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.     

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.     

The electronic structure of Rhodium: Angle-resolved studies of photoelectron and secondary electron emission

We report electron spectroscopic studies of the Rh(111) surface, with the aim to obtain bulk band-structure information. We have measured normal photoemision using tunable synchrotron radiation in the range of photon energies between 11 eV and 55 eV, and angle-dependent photoemission along the LUX and LKL azimuths using the He resonance lines (=21.2 eV, 40.8 eV). To complement these data, we studied angleresolved secondary electron emission after excitation with electrons and photons. We derive parts of the one-electron energy dispersionE(k) along L, and determine the energies of several bulk critical points (in eV):E(> ₇₊/₈₊)=–2.75±0.10,E(> ₈₊=–0.85±0.10,E(> _7–=16.1±0.5,E(> _6–/> _8–)=20.5±0.5,E(X ₇₊)=–5.0±0.1,E(L ₆₊)=–5.6±0.5,E(L ₆₊/L ₄₊₊₅₊)=–2.65±0.10,E(L ₆₊)=9.0±0.5 eV. Our results are compared to several available band structure calculations.     

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.     

Antisymmetry and analytic structure in the spectrum of a uniform Fréchet algebra

Let M be a C-smooth submanifold of a domain GCⁿ. Denote by 0(M) the algebra of germs of holomorphic functions on M, that is, each f0(M) is holomorphic in some neighbourhood of M, the neighbourhood dependent of f. Now define A(M) as the closure of 0(M) with respect to the topology of compact convergence on M.If M coincides with A(M), the spectrum of A(M), we give a necessary and sufficient condition for A(M) such that M is a complex manifold.     

Momentum-resolved bremsstrahlung isochromat spectroscopy of silver surfaces

Angle-resolved bremsstrahlung isochromat spectra of the Ag(100), Ag(110) and Ag(111) surfaces have been measured. Our work extends and complements several earlier investigations of other authors. The data are summarized in the form of final state dispersionsE(k ). Comparison is made to the available theoretical and experimental information. The results for the bulk as well as for the surface-specific features are in excellent to reasonable agreement among each others and with recent calculations.