A priori-Schranken für diskrete Lösungen monotoner Operatorgleichungen und Anwendungen

Summary Operator equationsTu=f are approximated by Galerkin's method, whereT is a monotone operator in the sense of Browder and Minty, so that existence results are available in a reflexive Banach spaceX. In a normed spaceY error estimates are established, which require a priori bounds for the discrete solutionsu _h in the norm of a suitable space . Sufficient conditions for the uniform boundedness u _{h Z} =O(1) ash0 are proved. Well-known error estimates in [3] for the special caseX=Y=Z are generalized by this. The theory is applied to quasilinear elliptic boundary value problems of order 2m in a bounded domain . The approximating subspaces are finite element spaces. Especially the caseX=W ₀ ^{m, p} (), 1<p<,Y=W ₀ ^{m. 2} (),Z=W ₀ ^{m. max (2,p)} ()W^m, () is treated. Some examples for 1<p<2 are considered. Forp2 a refined technique is introduced in the author's paper [7].

     

A Kinetic Evidence for the Nitroxyl Radicals Recycling Mechanism in the Photostabilizing Process of HALS

The photoinduced bulk polymerization of a reactive-hindered amine fight stabilizers(r-HALS), 4-acryloyl-2, 2, 6, 6-tetramethylpiperidinyl (ATMP), was performed at 80℃ by using a DPC technique. An unique periodic exponential attenuation-type oscillating curve was found when the polymerization was carried out in air, but this phenomenon was not found in nitrogen.It is supposed that this unique kinetic performance may be attributed to nitroxyl radicals that are produced in situ from the oxidation of ATMP. ATMP polymer with narrow polydispersity (d =1.03) can be obtained by photoinduced solution polymerization of ATMP. The signal detected in ESR may be assigned to the nitroxyl radicals in the matrix of ATMP polymer. Since this kind of recycling of nitroxyl radicals is well documented for the photostabilizing mechanism of HALS, the present results may serve as a kinetic evidence for this mechanism.     

High purity gadolinium by the electrolysis of GdF3

The anodic overvoltage on carbon and platinum electrodes in the electrochemical production of high purity gadolinium from molten 75 LiF-25 mol% GdF₃ solutions is discussed. At the cell temperature of 840°C calciumimpregnated anodes led to the reduction of inert electrode films and to a current yield of nearly 100%.The deposited gadolinium contained 75, 22, 54 and less than 100 ppm of the interstitial elements H, N, O and C respectively; the concentrations of the highest other analysed impurities were: Si (89), Fe (15), Y (5), Zr (3), Nd (3), Tb (71), Ta (49), W (23) and Re (<3 ppm).Partly performed at the Ames Laboratory—U.S. Department of Energy.     

Modeling of recombination kinetics of radical pairs in magnetic field. Comparison with experimental dependences on the frequency of encounters in biradicals

The recombination kinetics of spin-correlated radical pairs (RPs) with three nonequivalent magnetic nuclei were calculated under conditions of enforced encounters between radicals at time-independent frequency n_dif. The simplest two-position model of a RP was used, which includes two states (contact state and distance-separated state) of the RP, differing in magnitude of isotropic spin-spin exchange interaction between radicals. The calculated kinetic curves were treated in terms of a three-exponential model. The dependences of corresponding rate constants (k _rec) on n_dif, external magnetic field strength (B ₀), and intensity, A _eff, of isotropic hyperfine coupling (HFC) were obtained. The k _rec-vs.-n_dif or k _rec-vs.-viscosity (n_dif varies simultaneously with the inverse lifetime of the contact state) plots pass through maxima whose positions are shifted from the n_dif region near the A _eff value at B ₀ = 0.5 G toward high n_dif values with an increase in B ₀. At n_dif ≫ A _eff, the k _rec-vs.-B ₀ plots pass through maxima in the region B ₀ = A _eff. The calculated dependences are compared with experimental data on recombination of biradicals. The results of calculations show that the experimentally observed maxima on the k _rec-vs.-B ₀ or k _rec-vs.-n_dif plots can be due to peculiar features of the spin dynamics induced by the hyperfine coupling rather than the exchange interaction effects, as is commonly accepted. __________ Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 5, pp. 1103–1110, May, 2005.     

Absence of p,π-conjugation in the Cl2C=CHOMe molecule from data ofab initio calculations

ab initio Calculation of the Cl₂C=CHOMe molecule has been carried out with geometrical optimization in the split valence basis set in the RHF/6-31G^*//RHF/6-31G^* approximation. An analysis of the populations of the p-orbitals of the Cl atoms implies the absence of p,-conjugation between the unshared electron pairs of these atoms and the -bond. The asymmetry parameters of the electric field gradient at the³⁵Cl nuclei, calculated from the 3p-orbital populations of the Cl atoms, practically coincide with the experimental values.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 12, pp. 2369–2372, December, 1995.The authors are grateful to G. S. Beloglazov for assistance in accomplishingab initio calculations.     

Molecular shape effects and quantum theory

Certain features of the chemist's molecular structure model, viz. size and shape, are retrieved even in the best non-adiabatic variational calculations thus far carried out for ground states of H ₂ ⁺ and H₂. Those features do not conflict with the full symmetry of exact molecular eigenstates, once they are properly understood as correlation effects.     

Quantitative surface analysis by Auger and x-ray photoelectron spectroscopy

Recent developments in quantitative surface analysis by Auger (AES) and x-ray photoelectron (XPS) spectroscopies are reviewed and problems relating to a more accurate quantitative interpretation of AES/XPS experimental data are discussed. Special attention is paid to consideration of elementary physical processes involved and influence of multiple scattering effects on signal line intensities. In particular, the major features of core-shell ionization by electron impact, Auger transitions and photoionization are considered qualitatively and rigorous approaches used to calculate the respective transition probabilities are analysed. It is shown that, in amorphous and polycrystalline targets, incoherent scattering of primary and signal Auger and photoelectrons can be described by solving analytically a kinetic equation with appropriate boundary conditions. The analytical results for the angular and energy distribution, the mean escape depth, and the escape probability as a function of depth of origin of signal electrons as well as that for the backscattering factor in AES are in good agreement with the corresponding Mote Carlo simulation data. Methods for inelastic background subtraction, surface composition determination and depth-profile reconstructions by angle-resolved AES/XPS are discussed. Examples of novel techniques based on x-ray induced photoemission are considered.     

Dirhodium(II)-catalyzed carbonyl ylide generation. Stereoelectronic control in dioxolane formation

The combination of ethyl diazoacetate with aryl aldehydes in the presence of copper(I) or rhodium(II) catalysts results in the formation of 1,3-dioxolane products in moderate to good yields. These reactions occur through a pathway that involves ylide intermediates. Catalyst-dependent diastereocontrol is observed and suggests that metal-associated ylides are involved in the product-determining step. The influence of aryl aldehyde substituents has been determined. Current address. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 5, pp. 961–965, May, 1998.