A constructive characterization of the split closure of a mixed integer linear program

Two independent proofs of the polyhedrality of the split closure of mixed integer linear program have been previously presented. Unfortunately neither of these proofs is constructive. In this paper, we present a constructive version of this proof. We also show that split cuts dominate a family of inequalities introduced by Köppe and Weismantel.     

An alternative approach for non-linear optimal control problems based on the method of moments

We propose an alternative method for computing effectively the solution of non-linear, fixed-terminal-time, optimal control problems when they are given in Lagrange, Bolza or Mayer forms. This method works well when the nonlinearities in the control variable can be expressed as polynomials. The essential of this proposal is the transformation of a non-linear, non-convex optimal control problem into an equivalent optimal control problem with linear and convex structure. The method is based on global optimization of polynomials by the method of moments. With this method we can determine either the existence or lacking of minimizers. In addition, we can calculate generalized solutions when the original problem lacks of minimizers. We also present the numerical schemes to solve several examples arising in science and technology.     

Multi-scale Young measures

We introduce multi-scale Young measures to deal with problems where multi-scale phenomena are relevant. We prove some interesting representation results that allow the use of these families of measures in practice, and illustrate its applicability by treating, from this perspective, multi-scale convergence and homogenization of multiple integrals.

     

On the Cartan–Jacobson Theorem

The well-known Cartan–Jacobson theorem claims that the Lie algebra of derivations of a Cayley algebra is central simple if the characteristic is not 2 or 3. In this paper we have studied these two cases, with the following results: if the characteristic is 2, the theorem is also true, but, if the characteristic is 3, the derivation algebra is not simple. We have also proved that in this last case, there is a unique nonzero proper seven-dimensional ideal, which is a central simple Lie algebra of type A₂, and the quotient of the derivation algebra modulo this ideal turns out to be isomorphic, as a Lie algebra, to the ideal itself. The original motivation of this work was a series of computer-aided calculations which proved the simplicity of derivation algebras of Cayley algebras in the case of characteristic not 3. These computations also proved the existence of a unique nonzero proper ideal (which turns out to be seven-dimensional) in the algebra of derivations of split Cayley algebras in characteristic 3.     

Effect of excess halide on the palladium‐catalyzed insertion‐triggered radical copolymerization of methyl acrylate and 1‐hexene

[Pd₂(μ‐Cl)₂(C₆F₅)₂(tht)₂] ( 1 ) is a very efficient initiator of the radical polymerization of methyl acrylate, but it is not active in the polymerization of methyl methacrylate or in the copolymerization with 1‐hexene. The addition of an excess of NBu₄Cl to solutions of [Pd₂(μ‐Cl)₂(C₆F₅)₂(tht)₂] ( 1 ) provides an initiator system that copolymerizes methyl acrylate and 1‐hexene by an insertion‐triggered radical mechanism. Random copolymers are obtained with 11% incorporation of 1‐hexene in moderate yields (about 35%). Studies of the decomposition products obtained after the first insertion of methyl acrylate in the Pd? C₆F₅ bond of 1 show that the addition of excess halide in the presence of monomer favors the homolytic cleavage of the Pd? C bond, and the generation of the radicals that are active species in the polymerization, versus alternative evolution pathways. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 5682–5691, 2006     

Multiscale Finite Element Modeling of Arc Dynamics in a DC Plasma Torch

The dynamics of the electric arc inside a direct current non-transferred arc plasma torch are simulated using a three-dimensional, transient, equilibrium model. The fluid and electromagnetic equations are solved numerically in a fully coupled approach by a multiscale finite element method. Simulations of a torch operating with argon and argon–hydrogen under different operating conditions are presented. The model is able to predict the operation of the torch in steady and takeover modes without any further assumption on the reattachment process except for the use of an artificially high electrical conductivity near the electrodes, needed because of the equilibrium assumption. The results obtained indicate that the reattachment process in these operating modes may be driven by the movement of the arc rather than by a breakdown-like process. It is also found that, for a torch operating in these modes and using straight gas injection, the arc will tend to re-attach to the opposite side of its original attachment. This phenomenon seems to be produced by a net angular momentum on the arc due to the imbalance between magnetic and fluid drag forces.     

Ambiphilic boryl groups in a neutral Ni(ii) complex: a new activation mode of H2

The concept of metal–ligand cooperation opens new avenues for the design of catalytic systems that may offer alternative reactivity patterns to the existing ones. Investigations of this concept with ligands bearing a boron center in their skeleton established mechanistic pathways for the activation of small molecules in which the boron atom usually performs as an electrophile. Here, we show how this electrophilic behavior can be modified by the ligand trans to the boron center, evincing its ambiphilic nature. Treatment of diphosphinoboryl (PBP) nickel–methyl complex 1 with bis(catecholato)diboron (B₂Cat₂) allows for the synthesis of nickel(ii) bis-boryl complex 3 that promotes the clean and reversible heterolytic cleavage of dihydrogen leading to the formation of dihydroborate nickel complex 4. Density functional theory analysis of this reaction revealed that the heterolytic activation of H₂ is facilitated by the cooperation of both boryl moieties and the metal atom in a concerted mechanism that involves a Ni(ii)/Ni(0)/Ni(ii) process. Contrary to 1, the boron atom from the PBP ligand in 3 behaves as a nucleophile, accepting a formally protic hydrogen, whereas the catecholboryl moiety acts as an electrophile, receiving the attack from the hydride-like fragment. This manifests the dramatic change in the electronic properties of a ligand by tuning the substituent trans to it and constitutes an unprecedented cooperative mechanism that involves two boryl ligands in the same molecule operating differently, one as a Lewis acid and the other one as a Lewis base, in cooperation with the metal. In addition, reactivity towards different nucleophiles such as amines or ammonia confirmed the electrophilic nature of the Bcat moiety, allowing the formation of aminoboranes.

A bis(boryl)nickel complex promotes the facile and reversible activation of H₂ through a cooperative mechanism that involves the metal and both boryl moieties in a concerted five-center process.