Games and general distributive laws in Boolean algebras

The games and are played by two players in -complete and max -complete Boolean algebras, respectively. For cardinals such that or , the -distributive law holds in a Boolean algebra iff Player 1 does not have a winning strategy in . Furthermore, for all cardinals , the -distributive law holds in iff Player 1 does not have a winning strategy in . More generally, for cardinals such that , the -distributive law holds in iff Player 1 does not have a winning strategy in . For regular and , implies the existence of a Suslin algebra in which is undetermined.

     

The hydrogenation of α-methylstyrene by tricarbonyl(cyclopentadienyl)hydride compounds of tungsten and molybdenum; support for a radical mechanism

Rates of reaction of the hydrides of tungsten and molybdenum of the form HM(η5-C₅H₅(CO)₃, with β-methylstyrene have been determined. The rate law is first order in olefin and in hydride. A mechanism involving a rate limiting step of hydrogen atom transfer to the olefin is consistent with the rate law, isotope effect and the absence of CO inhibition. The activation enthalpy for the reactions of HW(η5-C₅H₅)(CO)₃ and HMo(η5-C₅H₅)(CO)₃ are 97.5 ± 4.2 and 89.1 ± 3.3 kJ/mol, respectively. The rate constant for the reaction of styrene and HW(β5-C₅H₅)(CO)₃ is approximately that of β-methylstyrene, while β-methylstyrene was not observed to react under the conditions of the previous determinations. This suggests that attack by the hydride occurs at the β-carbon and this process is inhibited by substituents at that location.     

Some new inequalities involving the Hardy operator

In this paper we derive some new inequalities involving the Hardy operator, using some estimates of the Jensen functional, continuous form generalization of the Bellman inequality and a Banach space variant of it. Some results are generalized to the case of Banach lattices on $(0,b],0<b\le \infty$.     

The robustness in dynamics of out of equilibrium bidirectional transport systems with constrained entrances

Macroscopic and microscopic long-distance bidirectional transfer depends on connections between entrances and exits of various transport mediums. Persuaded by the associations, we introduce a small system module of Totally Asymmetric Simple Exclusion Process including oppositely directed species of particles moving on two parallel channels with constrained entrances. The dynamical rules which characterize the system obey symmetry between the two species and are identical for both the channels. The model displays a rich steady-state behavior, including symmetry breaking phenomenon. The phase diagram is analyzed theoretically within the mean-field approximation and substantiated with Monte Carlo simulations. Relevant mean-field calculations are also presented. We further compared the phase segregation with those observed in previous works, and it is examined that the structure of phase separation in proposed model is distinguished from earlier ones. Interestingly, for phases with broken symmetry, symmetry with respect to channels has been observed as the distinct particles behave differently while the similar type of particles exhibits the same conduct in the system. For symmetric phases, significant properties including currents and densities in the channels are identical for both types of particles. The effect of symmetry breaking occurrence on the Monte Carlo simulation results has also been examined based on particle density histograms. Finally, phase properties of the system having strong size dependency have been explored based on simulations findings.     

The size-Ramsey number of powers of paths

Given graphs and and a positive integer , say that is -Ramsey for , denoted , if every -coloring of the edges of contains a monochromatic copy of . The size-Ramsey number of a graph is defined to be . Answering a question of Conlon, we prove that, for every fixed , we have , where is the th power of the -vertex path (ie, the graph with vertex set and all edges such that the distance between and in is at most ). Our proof is probabilistic, but can also be made constructive.     

Weighted Hardy and singular operators in Morrey spaces

We study the weighted boundedness of the Cauchy singular integral operator SΓ in Morrey spaces Lp,λ(Γ) on curves satisfying the arc-chord condition, for a class of “radial type” almost monotonic weights. The non-weighted boundedness is shown to hold on an arbitrary Carleson curve. We show that the weighted boundedness is reduced to the boundedness of weighted Hardy operators in Morrey spaces Lp,λ(0,?), ?>0. We find conditions for weighted Hardy operators to be bounded in Morrey spaces. To cover the case of curves we also extend the boundedness of the Hardy-Littlewood maximal operator in Morrey spaces, known in the Euclidean setting, to the case of Carleson curves.     

Surface structures of SrTiO3 (001): a TiO2-rich reconstruction with a c(4 x 2) unit cell

We report the solution of the c(4 x 2) reconstruction of SrTiO(3) (001), obtained through a combination of high-resolution transmission electron microscopy, direct methods analysis, and density functional theory. The structure is characterized by a single overlayer of TiO(2) stoichiometry in which TiO(5) polyhedra are arranged into edge-shared structures, in contrast to the corner-shared TiO(6) polyhedra in bulk. This structural pattern is similar to that reported by us earlier for the (2 x 1) reconstruction of the same crystal face formed at higher temperature. We discuss probable mechanisms of surface stabilization as revealed by these two solutions which are likely to apply to other reconstructions of SrTiO(3) (001) and, possibly, other perovskites in general.     

On the Role of Interacting Particles and Limited Resources in the Regulation of Lattice Length Dynamics

Journal of Statistical Physics - Motivated by the significant effect of particle–particle interactions on the driven stochastic transport system, we examine how interacting particles control...     

The Retaining Pse5Ac7Ac Pseudaminyltransferase KpsS1 Defines a Previously Unreported glycosyltransferase family (GT118)

Cell surface sugar 5,7-diacetyl pseudaminic acid (Pse5Ac7Ac) is a bacterial analogue of the ubiquitous sialic acid, Neu5Ac, and contributes to the virulence of a number of multidrug resistant bacteria, including ESKAPE pathogens Pseudomonas aeruginosa, and Acinetobacter baumannii. Despite its discovery in the surface glycans of bacteria over thirty years ago, to date no glycosyltransferase enzymes (GTs) dedicated to the synthesis of a pseudaminic acid glycosidic linkage have been unequivocally characterised in vitro. Herein we demonstrate that A. baumannii KpsS1 is a dedicated pseudaminyltransferase enzyme (PseT) which constructs a Pse5Ac7Ac-α(2,6)-Glcp linkage, and proceeds with retention of anomeric configuration. We utilise this PseT activity in tandem with the biosynthetic enzymes required for CMP-Pse5Ac7Ac assembly, in a two-pot, seven enzyme synthesis of an α-linked Pse5Ac7Ac glycoside. Due to its unique activity and protein sequence, we also assign KpsS1 as the prototypical member of a previously unreported GT family (GT118).     

Reactions of Ru(CCPh)(L2)Cp* (L2=dppm, dppe) with tetracyanoethene: cycloaddition, formation of monodentate dppm and dppmO complexes and migration of CN to ruthenium

Reactions of FcCCH (a), HCCCCFc (b) and FcCCCCFc (c) with Ru₃(CO)₁₀(NCMe)₂ (all) and Ru₃(μ-dppm)(CO)₁₀ (b and c only) are described. Among the products, the complexes Ru₃(μ₃-RC₂R′)(μ-CO)(CO)₉ (R=H, R′=Fc 1, CCFc 2; R=R′=Fc 5), Ru₃(μ-H)(μ₃-C₂CCFc)(μ-dppm)(CO)₇ 3, Ru₃(μ₃-FcC₂CCFc)(μ-dppm)(μ-CO)(CO)₇ 6 and Ru₃{μ₃-C₄Fc₂(CCFc)₂}(μ-dppm)(μ-CO)(CO)₅ 7 were characterised, including single-crystal structure determinations for 1, 3, 5 and 7; that of 7 did not differ significantly from an earlier study of a mixed CH₂Cl₂–C₆H₆ solvate.