@unpublished{FedosovTarkhanov2015, author = {Fedosov, Boris and Tarkhanov, Nikolai Nikolaevich}, title = {Deformation quantisation and boundary value problems}, volume = {4}, number = {5}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-77150}, pages = {27}, year = {2015}, abstract = {We describe a natural construction of deformation quantisation on a compact symplectic manifold with boundary. On the algebra of quantum observables a trace functional is defined which as usual annihilates the commutators. This gives rise to an index as the trace of the unity element. We formulate the index theorem as a conjecture and examine it by the classical harmonic oscillator.}, language = {en} } @unpublished{FedosovSchulzeTarkhanov1999, author = {Fedosov, Boris and Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich}, title = {A general index formula on tropic manifolds with conical points}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25501}, year = {1999}, abstract = {We solve the index problem for general elliptic pseudodifferential operators on toric manifolds with conical points.}, language = {en} } @unpublished{FedosovSchulzeTarkhanov1998, author = {Fedosov, Boris and Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich}, title = {A remark on the index of symmetric operators}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25169}, year = {1998}, abstract = {We introduce a natural symmetry condition for a pseudodifferential operator on a manifold with cylindrical ends ensuring that the operator admits a doubling across the boundary. For such operators we prove an explicit index formula containing, apart from the Atiyah-Singer integral, a finite number of residues of the logarithmic derivative of the conormal symbol.}, language = {en} } @unpublished{FedosovSchulzeTarkhanov1997, author = {Fedosov, Boris and Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich}, title = {The index of elliptic operators on manifolds with conical points}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25096}, year = {1997}, abstract = {For general elliptic pseudodifferential operators on manifolds with singular points, we prove an algebraic index formula. In this formula the symbolic contributions from the interior and from the singular points are explicitly singled out. For two-dimensional manifolds, the interior contribution is reduced to the Atiyah-Singer integral over the cosphere bundle while two additional terms arise. The first of the two is one half of the 'eta' invariant associated to the conormal symbol of the operator at singular points. The second term is also completely determined by the conormal symbol. The example of the Cauchy-Riemann operator on the complex plane shows that all the three terms may be non-zero.}, language = {en} } @unpublished{FedosovSchulzeTarkhanov1998, author = {Fedosov, Boris and Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich}, title = {The index of higher order operators on singular surfaces}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25127}, year = {1998}, abstract = {The index formula for elliptic pseudodifferential operators on a two-dimensional manifold with conical points contains the Atiyah-Singer integral as well as two additional terms. One of the two is the 'eta' invariant defined by the conormal symbol, and the other term is explicitly expressed via the principal and subprincipal symbols of the operator at conical points. In the preceding paper we clarified the meaning of the additional terms for first-order differential operators. The aim of this paper is an explicit description of the contribution of a conical point for higher-order differential operators. We show that changing the origin in the complex plane reduces the entire contribution of the conical point to the shifted 'eta' invariant. In turn this latter is expressed in terms of the monodromy matrix for an ordinary differential equation defined by the conormal symbol.}, language = {en} } @unpublished{FedosovSchulzeTarkhanov1997, author = {Fedosov, Boris and Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich}, title = {On the index formula for singular surfaces}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25116}, year = {1997}, abstract = {In the preceding paper we proved an explicit index formula for elliptic pseudodifferential operators on a two-dimensional manifold with conical points. Apart from the Atiyah-Singer integral, it contains two additional terms, one of the two being the 'eta' invariant defined by the conormal symbol. In this paper we clarify the meaning of the additional terms for differential operators.}, language = {en} } @unpublished{FedosovSchulzeTarkhanov2003, author = {Fedosov, Boris and Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich}, title = {On index theorem for symplectic orbifolds}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26550}, year = {2003}, abstract = {We give an explicit construction of the trace on the algebra of quantum observables on a symplectic orbifold and propose an index formula.}, language = {en} } @unpublished{Fedosov1999, author = {Fedosov, Boris}, title = {Pseudo-differential operators and deformation quantization}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25651}, year = {1999}, abstract = {Using the Riemannian connection on a compact manifold X, we show that the algebra of classical pseudo-differential operators on X generates a canonical deformation quantization on the cotangent manifold T*X. The corresponding Abelian connection is calculated explicitly in terms of the of the exponential mapping. We prove also that the index theorem for elliptic operators may be obtained as a consequence of the index theorem for deformation quantization.}, language = {en} } @unpublished{Fedosov1997, author = {Fedosov, Boris}, title = {Non-Abelian reduction in deformation quantization}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25101}, year = {1997}, abstract = {We consider a G-invariant star-product algebra A on a symplectic manifold (M,ω) obtained by a canonical construction of deformation quantization. Under assumptions of the classical Marsden-Weinstein theorem we define a reduction of the algebra A with respect to the G-action. The reduced algebra turns out to be isomorphic to a canonical star-product algebra on the reduced phase space B. In other words, we show that the reduction commutes with the canonical G-invariant deformation quantization. A similar statement in the framework of geometric quantization is known as the Guillemin-Sternberg conjecture (by now completely proved).}, language = {en} } @unpublished{Fedosov1998, author = {Fedosov, Boris}, title = {Moduli spaces and deformation quantization in infinite dimensions}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25396}, year = {1998}, abstract = {We construct a deformation quantization on an infinite-dimensional symplectic space of regular connections on an SU(2)-bundle over a Riemannian surface of genus g ≥ 2. The construction is based on the normal form thoerem representing the space of connections as a fibration over a finite-dimensional moduli space of flat connections whose fibre is a cotangent bundle of the infinite-dimensional gauge group. We study the reduction with respect to the gauge groupe both for classical and quantum cases and show that our quantization commutes with reduction.}, language = {en} } @unpublished{Fedosov2006, author = {Fedosov, B.}, title = {On a spectral theorem for deformation quantization}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30161}, year = {2006}, abstract = {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.}, language = {en} } @article{Fedorowicz2020, author = {Fedorowicz, Magdalena}, title = {Finanzierung der b{\"u}rgerlichen Partizipation am Beispiel des B{\"u}rgerhaushalts}, series = {KWI Schriften}, journal = {KWI Schriften}, number = {12}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, isbn = {978-3-86956-486-9}, doi = {10.25932/publishup-48530}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-485306}, pages = {67 -- 76}, year = {2020}, language = {de} } @phdthesis{Federico2011, author = {Federico, Stefania}, title = {Synthetic peptides derived from decorin as building blocks for biomaterials based on supramolecular interactions}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-59661}, school = {Universit{\"a}t Potsdam}, year = {2011}, abstract = {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.}, language = {en} } @phdthesis{Federici2014, author = {Federici, Simone}, title = {Gamma-ray studies of the young shell-type SNR RX J1713.7-3946}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-71734}, school = {Universit{\"a}t Potsdam}, year = {2014}, abstract = {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.}, language = {en} } @misc{FedericiPohlRuppeletal.2011, author = {Federici, S. and Pohl, Martin and Ruppel, J. and Telezhinsky, Igor O. and Hofmann, Werner and Martinez, M. and Knapp, J.}, title = {Design concepts for the Cherenkov Telescope Array CTA}, series = {Zweitver{\"o}ffentlichungen der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe}, volume = {32}, journal = {Zweitver{\"o}ffentlichungen der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe}, number = {1325}, issn = {1866-8372}, doi = {10.25932/publishup-43014}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-430149}, pages = {124}, year = {2011}, abstract = {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.}, language = {en} } @unpublished{FedchenkoTarkhanov2017, author = {Fedchenko, Dmitry and Tarkhanov, Nikolai Nikolaevich}, title = {A Rad{\´o} Theorem for the Porous Medium Equation}, series = {Preprints des Instituts f{\"u}r Mathematik der Universit{\"a}t Potsdam}, volume = {6}, journal = {Preprints des Instituts f{\"u}r Mathematik der Universit{\"a}t Potsdam}, number = {1}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-102735}, pages = {12}, year = {2017}, abstract = {We prove that each locally Lipschitz continuous function satisfying the porous medium equation away from the set of its zeroes is actually a weak solution of this equation in the whole domain.}, language = {en} } @unpublished{FedchenkoTarkhanov2014, author = {Fedchenko, Dmitry and Tarkhanov, Nikolai Nikolaevich}, title = {An index formula for Toeplitz operators}, volume = {3}, number = {12}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-72499}, pages = {24}, year = {2014}, abstract = {We prove a Fedosov index formula for the index of Toeplitz operators connected with the Hardy space of solutions to an elliptic system of first order partial differential equations in a bounded domain of Euclidean space with infinitely differentiable boundary.}, language = {en} } @unpublished{FedchenkoTarkhanov2013, author = {Fedchenko, Dmitry and Tarkhanov, Nikolai Nikolaevich}, title = {A Class of Toeplitz Operators in Several Variables}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-68932}, year = {2013}, abstract = {We introduce the concept of Toeplitz operator associated with the Laplace-Beltrami operator on a compact Riemannian manifold with boundary. We characterise those Toeplitz operators which are Fredholm, thus initiating the index theory.}, language = {en} } @unpublished{FedchenkoTarkhanov2016, author = {Fedchenko, Dmitry and Tarkhanov, Nikolai Nikolaevich}, title = {Boundary value problems for elliptic complexes}, volume = {5}, number = {3}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-86705}, pages = {12}, year = {2016}, abstract = {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.}, language = {en} } @phdthesis{Fechler2012, author = {Fechler, Nina}, title = {Salts as highly diverse porogens : functional ionic liquid-derived carbons and carbon-based composites for energy-related applications}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-64775}, school = {Universit{\"a}t Potsdam}, year = {2012}, abstract = {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.}, language = {en} }