Refine
Year of publication
- 1997 (453) (remove)
Document Type
- Article (348)
- Monograph/Edited Volume (63)
- Preprint (25)
- Doctoral Thesis (11)
- Review (5)
- Other (1)
Language
- English (453) (remove)
Keywords
- manifolds with singularities (3)
- pseudodifferential operators (3)
- Fredholm property (2)
- Mellin transform (2)
- conical singularities (2)
- elliptic operators (2)
- index (2)
- 'eta' invariant (1)
- APS problem (1)
- Atiyah-Bott condition (1)
Institute
- Institut für Physik und Astronomie (125)
- Institut für Mathematik (93)
- Institut für Biochemie und Biologie (55)
- Institut für Chemie (39)
- Wirtschaftswissenschaften (27)
- Institut für Geowissenschaften (25)
- Institut für Informatik und Computational Science (23)
- Department Psychologie (12)
- Institut für Anglistik und Amerikanistik (11)
- Interdisziplinäres Zentrum für Dünne Organische und Biochemische Schichten (10)
Clones and Hyperidentities
(1997)
Hyperequational theory
(1997)
And/Or reasoning graphs for determining prime implicants in multi-level combinational networks
(1997)
In modern political philosophy social contract theory is the most prominent approach to individual rights and fair institutions. According to social contract theory the system of rights in a society ought to be justified by reconstructing its basic features as a contract between the mutually unconcerned members of society. This paper explores whether social contract theory can successfully be applied to justify rights of future generations. Three competing views are analysed: Rawls's theory of justice, Hobbes's radical liberalism and Gauthier's bargaining framework based on the Lockean proviso.
The paper is an enquiry into dynamic social contract theory. The social contract defines the rules of resource use. An intergenerational social contract in an economy with a single exhaustible resource is examined within a framework of an overlapping generations model. It is assumed that new generations do not accept the old social contract, and access to resources will be renegotiated between any incumbent generation and their successors. It turns out that later generations will be in an unfortunate position regardless of their bargaining power.
The paper contains the proof of the index formula for manifolds with conical points. For operators subject to an additional condition of spectral symmetry, the index is expressed as the sum of multiplicities of spectral points of the conormal symbol (indicial family) and the integral from the Atiyah-Singer form over the smooth part of the manifold. The obtained formula is illustrated by the example of the Euler operator on a two-dimensional manifold with conical singular point.
It is shown that the Hankel transformation Hsub(v) acts in a class of weighted Sobolev spaces. Especially, the isometric mapping property of Hsub(v) which holds on L²(IRsub(+),rdr) is extended to spaces of arbitrary Sobolev order. The novelty in the approach consists in using techniques developed by B.-W. Schulze and others to treat the half-line Rsub(+) as a manifold with a conical singularity at r = 0. This is achieved by pointing out a connection between the Hankel transformation and the Mellin transformation.The procedure proposed leads at the same time to a short proof of the Hankel inversion formula. An application to the existence and higher regularity of solutions, including their asymptotics, to the 1-1-dimensional edge-degenerated wave equation is given.
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.
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.
We construct a theory of general boundary value problems for differential operators whose symbols do not necessarily satisfy the Atiyah-Bott condition [3] of vanishing of the corresponding obstruction. A condition for these problems to be Fredholm is introduced and the corresponding finiteness theorems are proved.
For elliptic operators on manifolds with boundary, we define spectral boundary value problems, which generalize the Atiyah-Patodi-Singer problem to the case of nonhomogeneous boundary conditions, operators of arbitrary order, and nonself-adjoint conormal symbols. The Fredholm property is proved and equivalence with certain elliptic equations on manifolds with conical singularities is established.
The dynamics of noisy bistable systems is analyzed by means of Lyapunov exponents and measures of complexity. We consider both the classical Kramers problem with additive white noise and the case when the barrier fluctuates due to additional external colored noise. In case of additive noise we calculate the Lyapunov exponents and all measures of complexity analytically as functions of the noise intensity resp. the mean escape time. For the problem of fluctuating barrier the usual description of the dynamics with the mean escape time is not sufficient. The application of the concept of measures of complexity allows to describe the structures of motion in more detail. Most complexity measures sign the value of correlation time at which the phenomenon of resonant activation occurs with an extremum.
The ill-posed problem of aerosol size distribution determination from a small number of backscatter and extinction measurements was solved successfully with a mollifier method which is advantageous since the ill-posed part is performed on exactly given quantities, the points r where n(r) is evaluated may be freely selected. A new twodimensional model for the troposphere is proposed.
The influence of polyelectrolytes on structure formation in liquid crystalline Na-dodecylsulfate/decanol/water systems was investigated by means of small angle X-ray diffraction, rheology, NMR spectroscopy, and microscopy. By adding Na-polyacrylate (PAA) into the mesophase, the one-phase region is left and phenomena of phase separation into a solvent-rich and a polymer/surfactantrich phase occurs. By incoporating an anionic and cationic polyelectrolyte step by step the tendency of phase separation is increased drastically. The self-organization process can be regulated directly by varying the water content of the system. However, at a water content of 30% the properties of the resulting liquid crystal were changed drastically. X-ray diffraction shows a multitude of Bragg peaks, NMR shows a peak-splitting, and rheology shows a change from non-Newtonian to Newtonian-flow behavior. On the basis of the experimental results an ordered multilayer associate structure can be assumed.