For P a poset or lattice, let Id(P ) denote the poset, respectively, lattice, of upward directed downsets in P, including the empty set, and let id(P ) = Id(P )−{∅}. This note obtains various results to the effect that Id(P ) is always, and id(P ) often, “essentially larger” than P. In the first vein, we find that a poset P admits no <-respecting map (and so in particular, no one-to-one isotone...

This paper shows that any compactly generated lattice is a subdirect product of subdirectly irreducible lattices which are complete and upper continuous. An example of a compactly generated lattice which cannot be subdirectly decomposed into subdirectly irreducible compactly generated lattices is given. In the case of an ideal lattice of a lattice L, the decomposition into subdirectly irreducib...

The generalized gradient correction method for positron-electron correlation effects in solids @B. Barbiellini et al., Phys. Rev. B 51, 7341 ~1995!# is applied in several test cases. The positron lifetime, energetics, and momentum distribution of the annihilating electron-positron pairs are considered. The comparison with experiments shows systematic improvement in the predictive power of the t...

In this paper we review the hypothesis that a substantial part of the cosmic ray ux observed above about 10 19 eV may be produced by decaying or annihilating topo-logical defects left over from phase transitions in the early universe at grand uniication energy scales (10 16 GeV). Possible signatures of cosmic ray producing defect models are discussed which could be tested experimentally in the ...

A new theoretical framework for computation of the relic abundance of cold dark matter particles such as LSP is presented and some generic features of new results are discussed. The most important is a generalization of the Boltzmann equation to include off-shell effects and its thermal average over cosmic medium. It is shown that at very low temperatures, much below the mass of annihilating pa...