The clamped-plate equation for the limaçon

Hadamard claimed in 1907 that the clamped-plate equation is positivity preserving for domains which are bounded by a Limaçon de Pascal. We will show that this claim is false in its full generality. However, we will also prove that there are nonconvex limaçons for which the clamped-plate equation has the sign-preserving property. In fact we will give an explicit bound for the parameter of the limaçon where sign change may occur. Mathematics Subject Classification (2000) 35J40, 35Q72, 35B50     

Interior penalty method for the indefinite time-harmonic Maxwell equations

Summary In this paper, we introduce and analyze the interior penalty discontinuous Galerkin method for the numerical discretization of the indefinite time-harmonic Maxwell equations in the high-frequency regime. Based on suitable duality arguments, we derive a-priori error bounds in the energy norm and the L²-norm. In particular, the error in the energy norm is shown to converge with the optimal order (h^min{s,}) with respect to the mesh size h, the polynomial degree , and the regularity exponent s of the analytical solution. Under additional regularity assumptions, the L²-error is shown to converge with the optimal order (h⁺¹). The theoretical results are confirmed in a series of numerical experiments.Supported by the EPSRC (Grant GR/R76615).Supported by the Swiss National Science Foundation under project 21-068126.02.Supported in part by the Natural Sciences and Engineering Council of Canada.     

Direct measurement of 1J(13C13C) in coordinated double bonds

¹J(¹³C¹³C) has been determined in naturally abundant samples of η¹,η² -alkenyl-η⁵ -cyclopentadienylnickel complexes; for the coordinated double bonds ¹J(CC) lies between the value for free ethylene and cyclopropane, and therefore gives direct insight into the relevant bonding situation.     

Crystal and molecular structure of 17-β-methyllupanine perchlorate

The formula of the title compound is C₁₆H₂₇ClN₂O₅,MW = 362.9 orthorhombic,P2₁2₁2₁,a = 8.403(1),b= 13.133(1),c= 15.972(2) Å,Z = 4,D _x = 1.37 g cm^–3, (CuK) = 2.2 mm^-1. The lupanine skeleton has atrans-trans configuration. The ringA has a half-chair conformation, theB andD rings adopt a chair form, and theC ring forms a boat. The lupanine cations are linked together by the intermolecular hydrogen bonds forming infinite chains alongb. The N(16) ... O(C2) distance is 2.763(7) Å.     

Proton addition to excited diazaphenanthrenes topology determined molecular properties

Absorption and luminescence spectra, depopulation kinetics of the lowest excited singlet and triplet states and acid-base equilibria were investigated for neutral and protonated diazaphenanthrenes: 2,3-, 1,4- and 5,6-DAF. The spectroscopical results are correlated with CNDO/S calculations. Profound influence of topology upon photophysical and chemical (basicity) properties has been stated and discussed.     

The crystal and molecular structure of diaquadichlorotheophyllinecopper(II)

Summary The crystal structure of CuCl₂(C₇H₈N₄O₂)(H₂O)₂ has been determined from diffractometer data by Patterson and Fourier methods and refined by full-matrix least-squares to R=0.067 for 2123 observed reflections. Unit cell constants are:a=9.930(8),b=9.987(8),c=7.483(6) Å,=123.2(1),=94.5(1),= 83.9(1)°. The space group is P¯1 withZ=2. The structure consists of diaquadichlorotheophyllinecopper(II) complexes linked by hydrogen bonds. The coordination polyhedron of copper is a square pyramid whose base, severely tetrahedrally distorted, is formed by a water molecule [Cu-Ow=2.025(7) Å], two chlorines [Cu-Cl=2.273(4), 2.296(4) Å] and an imidazole nitrogen [Cu-N=1.983(9) Å] from the theophylline ligand. A second water molecule is at the apex of the pyramid [Cu-Ow=2.292(7) Å]. Coordination is completed to a distorted octahedral one by a long Cu ... O=3.164(7) Å contact involving the exocyclic oxygen at C₆ of the theophylline ligand.     

Charakteristik der Methansulfonyloxygruppe als ein desaktivierender o-,p-dirigierender Substituent durch ihr UV-Absorptionsspektrum

Ohne ZusammenfassungMit 1 Abbildung     

Sulla influenza della polarizzazione delle radio-onde nei fenomeni di interazione ionosferica

Riassunto Si studia l'influenza della polarizzazione delle radio-onde su alcuni fenomeni non lineari nella ionosfera tramite una nuova e più completa relazione funzionale fra i vettori densità di corrente e campo elettrico. Tale studio riguarda la comparsa di onde di banda laterale e la loro dipendenza dalle direzioni di polarizzazione delle onde interagenti.

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Summary The influence of radio wave polarization on some nonlinear phenomena in the inosphere is studied through a new and more complete functional relation between current density and electric field vectors. This study is concerned with the occurrence of ?sideband? waves and their dependence on the polarization directions of interacting waves.

     

Quantitative determination of mesomorphic regions in oriented polymers from wide-angle X-ray diffraction

A method for quantitative characterization of the noncrystalline region in poly(ethylene terephthalate) (PET) fibers based on x-ray wide-angle diffraction data is elaborated. The procedure consists in a computational resolution of the diffracted intensity into individual peaks for 010, 11 0, and 100 planes and into isotropic and anisotropic components of diffuse scattering. The results show that the content of mesomorphic regions in the noncrystalline part of PET fibers with draw ratio of λ = 3.0 varies from 12% to 32% depending on the temperature of heat treatment.     

A 3D QSAR approach to the search for geometrical similarity in a series of nonpeptide angiotensin II receptor antagonists

Summary A 3D QSAR methodology based on the combined use of conformational analysis and chemometrics was applied to perform a comparative analysis of the 3D conformational features of 13 nonpeptide angiotensin II receptor antagonists showing different levels of binding affinity. Conformational analysis by using a molecular mechanics MM2 method was carried out for each of these structures to obtain conformational minima. These minima were described by ten interatomic distances which define the relative spatial disposition of five significant atoms belonging to relevant functional groups present in all the 13 molecules. The structure-activity relationship between the interatomic distances and the biological activity was then assessed by using chemometric methods (cluster analysis, principal component analysis, classification methods). With our indirect approach based on the search for geometrical similarity it was possible, even though structural information on the receptor active site was lacking, to identify the 3D geometrical requirements for the binding affinity of nonpeptide angiotensin II receptor inhibitors.