An algebra of meromorphic corner symbols

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.     

Resonant Raman scattering by strained and relaxed germanium quantum dots

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.     

New strong interactions: From QCD to LHC

The concept of strong interactions need not be limited to the sector of physics taken by QCD. While this domain is investigated by RHIC, LHC will be able to probe potential new strong interactions simultaneously: Finding the precise mechanism for electroweak symmetry breaking is one of the prime problems of physics. Intricately linked to this point is the question after the true nature or even the existence of the Higgs boson. Here, we present stronly interacting theories providing an explanation for the hierarchy problem and leading to a light composite Higgs boson, favoured by experimental data. Our variation of the standard model is consistent with precision data. We achieve this accordance by using technifermions in a higher representation of their gauge group. Anomaly conditions require at least one extra lepton family for some of the theories whereby they contain a natural dark matter candidate. We can accurately determine the masses of said leptons from experimental data.     

Growth of copper phthalocyanine on hydrogen passivated vicinal silicon(1 1 1) surfaces

Using ultra-high vacuum scanning tunneling microscopy (UHV-STM), we show that copper-phthalocyanine (CuPc) grows in a well ordered manner on hydrogen passivated vicinal silicon surfaces. CuPc grows one-dimensionally parallel to the monatomic steps on the vicinal silicon surface. Surprisingly, elongated clusters of the CuPc parallel to the step directions are formed even on the middle of the terraces well away from the step edges. The one-dimensional growth mode continues even after the full monolayer coverage on the substrate which results in strongly oriented growth mode of a thin film of CuPc on the vicinal silicon surfaces.     

Synthesis and Photochemistry of Novel 3,5-Diacetyl-1,4-dihydropyridines. II [1]

In continuation of previous work some novel 3,5-diacetyl-1,4-dihydropyridine derivatives were synthesized and their photochemical behavior was studied under oxygen and argon atmosphere. Oxidation of the dihydropyridine ring and formation of pyridine derivatives was the result of the reaction. The presence of oxygen affects not only on the rate of oxidation, but also the formation of some unidentified by-products was observed on irradiation under this atmosphere.     

Stability of translating solutions to mean curvature flow

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”.     

Formation of Fe i –B pairs in silicon at high temperatures

We report on the detection of Fe _i –B pairs in heavily B doped silicon using ⁵⁷Fe emission Mössbauer spectroscopy following implantation of radioactive ⁵⁷Mn⁺ parent ions (T _1/2?=?1.5 min) at elevated temperatures >?850 K. The Fe _i –B pairs are formed upon the dissociation of Fe _i –V pairs during the lifetime of the Mössbauer state (T _1/2?=?100 ns). The resulting free interstitial Fe_i diffuses over sufficiently large distances during the lifetime of the Mössbauer state to encounter a substitutional B impurity atom, forming Fe _i –B pairs, which are stable up to ～1,050 K on that time scale.     

Untersuchung von Textilien und Textilrohstoffen

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