Reduction of the n-dimensional static vacuum Einstein equation and generalized Schwarzschild solutions

We consider the static vacuum Einstein spacetime when the spatial factor is conformal to a n-dimensional pseudo-Euclidean space. The most general ansatz that reduces the resulting system of partial differential equations to a system of ordinary differential equations is completely described. We obtain the entire set of solutions of the reduced system, where the classical Schwarzschild solution arises as a particular solution. In addition, we show that the Riemannian spatial factors associated to these solutions are foliated by parallel hypersurfaces of constant mean curvature.     

Transfer behaviors of 90Sr and 137Cs from soil to grass to cow milk under natural conditions in Central Italy and their exposure risk

Journal of Radioanalytical and Nuclear Chemistry - Based on the newly-developed techniques, the transfer behaviors of 90Sr and 137Cs under natural conditions were studied. The concentrations of...     

A Computer Simulation Insight into the Formation of Apocarotenoids: Study of the Carotenoid Oxygenases BCO1 and BCO2 and Their Interaction with Putative Substrates

Carotenoids are isoprenoid pigments, and sources of vitamin A in humans. The first metabolic pathway for their synthesis is mediated by the enzymes β,β-carotene-15,15′-dioxygenase (BCO1) and β,β-carotene-9′,10′-dioxygenase (BCO2), which cleave carotenoids into smaller compounds, called apocarotenoids. The objective of this study is to gain insight into the interaction of BCO1 and BCO2 with carotenoids, adding structural diversity and importance in the agro-food and/or health sectors. Homology modeling of BCO1 and BCO2, and the molecular dynamics of complexes with all carotenoids were performed. Interaction energy and structures were analyzed. For both enzymes, the general structure is conserved with a seven beta-sheet structure, and the β-carotene is positioned at an optimal distance from the catalytic center. Fe²⁺ forms in an octahedral coordination sphere with four perfectly conserved histidine residues. BCO1 finds stability in a structure in which the β-carotene is positioned ready for enzymatic catalysis at the 15–15′ bond, and BCO2 in positioning the bond to be cleaved (C9–C10) close to the active site. In BCO1 the carotenoids interact with only seven residues with aromatic rings, while the interaction of BCO2 is much more varied in terms of the type of interaction, with more residues of different chemical natures.     

A new synthesis of some indolecarboxylic acids

1-Substituted isatins are transformed into indole derivatives by means of ethyl chloroacetate. In fact, under the conditions of the Darzens reaction they give two glycidic ester isomers 4 and 5 which, by hydrolysis in alkaline medium, undergo a transposition to indole-2,3-dicarboxylic acids 2 together with minor amounts of indole-3-carboxylic acids 3 . From isatin itself, 2,3-dicarboxyindole-1-acetic acid ( 6 ) was obtained.     

Microbial hydroxylation of sclareol by Rhizopus stolonifer

Incubation of sclareol with Rhizopus stolonifer affords in high yield a mixture of triols with 18-hydroxy-sclareol as the main component.     

Synthesis, characterization and semi-empirical calculations for the thiocyanate linkage isomers of an (alpha-iminooxime)cobalt(III) macrocyclic complex

Herein we report the synthetic route and detailed characterization of the macrocyclic complex [Co(dohpn)(SCN)2] and its linkage isomer (dohpn=2,3,9,10-tetramethyl-1,4,8,11-tetraazaundecane-1,3,8,10-tetraen-11-ol-1-olate and py=pyridine) based on analytical, spectroscopic and electrochemical methods. Structural, vibrational and electronic features are discussed and a coherent assignment is proposed on the basis of semi-empirical theoretical calculations.     

Tightness games with bounded finite selections

For a topological space X and a point x ∈ X, consider the following game—related to the property of X being countably tight at x. In each inning n ∈ ω, the first player chooses a set A _n that clusters at x, and then the second player picks a point a _n ∈ A _n ; the second player is the winner if and only if \(x \in \overline {\left\{ {{a_n}:n \in \omega } \right\}} \).In this work, we study variations of this game in which the second player is allowed to choose finitely many points per inning rather than one, but in which the number of points they are allowed to choose in each inning has been fixed in advance. Surprisingly, if the number of points allowed per inning is the same throughout the play, then all of the games obtained in this fashion are distinct. We also show that a new game is obtained if the number of points the second player is allowed to pick increases at each inning.     

C k -solvability near the characteristic set for a class of planar complex vector fields of infinite type

This paper deals with semi-global C ^k -solvability of complex vector fields of the form ${\mathsf{L}=\partial/\partial t+x^r(a(x)+ib(x))\partial/\partial x,}This paper deals with semi-global C ^k -solvability of complex vector fields of the form L=?/?t+x^r(a(x)+ib(x))?/?x,{\mathsf{L}=\partial/\partial t+x^r(a(x)+ib(x))\partial/\partial x,}, r ≥ 1, defined on W_e=(-e,e)×S¹{\Omega_\epsilon=(-\epsilon,\epsilon)\times S^1}, ${\epsilon >0 }${\epsilon >0 }, where a and b are C ^∞ real-valued functions in (-e,e){(-\epsilon,\epsilon)}. It is shown that the interplay between the order of vanishing of the functions a and b at x = 0 influences the C ^k -solvability at Σ = {0} × S ¹. When r = 1, it is permitted that the functions a and b of L{\mathsf L}depend on the x and t variables, that is, L=?/?t+x(a(x,t)+ib(x,t))?/?x,{\mathsf{L}=\partial/\partial t+x(a(x,t)+ib(x,t))\partial/\partial x,}where (x, t) ? W_e{(x, t)\in\Omega_\epsilon}.     

On the Lattice Structure of Probability Spaces in Quantum Mechanics

Let $\mathcal{C}$ be the set of all possible quantum states. We study the convex subsets of $\mathcal{C}$ with attention focused on the lattice theoretical structure of these convex subsets and, as a result, find a framework capable of unifying several aspects of quantum mechanics, including entanglement and Jaynes’ Max-Ent principle. We also encounter links with entanglement witnesses, which leads to a new separability criteria expressed in lattice language. We also provide an extension of a separability criteria based on convex polytopes to the infinite dimensional case and show that it reveals interesting facets concerning the geometrical structure of the convex subsets. It is seen that the above mentioned framework is also capable of generalization to any statistical theory via the so-called convex operational models’ approach. In particular, we show how to extend the geometrical structure underlying entanglement to any statistical model, an extension which may be useful for studying correlations in different generalizations of quantum mechanics.