solution of self adjoint elliptic partial differential equations. The derived iterative methods are shown to be both competitive and computationally efficient in comparison with existing schemes. The application of the methods to a linear and non-linear elliptic boundary value problem in 2 dimensions is discussed and numerical results given.     

Hydrazine determination in sludge samples by high-performance liquid chromatography

A relatively simple and cost-effective method utilizing HPLC with UV detection was developed to detect and quantify hydrazine in sludge samples. The method was developed primarily for sludge samples, but it can also be applicable to soil and other environmental samples. The hydrazines in the matrices were derivatized to hydrazones with benzaldehyde. The hydrazones were separated using HPLC with an RP C-18 column in an isocratic mode with methanol-water (95:5 v/v) and detected with UV detection at 313 nm. The detection limit (25 microL injection) for the method is 0.02 microg/mL of hydrazine.     

Fluidized beds in flow analysis: use with ion-exchange separation for spectrophotometric determination of zinc in plant digests

A novel strategy for utilization of solid reagents in flow analysis is proposed. Establishment of diffuse and reproducible geometry enables the solid particles to be maintained in constant floating, reflux, and circulating motion inside a mini-chamber. This is efficiently accomplished with pulsed flows, a characteristic of multi-pumping flow systems. Drawbacks inherent in solid-phase packed columns, for example backpressure, preferential pathways, swelling, etc., and some limitations inherent in immobilized reagents are minimised. Spectrophotometric determination of zinc in plants was selected as an application of the technique. Dowex 1-X8 anionic resin was kept freely inside a mini-chamber. Zinc chloro-complexes were adsorbed on the moving particles and derivatization with zincon was performed after elution. Analytical figures of merit and the potential and limitations of the approach are discussed.     

Discreteness of space from GUP II: Relativistic wave equations

Various theories of Quantum Gravity predict modifications of the Heisenberg Uncertainty Principle near the Planck scale to a so-called Generalized Uncertainty Principle (GUP). In some recent papers, we showed that the GUP gives rise to corrections to the Schrödinger equation, which in turn affect all quantum mechanical Hamiltonians. In particular, by applying it to a particle in a one-dimensional box, we showed that the box length must be quantized in terms of a fundamental length (which could be the Planck length), which we interpreted as a signal of fundamental discreteness of space itself. In this Letter, we extend the above results to a relativistic particle in a rectangular as well as a spherical box, by solving the GUP-corrected Klein–Gordon and Dirac equations, and for the latter, to two and three dimensions. We again arrive at quantization of box length, area and volume and an indication of the fundamentally grainy nature of space. We discuss possible implications.     

Comparing predator–prey models with hidden and explicit resources

In this paper two mathematical models are proposed and analyzed to elucidate the influence on a generalist predator of its hidden and explicit resources. Boundedness of the system’s trajectories, feasibility, local and global stability of the equilibria for both models are established, as well as possible local bifurcations. The findings indicate that the relevant behaviour of the system, including switching of stability, extinction and persistence of the involved populations, depends mainly on the reproduction rate of the favorite prey. To achieve full ecosystem survival some balance between the respective grazing pressures exerted by the predator on the prey populations needs to be maintained, while higher grazing pressure just on one species always leads to its extinction.     

A fast gradient and function sampling method for finite-max functions

This paper proposes an algorithm for the unconstrained minimization of a class of nonsmooth and nonconvex functions that can be written as finite-max functions. A gradient and function-based sampling method is proposed which, under special circumstances, either moves superlinearly to a minimizer of the problem of interest or improves the optimality certificate. Global and local convergence analysis are presented, as well as examples that illustrate the obtained theoretical results.