“Neglect of Diatomic Differential Overlap” in nonempirical quantum chemical orbital theories. II. A polynomial expansion for Δ−1/2 in terms of Legendre and Chebyshev polynomials

Several attempts to justify the Neglect of Diatomic Differential Overlap (NDDO ) approximation in terms of a power series expansion for Δ^?1/2 (Δ is the overlap matrix) have been made (cf. Part I). The new approach for attaining an optimal approximation of Δ^?1/2 represented here transfers the problem of finding an optimal matrix polynomial to an approximation problem of real functions within the spectrum of Δ. Best approximations are derived by use of Legendre and Chebyshev polynomials. © 1995 John Wiley & Sons, Inc.     

Convergence of bivariate cardinal interpolation

We give necessary and sufficient conditions for the convergence of cardinal interpolation with bivariate box splines as the degree tends to infinity.     

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Die Elektronenstruktur des Dicyclohepta[c d,g h]pentalens

Dicyclohepta[cd, gh]pentalene is shown by ESR.- and NMR.-spectroscopic evidence to be best represented as a perturbed [14] annulene. The orbital interaction between the π-perimeter and the ethylene-“bridge” is discussed.     

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Notices bibliographiques

     

EFFECT OF U.V.-IRRADIATION ON SEDIMENTATION BEHAVIOR OF VARIOUS PROTEINS

Abstract— Moderate u.v.-doses (2537 Å) sufficient to reduce enzymatic activities of native enzymes up to about 90 per cent, in general do not produce measurable amounts of smaller dialyzable fragments.
The disappearance of the original boundary in sedimentation diagrams is mostly due to the formation of rapidly sedimenting polydispersed material. Generally the sedimentation constants of the native proteins are not significantly changed. The boundaries, however, often loose their symmetry. The quantum yields for the disappearance of the original boundaries are roughly inversely proportional to the molecular weights. The number of molecules disappearing from the main peak is smaller than the number of molecules inactivated by a given dose. The data indicate that ultracentrifugation provides no satisfactory method for separation of native molecules from the damaged and inactivated. Proteins with labile quaternary structures (e.g. thyroglobulin or hemocyanine) which tend to dissociate under very mild conditions show an enhanced dissociation after u. v.-irradiation.