On the existence and convergence of the solution of PML equations

In this article we study the mesh termination method in computational scattering theory known as the method of Perfectly Matched Layer (PML). This method is based on the idea of surrounding the scatterer and its immediate vicinity with a fictitious absorbing non-reflecting layer to damp the echoes coming from the mesh termination surface. The method can be formulated equivalently as a complex stretching of the exterior domain. The article is devoted to the existence and convergence questions of the solutions of the resulting equations. We show that with a special choice of the fictitious absorbing coefficient, the PML equations are solvable for all wave numbers, and as the PML layer is made thicker, the PML solution converge exponentially towards the actual scattering solution. The proofs are based on boundary integral methods and a new type of near-field version of the radiation condition, called here the double surface radiation condition. Partly supported by the Finnish Academy, project 37692.     

FREE NUCLEOTIDES IN RESTING AND METABOLIZING BAKER'S YEAST*

The free nucleotides of semi-aerobically and aerobically cultured baker's yeast in different industrial stages have been investigated under different conditions: during growth and at rest, and during respiration and fermentation of different substrates. The amounts of protein and nucleic acids diminish progressively during industrial propagation, while the amount of free nucleotides falls only during the last stage of propagation. In yeasts cultured under different conditions of aeration and nutrient addition, the nucleotide spectra were rather similar, but the proportions of the free nucleotides change considerably when the yeast passes from the resting state to growth or metabolism. On transfer from respiration to fermentation the nucleotide spectrum remained practically unchanged. However, a small addition of ethanol to a respiring yeast suspension caused clear alterations in the spectrum, the most obvious being the reduced amount of nucleotides with energy-rich phosphate bonds.     

Clustering properties of hierarchical self-organizing maps

A multilayer hierarchical self-organizing map (HSOM) is discussed as an unsupervised clustering method. The HSOM is shown to form arbitrarily complex clusters, in analogy with multilayer feedforward networks. In addition, the HSOM provides a natural measure for the distance of a point from a cluster that weighs all the points belonging to the cluster appropriately. In experiments with both artificial and real data it is demonstrated that the multilayer SOM forms clusters that match better to the desired classes than do direct SOM's, classical k-means, or Isodata algorithms.     

Quantum Correlations and Cyclic Structures

This article is a tribute to Professor Ruben Pauncz on his septuagenary. We discuss the close connection between the theory of quantum correlations and near cyclic structures in theoretical chemistry. A brief review of the essential transformation properties in condensed matter physics is given and some suggestions for the future are indicated.     

Recovery of manganese from iron containing sulfate solutions by precipitation

Worldwide consumption of manganese is increasing, nevertheless huge amounts of manganese from hydrometallurgical processes still end up as waste since the recovery of manganese from multi-metal solutions at low concentrations is not considered feasible. Poor iron control typically prevents the production of high purity manganese. This work studies a number of precipitants in manganese recovery and iron separation from sulfate solutions. The precipitation reagents were compared from the point of view of selectivity and economy. Carbonate precipitation is a fast and effective method for the recovery of manganese from bulk solutions. Subsequent leaching of metal carbonate is also easier and consumes less acid than, for example, hydroxide or sulfide precipitates. In order to avoid gypsum formation, soda ash should be used instead of limestone. It was found that efficient selective iron removal from MnSO₄ solutions is achieved with combined O₂ or air oxidation and CaCO₃ precipitation at pH >5.8 and at a redox potential of >200 mV. Effective mixing and sufficient retention time are essential to make the method technically efficient and economically feasible.     

Polycyclic aromatic hydrocarbons (PAHs) in soot produced by combustion of polystyrene,polypropylene, and wood

The smoke and soot produced by the combustion of plastics or wood in a domestic stove or fireplace contain many poisonous compounds, including the polycyclic aromatic hydrocarbons (PAHs), many of which are carcinogenic. PAHs were selected as the subject of our study to gain a better sense of the hazards of burning plastics. Small samples of polystyrene, polypropylene, and wood underwent combustion in a tubular oven at 700°C; in addition, polystyrene and wood were combusted at room temperature. After their extraction and purification, the PAHs were analyzed by gas chromatography and mass spectrometry. Conditions in the hot oven promoted soot production, whereas combustion at room temperature led to somewhat more complete combustion. The PAH profiles of the examined materials resembled each other to some extent, though the original chemical structure of the polymeric materials varied a great deal. However, clear differences between the materials could be detected from the soot extracts, the soot of polystyrene being especially rich in compounds containing remnants of the polymer structure. Carcinogenic activity caused by the PAHs can be assumed to be of the same order of magnitude as soot from the combustion of wood.