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We give a construction of an eigenstate for a non-critical level of the Hamiltonian function, and investigate the contribution of Morse critical points to the spectral decomposition. We compare the rigorous result with the series obtained by a perturbation theory. As an example the relation to the spectral asymptotics is discussed.
In this work, the development of a new molecular building block, based on synthetic peptides derived from decorin, is presented. These peptides represent a promising basis for the design of polymer-based biomaterials that mimic the ECM on a molecular level and exploit specific biological recognition for technical applications. Multiple sequence alignments of the internal repeats of decorin that formed the inner and outer surface of the arch-shaped protein were used to develop consensus sequences. These sequences contained conserved sequence motifs that are likely to be related to structural and functional features of the protein. Peptides representative for the consensus sequences were synthesized by microwave-assisted solid phase peptide synthesis and purified by RP-HPLC, with purities higher than 95 mol%. After confirming the desired masses by MALDI-TOF-MS, the primary structure of each peptide was investigated by 1H and 2D NMR, from which a full assignment of the chemical shifts was obtained. The characterization of the peptides conformation in solution was performed by CD spectroscopy, which demonstrated that using TFE, the peptides from the outer surface of decorin show a high propensity to fold into helical structures as observed in the original protein. To the contrary, the peptides from the inner surface did not show propensity to form stable secondary structure. The investigation of the binding capability of the peptides to Collagen I was performed by surface plasmon resonance analyses, from which all but one of the peptides representing the inner surface of decorin showed binding affinity to collagen with values of dissociation constant between 2•10-7 M and 2.3•10-4 M. On the other hand, the peptides representative for the outer surface of decorin did not show any significant interaction to collagen. This information was then used to develop experimental demonstration for the binding capabilities of the peptides from the inner surface of decorin to collagen even when used in more complicated situations close to possible appications. With this purpose, the peptide (LRELHLNNN) which showed the highest binding affinity to collagen (2•10-7 M) was functionalized with an N-terminal triple bond in order to obtain a peptide dimer via copper(I)-catalyzed cycloaddition reaction with 4,4'-diazidostilbene-2,2'-disulfonic acid. Rheological measurements showed that the presence of the peptide dimer was able to enhance the elastic modulus (G') of a collagen gel from ~ 600 Pa (collagen alone) to ~ 2700 Pa (collagen and peptide dimer). Moreover, it was shown that the mechanical properties of a collagen gel can be tailored by using different molar ratios of peptide dimer respect to collagen. The same peptide, functionalized with the triple bond, was used to obtain a peptide-dye conjugate by coupling it with N-(5'-azidopentanoyl)-5-aminofluorescein. An aqueous solution (5 vol% methanol) of the peptide dye conjugate was injected into a collagen and a hyaluronic acid (HA) gel and images of fluorescence detection showed that the diffusion of the peptide was slower in the collagen gel compared to the HA gel. The third experimental demonstration was gained using the peptide (LSELRLHNN) which showed the lower binding affinity (2.3•10-4 M) to collagen. This peptide was grafted to hyaluronic acid via EDC-chemistry, with a degree of functionalization of 7 ± 2 mol% as calculated by 1H-NMR. The grafting was further confirmed by FTIR and TGA measurements, which showed that the onset of decomposition for the HA-g-peptide decreased by 10 °C compared to the native HA. Rheological measurements showed that the elastic modulus of a system based on collagen and HA-g-peptide increased by almost two order of magnitude (G' = 200 Pa) compared to a system based on collagen and HA (G' = 0.9 Pa). Overall, this study showed that the synthetic peptides, which were identified from decorin, can be applied as potential building blocks for biomimetic materials that function via biological recognition.
One of the most significant current discussions in Astrophysics relates to the origin of high-energy cosmic rays. According to our current knowledge, the abundance distribution of the elements in cosmic rays at their point of origin indicates, within plausible error limits, that they were initially formed by nuclear processes in the interiors of stars. It is also believed that their energy distribution up to 1018 eV has Galactic origins. But even though the knowledge about potential sources of cosmic rays is quite poor above „ 1015 eV, that is the “knee” of the cosmic-ray spectrum, up to the knee there seems to be a wide consensus that supernova remnants are the most likely candidates. Evidence of this comes from observations of non-thermal X-ray radiation, requiring synchrotron electrons with energies up to 1014 eV, exactly in the remnant of supernovae. To date, however, there is not conclusive evidence that they produce nuclei, the dominant component of cosmic rays, in addition to electrons. In light of this dearth of evidence, γ-ray observations from supernova remnants can offer the most promising direct way to confirm whether or not these astrophysical objects are indeed the main source of cosmic-ray nuclei below the knee. Recent observations with space- and ground-based observatories have established shell-type supernova remnants as GeV-to- TeV γ-ray sources. The interpretation of these observations is however complicated by the different radiation processes, leptonic and hadronic, that can produce similar fluxes in this energy band rendering ambiguous the nature of the emission itself. The aim of this work is to develop a deeper understanding of these radiation processes from a particular shell-type supernova remnant, namely RX J1713.7–3946, using observations of the LAT instrument onboard the Fermi Gamma-Ray Space Telescope. Furthermore, to obtain accurate spectra and morphology maps of the emission associated with this supernova remnant, an improved model of the diffuse Galactic γ-ray emission background is developed. The analyses of RX J1713.7–3946 carried out with this improved background show that the hard Fermi-LAT spectrum cannot be ascribed to the hadronic emission, leading thus to the conclusion that the leptonic scenario is instead the most natural picture for the high-energy γ-ray emission of RX J1713.7–3946. The leptonic scenario however does not rule out the possibility that cosmic-ray nuclei are accelerated in this supernova remnant, but it suggests that the ambient density may not be high enough to produce a significant hadronic γ-ray emission. Further investigations involving other supernova remnants using the improved back- ground developed in this work could allow compelling population studies, and hence prove or disprove the origin of Galactic cosmic-ray nuclei in these astrophysical objects. A break- through regarding the identification of the radiation mechanisms could be lastly achieved with a new generation of instruments such as CTA.
Ground-based gamma-ray astronomy has had a major breakthrough with the impressive results obtained using systems of imaging atmospheric Cherenkov telescopes. Ground-based gamma-ray astronomy has a huge potential in astrophysics, particle physics and cosmology. CTA is an international initiative to build the next generation instrument, with a factor of 5-10 improvement in sensitivity in the 100 GeV-10 TeV range and the extension to energies well below 100 GeV and above 100 TeV. CTA will consist of two arrays (one in the north, one in the south) for full sky coverage and will be operated as open observatory. The design of CTA is based on currently available technology. This document reports on the status and presents the major design concepts of CTA.
The aim of this paper is to bring together two areas which are of great importance for the study of overdetermined boundary value problems. The first area is homological algebra which is the main tool in constructing the formal theory of overdetermined problems. And the second area is the global calculus of pseudodifferential operators which allows one to develop explicit analysis.
The present thesis is to be brought into line with the current need for alternative and sustainable approaches toward energy management and materials design. In this context, carbon in particular has become the material of choice in many fields such as energy conversion and storage. Herein, three main topics are covered: 1)An alternative synthesis strategy toward highly porous functional carbons with tunable porosity using ordinary salts as porogen (denoted as “salt templating”) 2)The one-pot synthesis of porous metal nitride containing functional carbon composites 3)The combination of both approaches, enabling the generation of highly porous composites with finely tunable properties All approaches have in common that they are based on the utilization of ionic liquids, salts which are liquid below 100 °C, as precursors. Just recently, ionic liquids were shown to be versatile precursors for the generation of heteroatom-doped carbons since the liquid state and a negligible vapor pressure are highly advantageous properties. However, in most cases the products do not possess any porosity which is essential for many applications. In the first part, “salt templating”, the utilization of salts as diverse and sustainable porogens, is introduced. Exemplarily shown for ionic liquid derived nitrogen- and nitrogen-boron-co-doped carbons, the control of the porosity and morphology on the nanometer scale by salt templating is presented. The studies within this thesis were conducted with the ionic liquids 1-Butyl-3-methyl-pyridinium dicyanamide (Bmp-dca), 1-Ethyl-3-methyl-imidazolium dicyanamide (Emim-dca) and 1 Ethyl 3-methyl-imidazolium tetracyanoborate (Emim-tcb). The materials are generated through thermal treatment of precursor mixtures containing one of the ionic liquids and a porogen salt. By simple removal of the non-carbonizable template salt with water, functional graphitic carbons with pore sizes ranging from micro- to mesoporous and surface areas up to 2000 m2g-1 are obtained. The carbon morphologies, which presumably originate from different onsets of demixing, mainly depend on the nature of the porogen salt whereas the nature of the ionic liquid plays a minor role. Thus, a structural effect of the porogen salt rather than activation can be assumed. This offers an alternative to conventional activation and templating methods, enabling to avoid multiple-step and energy-consuming synthesis pathways as well as employment of hazardous chemicals for the template removal. The composition of the carbons can be altered via the heat-treatment procedure, thus at lower synthesis temperatures rather polymeric carbonaceous materials with a high degree of functional groups and high surface areas are accessible. First results suggest the suitability of the materials for CO2 utilization. In order to further illustrate the potential of ionic liquids as carbon precursors and to expand the class of carbons which can be obtained, the ionic liquid 1-Ethyl-3-methyl-imidazolium thiocyanate (Emim-scn) is introduced for the generation of nitrogen-sulfur-co-doped carbons in combination with the already studied ionic liquids Bmp-dca and Emim-dca. Here, the salt templating approach should also be applicable eventually further illustrating the potential of salt templating, too. In the second part, a one-pot and template-free synthesis approach toward inherently porous metal nitride nanoparticle containing nitrogen-doped carbon composites is presented. Since ionic liquids also offer outstanding solubility properties, the materials can be generated through the carbonization of homogeneous solutions of an ionic liquid acting as nitrogen as well as carbon source and the respective metal precursor. The metal content and surface area are easily tunable via the initial metal precursor amount. Furthermore, it is also possible to synthesize composites with ternary nitride nanoparticles whose composition is adjustable by the metal ratio in the precursor solution. Finally, both approaches are combined into salt templating of the one-pot composites. This opens the way to the one-step synthesis of composites with tunable composition, particle size as well as precisely controllable porosity and morphology. Thereby, common synthesis strategies where the product composition is often negatively affected by the template removal procedure can be avoided. The composites are further shown to be suitable as electrodes for supercapacitors. Here, different properties such as porosity, metal content and particle size are investigated and discussed with respect to their influence on the energy storage performance. Because a variety of ionic liquids, metal precursors and salts can be combined and a simple closed-loop process including salt recycling is imaginable, the approaches present a promising platform toward sustainable materials design.