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1.
Operators on manifolds with corners that have base configurations with geometric singularities can be analysed in the frame of a conormal symbolic structure which is in spirit similar to the one for conical singularities of Kondrat'ev's work. Solvability of elliptic equations and asymptotics of solutions are determined by meromorphic conormal symbols. We study the case when the base has edge singularities which is a natural assumption in a number of applications. There are new phenomena, caused by a specific kind of higher degeneracy of the underlying symbols. We introduce an algebra of meromorphic edge operators that depend on complex parameters and investigate meromorphic inverses in the parameter-dependent elliptic case. Among the examples are resolvents of elliptic differential operators on manifolds with edges.  相似文献   
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This paper reports on the results of resonant Raman scattering investigations of the fundamental vibrations in Ge/Si structures with strained and relaxed germanium quantum dots. Self-assembled strained Ge/Si quantum dots are grown by molecular-beam epitaxy on Si(001) substrates. An ultrathin SiO2 layer is grown prior to the deposition of a germanium layer with the aim of forming relaxed germanium quantum dots. The use of resonant Raman scattering (selective with respect to quantum dot size) made it possible to assign unambiguously the line observed in the vicinity of 300 cm?1 to optical phonons confined in relaxed germanium quantum dots. The influence of confinement effects and mechanical stresses on the vibrational spectra of the structures with germanium quantum dots is analyzed.  相似文献   
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We prove stability of rotationally symmetric translating solutions to mean curvature flow. For initial data that converge spatially at infinity to such a soliton, we obtain convergence for large times to that soliton without imposing any decay rates. The authors are members of SFB 647/B3 “Raum – Zeit – Materie: Singularity Structure, Long-time Behaviour and Dynamics of Solutions of Non-linear Evolution Equations”.  相似文献   
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TiCx-PECVD-layers were characterized by TEM. EDX analysis and electron diffraction. TiCx-layers deposited using benzene showed a columnar structure, at which the column size decreases with rising excess carbon content. TiCx-layers deposited using n-heptane presented a lamellar structure, at which the lamellar thickness diminishes with an increasing excess carbon content. In dependence on the layer thickness a periodic progress of the element contents was observed, at which a maximum for Ti and Cl correlates with a minimum for C. It was found that the incorporated chlorine is bonded to titanium. The lattice parameter depends on the chlorine content. Using TiCl4/H2/Ar-gas mixtures without any hydrocarbon, layers containing TiH2 are formed.  相似文献   
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New indides Ce3Ge0.66In4.34 and Ce11Ge4.74In5.26 were synthesized from the elements by arc‐melting and subsequent annealing at 870 K. Single crystals were grown through special annealing procedures in sealed tantalum tubes in a high‐frequency furnace. Both compounds were investigated on the basis of X‐ray powder and single crystal data: I4/mcm, La3GeIn4 type, a = 848.8(1), c = 1192.0(2) pm, Z = 4, wR2 = 0.0453, 499 F2 values, 17 variables for Ce3Ge0.66In4.34 and I4/mmm, Sm11Ge4In6 type (ordered version of the Ho11Ge10 type), a = 1199.3(2), c = 1662.0(3) pm, wR2 = 0.0507, 1217 F2 values, 41 variables for Ce11Ge4.74In5.26. The Ce3Ge0.66In4.34 structure shows a mixed Ge/In occupancy on the 4c Wyckoff position. This site is octahedrally coordinated by cerium atoms. These octahedra share all edges, leading to a three‐dimensional network. The latter is penetrated by a two‐dimensional indium substructure which consists of flattened tetrahedra at In–In distances of 291 and 300 pm. The Ce11Ge4.74In5.26 structure contains three crystallographically independent germanium sites. The latter are coordinated by eight or nine cerium neighbors. These CN8 and CN9 polyhedra are condensed to a complex network which is penetrated by a three‐dimensional indium network with In–In distances of 301–314 pm. The 16m site shows a mixed In/Ge occupancy. Chemical bonding in both compounds is dominated by the p elements. Both ternaries studied exhibit localized magnetism due to the presence of Ce3+ ions. The compound Ce3GeIn4 remains paramagnetic down to 1.72 K, whereas Ce11Ge4In6 orders ferromagnetically at TC = 7.5 K.  相似文献   
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On the Dispersion of Metals in Supported Catalysts. II. Small Angle X-ray Investigation. on Platinum/Alumina and Palladium/Alumina Catalysts The metal dispersion in 0.5% Pd/A12O3. 0.5°% Pt/Al2O3 abd 1.5% Pt/Al2O3 catalysts was investigated by small angle X-ray scattering, Using a Kratky camera the difference scattering curves catalyst-carrier were evaluated. The assumption was made that the scattering centres are globular and that there is no interparticular scattering. From the Guinier approximation the Guinier radii RG of the metal particles were determined. With the Pd catalyst always positive difference scattering curves were found, whereas negative values were found with the Pt catalysts at a scattering angle greater than 0.022 rad. Therefore only for the sample with 0.5% Pd the Porod invariant \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm \tilde Q}$\end{document} and the Porod radius RP could be determined. From RG and RP the parameters of a two- and of a one-parametric distribution were calculated. The results are in good agreement with data from wide angle X-ray diffraction measurements.  相似文献   
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