Topological entropy of continuous self-maps on closed surfaces

The objective of this work is to present sufficient conditions for having positive topological entropy for continuous self-maps defined on a closed surface by using the action of this map on the homological groups of the closed surface.     

Periodic Solutions of the Duffing Differential Equation Revisited via the Averaging Theory

We use three different results of the averaging theory of first order for studying the existence of new periodic solutions in the two Duffing differential equations $\ddot y+ a \sin y= b \sin t$ and $\ddot y+a y-c y^3=b\sin t$, where $a$, $b$ and $c$ are real parameters.     

A three-dimensional lanthanide-organic radical open-framework

The reaction of a 3-connecting PTMTC radical with Tb(III) ions forms a three-dimensional open-framework with the formula [Tb(PTMTC)(DMF)(3)] (1), which associates a lattice complex T topology with large channels, guest-induced reversible crystal to amorphous transformations and ferromagnetic metal-radical interactions.     

Efficient preparation of N-phenylsulfenyl ketimines from oximes or nitro compounds without racemization of alpha-stereocenters

As N-sulfenyl imines (e.g., RR'C=N-SAr) can be readily transformed to their N-sulfinyl imines (RR'C=N-SOAr), N-sulfonyl imines (RR'C=N-SO2Ar), and N-sulfonyl oxaziridines, the very mild procedure developed to convert ketoximes and secondary nitro derivatives to N-arenesulfenyl ketimines constitutes a new and efficient route to all these series of compounds. The configuration of the alpha-stereocenters is retained.     

Quadratic systems with a rational first integral of degree 2: A complete classification in the coefficient space $$\mathbb{R}^{12} $$

A quadratic polynomial differential system can be identified with a single point of through the coefficients. Using the algebraic invariant theory we classify all the quadratic polynomial differential systems of having a rational first integral of degree 2. We show that there are only 24 topologically different phase portraits in the Poincaré disc associated to this family of quadratic systems up to a reversal of the sense of their orbits, and we provide a unique representative of every class modulo an affine change of variables and a rescalling of the time variable. Moreover, each one of these 24 representatives is determined by a set of invariant conditions and each respective first integral is given in invariant form directly in The authors are partially supported by a MEC/FEDER grant MTM2005-06098-C02-01, and a CONACIT grant number 2005SGR-00550. Partially supported by CRDF-MRDA CERIM-1006-06     

Transition metal bisdithiolene complexes based on extended ligands with fused tetrathiafulvalene and thiophene moieties: new single-component molecular metals

The gold and nickel bisdithiolene complexes based on new highly extended ligands incorporating fused tetrathiafulvalene and thiophene moieties (alpha-tdt=thiophenetetrathiafulvalenedithiolate and dtdt=dihydro- thiophenetetrathiafulvalenedithiolate), were prepared and characterised by using cyclic voltammetry, single crystal X-ray diffraction, EPR, magnetic susceptibility and electrical transport measurements. These complexes, initially obtained under anaerobic conditions as diamagnetic gold monoanic [nBu(4)N][Au(alpha-tdt)(2)] (4), [nBu(4)N][Au(dtdt)(2)] (3) and nickel dianionic species [(nBu(4)N)(2)][Ni(alpha-tdt)(2)] (8), [(nBu(4)N)(2)][Ni(dtdt)(2)] (7), can be easily oxidised to the stable neutral state just by air or iodine exposure. The monoanionic complexes crystallise in at least two polymorphs, all of which have good cation and anion segregation in alternated layers, the anion layers making a dense 2D network of short SS contacts. All of the neutral complexes, obtained as microcrystalline or quasi amorphous fine powder, present relatively large magnetic susceptibilities that correspond to effective magnetic moments in the range 1-3 mu(B) indicative of high spin states and very high electrical conductivity that in case of the Ni compound can reach sigma(RT) approximately 250 S cm(-1) with a clear metallic behaviour. These compounds are new examples of the still rare single-component molecular metals.     

Electroactive thiazole derivatives capped with ferrocenyl units showing charge-transfer transition and selective ion-sensing properties: a combined experimental and theoretical study

The synthesis, optical and electrochemical properties, and X-ray characterization of two thiazole derivatives capped by ferrocenyl groups (5 and 7) and their model compounds with one ferrocenyl, either at 2 or 5 position of the mono- or bis-thiazolyl rings (3, 9, 11, and 14), are presented. Bisferrocenyl thiazole 5 forms the mixed-valence species 5*+ by partial oxidation which, interestingly, shows an intramolecular electron-transfer phenomenon. Moreover, the reported heteroaromatic compounds show selective ion-sensing properties. Thus, ferrocenylthiazoles linked across the 5 position of the heteroaromatic ring are selective chemosensors for Hg2+ and Pb2+ metal ions; 5-ferrocenylthiazole 3 operates through two channels, optical and redox, for Hg2+ and only optical for Pb2+, whereas 1,1'-bis(thiazolyl)ferrocene 14 is only an optical sensor for both metal ions. Moreover, complex 3 behaves as an electrochemically induced switchable chemosensor because of the low metal-ion affinity of the oxidized 3*+ species. On the other hand, ferrocenylthiazole 9, in which the heterocyclic ring and the ferrocene group are linked across the 2 position, is a selective redox sensor for Hg2+ metal ions, and it responds optically, as does bis(thiazolyl)ferrocene 11, to a narrow range of cations (Zn2+, Cd2+, Hg2+, Ni2+, and Pb2+). Finally, bis(ferrocenyl)thiazole 5 is a dual optical and redox sensor for Zn2+, Cd2+, Hg2+, Ni2+, and Pb2+, whereas bis(ferrocenyl) compound 7, bearing a bis(thiazole) unit as a bridge, is only a chromogenic sensor for Zn2+, Cd2+, Hg2+, Ni2+, and Pb2+. The experimental data and conclusions about both the electronic and ion-sensing properties are supported by DFT calculations which show, in addition, an unprecedented intramolecular electron-transfer reorganization after the first one-electron oxidation of compound 5.