Bivariate Free Knot Splines

We consider the least squares approximation of gridded 2D data by tensor product splines with free knots. The smoothing functional to be minimized—a generalization of the univariate Schoenberg functional—is chosen in such a way that the solution of the bivariate problem separates into the solution of a sequence of univariate problems in case of fixed knots. The resulting optimization problem is a constrained separable least squares problem with tensor product structure. Based on some ideas developed by the authors for the univariate case, an efficient method for solving the specially structured 2D problem is proposed, analyzed and tested on hand of some examples from the literature.     

Low-temperature hydride furnace modified for the atomic absorption spectrometric determination of metals with low appearance temperatures

The sample is vaporized from tungsten filament coils (150 W) and transported by an argon stream to the cell of a modified hydride furnace for atomic absorption spectrometry (a.a.s.). The system provides almost the same sensitivity for elements with low appearance temperatures (e.g., Bi, Cd, Pb, Tl, Zn) as graphite-furnace a.a.s. The detection limits are between 0.1 and 5 ng ml^?1, depending on the element.     

ROBUSTNESS OF AN UPWIND FINITE DIFFERENCE SCHEME FOR SEMILINEAR CONVECTION-DIFFUSION PROBLEMS WITH BOUNDARY TURNING POINTS

We consider a singularly perturbed semilinear convection-diffusion problem with a boundary layer of attractive turning-point type. It is shown that its solution can be decomposed into a regular solution component and a layer component. This decomposi-tion is used to analyse the convergence of an upwinded finite difference scheme on Shishkin meshes.     

Analysis of a finite-difference scheme for a singularly perturbed problem with two small parameters

We study a model linear convection-diffusion-reaction problem where both the diffusion term and the convection term are multiplied by small parameters ε_d and ε_c, respectively. Depending on the size of the parameters the solution of the problem may exhibit exponential layers at both end points of the domain. Sharp bounds for the derivatives of the solution are derived using a barrier-function technique. These bounds are applied in the analysis of a simple upwind-difference scheme on Shishkin meshes. This method is established to be almost first-order convergent, independently of the parameters ε_d and ε_c.     

Synthesis,Vibrational Spectrum and Structure of the Tetracyanoborate K[B(CN)4]·CH3CN

The new tetracyanoborate K[B(CN)₄]·CH₃CN was synthesized by dissolution of the solvent‐free K[B(CN)₄] in acetonitrile and subsequent careful crystallization. The crystal structure has been determined by single‐crystal X‐ray diffraction. It crystallizes in the orthorhombic space group P2₁2₁2₁ with Z = 4. Some comparisons with related structures are made, and the vibrational spectrum is discussed.     

Rhodium and palladium β-diketonate determination with on-line supercritical fluid extraction-high performance liquid chromatography via solid phase extraction

 An on-line system of supercritical fluid extraction (SFE) and high performance liquid chromatography (HPLC) via solid phase extraction (SPE) is described for the determination of palladium and rhodium 2,2,6,6-tetramethyl-3,5-heptanedione-(thd) as well as rhodium-acetylacetonate-(acac) and benzylacetonate-(bzac) chelates. The chelates were extracted with supercritical CO₂ from sand and humic acid, concentrated on SPE cartridges and analysed with HPLC. Two cartridge materials were tested and compared to off-line trapping. The percentage of the breakthrough and cartridge retained material were measured in liquid dichloromethane. The SFE conditions could be optimized to separate metal chelates during the extraction. The supercritical fluid (SF) behaviour of different ligands on rhodium were investigated. Received: 19 July 1996/Revised: 11 December 1996/Accepted: 14 December 1996     

Kristallstrukturen der Fluorochloroplatinate(IV) cis-[(C5H5N)2CH2][PtF4Cl2], trans-[(C5H5N)2CH2][PtF4Cl2] · H2O und [(C5H5N)2CH2][PtF5Cl]

Crystal Structures of the Fluorochloroplatinates(IV) cis-[(C₅H₅N)₂CH₂][PtF₄Cl₂], trans-[(C₅H₅N)₂CH₂][PtF₄Cl₂] · H₂O, and [(C₅H₅N)₂CH₂][PtF₅Cl] The complex ions cis-[PtF₄Cl₂]^2?, trans-[PtF₄Cl₂]^2? and [PtF₅Cl]^2? have been synthesized by stereoselective ligand exchange reactions utilizing the trans effect and are separated by ion exchange chromatography on diethylaminoethyl cellulose. These anions form stable AB-type salts with the doubly charged cation dipyridiniomethane, [(C₅H₅N)₂CH₂]²⁺. X-ray structure determinations on single crystals of cis-[(C₅H₅N)₂CH₂][PtF₄Cl₂] ( 1 ) (monoclinic, space group P2₁/n with a = 10.379(10), b = 9.635(2), c = 13.738(2) Å, β = 99.142(10)°, Z = 4), trans-[(C₅H₅N)₂CH₂][PtF₄Cl₂] · H₂O ( 2 ) (triclinic, space group P1 with a = 7.757(4), b = 10.059(7), c = 10.408(6) Å, α = 82.49(5), β = 68.92(4), γ = 75.46(4)°, Z = 2) and [(C₅H₅N)₂CH₂][PtF₅Cl] ( 3 ) (orthorhombic, space group Pnma with a = 10.394(3), b = 13.320(2), c = 9.2694(10) Å, Z = 4), reveal the perfect ordering of the anion sublattice. The stronger trans influence of Cl compared with F is observed in asymmetric axes $ {\rm F}^ \bullet $? Pt? Cl′. The bond lengths Pt? $ {\rm F}^ \bullet $ are 0.026 Å (1.4%) longer and the Pt? Cl′ distances are 0.078 Å (3,3%) shorter in comparison with those of symmetrically coordinated axes. The weakening of the Pt? $ {\rm F}^ \bullet $ bond and the strengthening of the Pt? Cl′ bond is better recognizable from shifts of the stretching vibrations by 8% to lower and by 13% to higher frequencies, respectively. Correspondingly, the valence force constants are found to be 15% lower and 22% higher. The trans influence is observed most distinctly in the ¹⁹F-nmr spectra exhibiting the coupling constant ¹J($ {\rm F}^ \bullet $Pt) to be 29% smaller than ¹J(FPt).