Meshfree First-order System Least Squares

We prove convergence for a meshfree first-order system least squares （FOSLS） partition of unity finite element method （PUFEM）. Essentially, by virtue of the partition of unity, local approximation gives rise to global approximation in H（div）∩H（curl）. The FOSLS formulation yields local a posteriori error estimates to guide the judicious allotment of new degrees of freedom to enrich the initial point set in a meshfree discretization. Preliminary numerical results are provided and remaining challenges are discussed.     

MO-Calculation of the Optical Activity of Oligopeptides. II. Open-chain conformations. Comparison with some cyclic systems

Using the Frozen Core (FC) MO procedure described in a previous communication, we have computed the long-wavelength chiroptic properties of oligopeptides in the parallel-chain (PC) pleated sheet conformation, in the poly (L -proline) I and poly (L -proline) II conformations. The main features of the computed results are: (a) In the PC pleated sheet conformation the π–π* transition with the highest positive rotatory strength appears at shorter wavelength than the π–π* transition with highest negative rotatory strength and is polarized mainly perpendicularly to the chain axis. There is an analogy between the computed PC pleated sheet spectrum and that calculated for a cyclohexapeptide of low symmetry, in a conformation which is probably stabilized by intra-annular hydrogen bonds. (b) In the polyproline I conformation the computed π–π* transition with highest positive rotatory strength is also the longest-wavelength π–π* transition and is polarized mainly along the helix axis. There is an analogy between this spectrum and that calculated for cyclo(tri-L -proline) of symmetry C₃. (c) The poly-proline II CD. spectrum may be qualitatively reproduced only by invoking very strong n – π interaction. The local n –π mixing parameter Λ must take on values ?3 eV, which is of the order of a nearest-neighbor core resonance integral between atomic 2p orbitals of same spatial orientation. The question concerning the structural reasons for this situation is raised. As far as comparisons with experimental data are possible, qualitative agreement is obtained.     

Determination of drug-macromolecule binding parameters by numerical analysis

A method is described for calculating the binding parameters of a drug to a macromolecule from data obtained by indirect techniques, such as spectroscopy, assuming the existence of only one class of binding sites. A critical evaluation of the performance of the method is presented, showing that the errors which previously reported methods may produce are avoided. Some examples that make use of experimental data determined for phenylbutazone and oxyphenbutazone by means of UV difference spectroscopy are given.     

Numerisch genaue Lösungen des nichtlokalen Schalenmodells

The nonlocal Schrödinger-equation has been solved in the shell model case with a kernel-function, which is well known from optical model calculations. Now in the eigenvalue region the energies, as well as the wave-functions, of the exact and the approximate nonlocal calculations (E andE ₀) differ slightly on the average. The exact solutions show in general larger energy-level distances. Although these differences are small, fitting of experimental neutron binding-energies requires nevertheless a relatively big change of the set of physical parameters; the exact nonlocal calculations tend to larger potential depthV and smaller radius constantr ₀ than the approximate nonlocal ones. For the wave-functions (Φ andΦ ₀) it can be shown that an application of the Perey-effect leads to a wrong result in the shell model case. Here the difference function shows two inflection points, whereas there is only one in the optical model. The form of nuclear matter distribution thus becomes more potential-like. The eigenfunctions of the exact nonlocal calculation are orthogonal, whereas the local equivalent ones are not.