Partition of graphs with condition on the connectivity and minimum degree

C. Thomassen and M. Szegedy proved the existence of a functionf(s, t) such that the points of anyf(s, t)-connected graph have a decomposition into two non-empty sets such that the subgraphs induced by them ares-connected andt-connected, respectively. We prove, thatf(s, t) ≦ 4s+4t − 13 and examine a similar problem for the minimum degree.     

When is a Pixley-Roy hyperspace CCC?

A space X is said to satisfy condition (C) if for every Y?X with |Y|=ω₁, any family $\text{G}$ of open subsets of Y with |$\text{G}$|=ω₁ has a countable network. It is easy to see that if X satisfies condition (C), then its Pixley-Roy hyperspace $\text{F}$[X] is CCC. We show that under MA_ω1 condition (C) is also necessary for $\text{F}$[X] to be CCC, but under CH it is not.     

The adsorption of sulfur on the platinum (100) surface

Clean platinum (100) surfaces of 1× 1 and 5 × 20 structure were exposed to H₂S. Surface coverage with Sulfur followed Langmuir kinetics, which, together with LEED data, points to a repulsive interaction between sulfur atoms. Sulfur adsorption causes a decrease in the work function of platinum by 0.7 eV at saturation coverage. This is attributed to polarization, rather than ionization, of the adsorbed sulfur. Photoemission measurements are difficult to interpret because of two-dimensional periodicity and the overlap of electronic structure of the adsorbate with the platinum d band. We observe peaks due to sulfur at 6.3, 4.5, and 2.5 eV below the Fermi level for the c(2 × 2) overlayer and at 6.8, 4.5, and 2.0 eV below E_F for the p(2 × 2) surface. A tentative interpretation in terms of sulfur orbitals is given. The decrease in work function and analogy with the properties of PtS₂ lead us to propose covalent bonding of sulfur to platinum, in which every sulfur atom is bonded to four Pt neighbors in both structures. The repulsive interaction between sulfur atoms is indirect through the platinum substrate.     

Interfacial water structure controls protein conformation

A phenomenological theory of salt-induced Hofmeister phenomena is presented, based on a relation between protein solubility in salt solutions and protein-water interfacial tension. As a generalization of previous treatments, it implies that both kosmotropic salting out and chaotropic salting in are manifested via salt-induced changes of the hydrophobic/hydrophilic properties of protein-water interfaces. The theory is applied to describe the salt-dependent free energy profiles of proteins as a function of their water-exposed surface area. On this basis, three classes of protein conformations have been distinguished, and their existence experimentally demonstrated using the examples of bacteriorhodopsin and myoglobin. The experimental results support the ability of the new formalism to account for the diverse manifestations of salt effects on protein conformation, dynamics, and stability, and to resolve the puzzle of chaotropes stabilizing certain proteins (and other anomalies). It is also shown that the relation between interfacial tension and protein structural stability is straightforwardly linked to protein conformational fluctuations, providing a keystone for the microscopic interpretation of Hofmeister effects. Implications of the results concerning the use of Hofmeister effects in the experimental study of protein function are discussed.     

Bis-[3]Ferrocenophanes with Central >E−E’< Bonds (E,E’=P,SiH): Preparation,Properties, and Thermal Activation

A series of bis-[3]ferrocenophanes of the general type Fe(C₅H₄E’)₂E−E(E'C₅H₄)₂Fe (E=P, SiH and E’=PtBu, NneoPentyl, NSi(CH₃)₃) with an isolobal molecular framework have been prepared and characterized by heteronuclear NMR spectroscopy and X-ray crystallography. The thermal dissociation behavior with respect to homolytic fission of the central bond generating phosphorus centered radicals was investigated using EPR spectroscopy and quantum chemical calculations.