The full basis theorem does not imply analytic wellordering

A finite support product of ${\omega }_1$ clones of Jensen's minimal ${\Pi }_2^1$ singleton forcing is used to define a model in which any non-empty analytically definable set of reals contains an analytically definable real (the full basis theorem), but there is no analytically definable wellordering of the reals.     

Reactions of 2,4-hexadiyne-1,6-diol with [H2Os3(CO)9(PR3)] clusters. Cyclization of the diyne and reversible exchange of the phosphine ligands between different positions of the "Os3C3" framework

Reactions between unsaturated [H(2)Os(3)(CO)(9)(PR(3))] clusters (PR(3)= PPh(3), P(4-CF(3)-C(6)H(4))(3), PEt(3)) and 2,4-hexadiyne-1,6-diol have been studied. It was found that the diyne ligand easily reacts with all these complexes to give [HOs(3)(CO)8(PR3)-[mu3, eta1:eta3:eta1)-(CH(3)-C-C=CH-CH=C-O)]] complexes (V, VI and VII, respectively) containing the "Os3C3" pentagonal pyramid cluster framework. This structural pattern is formed through the diyne cyclization, dissociation of a CO ligand and eventual coordination of the cyclized organic moiety to the osmium triangle in the [mu3, eta1:eta3:eta1) manner. In the case of the PEt(3) substituted cluster the second hydride transfer onto the organic fragment occurs to afford the nonhydride [Os(3)(CO)(8)(PR3)[mu3), eta1:eta2:eta1)-(CH(3)-CH-C=CH-CH=C-O)]] cluster, VIII, containing distorted pentagonal pyramid framework with a broken Os-C bond. Heating V, VI of VII and in hexane solutions results in formation of the regioisomers (Va, VIa and VIIa) with the phosphine ligand located at adjacent osmium atoms across the Os-Os bond bridged by the coordinated organic fragment. The most probable mechanism of the isomerization includes reversible phosphine migration between these metal centres. Solid-state structure of V, Va, VI, VIIa and VIII have been established by single crystal X-ray diffraction. A general mechanistic scheme for the diyne ligand cyclization and cluster framework transformations is suggested and discussed.     

Unbiased Estimation for a Multivariate Exponential whose Components have a Common Shift

It is shown that for independent and identically distributed random vectors, for which the components are independent and exponentially distributed with a common shift, we can construct unbiased estimators of their density, derived from the Uniform Minimum Variance Unbiased Estimator (UMVUE) of their distribution function. As direct applications of the UMVUEs of the density functions we present a Chi-square goodness of fit test of the model, and give two tables of the UMVUEs of some commonly used functions of the unknown parameters of the multivariate exponential model considered in this paper.     

Results of a higgs boson searches in the ATLAS and CMS experiments at the large hadron collider at energies 7 and 8 TeV

Recent achievements of the ATLAS and CMS experiments at the Large Hadron Collider searching for a Higgs boson are summarized. A new particle with the mass of 125 GeV and properties expected for the Standard Model Higgs boson was discovered three years ago in these experiments in proton-proton collisions when analyzing part of the data taken at the centre-of-mass energies 7 TeV and 8 TeV in 2011 and 2012 year exposures. Today all the data are processed and fully analyzed. Experimental results of studies of individual Higgs boson decay channels as well as their combination to extract such properties as mass, signal strength, coupling constants, spin and parity are reviewed. All experimental results are found to be compatible with the Standard Model predictions.     

On effective σ‐boundedness and σ‐compactness

We prove several dichotomy theorems which extend some known results on σ‐bounded and σ‐compact pointsets. In particular we show that, given a finite number of $\Delta ^{1}_{1}$ equivalence relations $\mathrel {\mathsf {F}}_1,\dots ,\mathrel {\mathsf {F}}_n$, any $\Sigma ^{1}_{1}$ set A of the Baire space either is covered by compact $\Delta ^{1}_{1}$ sets and lightface $\Delta ^{1}_{1}$ equivalence classes of the relations $\mathrel {\mathsf {F}}_i$, or A contains a superperfect subset which is pairwise $\mathrel {\mathsf {F}}_i$‐inequivalent for all i = 1, …, n. Further generalizations to $\Sigma ^{1}_{2}$ sets A are obtained.     

Theoretical considerations and computational analysis of the complexity in polyketide synthesis pathways

The emergence of antimicrobial resistance has led to an increase in research directed toward the engineering of novel polyketides. To date, less than 10 000 polyketide structures have been discovered experimentally; however, the theoretical analysis of polyketide biosynthesis performed suggests that over a billion possible structures can be synthesized. Polyketide synthesis, which involves the formation of a linear chain and its subsequent cyclization, is catalyzed by an enzyme complex called polyketide synthase (PKS). There are a number of variables in the linear chain synthesis controlled by the PKS: the number, identity, stereochemistry and sequence of the monomer units used in the elongation steps, and the degree of reduction that occurs after each of the condensation reactions. The theoretical analysis performed demonstrates that changes in these variables lead to the formation of different polyketide linear chains and, consequently, a high diversity of polyketide structures. The complexity in the number of possible structures led to the implementation of this system in BNICE, a computational framework that generates all possible biochemical pathways using a given set of enzyme reaction rules. This formulation allowed the analysis of the evolution of diversity in the synthesis mechanism and the construction of the pathway architecture of polyketide biosynthesis. It is expected that, after future implementation of the cyclization reactions, this framework can be used to identify all possible polyketides and their corresponding synthesis pathways. Consequently, this formulation would prove useful in guiding experimental approaches to engineer novel polyketides, a number of which will likely have medicinal properties.     

Reasonable non-Radon-Nikodym ideals

Following a research line suggested by Ilijas Farah, we prove that for any abelian Polish σ-compact group H there exists an Fσ Radon-Nikodym ideal, that is, an ideal Z⊆P(N) together with a Borel Z-approximate homomorphism which is not Z-approximable by a continuous true homomorphism .     

Homotopy Gerstenhaber Structures and Vertex Algebras

We provide a simple construction of a G _∞-algebra structure on an important class of vertex algebras V, which lifts the Gerstenhaber algebra structure on BRST cohomology of V introduced by Lian and Zuckerman. We outline two applications to algebraic topology: the construction of a sheaf of G _∞ algebras on a Calabi–Yau manifold M, extending the operations of multiplication and bracket of functions and vector fields on M, and of a Lie_∞ structure related to the bracket of Courant (Trans Amer Math Soc 319:631–661, 1990).