Enantio- and diastereocontrol in intermolecular cyclopropanation reaction of styrene catalyzed by dirhodium(II) complexes with bulky ortho-metalated aryl phosphines

Enantiomerically pure dirhodium(II) complexes with ortho-metalated p-substituted aryl phosphines have been shown to be enantio- and diastereoselective in the cyclopropanation of styrene by ethyl diazoacetate. Enantioselectivities up to 91% and diastereoselectivities up to 90% are observed for ethyl cis-2-phenylcyclopropanecarboxylate.     

Polynomial differential systems having a given Darbouxian first integral

The Darbouxian theory of integrability allows to determine when a polynomial differential system in has a first integral of the kind f₁^λ₁?f_p^λ_pexp(g/h) where f_i, g and h are polynomials in , and for i=1,…,p. The functions of this form are called Darbouxian functions. Here, we solve the inverse problem, i.e. we characterize the polynomial vector fields in having a given Darbouxian function as a first integral.On the other hand, using information about the degree of the invariant algebraic curves of a polynomial vector field, we improve the conditions for the existence of an integrating factor in the Darbouxian theory of integrability.     

On the parameter dependence of the real cubic surfaces in arnold’s form

We consider the topological classification of cubic surfaces which are obtained as intersection of the sphere with the algebraic variety defined by the zeroes of a homogeneous cubic polynomial in Arnold’s normal form. This classification is based on the parameters appearing in this normal form, obtaining a correspondence between the parameters of the surface and its topological type. General classifications of cubic surfaces are made in the projective space ℙ³(ℝ), but our method, based on a very simple combinatorial procedure is easier to implement in . We split the cubic surfaces parameter space into ten equivalence classes.     

Use of combinatorial chemistry to develop photocurable thermoplastic polyurethane elastomers (TPUs)

Combinatorial chemistry was used to develop photocurable thermoplastic polyurethane elastomers through the incorporation of photoreactive diacetylene diols as chain extenders. The methodology applied allowed, in 36 experiments, the choice of the best compromise between mechanical properties and lack of colour. The combinations chosen were scaled up and their properties were evaluated in terms of mechanical properties. The combinatorial approach reduced the estimated time tenfold in developing such type of materials.     

Supersymmetric three-body decays of the top quark in the MSSM

We survey all possible supersymmetric three-body decays of the top quark in the framework of the MSSM and present detailed numerical analyses of the most relevant cases. Although the two-body channels are generally dominant, it is not inconceivable that some or all of our most favourite two-body SUSY candidates could be suppressed. In this event there is still the possibility that some of the available three-body SUSY modes might exhibit a substantial branching fraction and/or carry exotic signatures that would facilitate their identification. Furthermore, in view of the projected inclusive measurement of the top-quark width Г _t in future colliders, one should have at one’s disposal the full second order correction (electroweak and strong) to the value of that parameter in the MSSM. Our analysis confirms that some supersymmetric three-body decays could be relevant and thus contribute to Г _t at a level comparable to the largest one loop supersymmetric effects on two-body modes recently computed in the literature.     

Periodic points of holomorphic maps via Lefschetz numbers

In this paper we study the set of periods of holomorphic maps on compact manifolds, using the periodic Lefschetz numbers introduced by Dold and Llibre, which can be computed from the homology class of the map. We show that these numbers contain information about the existence of periodic points of a given period; and, if we assume the map to be transversal, then they give us the exact number of such periodic orbits. We apply this result to the complex projective space of dimension and to some special type of Hopf surfaces, partially characterizing their set of periods. In the first case we also show that any holomorphic map of of degree greater than one has infinitely many distinct periodic orbits, hence generalizing a theorem of Fornaess and Sibony. We then characterize the set of periods of a holomorphic map on the Riemann sphere, hence giving an alternative proof of Baker's theorem.     

Exploring the interaction of mercury(II) by N(2)S(2) and NS(3) anthracene-containing macrocyclic ligands: photophysical, analytical, and structural studies

The complexation properties toward Hg(II) of six macrocyclic ligands, 3,11-dithia-7,17-diazabicyclo[11.3.1]heptadeca-1(17),13,15-triene (L1), 7-(9-anthracenylmethyl)-3,11-dithia-7,17-diazabicyclo[11.3.1]heptadeca-1(17),13,15-triene (L2), 7-(10-methyl-9-anthracenylmethyl)-3,11-dithia-7,17-diazabicyclo[11.3.1]heptadeca-1(17),13,15-triene (L3), 7,7'-[9,10-anthracenediylbis(methylene)]bis-3,11-dithia-7,17-diazabicyclo[11.3.1]heptadeca-1(17),13,15-triene (L4), 1,4,7-trithia-11-azacyclotetradecane (L5), and 11,-(anthracen-9-ylmethyl)-1,4,7-trithia-11-azacyclotetradecane (L6), were studied. The stoichiometries of the formed species were determined from absorption and fluorescence titrations. In these anthracene-containing macrocycles, a fluorescent quenching of the emission was found upon Hg(II) addition. The X-ray crystal structure of [HgCl2(L2)] x 1/2CH2Cl2 was determined. The asymmetric unit contains two independent [HgCl2(L2)] molecules and one dichloromethane molecule. Each Hg(II) ion is coordinated by the pyridine nitrogen, the two sulfur atoms of one L2 molecule, and two chloride ions. Analytical studies using solvent extraction separation of Hg(II) from aqueous solutions were performed to determine the Hg(II) extraction capability of ligands L1, L2, and L5.