This paper is centered on an extremely general problem: Problem. Is it consistent (perhaps modulo large cardinals) that a locally compact space X must be the union of countably many ω-bounded subspaces if every closed discrete subspace of X is countable [in other words, if X is ω1-compact]? A space is ω-bounded if every countable subset has compact closure. This is a strengthening of countable ...

We prove the first polynomial bound on number of monotonic homotopy moves required to tighten a collection closed curves any compact orientable surface, where crossings in curve is not allowed increase at time during process. The best known upper before was exponential, which can be obtained by combining algorithm De Graaf and Schrijver [ J. Comb. Theory Ser. B , 1997] together with an exponent...

A framework is developed to rigorously test an entire class of memory retention functions by examining hazard properties. Evidence is provided that the memory hazard function is not monotonically decreasing. Yet most of the proposals for retention functions, which have emerged from the psychological literature, imply that memory hazard is monotonically decreasing over the entire temporal range....

The purpose of this paper is to introduce monotonization in the setting of pointfree topology. More specifically, monotonically normal locales are characterized in terms of monotone insertion and monotone extensions theorems.

An iterative method LSMR is presented for solving linear systems Ax = b and leastsquares problems min ‖Ax−b‖2, with A 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 ATAx = ATb, so that the quantities ‖Ark‖ are monotonically decreasing (where rk = b−Axk is the re...