134,091 research outputs found
Pairwise monotonically normal spaces
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
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
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 -separable spaces may not be perfect
summary:A topological space is said to be -separable if has a -closed-discrete dense subset. Recently, G. Gruenhage and D. Lutzer showed that -separable PIGO spaces are perfect and asked if -separable monotonically normal spaces are perfect in general. The main purpose of this article is to provide examples of -separable monotonically normal spaces which are not perfect. Extremely normal -separable spaces are shown to be stratifiable
LSMR: An iterative algorithm for sparse least-squares problems
An iterative method LSMR is presented for solving linear systems and
least-squares problem \min \norm{Ax-b}_2, with 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 is the residual for the current iterate
). 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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