On the mechanism of the copper-catalyzed enantioselective 1,4-addition of grignard reagents to alpha,beta-unsaturated carbonyl compounds

The mechanism of the enantioselective 1,4-addition of Grignard reagents to alpha,beta-unsaturated carbonyl compounds promoted by copper complexes of chiral ferrocenyl diphosphines is explored through kinetic, spectroscopic, and electrochemical analysis. On the basis of these studies, a structure of the active catalyst is proposed. The roles of the solvent, copper halide, and the Grignard reagent have been examined. Kinetic studies support a reductive elimination as the rate-limiting step in which the chiral catalyst, the substrate, and the Grignard reagent are involved. The thermodynamic activation parameters were determined from the temperature dependence of the reaction rate. The putative active species and the catalytic cycle of the reaction are discussed.     

Vapor-liquid equilibrium of hexadecapolar fluids from a perturbation-based equation of state

In this work a numerically tractable expression for the interaction potential between two point hexadecapoles with octahedral symmetry and a molecular-based equation of state derived by perturbation theory for hexadecapolar fluids are presented. The polar system is modeled by square-well particles with a point hexadecapole with octahedral symmetry at their centers. This equation of state is analytical in the state variables and in the potential parameters and allows us to study the effects of the hexadecapolar moment strength on the thermodynamic properties and liquid-vapor phase diagram. The equation presented here is applied to the thermodynamics of sulfur hexafluoride and gives very good predictions for the saturation pressures and the vapor-liquid phase diagram.     

Unprecedented reactivity pattern of chromium fischer carbene complexes. Direct application to one-pot synthesis of 4-aryl-3,4-dihydrocoumarins on a multigram scale

[reaction: see text] Reaction of alkenyl carbene chromium(0) complexes and ketene acetals triggers the formation of 4-aryl-3,4-dihydrocoumarins. The reaction can be carried out as a simple one-pot protocol in air atmosphere. The huge interest of dihydrocoumarins has prompted us to optimize a multigram-scale process.     

Completion problems for real matrices, II

Thirty years ago, G. N. de Oliveira has proposed the following completion problems: Describe the possible characteristic polynomials of , where C_1,1 and C_2,2 are square submatrices, when some of the blocks C_i,j are fixed and the others vary. Several of these problems remain unsolved. This paper gives the solution, over the field of real numbers, of Oliveira’s problem where the blocks C_1,1,C_2,2 are fixed and the others vary.     

First order spectral perturbation theory of square singular matrix polynomials

We develop first order eigenvalue expansions of one-parametric perturbations of square singular matrix polynomials. Although the eigenvalues of a singular matrix polynomial P(λ) are not continuous functions of the entries of the coefficients of the polynomial, we show that for most perturbations they are indeed continuous. Given an eigenvalue λ₀ of P(λ) we prove that, for generic perturbations M(λ) of degree at most the degree of P(λ), the eigenvalues of P(λ)+?M(λ) admit covergent series expansions near λ₀ and we describe the first order term of these expansions in terms of M(λ₀) and certain particular bases of the left and right null spaces of P(λ₀). In the important case of λ₀ being a semisimple eigenvalue of P(λ) any bases of the left and right null spaces of P(λ₀) can be used, and the first order term of the eigenvalue expansions takes a simple form. In this situation we also obtain the limit vector of the associated eigenvector expansions.     

Analysis of multiple scattering iterations for high-frequency scattering problems. II: The three-dimensional scalar case

In this paper, we continue our analysis of the treatment of multiple scattering effects within a recently proposed methodology, based on integral-equations, for the numerical solution of scattering problems at high frequencies. In more detail, here we extend the two-dimensional results in part I of this work to fully three-dimensional geometries. As in the former case, our concern here is the determination of the rate of convergence of the multiple-scattering iterations for a collection of three-dimensional convex obstacles that are inherent in the aforementioned high-frequency schemes. To this end, we follow a similar strategy to that we devised in part I: first, we recast the (iterated, Neumann) multiple-scattering series in the form of a sum of periodic orbits (of increasing period) corresponding to multiple reflections that periodically bounce off a series of scattering sub-structures; then, we proceed to derive a high-frequency recurrence that relates the normal derivatives of the fields induced on these structures as the waves reflect periodically; and, finally, we analyze this recurrence to provide an explicit rate of convergence associated with each orbit. While the procedure is analogous to its two-dimensional counterpart, the actual analysis is significantly more involved and, perhaps more interestingly, it uncovers new phenomena that cannot be distinguished in two-dimensional configurations (e.g. the further dependence of the convergence rate on the relative orientation of interacting structures). As in the two-dimensional case, and beyond their intrinsic interest, we also explain here how the results of our analysis can be used to accelerate the convergence of the multiple-scattering series and, thus, to provide significant savings in computational times.     

Eigenfunction Expansions and Transformation Theory

Generalized eigenfunctions may be regarded as vectors of a basis in a particular direct integral of Hilbert spaces or as elements of the antidual space Φ^× in a convenient Gelfand triplet Φ⊆ℋ⊆Φ^×. This work presents a fit treatment for computational purposes of transformations formulas relating different generalized bases of eigenfunctions in both frameworks direct integrals and Gelfand triplets. Transformation formulas look like usual in Physics literature, as limits of integral functionals but with well defined kernels. Several approaches are feasible. Vitali approach is used.     

Uniqueness of unconditional basis in quasi-Banach spaces which are not sufficiently Euclidean

Strongly absolute bases are, roughly speaking, purely nonlocally convex bases in quasi-Banach spaces. When, in addition, they are unconditional then the discrete lattice structure they induce in the space is lattice anti-Euclidean. In this brief note we characterize the complemented unconditional basic sequences in those quasi-Banach spaces with strongly absolute unconditional basis, and use this result to derive the uniqueness of unconditional basis in many classical quasi-Banach spaces.     

Fujita exponents for evolution problems with nonlocal diffusion

We prove the existence of a critical exponent of Fujita type for the nonlocal diffusion problem

The dual geometry of Boolean semirings

It is well known that the variety of Boolean semirings, which is generated by the three element semiring ${\mathbb{S}}$ , is dual to the category of partially Stone spaces. We place this duality in the context of natural dualities. We begin by introducing a topological structure S? and obtain an optimal natural duality between the quasi-variety ISP( ${\mathbb{S}}$ ) and the category IS _c P+(S?). Then we construct an optimal and very small structure S? _os that yields a strong duality. The geometry of some of the partially Stone spaces that take part in these dualities is presented, and we call them “hairy cubes”, as they are n-dimensional cubes with unique incomparable covers for each element of the cube. We also obtain a polynomial representation for the elements of the hairy cube.