Embedding in R-closed spaces

Some problems in the theory of R-closed spaces are solved by showing that every regular space can be embedded in a minimal regular space and there is an R-closed space with no coarser minimal regular topology. A class of spaces is found so that when fed into the Jone's machinery for producing non-Tychonoff, regular spaces, the output is non-tychonoff R-closed and minimal regular spaces. Also, an example of a strongly minimal regular space that is not locally R-closed is given.     

Model calculations of the spectra of rare-gas impurities in alkali hosts

Summary The spectra of rare-gas impurities in alkali hosts are evaluated for a change of mean-field (ΔMF) model. The model produces absorption and emission edge anomalies and asymmetric X-ray photoemission line shapes, but the threshold shapes are different from those observed by Tilton, Phelps and Flynn. The resolution of the discrepancy between theory and experiment appears to lie beyond this ΔMF model.

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Riassunto Si sono calcolati gli spettri di impurità di gas rari in ospiti alcalini per un cambiamento del modello di campo medio (ΔMF). Il modello produce anomalie di bordo di assorbimento ed emissione e forme della linea di emissione dei raggi X asimmetriche, ma le forme sulla soglia sono differenti da quelle osservate da Tilton, Phelps e Flynn. La risoluzione della discrepanza tra teoria ed esperimenti appare al di là di questo modello ΔMF.

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Резюме Оцениваются спектры разреженных газовых примесей в щелочных кристаллах для изменения модели среднего поля (ΔMF). Предложенная моделъ дает поглощение и аномалии края испускания и асимметричнЫе формы линии фотоиспускания ренттеновского излучения, но формы порогов отличаются от резуљтатов, полчч∈нных Тилтоном Фелпсом и Флином. Возможностя разрешения расхождений между теорией и зкспериментом, оказьивается, лежит за пределами зтой ΔMF модели.

     

Conformational memories with variable bond angles

Conformational Memories (CM) is a simulated annealing/Monte Carlo method that explores peptide and protein dihedral conformational space completely and efficiently, independent of the original conformation. Here we extend the CM method to include the variation of a randomly chosen bond angle, in addition to the standard variation of two or three randomly chosen dihedral angles, in each Monte Carlo trial of the CM exploratory and biased phases. We test the hypothesis that the inclusion of variable bond angles in CM leads to an improved sampling of conformational space. We compare the results with variable bond angles to CM with no bond angle variation for the following systems: (1) the pentapeptide Met-enkephalin, which is a standard test case for conformational search methods; (2) the proline ring pucker in a 17mer model peptide, (Ala)(8)Pro(Ala)(8); and (3) the conformations of the Ser 7.39 chi(1) in transmembrane helix 7 (TMH7) of the cannabinoid CB1 receptor, a 25-residue system. In each case, analysis of the CM results shows that the inclusion of variable bond angles results in sampling of regions of conformational space that are inaccessible to CM calculations with only variable dihedral angles, and/or a shift in conformational populations from those calculated when variable bond angles are not included. The incorporation of variable bond angles leads to an improved sampling of conformational space without loss of efficiency. Our examples show that this improved sampling leads to better exploration of biologically relevant conformations that have been experimentally validated.     

Saturated boolean algebras and their stone spaces

For an infinite cardinal κ, we call a compact zero-dimensional space a κ-Parovicenko space if its boolean algebra of clopen sets is κ-saturated and has cardinality κ^<κ. We answer some questions about these spaces which were posed in [14]. For instance, it is shown that a κ⁺-Parovicenko spacé can be a Stone-Cech remainder in a natural way. We show that some of the results in [14] which used the assumption κ^<κ=κ, do indeed require this assumption. We also show that if 2^κ=κ⁺ then each compact F_κ⁺-space with weight κ⁺ can be embedded into a κ⁺-Parovicenko space (and so into an extremally disconnected space).     

Homogeneity in powers of zero-dimensional first-countable spaces

A construction of L. Brian Lawrence is extended to show that the -power of every subset of the Cantor set is homogeneous via a continuous translation modulo a dense set. It follows that every zero-dimensional first-countable space has a homogeneous -power.