Composition Operators and Endomorphisms

If $b$ is an inner function, then composition with $b$ induces an endomorphism, $\beta$, of $L^\infty(\mathbb{T})$ that leaves $H^\infty(\mathbb{T})$ invariant. We investigate the structure of the endomorphisms of $B(L^2(\mathbb{T}))$ and $B(H^2(\mathbb{T}))$ that implement $\beta$ through the representations of $L^\infty(\mathbb{T})$ and $H^\infty(\mathbb{T})$ in terms of multiplication operators on $L^2(\mathbb{T})$ and $H^2(\mathbb{T})$. Our analysis, which is based on work of R. Rochberg and J. McDonald, will wind its way through the theory of composition operators on spaces of analytic functions to recent work on Cuntz families of isometries and Hilbert $C^*$-modules

Evidence for electromagnetic granularity in polycrystalline Sm1111 iron-pnictides with enhanced phase purity

We prepared polycrystalline SmFeAsO1-xFx (Sm1111) bulk samples by sintering and hot isostatic pressing (HIP) in order to study the effects of phase purity and relative density on the intergranular current density. Sintered and HIPped Sm1111 samples are denser with fewer impurity phases, such as SmOF and the grain boundary wetting phase, FeAs. We found quite complex magnetization behavior due to variations of both the inter and intragranular current densities. Removing porosity and reducing second phase content enhanced the intergranular current density, but HIPping reduced Tc and the intragranular current density, due to loss of fluorine and reduction of Tc. We believe that the HIPped samples are amongst the purest polycrystalline 1111 samples yet made. However, their intergranular current densities are still small, providing further evidence that polycrystalline pnictides, like polycrystalline cuprates, are intrinsically granular.Comment: 14 pages, 6 figure

Neutron Irradiation of Sm-1111

SmFeAsO$_{1-x}$F$_x$ was irradiated in a fission reactor to a fast (E > 0.1 MeV) neutron fluence of 4x10^${21}$ m$^{-2}$. The introduced defects increase the normal state resistivity due to a reduction in the mean free path of the charge carriers. This leads to an enhancement of the upper critical field at low temperatures. The critical current density within the grains, Jc, increases upon irradiation. The second maximum in the field dependence of Jc disappears and the critical current density becomes a monotonically decreasing function of the applied magnetic field

New Fe-based superconductors: properties relevant for applications

Less than two years after the discovery of high temperature superconductivity in oxypnictide LaFeAs(O,F) several families of superconductors based on Fe layers (1111, 122, 11, 111) are available. They share several characteristics with cuprate superconductors that compromise easy applications, such as the layered structure, the small coherence length, and unconventional pairing, On the other hand the Fe-based superconductors have metallic parent compounds, and their electronic anisotropy is generally smaller and does not strongly depend on the level of doping, the supposed order parameter symmetry is s wave, thus in principle not so detrimental to current transmission across grain boundaries. From the application point of view, the main efforts are still devoted to investigate the superconducting properties, to distinguish intrinsic from extrinsic behaviours and to compare the different families in order to identify which one is the fittest for the quest for better and more practical superconductors. The 1111 family shows the highest Tc, huge but also the most anisotropic upper critical field and in-field, fan-shaped resistive transitions reminiscent of those of cuprates, while the 122 family is much less anisotropic with sharper resistive transitions as in low temperature superconductors, but with about half the Tc of the 1111 compounds. An overview of the main superconducting properties relevant to applications will be presented. Upper critical field, electronic anisotropy parameter, intragranular and intergranular critical current density will be discussed and compared, where possible, across the Fe-based superconductor families

Preparation of amino-substituted indenes and 1,4-dihydronaphthalenes using a one-pot multireaction approach: total synthesis of oxybenzo[c]phenanthridine alkaloids

Allylic trichloroacetimidates bearing a 2-vinyl or 2-allylaryl group have been designed as substrates for a one-pot, two-step multi-bond-forming process leading to the general preparation of aminoindenes and amino-substituted 1,4-dihydronaphthalenes. The synthetic utility of the privileged structures formed from this one-pot process was demonstrated with the total synthesis of four oxybenzo[c]phenanthridine alkaloids, oxychelerythrine, oxysanguinarine, oxynitidine, and oxyavicine. An intramolecular biaryl Heck coupling reaction, catalyzed using the Hermann–Beller palladacycle was used to effect the key step during the synthesis of the natural products

Search for dinucleon decay into pions at Super-Kamiokande

A search for dinucleon decay into pions with the Super-Kamiokande detector has been performed with an exposure of 282.1 kiloton-years. Dinucleon decay is a process that violates baryon number by two units. We present the first search for dinucleon decay to pions in a large water Cherenkov detector. The modes $^{16}$O$(pp) \rightarrow$ $^{14}$C$\pi^{+}\pi^{+}$, $^{16}$O$(pn) \rightarrow$ $^{14}$N$\pi^{+}\pi^{0}$, and $^{16}$O$(nn) \rightarrow$ $^{14}$O$\pi^{0}\pi^{0}$ are investigated. No significant excess in the Super-Kamiokande data has been found, so a lower limit on the lifetime of the process per oxygen nucleus is determined. These limits are: $\tau_{pp\rightarrow\pi^{+}\pi^{+}} > 7.22 \times 10^{31}$ years, $\tau_{pn\rightarrow\pi^{+}\pi^{0}} > 1.70 \times 10^{32}$ years, and $\tau_{nn\rightarrow\pi^{0}\pi^{0}} > 4.04 \times 10^{32}$ years. The lower limits on each mode are about two orders of magnitude better than previous limits from searches for dinucleon decay in iron.Comment: 20 pages, 17 figures. Accepted for publication in Physical Review D on March 30, 201