The Chemistry of Stable Carbenes. Part 2. Benzoin-type condensations of formaldehyde catalyzed by stable carbenes

Stable carbenes derived from thiazole, 1H-imidazole, and 4H-1,2,4-triazole are efficient catalysts for benzointype condensations of formaldehyde. Catalysts derived from N-substituted thiazolium salts trimerize formaldehyde to dihydroxyacetone ( II ). Catalysts based on 1,4-disubstituted 4H-1,2,4-triazol-1-ium salts give glycolaldehyde ( I ) as the main product and no II , whereas N,N′-disubstituted 1H-imidazol-3-ium salts yield mixtures of both products. The isolation of several intermediates in the catalytic cycle provide a better insight into the reaction mechanism.     

Height estimates and topology at infinity of hypersurfaces immersed in a certain class of warped products

Height estimates are given for hypersurfaces immersed in a class of warped products of the type \(\mathbb {R}\times _{\rho } M^n\), under the assumption that some higher order mean curvatures are linearly related. When the fiber \(M^n\) is compact and such a hypersurface \(\Sigma ^n\) is noncompact, two-sided and properly immersed, we apply our height estimates in order to get information concerning the topology at infinity of \(\Sigma ^n\). Furthermore, when \(M^n\) is not necessarily compact, using a generalized version of the Omori–Yau maximum principle we establish new half-space theorems for these hypersurfaces.     

Stable hypersurfaces via the first eigenvalue of the anisotropic Laplacian operator

In this paper we provide a characterization for stable hypersurfaces with constant anisotropic mean curvature immersed in the Euclidean space \(\mathbb {R}^{n+1}\) through the analysis of the first eigenvalue of the anisotropic Laplacian operator.     

Integer programming models and linearizations for the traveling car renter problem

The traveling car renter problem (CaRS) is an extension of the classical traveling salesman problem (TSP) where different cars are available for use during the salesman’s tour. In this study we present three integer programming formulations for CaRS, of which two have quadratic objective functions and the other has quadratic constraints. The first model with a quadratic objective function is grounded on the TSP interpreted as a special case of the quadratic assignment problem in which the assignment variables refer to visitation orders. The second model with a quadratic objective function is based on the Gavish and Grave’s formulation for the TSP. The model with quadratic constraints is based on the Dantzig–Fulkerson–Johnson’s formulation for the TSP. The formulations are linearized and implemented in two solvers. An experiment with 50 instances is reported.     

Non-autonomous periodic systems with Allee effects

A new class of maps called unimodal Allee maps are introduced. Such maps arise in the study of population dynamics in which the population goes extinct if its size falls below a threshold value. A unimodal Allee map is thus a unimodal map with three fixed points, a zero fixed point, a small positive fixed point, called threshold point, and a bigger positive fixed point, called the carrying capacity. In this paper, the properties and stability of the three fixed points are studied in the setting of non-autonomous periodic dynamical systems or difference equations. Finally, we investigate the bifurcation of periodic systems/difference equations when the system consists of two unimodal Allee maps.     

Implementation of REDIM reduced chemistry to model an axisymmetric laminar diffusion methane–air flame

The goal of this work is to analyze the use of automatically reduced chemistry by the Reaction–Diffusion Manifold (REDIM) method in simulating axisymmetric laminar coflow diffusion flames. Detailed chemical kinetic models are usually computationally prohibitive for simulating complex reacting flows, and therefore reduced models are required. Automatic reduction model approaches usually exploit the natural multi-scale structure of combustion systems. The novel REDIM approach applies the concept of invariant manifolds to treat also the influence of the transport processes on the reduced model, which overcomes a fundamental problem of model reduction in neglecting the coupling of molecular transport with thermochemical processes. We have considered a previously well studied atmospheric pressure nitrogen-diluted methane–air flame as a test case to validate the methodology presented here. First, one-dimensional and two-dimensional REDIMs were computed and tabulated in lookup tables. Then, the full set of governing equations are projected on the REDIM and implemented in the object-oriented C++ Gascoigne code with a new add-on library to deal with the REDIM tables. The projected set of governing equations have been discretized by the Finite Element Method (FEM) and solved by a GMRES iteration preconditioned by a geometric multigrid method. Local grid refinement, adaptive mesh and parallelization are applied to ensure efficiency and precision. The numerical results obtained using the REDIM approach have shown very good agreement with detailed numerical simulations and experimental data.     

First total synthesis of (±)-floribundane B: An approach based on Johnson-Claisen rearrangement of a Morita-Baylis-Hillman adduct

The first total synthesis of (±)-floribundane B is reported. Johnson-Claisen rearrangement of a Morita-Baylis-Hillman adduct assembled all of the stereochemical features of this secoiridoid. The formal synthesis of (±)-oleocanthal and the synthesis of a chemical constituent of olive press juice is also reported.     

Structural and electronic effects in metallocene catalysts studied by x‐ray techniques

A series of metallocenes, namely, [Cp₂ZrCl₂], [(MeCp)₂ZrCl₂], [(nBuCp)₂ZrCl₂], [(iBuCp)₂ZrCl₂], [(tBuCp)₂ZrCl₂], [Et(Ind)₂ZrCl₂], [Et(IndH₄)₂ZrCl₂], and [MeSi₂(Ind)₂ZrCl₂)] were analyzed by extended x‐ray absorption fine structure (EXAFS) and x‐ray photoelectron spectroscopy (XPS). Complementary techniques, UV–vis spectroscopy and cyclic and differential pulse voltammetry, were employed to characterize the organometallic complexes. The catalysts were evaluated in ethylene polymerization, having methylaluminoxane (MAO) as the cocatalyst, and the resulting polymers were characterized by gel permeation chromatography. The structural and electronic effects caused by the coordination sphere around the metal center and their effects on the catalytic activity and polymer characteristics are discussed. Copyright © 2008 John Wiley & Sons, Ltd.