Numerical stability of biorthogonal wavelet transforms

For orthogonal wavelets, the discrete wavelet and wave packet transforms and their inverses are orthogonal operators with perfect numerical stability. For biorthogonal wavelets, numerical instabilities can occur. We derive bounds for the 2-norm and average 2-norm of these transforms, including efficient numerical estimates if the numberL of decomposition levels is small, as well as growth estimates forL . These estimates allow easy determination of numerical stability directly from the wavelet coefficients. Examples show that many biorthogonal wavelets are in fact numerically well behaved.     

Bildung Siliciumorganischer Verbindungen. LV. Die Konformeren des 1,3,5,7-Tetrasila-bicyclo[3,3,1]nonans und 2,4,6,8,9-Pentasila-bicyclo[3,3,1]nonans

Formation of Organosilicon Compounds. LV. Conformeres of the 1,3,5,7-Tetrasilabicyclo [3,3,1] nonane and 2,4,6,8,9-Pentasila-bicyclo [3,3,1] nonane Two types of carbosilanes with a bicyclo [3,3,1] nonane structure are reported, derivatives of 1,3,5,7-Tetrasila-bicyclo-[3,3,1] nonane (a) and of 2,4,6,8,9-Pentasila-bicyclo [3,3,1] nonane (b) with an inverse structure in respect to the Si- and C-atoms. By means of NMR-investigations the structure can be determined. Derivatives of (a) are present in the Si₄C₁₁H₂₈ with fully methylated Si-atoms, the 1,5 dichloro-1,3,5,7-tetrasila-bicyclo [3,3,1] nonane and Si₄Cl₆C₅H₁₀ with fully chlorinated Si-atoms with twofold boat conformation. In the derivatives of type (b) as Si₅H₁₀C₄H₆ with hydrogenated Si-atoms as well as in 9,9-dichloro-2,4,6,8,9-pentasila-bicyclo [3,3,1] nonane a change in conformation is observed, whereas a rigid chair conformation is found for both rings in the Si-chlorimated derivative Si₅Cl₁₀C₄H₁₀. A comparison of atom-resp. H? H distances in cyclohexane and 1,3,5-Trisilacyclohexane gives evidence that the boat conformation is more preferable for the 1,3,5-Trisilacyclohexane than for cyclohexane due to larger H? H-distances (caused by Si? C-distances).     

The Gas-Solid Interface the adsorption of nitrogen,argon, neopentane,sulfur dioxide,carbon dioxide and sulfur hexafluoride on rhombic sulfur

Physical adsorption of the title compounds on rhombic sulfur of 0.4 to 0.5 m²/g is reported. The isotherms are of type II for N₂, Ar and C₅H₁₂, of type III for SO₂ and CO₂, and linear for SF₆. There is no hysteresis. The method of Ross & Olivier shows that the surface is relatively heterogenous (γ 17). Isosteric heats of adsorption and c values of the B.E.T. equation are also reported.     

Stereochemistry of Polynuclear Cadmium(II)thioglycolates: Crystal Structure of [ICd8(SCH2CH2OH)12]3+ · 3I− · H2O

Crystals of the title compound are triclinic, a = 27.87 Å, b = 10.77 Å, c = 12.94 Å, α 73.1°, β 116.1°, γ 120.0°, space group P1 . The structure consists of octanuclear ions: Eight Cd(II) ions are found at the corners of a distorted cube, the center of the cube is occupied by an iodide, the twelve thioglycolate sulfur atoms bridge the twelve edges of the cube thereby forming a distorted icosahedron. Cadmium ions are either five or seven coordinate. The phase problem for this structure was solved using a combination of very high and very low E-values.     

Concentration and determination of trace organic pollutants in water

Organic pollutants in water are isolated on a mini-sampler tube containing a macroporous resin. The sorbed pollutants are next thermally transferred to a second sorption tube and then to an analytical column where they are separated and determined by temperature-programmed gas chromatography. Excellent recoveries were obtained for tests in which model organic compounds of various classes were added to water. The water sample is much smaller than that required with previous analytical methods.