Mixed variational formulations in locally convex spaces

The main purpose of this paper is to extend to the setting of locally convex spaces the study of the mixed variational formulation of some elliptic boundary value problems, the so-called Babuška–Brezzi theory. This study consists of characterizing the existence of a solution and giving conditions that guarantee the stability of the corresponding Galerkin method.     

α-Arylation and Ring Expansion of Annulated Cyclobutanones: Stereoselective Synthesis of Functionalized Tetralones

α-Arylcyclobutanones display unique reactivity that makes them valuable synthetic intermediates and target molecules. We describe the preparation of α-aryl- and α-heteroarylcyclobutanones through a direct α-arylation reaction. Problematic fragmentations are avoided by the use of LiO^tBu, which promotes a rapid but reversible self-aldol reaction that slowly releases the enolate required for α-arylation. We also demonstrate the ring expansion of α-arylcyclobutanones, a process that is highlighted in the stereoselective synthesis of 1-methoxy coniothyrinone D.     

Solving stochastic convex feasibility problems in hilbert spaces

In a stochastic convex feasibility problem connected with a complete probability space (Ω,A,μ) and a family of closed convex sets (C_ω)_ωεΩ in a real Hilbert space H, one wants to find a point that belongs to C_ω for μ almost all ω ε Ω. We present a projection based method where the variable relaxation parameter is defined by a geometrical condition, leading to an iteration sequence that is always weakly convergent to a μ almost common point. We then give a general condition assuring norm convergence of this equation to that μ almost common point     

Variational Analysis of Toda Systems

The author surveys some recent progress on the Toda system on a two-dimensional surface Σ,arising in models from self-dual non-abelian Chern-Simons vortices,as well as in differential geometry.In particular,its variational structure is analysed,and the role of the topological join of the barycentric sets of Σ is shown.     

Birthrates and delay times of Type Ia supernovae

Type Ia supernovae (SNe Ia) play an important role in diverse areas of astrophysics, from the chemical evolution of galaxies to observational cosmology. However, the nature of the progenitors of SNe Ia is still unclear. In this paper, according to a detailed binary population synthesis study, we obtained SN Ia birthrates and delay times from different progenitor models, and compared them with observations. We find that the Galactic SN Ia birthrate from the double-degenerate (DD) model is close to those infe...     

One‐pot carboxylative cyclization of propargylic alcohols and CO2 catalysed by N‐heterocyclic carbene/Ag systems

A series of N ‐heterocyclic carbene (NHC)/Ag systems were developed for the carboxylative assembly of propargylic alcohols and carbon dioxide (CO₂). With the catalysis of these catalytic systems, a variety of target α‐alkylidene cyclic carbonates could be obtained smoothly under atmospheric CO₂ pressure in straightforward one‐pot processes. Particularly, these reactions could be performed without any stoichiometric addition of bases or additives. Further mechanistic investigation reveals that the excellent activities are attributed to the effective activations of CO₂ accomplished by the NHCs via the formation of the NHC‐CO₂ adducts.     

A note on simultaneous preconditioning and symmetrization of non‐symmetric linear systems

Motivated by the theory of self‐duality that provides a variational formulation and resolution for non‐self‐adjoint partial differential equations (Ann. Inst. Henri Poincaré (C) Anal Non Linéaire 2007; 24 :171–205; Selfdual Partial Differential Systems and Their Variational Principles. Springer: New York, 2008), we propose new templates for solving large non‐symmetric linear systems. The method consists of combining a new scheme that simultaneously preconditions and symmetrizes the problem, with various well‐known iterative methods for solving linear and symmetric problems. The approach seems to be efficient when dealing with certain ill‐conditioned, and highly non‐symmetric systems. The numerical and theoretical results are provided to show the efficiency of our approach. Copyright © 2010 John Wiley & Sons, Ltd.