Efficient Collocation Schemes for Singular Boundary Value Problems

We discuss an error estimation procedure for the global error of collocation schemes applied to solve singular boundary value problems with a singularity of the first kind. This a posteriori estimate of the global error was proposed by Stetter in 1978 and is based on the idea of Defect Correction, originally due to Zadunaisky. Here, we present a new, carefully designed modification of this error estimate which not only results in less computational work but also appears to perform satisfactorily for singular problems. We give a full analytical justification for the asymptotical correctness of the error estimate when it is applied to a general nonlinear regular problem. For the singular case, we are presently only able to provide computational evidence for the full convergence order, the related analysis is still work in progress. This global estimate is the basis for a grid selection routine in which the grid is modified with the aim to equidistribute the global error. This procedure yields meshes suitable for an efficient numerical solution. Most importantly, we observe that the grid is refined in a way reflecting only the behavior of the solution and remains unaffected by the unsmooth direction field close to the singular point.     

Multipole expansion of diatomic overlap

A systematic extension of Ruedenberg's expansion formula is applied to evaluate two-electron integrals occurring in calculations on molecular structure. Minimum STO basis sets are used for all SCF-calculations within the framework of the MEDO-method (Multipole Expansion of Diatomic Overlap). The errors due to this approximation scheme are almost negligible compared to those introduced by the truncated basis set: LiH, Li₂ and N₂ are chosen as examples.     

Synthesis of angiotensins,bradykinins and substance P octapeptides in which the residues Phe and Tyr have been replaced with car and of [Car1, Leu5]-enkephalin

Thirteen peptides, analogues of bradykinin (BK), enkephalin, Substance P (SP) and [Sar¹]-angiotensin II ([Sar¹]-AT_II) have been synthesized by the solid-phase method. In all these peptides the residue Phe and Tyr were substituted with the boron-containing amino-acid L -o-carboranylalanine (Car). The purity and identity of the peptides were established by TLC., cellulose-electrophoresis and amino acid analysis.     

Fractals and analytical chemistry — an old and a new look

Summary The impact of the concept of fractals on the foundations of analytical chemistry is discussed. Examples from such diverse subfields like geochemistry, reactions in turbulent flow systems or particle technology illustrate the new look, quantifying what was so far left to intuition of the expert — complexity. These developments led to philosophical problems resolvable in the unity of arts and sciences.     

Photocyclisierung von 1-[3-(Chloracetylamino)propyl]-3-methylindol. 12. Mitteilung über synthetische Indol-Verbindungen

Photochemical cyclization of 1-[3-(chloroacetylamino)propyl]-3-methyl-indole . Photochemical cyclization of 1-[3-(chloroacetylamino)propyl]-3-methyl-indole involving loss of HCl leads to the three isomers 2, 3 and 4 , the structures of which have been determined by physical and chemical methods.     

Synthesis of a eta 2-2,3-diphosphabutadiene complex of zerovalent platinum from the corresponding eta 2-phosphaalkyne complex

Hydrozirconation of the eta 2-phosphaalkyne complex [Pt(dppe)(eta 2-tBuCP)] with [ZrHCl(eta 5-C5H5)2], followed by treatment with the chlorophosphaalkene ClP=C(SiMe3)2 affords the eta 2-2,3-diphosphabutadiene complex [Pt(dppe)(eta 2-tBuC(H)=PP=C(SiMe3)2]. In the presence of [Pt(PPh3)2] the latter undergoes an addition reaction with water to afford the structurally characterised Pt(II) complex [Pt(dppe)(tBuCH2P(O)HPC(SiMe3)2].     

Zum Meusnierschen Satz

Ohne ZusammenfassungHerrnFriedrich Pfeiffer zum 60. Geburtstag gewidmet.