On a Topological Property of certain Calkin Algebras

Let X = 1^p, 1 p < , or X = c₀, B(X) be the algebra of allbounded linear operators on X, H(X) be the ideal of compactoperators in B(X), and C(X) = B(X)/H(X) be the Calkin algebraon X. For TB(X), let ||T||_c = dist(T, H(X)) be the essentialnorm of T that is the norm of T+H(X) in C(X). It is shown thatfor any operator TB(X) and any number 0 < t < 1, thereexists a closed infinite dimensional subspace Z Z X such that ||Tx|| t||T||_c, for all x Z. As a consequence, it is shown that every (not necessarily complete)submultiplicative norm on the Calkin algebra C(X) is equivalentto the quotient norm || ||_c on C(X).     

CoLab: A hybrid knowledge representation and compilation laboratory

Knowledge bases for real-world domains such as mechanical engineering require expressive and efficient representation and processing tools. We pursue a declarative-compilative approach to knowledge engineering.While Horn logic (as implemented in PROLOG) is well-suited for representing relational clauses, other kinds of declarative knowledge call for hybrid extensions: functional dependencies and higher-order knowledge should be modeled directly. Forward (bottom-up) reasoning should be integrated with backward (top-down) reasoning. Constraint propagation should be used wherever possible instead of search-intensive resolution. Taxonomic knowledge should be classified into an intuitive subsumption hierarchy.Our LISP-based tools provide directtranslators of these declarative representations into abstract machines such as an extended Warren Abstract Machine (WAM) and specialized inference engines that are interfaced to each other. More importantly, we provide source-to-sourcetransformers between various knowledge types, both for user convenience and machine efficiency.These formalisms with their translators and transformers have been developed as part of CoLab, acompilationlaboratory for studying what we call, respectively, vertical and horizontal compilation of knowledge, as well as for exploring the synergeticcolaboration of the knowledge representation formalisms.A case study in the realm of mechanical engineering has been an important driving force behind the development of CoLab. It will be used as the source of examples throughout the paper when discussing the enhanced formalisms, the hybrid representation architecture, and the compilers.Supported by BMFT Research Project ARC-TEC (grant ITW 8902 C4)     

Anion and cation vacancies in CdTe

The cadmium vacancy (V_Cd) and the tellurium vacancy (V_Te) in CdTe are identified by Electron Paramagnetic Resonance (EPR). The EPR spectrum of the singly ionised V_Te reveals cubic (unpertubed) symmetry and the hyperfine structure shows that the unpaired electron is equally spread over the four Cd neighbors. Further figand hyperfine interactions with the more distant neighbors are resolved by Electron Nuclear Double Resonance (ENDOR). The V_Cd is a double acceptor and the EPR spectrum is observed in its singly negative charge state. The symmerty is found to be trigonal, which can be explained in a model in which the hole occupies a dangling bondt ₂ orbital and the orbital degeneracy is removed by a static Jahn-Teller distortion. The hyperfine interaction shows that the hole is localised on one of the four Te neighbors.Paper presented at the 132nd WE-Heraeus-Seminar on Positron Studies of Semiconductor Defects, Halle, Germany, 29 August to 2 September 1994