Toeplitz CAR flows are a class of E0-semigroups including the first type III example constructed by R. T. Powers. We show that the Toeplitz CAR flows contain uncountably many mutually non cocycle conjugate E0-semigroups of type III. We also generalize the type III criterion for Toeplitz CAR flows employed by Powers (and later refined by W. Arveson), and show that Toeplitz CAR flows are always e...

Let κ be an inaccessible cardinal, and let E0 = {x ∈ Pκκ + : cf λx = cf κx} and E1 = {x ∈ Pκκ : κx is regular and λx = κ + x }. It is consistent that the set E1 is stationary and that every stationary subset of E0 reflects at almost every a ∈ E1. Supported by NSF grants DMS-9401275 and DMS 97-04477. Typeset by AMS-TEX 1 2 THOMAS JECH AND SAHARON SHELAH

1.1. Normal solvability. Consider a linear operator L acting from a Banach space E0(Ω) to another space E(Ω). Here Ω denotes a domain in Rn, and the notation E(Ω) is used for a Banach space of functions defined in Ω. We are basically interested in the case where the domain Ω is unbounded though all results remain applicable and in many cases even simpler for bounded domains. Suppose that E0(G) ...

The probability that a randomly accelerated particle in two dimensions has not yet left a simply connected domain A after a time t decays as e−E0t for long times. The same quantity E0 also determines the confinement free energy per unit length ∆f = kBT E0 of a semiflexible polymer in a narrow cylindrical pore with cross section A. From simulations of a randomly accelerated particle we estimate ...

Data for the inactivation of three Escherichia coli mutants by energetic heavy ions are fitted by the track theory of a one-hit detector in an extended target mode. The respective E0's are 46, 36.5, and 12.6 Gy for E. coli B, B/r, and Bs-1 and a0, the assumed target radius, is 0.5 microns for all three. The parameter E0, the D37 with gamma rays, is measured directly, while a0 is fitted to the d...

The local bonding environment of chlorine in silicate melts has a profound influence over the thermodynamic properties and structure melt, affecting viscosity, rheology, volatile degassing potential. To constrain Cl natural melts, we have determined K-edge X-ray absorption fine (XAFS) spectra for 44 experimentally produced glasses both near edge (XANES) extended (EXAFS) regions. In pre-edge reg...

The paper examines relationships between the Shannon entropy and the `α-norm for n-ary probability vectors, n ≥ 2. More precisely, we investigate the tight bounds of the `α-norm with a fixed Shannon entropy, and vice versa. As applications of the results, we derive the tight bounds between the Shannon entropy and several information measures which are determined by the `α-norm. Moreover, we app...

Where E0 is the standard electrode potential, R is the universal gas constant, T is the absolute temperature, z is the number of moles of electrons transferred in the cell reaction or halfreaction, F is the Faraday-constant, and cox and cred are the concentrations of the oxidized and reduced forms of the component. The potential of the hydrogen electrode is declared to be 0.000 V at all tempera...

Polar coding is a new technique introduced by Arıkan [1] based on a phenomenon called channel polarization. Polar codes are appealing as an error correction method since they are proved to achieve the symmetric capacity of any B-DMC using low complexity encoders and decoders, and their block error probability is shown to decrease exponentially in the square root of the block length. In fact, tw...