Symmetric recursive algorithms for surfaces: B-patches and the de boor algorithm for polynomials over triangles

Using the concept of a symmetric recursive algorithm, we construct a new patch representation for bivariate polynomials: the B-patch. B-patches share many properties with B-spline segments: they are characterized by their control points and by a three-parameter family of knots. If the knots in each family coincide, we obtain the Bézier representation of a bivariate polynomial over a triangle. Therefore B-patches are a generalization of Bézier patches. B-patches have a de Boor-like evaluation algorithm, and, as in the case of B-spline curves, the control points of a B-patch can be expressed by simply inserting a sequence of knots into the corresponding polar form. In particular, this implies linear independence of the blending functions. B-patches can be joined smoothly and they have an algorithm for knot insertion that is completely similar to Boehm's algorithm for curves.     

Effects of radiator motion on plasma-broadened hydrogen lyman-β

For the hydrogen line L-β, broadening in an Ar⁺-plasma (N_e = 7.2 × 10¹⁶ cm^?3, T = 12,200 K) has been investigated with the help of a computer simulation of ion broadening taking full account of radiator motion. The anisotropy in Stark broadening for a moving radiator is found to be negligible under these conditions, but Stark profiles depend markedly on the radiator speed. The final line profile (including Stark and Doppler broadening) is nearly the same as the profile obtained by convolution of the Doppler profile with the Stark profile for radiators at rest and fictitious ions with the reduced mass of the atom-ion pair.     

Identification of Cu(I) and Cu(II) oxides by electron spectroscopic methods: AES,ELS and UPS investigations

The externally prepared black-coloured copper oxide (T? 700 K, P_O2 ? 100 torr) on a Cu(100) surface is identified by electron spectroscopy as CuO. Compared to the red-coloured Cu(I) oxide (in situ oxidation at T ? 400 K, P_O2 ? 0.5 torr, ～ 10⁹ L), the He(I)- excited photoemisson from CuO reveals characteristic shake-up satellites 10–12 eV below E_F and a broadened emission from overlapping oxygen-induced 2p and Cu 3d states. From the AES and ELS results, in correlation with the data from core electron spectroscopy, chemical shifts of Cu 2p, Cu 3s and Cu 3p in CuO to higher binding energy and decreases in binding energy of the oxygen-induced states were deduced. The unoccupied electron states of Cu at 5 and 7.5 eV above E_F — postulated from the ELS results — are preserved in Cu₂O and CuO compounds. Annealing of the Cu(II) oxide at 670 K is accompanied by decomposition into Cu₂O due to the solid-state reaction following the scheme: 2CuO → 1/2 O₂ + Cu₂O.