134,091 research outputs found

    Pairwise monotonically normal spaces

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    summary:We introduce and study the notion of pairwise monotonically normal space as a bitopological extension of the monotonically normal spaces of Heath, Lutzer and Zenor. In particular, we characterize those spaces by using a mixed condition of insertion and extension of real-valued functions. This result generalizes, at the same time improves, a well-known theorem of Heath, Lutzer and Zenor. We also obtain some solutions to the quasi-metrization problem in terms of the pairwise monotone normality

    The basis problem for subspaces of monotonically normal compacta

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    We prove, assuming Souslin's Hypothesis, that each uncountable subspace of each zero-dimensional monotonically normal compact space contains an uncountable subset of the real line with either the metric, the Sorgenfrey, or the discrete topology.Comment: 12 page

    Pressure Study of BiS2-Based Superconductors Bi4O4S3 and La(O,F)BiS2

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    We report the electrical resistivity measurements under pressure for the recently discovered BiS2-based layered superconductors Bi4O4S3 and La(O,F)BiS2. In Bi4O4S3, the transition temperature Tc decreases monotonically without a distinct change in the metallic behavior in the normal state. In La(O,F)BiS2, on the other hand, Tc initially increases with increasing pressure and then decreases above ? 1 GPa. The semiconducting behavior in the normal state is suppressed markedly and monotonically, whereas the evolution of Tc is nonlinear. The strong suppression of the semiconducting behavior without doping in La(O,F)BiS2 suggests that the Fermi surface is located in the vicinity of some instability. In the present study, we elucidate that the superconductivity in the BiS2 layer favors the Fermi surface at the boundary between the semiconducting and metallic behaviors.Comment: 4 pages, 6 figures, Accepted for publication in J. Phys. Soc. Jp

    Monotonically normal ee-separable spaces may not be perfect

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    summary:A topological space XX is said to be ee-separable if XX has a σ\sigma-closed-discrete dense subset. Recently, G. Gruenhage and D. Lutzer showed that ee-separable PIGO spaces are perfect and asked if ee-separable monotonically normal spaces are perfect in general. The main purpose of this article is to provide examples of ee-separable monotonically normal spaces which are not perfect. Extremely normal ee-separable spaces are shown to be stratifiable

    LSMR: An iterative algorithm for sparse least-squares problems

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    An iterative method LSMR is presented for solving linear systems Ax=bAx=b and least-squares problem \min \norm{Ax-b}_2, with AA being sparse or a fast linear operator. LSMR is based on the Golub-Kahan bidiagonalization process. It is analytically equivalent to the MINRES method applied to the normal equation A\T Ax = A\T b, so that the quantities \norm{A\T r_k} are monotonically decreasing (where rk=b−Axkr_k = b - Ax_k is the residual for the current iterate xkx_k). In practice we observe that \norm{r_k} also decreases monotonically. Compared to LSQR, for which only \norm{r_k} is monotonic, it is safer to terminate LSMR early. Improvements for the new iterative method in the presence of extra available memory are also explored.Comment: 21 page
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