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.     

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.     

Phase Transition in Ferromagnetic Ising Models with Non-uniform External Magnetic Fields

In this article we study the phase transition phenomenon for the Ising model under the action of a non-uniform external magnetic field. We show that the Ising model on the hypercubic lattice with a summable magnetic field has a first-order phase transition and, for any positive (resp. negative) and bounded magnetic field, the model does not present the phase transition phenomenon whenever lim?inf?h _i >0, where \(\mathbf{h}=(h_{i})_{i\in \mathbb{Z}^{d}}\) is the external magnetic field.     

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.     

Soil δ15N patterns in old-growth forests of southern Chile as integrator for N-cycling

Old-growth forests of southern Chile represent an important reserve of temperate (rain) forests in the world. Wetter and colder forest ecosystems appear to be more efficient in conserving and recycling N such that mostly non-plant available N species are lost, which could be indicated by more depleted δ¹⁵N values of the soil and plants. Hydrological N loss from the old-growth forests in southern Chile occurs mainly via dissolved organic nitrogen and not via dissolved inorganic N. Forest disturbances (e.g. fire, clear-cutting or enhanced N deposition) cause (abrupt) changes in ecosystem N-cycling processes. In this study, we hypothesized that δ¹⁵N signatures of soil profiles under old-growth forests could be used as an integrator for ecosystem N-cycling, and changes of these δ¹⁵N profiles could be valuable to assess ecosystem resilience towards disturbances. Six old-growth forests were selected in the phytogeographical region of the Valdivian rain forest in southern Chile. One of the sites has been partly burned in February 2002. First, we observed that ecosystems with higher mean annual precipitation and lower mean annual temperature were relatively more depleted in ¹⁵N. Secondly, we found that a forest fire caused a 100-fold increase of the nitrate export and induced an enrichment of the soil δ¹⁵N signal in the upper 20 cm.     

Basic Module Theory for General Rings

We show how to construct a theory of modules over general rings (i.e., rings which do not necessarily have an identity element) in such a form that most of the known results of the usual theory of modules over unital rings are obtained by particularizing the results of the general theory.     

On the Iterated Biclique Operator

A biclique of a graph G is a maximal induced complete bipartite subgraph of G. The biclique graph of G, denoted by , is the intersection graph of the bicliques of G. We say that a graph G diverges (or converges or is periodic) under an operator F whenever ( for some m, or for some k and , respectively). Given a graph G, the iterated biclique graph of G, denoted by , is the graph obtained by applying the biclique operator k successive times to G. In this article, we study the iterated biclique graph of G. In particular, we classify the different behaviors of when the number of iterations k grows to infinity. That is, we prove that a graph either diverges or converges under the biclique operator. We give a forbidden structure characterization of convergent graphs, which yield a polynomial time algorithm to decide if a given graph diverges or converges. This is in sharp contrast with the situsation for the better known clique operator, where it is not even known if the corresponding problem is decidable. © 2012 Wiley Periodicals, Inc. J. Graph Theory 73: 181–190, 2013     

Kaurenoic acid extracted from Sphagneticola trilobata reduces acetaminophen-induced hepatotoxicity through inhibition of oxidative stress and pro-inflammatory cytokine production in mice

Acetaminophen (paracetamol) is a widely used analgesic and antipyretic drug that is safe at therapeutic doses. However, acetaminophen overdose can be fatal. Currently, the only treatment available is the N-acetyl cysteine. The diterpene kaurenoic acid (ent-kaur-16-en-19-oic acid, KA) is the major constituent of Sphagneticola trilobata (L.) Pruski. KA presents anti-inflammatory, anti-nociceptive and antioxidant properties. In this study, we evaluated the efficacy of KA in a model of acetaminophen-induced hepatotoxicity. KA increased, in a dose-dependent manner, the survival rate after acetaminophen overdose. KA reduced acetaminophen-induced hepatic necrosis and ALT and AST levels. KA decreased acetaminophen-induced neutrophil and macrophage recruitment, oxidative stress and the production of IL-33, TNF-α and IL-1β, alongside with normalisation of IL-10 levels in the liver. Therefore, KA showed preclinical efficacy in acetaminophen-induced hepatotoxicity and lethality.