Synthesis of γ-lactones from easily and accessible reactants catalyzed by Cu–MnOx catalysts

The mechanism of the oxidative [3+2] cycloaddition of alkenes with anhydrides using oxygen as an oxidant to synthesize γ-lactones has been studied using a heterogeneous dual copper-manganese–based catalyst. The cyclization takes place through two coexisting reaction mechanisms, the involvement of different reaction intermediates and a clear synergistic effect between copper and manganese. In fact it appears that CuO clusters dispersed on the surface of a manganese-based oxide increase the redox capability of manganese ions and leads to an increase in the release of oxygen from the surface.     

Analysis of Hückel's [4n + 2] rule through electronic delocalization measures

In the present work, we analyze the pi-electronic delocalization in a series of annulenes and their dications and dianions by using electron delocalization indices calculated in the framework of the quantum theory of atoms in molecules. The aim of our study is to discuss the Hückel's 4n + 2 rule from the viewpoint of pi-electronic delocalization. Our results show that there is an important increase of electronic delocalization (of about 1 e) when going from antiaromatic 4n pi systems to aromatic (4n + 2)pi systems. Less clear is the change in pi-electronic delocalization when we move from a (4n + 2)pi-aromatic to a 4n pi-antiaromatic species by adding or removing a pair of electrons.     

Matching Points with Squares

Given a class of geometric objects and a point set P, a -matching of P is a set of elements of such that each C _i contains exactly two elements of P and each element of P lies in at most one C _i . If all of the elements of P belong to some C _i , M is called a perfect matching. If, in addition, all of the elements of M are pairwise disjoint, we say that this matching M is strong. In this paper we study the existence and characteristics of -matchings for point sets in the plane when is the set of isothetic squares in the plane. A consequence of our results is a proof that the Delaunay triangulations for the L _∞ metric and the L ₁ metric always admit a Hamiltonian path.     

A Polynomial Bound for Untangling Geometric Planar Graphs

To untangle a geometric graph means to move some of the vertices so that the resulting geometric graph has no crossings. Pach and Tardos (Discrete Comput. Geom. 28(4): 585–592, 2002) asked if every n-vertex geometric planar graph can be untangled while keeping at least n ^ε vertices fixed. We answer this question in the affirmative with ε=1/4. The previous best known bound was \(\Omega(\sqrt{\log n/\log\log n})\). We also consider untangling geometric trees. It is known that every n-vertex geometric tree can be untangled while keeping at least \(\Omega(\sqrt{n})\) vertices fixed, while the best upper bound was \(\mathcal{O}((n\log n)^{2/3})\). We answer a question of Spillner and Wolff (http://arxiv.org/abs/0709.0170) by closing this gap for untangling trees. In particular, we show that for infinitely many values of n, there is an n-vertex geometric tree that cannot be untangled while keeping more than \(3(\sqrt{n}-1)\) vertices fixed.     

Braces and the Yang–Baxter Equation

Several aspects of relations between braces and non-degenerate involutive set-theoretic solutions of the Yang–Baxter equation are discussed and many consequences are derived. In particular, for each positive integer n a finite square-free multipermutation solution of the Yang–Baxter equation with multipermutation level n and an abelian involutive Yang–Baxter group is constructed. This answers a problem of Gateva-Ivanova and Cameron. It is proved that finite non-degenerate involutive set-theoretic solutions of the Yang–Baxter equation whose associated involutive Yang–Baxter group is abelian are multipermutation solutions. Earlier the authors proved this with the additional square-free hypothesis on the solutions. It is also proved that finite square-free non-degenerate involutive set-theoretic solutions associated to a left brace are multipermutation solutions.     

Efficiency of Site-Specific Clicked Laccase–Carbon Nanotubes Biocathodes towards O2 Reduction

A maximization of a direct electron transfer (DET) between redox enzymes and electrodes can be obtained through the oriented immobilization of enzymes onto an electroactive surface. Here, a strategy for obtaining carbon nanotube (CNTs) based electrodes covalently modified with perfectly control-oriented fungal laccases is presented. Modelizations of the laccase-CNT interaction and of electron conduction pathways serve as a guide in choosing grafting positions. Homogeneous populations of alkyne-modified laccases are obtained through the reductive amination of a unique surface-accessible lysine residue selectively engineered near either one or the other of the two copper centers in enzyme variants. Immobilization of the site-specific alkynated enzymes is achieved by copper-catalyzed click reaction on azido-modified CNTs. A highly efficient reduction of O₂ at low overpotential and catalytic current densities over −3 mA cm⁻² are obtained by minimizing the distance from the electrode surface to the trinuclear cluster.     

Synthetic hydromagnesite as flame retardant. Evaluation of the flame behaviour in a polyethylene matrix

Synthetic hydromagnesite obtained from an industrial by-product was evaluated as a non-halogenated flame retardant. It was used in combination with aluminium hydroxide (ATH) and compared with commercial flame retardants like magnesium hydroxide (MH) and natural hydromagnesite-huntite (U) in a polyolefin system of low-density polyethylene/poly(ethylene-co-vinyl acetate) (LDPE/EVA).The thermal stability and flame behaviour of the halogen free flame retarded composites were studied by thermogravimetric and differential thermal analysis (TG-DTA), limiting oxygen index (LOI), epiradiateur and cone calorimeter. It has been shown that synthetic hydromagnesite could be an alternative solution to the use of MH in non-halogenated flame retardant systems in EVA.