Isomorphisms of lattices of Bures-closed bimodules over Cartan MASAs

For i = 1; 2, let (Mi;Di) be pairs consisting of a Cartan MASA Di in a von Neumann algebra Mi, let atom(Di) be the set of atoms of Di, and let Si be the lattice of Bures-closed Di bimodules in Mi. We show that when Mi have separable preduals, there is a lattice isomorphism between S1 and S2 if and only if the sets f(Q1;Q2) 2 atom(Di) atom(Di) : Q1MiQ2 6= (0)g have the same cardinality. In particular, when Di is nonatomic, Si is isomorphic to the lattice of projections in L1([0; 1];m) where m is Lebesgue measure, regardless of the isomorphism classes of M1 and M2

Cartan Triples

We introduce the class of Cartan triples as a generalization of the notion of a Cartan MASA in a von Neumann algebra. We obtain a one-to-one correspondence between Cartan triples and certain Clifford extensions of inverse semigroups. Moreover, there is a spectral theorem describing bimodules in terms of their support sets in the fundamental inverse semigroup and, as a corollary, an extension of Aoi's theorem to this setting. This context contains that of Fulman's generalization of Cartan MASAs and we discuss his generalization in an appendix.Comment: 37 page

CARTAN TRIPLES

We introduce the class of Cartan triples as a generalization of the notion of a Car- tan MASA in a von Neumann algebra. We obtain a one-to-one correspondence between Cartan triples and certain Clifford extensions of inverse semigroups. Moreover, there is a spectral theorem describing bimodules in terms of their support sets in the fundamental inverse semigroup and, as a corollary, an extension of Aoi’s theorem to this setting. This context contains that of Fulman’s generalization of Cartan MASAs and we discuss his generalization in an appendix

A 15kWe (nominal) solar thermal electric power conversion concept definition study: Steam Rankine reheat reciprocator system

An evaluation was made of the potential of a steam Rankine reheat reciprocator engine to operate at high efficiency in a point-focusing distributed receiver solar thermal-electric power system. The scope of the study included the engine system and electric generator; not included was the solar collector/mirror or the steam generator/receiver. A parametric analysis of steam conditions was completed leading to the selection of 973 K 12.1 MPa as the steam temperature/pressure for a conceptual design. A conceptual design was completed for a two cylinder/ opposed engine operating at 1800 rpm directly coupled to a commercially available induction generator. A unique part of the expander design is the use of carbon/graphite piston rings to eliminate the need for using oil as an upper cylinder lubricant. The evaluation included a system weight estimate of 230 kg at the mirror focal point with the condenser mounted separately on the ground. The estimated cost of the overall system is $1932 or$90/kW for the maximum 26 kW output

Semicrossed Products of Operator Algebras by Semigroups

We examine the semicrossed products of a semigroup action by $*$-endomorphisms on a C*-algebra, or more generally of an action on an arbitrary operator algebra by completely contractive endomorphisms. The choice of allowable representations affects the corresponding universal algebra. We seek quite general conditions which will allow us to show that the C*-envelope of the semicrossed product is (a full corner of) a crossed product of an auxiliary C*-algebra by a group action. Our analysis concerns a case-by-case dilation theory on covariant pairs. In the process we determine the C*-envelope for various semicrossed products of (possibly nonselfadjoint) operator algebras by spanning cones and lattice-ordered abelian semigroups. In particular, we show that the C*-envelope of the semicrossed product of C*-dynamical systems by doubly commuting representations of $\mathbb{Z}^n_+$ (by generally non-injective endomorphisms) is the full corner of a C*-crossed product. In consequence we connect the ideal structure of C*-covers to properties of the actions. In particular, when the system is classical, we show that the C*-envelope is simple if and only if the action is injective and minimal. The dilation methods that we use may be applied to non-abelian semigroups. We identify the C*-envelope for actions of the free semigroup $\mathbb{F}_+^n$ by automorphisms in a concrete way, and for injective systems in a more abstract manner. We also deal with C*-dynamical systems over Ore semigroups when the appropriate covariance relation is considered.Comment: 100 pages; comments and references update

The art of being human : a project for general philosophy of science

Throughout the medieval and modern periods, in various sacred and secular guises, the unification of all forms of knowledge under the rubric of ‘science’ has been taken as the prerogative of humanity as a species. However, as our sense of species privilege has been called increasingly into question, so too has the very salience of ‘humanity’ and ‘science’ as general categories, let alone ones that might bear some essential relationship to each other. After showing how the ascendant Stanford School in the philosophy of science has contributed to this joint demystification of ‘humanity’ and ‘science’, I proceed on a more positive note to a conceptual framework for making sense of science as the art of being human. My understanding of ‘science’ is indebted to the red thread that runs from Christian theology through the Scientific Revolution and Enlightenment to the Humboldtian revival of the university as the site for the synthesis of knowledge as the culmination of self-development. Especially salient to this idea is science‘s epistemic capacity to manage modality (i.e. to determine the conditions under which possibilities can be actualised) and its political capacity to organize humanity into projects of universal concern. However, the challenge facing such an ideal in the twentyfirst century is that the predicate ‘human’ may be projected in three quite distinct ways, governed by what I call ‘ecological’, ‘biomedical’ and ‘cybernetic’ interests. Which one of these future humanities would claim today’s humans as proper ancestors and could these futures co-habit the same world thus become two important questions that general philosophy of science will need to address in the coming years

Application of pattern recognition techniques to the identification of aerospace acoustic sources

A pattern recognition system was developed that successfully recognizes simulated spectra of five different types of transportation noise sources. The system generates hyperplanes during a training stage to separate the classes and correctly classify unknown patterns in classification mode. A feature selector in the system reduces a large number of features to a smaller optimal set, maximizing performance and minimizing computation

Interaction of gases with lunar materials

The surface chemistry of Apollo 17 lunar fines samples 74220 (the orange soil) and 74241 (the gray control soil) has been studied by measuring the adsorption of nitrogen, argon, and oxygen (all at 77 K) and also water vapor (at 20 or 22 C). In agreement with results for samples from other missions, both samples had low initial specific surface areas, consisted of nonporous particles, and were attacked by water vapor at high relative pressure to give an increased specific surface area and create a pore system which gave rise to a capillary condensation hysteresis loop in the adsorption isotherms. In contrast to previous samples, both of the Apollo 17 soils were partially hydrophobic in their initial interaction with water vapor (both samples were completely hydrophilic after the reaction with water). The results are consistent with formation at high temperatures without subsequent exposure to significant amounts of water

Applications of Skylab EREP photographs to mapping landforms and environmental geomorphology in the Great Plains and Midwest

The following evaluations of Skylab photographs were undertaken: (1) the 1290 Skylab S190A and S190B photographs of Illinois, Iowa, Kansas, Missouri, Nebraska, and South Dakota were evaluated in detail in terms of coverage, cloud cover, photographic quality, endlap, detectability of roads and stereorelief, and utility for geomorphologic mapping, and (2) the utility of the Skylab photos were tested for interpretive analytic mapping of geomorphologic features over large areas representative of different parts of this region. Photointerpretative maps of analytic geomorphology were obtained for various test areas representative of the varied landscapes in the region. These maps are useful for regional land-use planning, ground-water exploration, and other environmental geomorphologic-geologic applications. Compared with LANDSAT-1 MSS images, Skylab photos afford almost as extensive overviews of large areas but in considerably greater detail, and for many SL photos, moderate stereorelief. However, repetitive multiseasonal, cloud-free coverage by high-quality photos is very limited and many areas have no coverage at all