BOOK REVIEW

Modeling Fluctuating Populations by R.M. Nisbet and W.S.C. Gurney, John Wiley and Sons, 1982, 379 pp.     

Qualitative properties of modified equations

Suppose that a consistent one-step numerical method of orderr is applied to a smooth system of ordinary differential equations.Given any integer m 1, the method may be shown to be of orderr + m as an approximation to a certain modified equation. Ifthe method and the system have a particular qualitative propertythen it is important to determine whether the modified equationsinherit this property. In this article, a technique is introducedfor proving that the modified equations inherit qualitativeproperties from the method and the underlying system. The techniqueuses a straightforward contradiction argument applicable toarbitrary one-step methods and does not rely on the detailedstructure of associated power series expansions. Hence the conclusionsapply, but are not restricted, to the case of Runge-Kutte methods.The new approach unifies and extends results of this type thathave been derived by other means: results are presented forintegral preservation, reversibility, inheritance of fixed points.Hamiltonian problems and volume preservation. The techniquealso applies when the system has an integral that the methodpreserves not exactly, but to order greater than r. Finally,a negative result is obtained by considering a gradient systemand gradient numerical method possessing a global property thatis not shared by the associated modified equations.     

The stereochemistry of transition metal cyclooctatetraenyl complexes: di-h3,h3′ cyclooctatetraenedinickel,a sandwich compound with two enveloped nickel atoms

The crystal structure of dicyclooctatetraenedinickel, [(COT)Ni]₂, has been determined from three-dimensional, single crystal X-ray data collected by counter methods. Crystals of [(COT)Ni]₂, belong to the monoclinic system with a = 8.2906(3), b = 11.4185(5), c = 7.2340(3) Å, β = 115.978(2)°, d(calc) = 1.757 gcm^?3, Z = 2. The space group is C²_2h-P2₁/a. The structure was refined anisotropically (hydrogen atoms and a nickel atom fragment isotropically) by fullmatrix least-squares techniques. Final values of R and R_w were 0.046 and 0.079, respectively, for the 1055 unique, absorption and extinction corrected reflections with I > 2σ(I). Crystals of [(COT)Ni]₂ consists of discrete molecules with crystallographic C_i ($\text{1}$) symmetry. The compound possesses a sandwich structure with both metal atoms between the COT rings. Each nickel atom forms π-allyl type bonds to three carbon atoms of each COT ring. The nickel atoms are disordered over three sites. The effect of this disorder on the interpretation of the derived structural parameters is discussed.     

Hydratstufen und Kristallstrukturen von Bariumchlorid

Hydrates and crystal Structure of Barium Chloride The dehydrating process of BaCl₂ · 2H₂O and the phase transformations of BaCl₂ were observed by using a modified high temperature X-ray camera. The following compounds appeared with increasing temperature: BaCl₂ · 2H₂O → BaCl₂ · 1H₂O → BaCl₂(cubT) [BaCl₂(hex)]→ α-BaCl₂(ortho) → β-BaCl₂(cubH). The phase BaCl₂(cubT) is supposed to be the metastable low temperature form of β-BaCl₂(cubH). Structural relationships were demonstrated by comparing the different phases of the BaCl₂? H₂O system.     

Hydratstufen und Kristallstrukturen von Strontiumchlorid und Europium(II)-chlorid

Hydrates and Crystal Structures of Strontium Chloride and Europium Dichloride The dehydrating processes of SrCl₂ · 6 H₂O and EuCl₂ · 2 H₂O and the phase transformations involved were observed using a high temperature X-ray camera. The following phases appeared with increasing temperatur in the SrCl₂? H₂O system: SrCl₂ · 6 H₂O → SrCl₂ · 2 H₂O → SrCl₂ · 1 H₂O → SrCl₂(cub), and in the EuCl₂? H₂O system: EuCl₂ · 2 H₂O → EuCl₂ · 1 H₂O → EuCl₂ · wH₂O → EuCl₂(ortho), [EuCl₂(kub)].     

Solubility of glasses in the system P2O5-CaO-MgO-Na2O-TiO2: Experimental and modeling using artificial neural networks

Phosphate glasses in the system P₂O₅-CaO-MgO-Na₂O-TiO₂ for use as degradable implant materials were produced. In order to classify their solubility behavior, dissolution experiments were performed in deionized water for 60 min at 98 °C. Resulting solutions were analyzed using ICP-OES. In addition, pH measurements were carried out in physiological NaCl solution. With increasing phosphorus oxide content, the glasses showed a higher solubility and gave lower pH values in aqueous solution. This was caused by changes in the glass structure, as long phosphate chains are more susceptible to hydration than smaller phosphate groups. These changes in glass structure were followed by ³¹P MAS-NMR experiments. Increasing sodium oxide concentrations in exchange for calcium or magnesium oxide also increased the glass solubility by disrupting ionic cross links between chains. By contrast, addition of titania made the glasses more stable towards dissolution by cross linking smaller phosphate groups. The aim of this study was to find a relationship between glass composition and solubility behavior. As classical linear methods of data analysis were unsuitable due to the complexity of the relationship, preliminary artificial neural networks analyses were performed and were found to be an interesting tool for modeling the solubility behavior of phosphate glasses.     

Zur Kenntnis des Ammoniumsalzes der Trifluormethyl-sulfonsäure,NH4(SO3CF3)

On the ammonium salt of trifluoromethyl sulfonic acid, NH₄(SO₃CF₃) The preparation of NH₄(SO₃CF₃) is described. The compound has been identified and characterised by chemical analysis, PMR and vibrational spectroscopy. Single crystals were investigated by microscopical and x-ray diffraction methods. The vibrational spectra could be assigned. The compound crystallizes at ?100°C in the space group P 4₁2₁2 (P 4₃2₁2) and at room temperature probably in P 4/nmm. From the preliminary results some properties of the structures are discussed.