Some remarks on singularities in quantum cosmology

We discuss to what extent classical singularities persist upon quantization in two simple cosmological models.Comment: 4 pps., LaTeX2e. Substantial revisions. To appear in: Proc. of the Second Conference on Constrained Dynamics and Quantum Gravity, Santa Margherita Ligure, Italy, 17-21 September 1996. Edited by V. de Alfaro et a

L2 regularity of measurable solutions of a finite-difference equation of the circle

We show that if $\varphi$ is a lacunary Fourier series and the equation $\psi (x) -\psi (x + \alpha) = \varphi(x), x \bmod 1$ has a measurable solution $\varphi$, then in fact the equation has a solution in L2. This work of Michel Herman (1942-2000) appeared only as a preprint of the Mathematics Institute, University of Warwick, dated May 1976. It was turned into TEX format by Claire Desescures. Minor editorial work was done by Albert Fathi

Explicit Representation of Exception Handling in the Development of Dependable Component-Based Systems

Exception handling is a structuring technique that facilitates the design of systems by encapsulating the process of error recovery. In this paper, we present a systematic approach for incorporating exceptional behaviour in the development of component-based software. The premise of our approach is that components alone do not provide the appropriate means to deal with exceptional behaviour in an effective manner. Hence the need to consider the notion of collaborations for capturing the interactive behaviour between components, when error recovery involves more than one component. The feasibility of the approach is demonstrated in terms of the case study of the mining control system

Probing singularities in quantum cosmology with curvature scalars

We provide further evidence that the canonical quantization of cosmological models eliminates the classical Big Bang singularity, using the {\it DeBroglie-Bohm} interpretation of quantum mechanics. The usual criterion for absence of the Big Bang singularity in Friedmann-Robertson-Walker quantum cosmological models is the non-vanishing of the expectation value of the scale factor. We compute the `local expectation value' of the Ricci and Kretschmann scalars, for some quantum FRW models. We show that they are finite for all time. Since these scalars are elements of general scalar polynomials in the metric and the Riemann tensor, this result indicates that, for the quantum models treated here, the `local expectation value' of these general scalar polynomials should be finite everywhere. Therefore, we have further evidence that the quantization of the models treated here eliminates the classical Big Bang singularity. PACS: 04.40.Nr, 04.60.Ds, 98.80.Qc.Comment: 9 pages, 6 figure

Quasiblack holes with pressure: General exact results

A quasiblack hole is an object in which its boundary is situated at a surface called the quasihorizon, defined by its own gravitational radius. We elucidate under which conditions a quasiblack hole can form under the presence of matter with nonzero pressure. It is supposed that in the outer region an extremal quasihorizon forms, whereas inside, the quasihorizon can be either nonextremal or extremal. It is shown that in both cases, nonextremal or extremal inside, a well-defined quasiblack hole always admits a continuous pressure at its own quasihorizon. Both the nonextremal and extremal cases inside can be divided into two situations, one in which there is no electromagnetic field, and the other in which there is an electromagnetic field. The situation with no electromagnetic field requires a negative matter pressure (tension) on the boundary. On the other hand, the situation with an electromagnetic field demands zero matter pressure on the boundary. So in this situation an electrified quasiblack hole can be obtained by the gradual compactification of a relativistic star with the usual zero pressure boundary condition. For the nonextremal case inside the density necessarily acquires a jump on the boundary, a fact with no harmful consequences whatsoever, whereas for the extremal case the density is continuous at the boundary. For the extremal case inside we also state and prove the proposition that such a quasiblack hole cannot be made from phantom matter at the quasihorizon. The regularity condition for the extremal case, but not for the nonextremal one, can be obtained from the known regularity condition for usual black holes.Comment: 18 pages, no figures; improved introduction, added references, calculations better explaine

Academic Panel: Can Self-Managed Systems be trusted?

Trust can be defined as to have confidence or faith in; a form of reliance or certainty based on past experience; to allow without fear; believe; hope: expect and wish; and extend credit to. The issue of trust in computing has always been a hot topic, especially notable with the proliferation of services over the Internet, which has brought the issue of trust and security right into the ordinary home. Autonomic computing brings its own complexity to this. With systems that self-manage, the internal decision making process is less transparent and the ‘intelligence’ possibly evolving and becoming less tractable. Such systems may be used from anything from environment monitoring to looking after Granny in the home and thus the issue of trust is imperative. To this end, we have organised this panel to examine some of the key aspects of trust. The first section discusses the issues of self-management when applied across organizational boundaries. The second section explores predictability in self-managed systems. The third part examines how trust is manifest in electronic service communities. The final discussion demonstrates how trust can be integrated into an autonomic system as the core intelligence with which to base adaptivity choices upon