Shift invariant preduals of ℓ₁(ℤ)

The Banach space ℓ<sub>1</sub>(ℤ) admits many non-isomorphic preduals, for example, C(K) for any compact countable space K, along with many more exotic Banach spaces. In this paper, we impose an extra condition: the predual must make the bilateral shift on ℓ<sub>1</sub>(ℤ) weak<sup>*</sup>-continuous. This is equivalent to making the natural convolution multiplication on ℓ<sub>1</sub>(ℤ) separately weak*-continuous and so turning ℓ<sub>1</sub>(ℤ) into a dual Banach algebra. We call such preduals <i>shift-invariant</i>. It is known that the only shift-invariant predual arising from the standard duality between C<sub>0</sub>(K) (for countable locally compact K) and ℓ<sub>1</sub>(ℤ) is c<sub>0</sub>(ℤ). We provide an explicit construction of an uncountable family of distinct preduals which do make the bilateral shift weak<sup>*</sup>-continuous. Using Szlenk index arguments, we show that merely as Banach spaces, these are all isomorphic to c<sub>0</sub>. We then build some theory to study such preduals, showing that they arise from certain semigroup compactifications of ℤ. This allows us to produce a large number of other examples, including non-isometric preduals, and preduals which are not Banach space isomorphic to c<sub>0</sub>

Unusual T_c variation with hole concentration in Bi_2Sr_{2-x}La_xCuO_{6+\delta}

We have investigated the $T_c$ variation with the hole concentration $p$ in the La-doped Bi 2201 system, Bi$_2$Sr$_{2-x}$La$_x$CuO$_{6+\delta}$. It is found that the Bi 2201 system does not follow the systematics in $T_c$ and $p$ observed in other high-$T_c$ cuprate superconductors (HTSC's). The $T_c$ vs $p$ characteristics are quite similar to what observed in Zn-doped HTSC's. An exceptionally large residual resistivity component in the inplane resistivity indicates that strong potential scatterers of charge carriers reside in CuO$_2$ planes and are responsible for the unusual $T_c$ variation with $p$, as in the Zn-doped systems. However, contrary to the Zn-doped HTSC's, the strong scatter in the Bi 2201 system is possibly a vacancy in the Cu site.Comment: RevTeX, 3 figures, to be published in the Physical Review

Notions of Infinity in Quantum Physics

In this article we will review some notions of infiniteness that appear in Hilbert space operators and operator algebras. These include proper infiniteness, Murray von Neumann's classification into type I and type III factors and the class of F{/o} lner C*-algebras that capture some aspects of amenability. We will also mention how these notions reappear in the description of certain mathematical aspects of quantum mechanics, quantum field theory and the theory of superselection sectors. We also show that the algebra of the canonical anti-commutation relations (CAR-algebra) is in the class of F{/o} lner C*-algebras.Comment: 11 page

Structural trends and bonding of the 5ƒ-elements (U-Am) with the oxoligand I03-.

The solid state chemistry of transuranium compounds has received considerably less attention than their uranium analogs owing to decreased availability and the highly specialized facilities needed to safely study long-lived {alpha}-emitters. However, understanding the behavior of the early transuranium elements is critical for assessing their environmental impact as long-term contributors to radioactive dose in nuclear waste repositories. Of particular interest is how these elements might react with fission product radionuclides such as 129I, or their derivatives. In fact, iodine can exist in solution in both oxidized and reduced forms, i .e. as I03 and F, and studies on the nature of129I in nuclear waste suggested the existence of iodate, 103.

Underspecification, Inherent Nondeterminism and Probability in Sequence Diagrams

Abstract. Nondeterminism in specifications may be used for at least two different purposes. One is to express underspecification, which means that the specifier for the same environment behavior allows several alterna-tive behaviors of the specified component and leaves the choice between these to those responsible for implementing the specification. In this case a valid implementation will need to implement at least one, but not nec-essarily all, alternatives. The other purpose is to express inherent nonde-terminism, which means that a valid implementation needs to reflect all alternatives. STAIRS is an approach to the compositional and incremental development of sequence diagrams supporting underspecification as well as inherent nondeterminism. Probabilistic STAIRS builds on STAIRS and allows probabilities to be included in the specifications. Underspecifica-tion with respect to probabilities is also allowed. This paper investigates the use of underspecification, inherent nondeterminism and probability in sequence diagrams, the relationships between these concepts, and how these are expressed in STAIRS and probabilistic STAIRS.

PCR diagnostics and monitoring of adenoviral infections in hematopoietic stem cell transplantation recipients

After stem cell transplantation, human patients are prone to life-threatening opportunistic infections with a plethora of microorganisms. We report a retrospective study on 116 patients (98 children, 18 adults) who were transplanted in a pediatric bone marrow transplantation unit. Blood, urine and stool samples were collected and monitored for adenovirus (AdV) DNA using polymerase chain reaction (PCR) and real-time PCR (RT-PCR) on a regular basis. AdV DNA was detected in 52 (44.8%) patients, with mortality reaching 19% in this subgroup. Variables associated with adenovirus infection were transplantations from matched unrelated donors and older age of the recipient. An increased seasonal occurrence of adenoviral infections was observed in autumn and winter. Analysis of immune reconstitution showed a higher incidence of AdV infections during periods of low T-lymphocyte count. This study also showed a strong interaction between co-infections of AdV and BK polyomavirus in patients undergoing hematopoietic stem cell transplantations