Maximum principle at infinity for complete minimal surfaces in flat 3-manifolds

The main result of this paper is the following maximum principle at infinity:Theorem.Let M ₁ and M ₂ be two disjoint properly embedded complete minimal surfaces with nonempty boundaries, that are stable in a complete flat 3-manifold. Then dist(M ₁,M ₂)=min(dist(M ₁,M ₂), dist(M ₂,M ₁)).In case one boundary is empty, e.g. M ₁,then dist(M ₁,M ₂)=dist(M ₂,M ₁).If both boundaries are empty, then M ₁ and M ₂ are flat.     

Twistor holomorphic Lagrangian surfaces in the complex projective and hyperbolic planes

We completely classify all the twistor holomorphic Lagrangian immersions in the complex projective plane ², i.e. those Lagrangian immersions such that their twistor lifts to the twistor space over ² are holomorphic. This classification provides a one-parameter family of examples of Lagrangian spheres in ².Research partially supported by a DGICYT grant No. PB91-0731.     

A two-phase algorithm for the partial accessibility constrained vehicle routing problem

In the partial accessibility constrained vehicle routing problem, a route can be covered by two types of vehicles, i.e. truck or truck + trailer. Some customers are accessible by both vehicle types, whereas others solely by trucks. After introducing an integer programming formulation for the problem, we describe a two-phase heuristic method which extends a classical vehicle routing algorithm. Since it is necessary to solve a combinatorial problem that has some similarities with the generalized assignment problem, we propose an enumerative procedure in which bounds are obtained from a Lagrangian relaxation. The routine provides very encouraging results on a set of test problems.     

Sur les metriques admettant les plans comme surfaces minimales

We establish the system of partial differential equations satisfied by the riemannian metrics on open subsets of which admit planes as minimal surfaces. This is a nonlinear system of 10 partial differential equations, with the euclidian metric as a particular solution. In a previous work, we solved this system for axially symmetrical metrics. In this paper we linearize the system at the euclidian metric and solve the linear system. We obtain a 20-dimensional space of solutions.

     

The role of radicals in metal-assisted oxygenation reactions

The oxo-functionalization of organic substrates with the aid of metal oxo moieties is of fundamental importance not only in nature but also in academic and industrial research. Nevertheless the corresponding reaction mechanisms remain among the most enigmatic in chemistry and few of them are understood in detail. Recent research efforts have resulted in significantly improved information: in the cases of many oxygenation reactions evidence has been provided for the occurrence radical intermediates, even though the high selectivity observed suggests to a different mechanism. Examples stem from various areas of chemistry and include processes involving molecular metal oxo complexes, gas-phase and matrix-isolated species, metalloenzymes, and solid-state oxide surfaces. This review treats this seemingly wide variety of systems with the aim of providing an overview of common reactivity patterns and principles, as well as open problems.     

Synthesis of tetrazolopiperazine building blocks by a novel multi-component reaction

A novel Ugi-five-centre-four-component reaction (U-5C-4CR) of aldehydes, primary amines, trimethylsilylazide and 2-isocyanoethyltosylate yielding tetrazolopiperazine building blocks is described.     

Corrugated single-layer graphite sheet as a model of stepped surface of a crystal

Electronic structure calculations have been performed for flat graphite sheets and periodically distorted sheets with different values of deformation angle and hydrogen adsorption. These characteristics do not all behave monotonically with increasing deformation angle. At small deformation angles, the electrons pass from the atoms of terraces to those of edges, while at larger angles the reverse pattern is observed. The position of the Fermi level also varies nonmonotonically. The binding energy of hydrogen depends significantly on the adsorption site, and the difference can be doubled. Based on the ata obtained, it was concluded that a priori statements derived from the “general concepts” on the difference in the physicochemical properties of, for example, terrace and edge atoms on high-index facets are unreliable.     

Solid-phase synthesis of liquid crystalline isoxazole library

Combinatorial library of isoxazoles was prepared by 1,3-dipolar cycloaddition on solid support. p-Cyano derivatives showed nematic and/or smectic A phases. A bilayer smectic phase for 2h is proposed by the combination of molecular mechanics calculation and X-ray diffraction experiment.     

Covalent-ionic nature of the potential energy surface of the Li-CO2 complex

Unrestricted Hartree-Fock calculations with large basis sets, including d-functions, and the estimation of the correlation energy, show that the potential energy surface for the Li-CO₂ complex is built from the crossing of two states, each of them corresponding to a different electron arrangement. One has a strong ionic character and the other is of van der Waals type. Each portion of the energy surface presents a minimum, which is stable in respect to the dissociation limit.     

组合电化学--电化学研究中的新策略

组合电化学是一种新的电化学研究策略，通过设计和构建大量多样性的电极阵列，并对其进行高通量筛选和表征，快速、高效地实现了体系的电化学研究。本文综述了近年来进行的组合电化学研究，重点介绍了组合光学筛选方法、组合电化学合成方法以及电化学平行筛选方法，并探讨了各种方法的优势和存在的问题。