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Toeplitz operators, and ellipticity of boundary value problems with global projection conditions
(2003)
Ellipticity of (pseudo-) differential operators A on a compact manifold X with boundary (or with edges) Y is connected with boundary (or edge) conditions of trace and potential type, formulated in terms of global projections on Y together with an additional symbolic structure. This gives rise to operator block matrices A with A in the upper left corner. We study an algebra of such operators, where ellipticity is equivalent to the Fredhom property in suitable scales of spaces: Sobolev spaces on X plus closed subspaces of Sobolev spaces on Y which are the range of corresponding pseudo-differential projections. Moreover, we express parametrices of elliptic elements within our algebra and discuss spectral boundary value problems for differential operators.
Mixed elliptic boundary value problems are characterised by conditions which have a jump along an interface of codimension 1 on the boundary. We study such problems in weighted edge Sobolev spaces and show the Fredholm property and the existence of parametrices under additional conditions of trace and potential type on the interface. Our methods from the calculus of boundary value problems on a manifold with edges will be illustrated by the Zaremba problem and other mixed problems for the Laplace operator.
During the past several decades polymer materials become widely used as components of medical devices and implants such as hemodialysers, bioartificial organs as well as vascular and recombinant surgery. Most of the devices cannot avoid the blood contact in their use. When the polymer materials come in contact with blood they can cause different undesired host responses like thrombosis, inflammatory reactions and infections. Thus the materials must be hemocompatible in order to minimize these undesired body responses. The earliest and one of the main problems in the use of blood-contacting biomaterials is the surface induced thrombosis. The sequence of the thrombus formation on the artificial surfaces has been well established. The first event, which occurs, after exposure of biomaterials to blood, is the adsorption of blood proteins. Surface physicochemical properties of the materials as wettability greatly influence the amount and conformational changes of adsorbed proteins. In turn the type, amount and conformational state of the adsorbed protein layer determines whether platelets will adhere and become activated or not on the artificial surface and thus to complete the thrombus formation. The adsorption of fibrinogen (FNG), which is present in plasma, has been shown to be closely related to surface induced thrombosis by participating in all processes of the thrombus formation such as fibrin formation, platelet adhesion and aggregation. Therefore study the FNG adsorption to artificial surfaces could contribute to better understanding of the mechanisms of platelet adhesion and activation and thus to controlling the surface induced thrombosis. Endothelization of the polymer surfaces is one of the strategies for improving the materials hemocompatibility, which is believed to be the most ideal solution for making truly blood-compatible materials. Since at physiological conditions proteins such as FNG and fibronectin (FN) are the usual extracellular matrix (ECM) for endothelial cells (EC) adhesion, precoating of the materials with these proteins has been shown to improve EC adhesion and growth in vitro. ECM proteins play an essential role not only like a structural support for cell adhesion and spreading, but also they are important factor in transmitting signals for different cell functions. The ability of cells to remodel plasma proteins such as FNG and FN in matrix-like structures together with the classical cell parameters such as actin cytoskeleton and focal adhesion formation could be used as an criteria for proper cell functioning. The establishment and the maintaining of delicate balance between cell-cell and cell-substrate contacts is another important factor for better EC colonization of the implants. The functionality of newly established endothelium in order to produce antithromotic substances should be always considered when EC seeding is used for improving the hemocompatibility of the polymer materials. Controlling the polymer surface properties such as surface wettability represents a versatile approach to manipulate the above cellular responses and therefore can be used in biomaterial and tissue engineering applications for producing better hemocompatible materials.
The quantum cosmological wavefunction for a quadratic gravity theory derived from the heterotic string effective action is obtained near the inflationary epoch and during the initial Planck era. Neglecting derivatives with respect to the scalar field, the wavefunction would satisfy a third-order differential equation near the inflationary epoch which has a solution that is singular in the scale factor limit a(t) → 0. When scalar field derivatives are included, a sixth-order differential equation is obtained for the wavefunction and the solution by Mellin transform is regular in the a → 0 limit. It follows that inclusion of the scalar field in the quadratic gravity action is necessary for consistency of the quantum cosmology of the theory at very early times.
The present work investigates the structure formation and wetting in two dimensional (2D) Langmuir monolayer phases in local thermodynamic equilibrium. A Langmuir monolayer is an isolated 2D system of surfactants at the air/water interface. It exhibits crystalline, liquid crystalline, liquid and gaseous phases differing in positional and/or orientational order. Permanent electric dipole moments of the surfactants lead to a long range repulsive interaction and to the formation of mesoscopic patterns. An interaction model is used describing the structure formation as a competition between short range attraction (bare line tension) and long range repulsion (surface potentials) on a scale Delta. Delta has the meaning of a dividing length between the short and long range interaction. In the present work the thermodynamic equilibrium conditions for the shape of two phase boundary lines (Young-Laplace equation) and three phase intersection points (Young′s condition) are derived and applied to describe experimental data: The line tension is measured by pendant droplet tensiometry. The bubble shape and size of 2D foams is calculated numerically and compared to experimental foams. Contact angles are measured by fitting numerical solutions of the Young-Laplace equation on micron scale. The scaling behaviour of the contact angle allows to measure a lower limit for Delta. Further it is discussed, whether in biological membranes wetting transitions are a way in order to control reaction kinetics. Studies performed in our group are discussed with respect to this question in the framework of the above mentioned theory. Finally the apparent violation of Gibbs′ phase rule in Langmuir monolayers (non-horizontal plateau of the surface pressure/area-isotherm, extended three phase coexistence region in one component systems) is investigated quantitatively. It has been found that the most probable explanation are impurities within the system whereas finite size effects or the influence of the long range electrostatics can not explain the order of magnitude of the effect.
Computational models such as E-Z Reader and SWIFT are ideal theoretical tools to test quantitatively our current understanding of eye-movement control in reading. Here we present a mathematical analysis of word skipping in the E-Z Reader model by semianalytic methods, to highlight the differences in current modeling approaches. In E-Z Reader, the word identification system must outperform the oculomotor system to induce word skipping. In SWIFT, there is competition among words to be selected as a saccade target. We conclude that it is the question of competitors in the “game” of word skipping that must be solved in eye movement research.
Content: I. The nature and form of international law 1. The acceptance of the existence of an international legal order 2. The legal position of the individual in international law II. Obligations of states in the protection of international human rights 1. Treaty-based human rights obligations 2. The nature of treaty-based human rights obligations 3. The ”absolute” and ”objective” character of human rights treaty obligations 4. Human rights conventions as self-contained regimes 5. The problem of characterisation of human rights obligations of states III. Human rights obligations arising from general principles of international law 1. Obligations erga omnes and human rights norms 2. The outlawing of genocide as obligation erga omnes 3. Protection from slavery as obligation erga omnes 4. The outlawing of acts of aggression as obligation erga omnes 5. Protection from racial discrimination as obligation erga omnes 6. The basic rights of the human person as obligation erga omnes 7. Jus Cogens and the search for peremptory norms of human rights 8. International crimes and human rights norms 9. The relationship between the concepts: erga omnes, jus cogens, international crime and human rights IV. International instruments for the coercive enforcement of state obligations to ‘respect and ensure’ human rights 1. Countermeasures as consequences of breach of treaties in international law 2. Application of reprisals for the enforcement of treaty-based human rights obligations 3. Intervention for the protection of human rights in international law 4. Intervention by the Security Council for the protection of human rights: the situation before the East-West détente 5. Humanitarian intervention after the end of the Cold War 6. The legal nature of ECOWAS intervention in the Liberian Civil War 7. The legality of NATO’s intervention in Kosovo 8. Some instances of intervention with mixed motives V. Non-forceful measures for the enforcement of states’ human rights obligations 1. Economic and financial pressure as means of enforcing states’ obligation to respect and observe human rights 2. The application of the clausula rebus sic stantibus for the protection of human rights 3. The enforcement of human rights through the World Bank 4. The enforcement of human rights through the ILO 5. Diplomatic recognition as an instrument for securing a state's respect and promotion of human rights 6. Refusal to comply with an extradition agreement as a means of enforcing a state’s human rights obligations 7. Denial of immunity as a means of enforcing a state’s human rights obligations 8. Publicity as an instrument for the enforcement of human rights VI. Judicial enforcement of state obligations to ‘respect and ensure’ human rights 1. Enforcement of human rights through International Criminal Tribunals 2. The International Criminal Tribunal for Yugoslavia 3. The International Criminal Tribunal for Rwanda 4. The International Special Court of Sierra Leone Résumé
We consider a nonparametric survival model with random censoring. To test whether the hazard rate has a parametric form the unknown hazard rate is estimated by a kernel estimator. Based on a limit theorem stating the asymptotic normality of the quadratic distance of this estimator from the smoothed hypothesis an asymptotic ®-test is proposed. Since the test statistic depends on the maximum likelihood estimator for the unknown parameter in the hypothetical model properties of this parameter estimator are investigated. Power considerations complete the approach.