Compactness in Banach space theory - selected problems

We list a number of problems in several topics related to compactness in nonseparable Banach spaces. Namely, about the Hilbertian ball in its weak topology, spaces of continuous functions on Eberlein compacta, WCG Banach spaces, Valdivia compacta and Radon-Nikod\'{y}m compacta

Generalization of entanglement to convex operational theories: Entanglement relative to a subspace of observables

We define what it means for a state in a convex cone of states on a space of observables to be generalized-entangled relative to a subspace of the observables, in a general ordered linear spaces framework for operational theories. This extends the notion of ordinary entanglement in quantum information theory to a much more general framework. Some important special cases are described, in which the distinguished observables are subspaces of the observables of a quantum system, leading to results like the identification of generalized unentangled states with Lie-group-theoretic coherent states when the special observables form an irreducibly represented Lie algebra. Some open problems, including that of generalizing the semigroup of local operations with classical communication to the convex cones setting, are discussed.Comment: 19 pages, to appear in proceedings of Quantum Structures VII, Int. J. Theor. Phy

Generalizations of entanglement based on coherent states and convex sets

Unentangled pure states on a bipartite system are exactly the coherent states with respect to the group of local transformations. What aspects of the study of entanglement are applicable to generalized coherent states? Conversely, what can be learned about entanglement from the well-studied theory of coherent states? With these questions in mind, we characterize unentangled pure states as extremal states when considered as linear functionals on the local Lie algebra. As a result, a relativized notion of purity emerges, showing that there is a close relationship between purity, coherence and (non-)entanglement. To a large extent, these concepts can be defined and studied in the even more general setting of convex cones of states. Based on the idea that entanglement is relative, we suggest considering these notions in the context of partially ordered families of Lie algebras or convex cones, such as those that arise naturally for multipartite systems. The study of entanglement includes notions of local operations and, for information-theoretic purposes, entanglement measures and ways of scaling systems to enable asymptotic developments. We propose ways in which these may be generalized to the Lie-algebraic setting, and to a lesser extent to the convex-cones setting. One of our original motivations for this program is to understand the role of entanglement-like concepts in condensed matter. We discuss how our work provides tools for analyzing the correlations involved in quantum phase transitions and other aspects of condensed-matter systems.Comment: 37 page

Processing real-world waste plastics by pyrolysis-reforming for hydrogen and high-value carbon nanotubes

Producing both hydrogen and high-value carbon nanotubes (CNTs) derived from waste plastics is reported here using a pyrolysis-reforming technology comprising a two-stage reaction system, in the presence of steam and a Ni-Mn-Al catalyst. The waste plastics consisted of plastics from a motor oil container (MOC), commercial waste high density polyethylene (HDPE) and regranulated HDPE waste containing polyvinyl chloride (PVC). The results show that hydrogen can be produced from the pyrolysis-reforming process, but also carbon nanotubes are formed on the catalyst. However, the content of 0.3 wt.% polyvinyl chloride in the waste HDPE (HDPE/PVC) has been shown to poison the catalyst and significantly reduce the quantity and purity of CNTs. The presence of sulfur has shown less influence on the production of CNTs in terms of quantity and CNT morphologies. Around 94.4 mmol H g plastic was obtained for the pyrolysis-reforming of HDPE waste in the presence of the Ni-Mn-Al catalyst and steam at a reforming temperature of 800 C. The addition of steam in the process results in an increase of hydrogen production and reduction of carbon yield; in addition, the defects of CNTs, for example, edge dislocations were found to be increased with the introduction of steam (from Raman analysis)

Hydrogen and Carbon Nanotubes from Pyrolysis-Catalysis of Waste Plastics: A Review

More than 27 million tonnes of waste plastics are generated in Europe each year representing a considerable potential resource. There has been extensive research into the production of liquid fuels and aromatic chemicals from pyrolysis-catalysis of waste plastics. However, there is less work on the production of hydrogen from waste plastics via pyrolysis coupled with catalytic steam reforming. In this paper, the different reactor designs used for hydrogen production from waste plastics are considered and the influence of different catalysts and process parameters on the yield of hydrogen from different types of waste plastics are reviewed. Waste plastics have also been investigated as a source of hydrocarbons for the generation of carbon nanotubes via the chemical vapour deposition route. The influences on the yield and quality of carbon nanotubes derived from waste plastics are reviewed in relation to the reactor designs used for production, catalyst type used for carbon nanotube growth and the influence of operational parameters