Friedel–Crafts acylation using bismuth triflate in [BMI][PF6]

Bismuth trifluoromethanesulfonate was found to be a good catalyst for the Friedel–Crafts acylation. Bismuth triflate immobilized in an ionic liquid was the most efficient catalytic system. Bismuth triflate in [BMI][PF₆] catalyzes this reaction under microwave irradiation allowing the rapid synthesis of aryl ketones in excellent yields. The catalyst system was easily recovered and reused several times.     

Monomer–Dimer Equilibrium for the 5′–5′ Stacking of Propeller‐Type Parallel‐Stranded G‐Quadruplexes: NMR Structural Study

Guanine‐rich sequence motifs, which contain tracts of three consecutive guanines connected by single non‐guanine nucleotides, are abundant in the human genome and can form a robust G‐quadruplex structure with high stability. Herein, by using NMR spectroscopy, we investigate the equilibrium between monomeric and 5′–5′ stacked dimeric propeller‐type G‐quadruplexes that are formed by DNA sequences containing GGGT motifs. We show that the monomer–dimer equilibrium depends on a number of parameters, including the DNA concentration, DNA flanking sequences, the concentration and type of cations, and the temperature. We report on the high‐definition structure of a simple monomeric G‐quadruplex containing three single‐residue loops, which could serve as a reference for propeller‐type G‐quadruplex structures in solution.     

Decentralized Model Predictive Control for Networks of Linear Systems with Coupling Delay

This paper presents a new dissipativity-based decentralized model predictive control strategy for networks of linear systems suffering from a bounded coupling delay. The notion of delay-robust dissipativity is introduced and applied to the development of interconnection stability conditions. The dissipation inequality of system trajectories is converted into a prognostic stability constraint for the optimization problem of model predictive control to guarantee the system stability. A recursive feasibility condition is derived for the constrained optimization problem, which is formulated in a semi-definite program. A numerical example of an interconnected three-unit process system is provided for illustrations.     

Path-following gradient-based decomposition algorithms for separable convex optimization

A new decomposition optimization algorithm, called path-following gradient-based decomposition, is proposed to solve separable convex optimization problems. Unlike path-following Newton methods considered in the literature, this algorithm does not require any smoothness assumption on the objective function. This allows us to handle more general classes of problems arising in many real applications than in the path-following Newton methods. The new algorithm is a combination of three techniques, namely smoothing, Lagrangian decomposition and path-following gradient framework. The algorithm decomposes the original problem into smaller subproblems by using dual decomposition and smoothing via self-concordant barriers, updates the dual variables using a path-following gradient method and allows one to solve the subproblems in parallel. Moreover, compared to augmented Lagrangian approaches, our algorithmic parameters are updated automatically without any tuning strategy. We prove the global convergence of the new algorithm and analyze its convergence rate. Then, we modify the proposed algorithm by applying Nesterov’s accelerating scheme to get a new variant which has a better convergence rate than the first algorithm. Finally, we present preliminary numerical tests that confirm the theoretical development.     

Optimizing a multi-stage production/inventory system by DC programming based approaches

This paper deals with optimizing the cost of set up, transportation and inventory of a multi-stage production system in presence of bottleneck. The considered optimization model is a mixed integer nonlinear program. We propose two methods based on DC (Difference of Convex) programming and DCA (DC Algorithm)—an innovative approach in nonconvex programming framework. The mixed integer nonlinear problem is first reformulated as a DC program and then DCA is developed to solve the resulting problem. In order to globally solve the problem, we combine DCA with a Branch and Bound algorithm (BB-DCA). A convex minorant of the objective function is introduced. DCA is used to compute upper bounds while lower bounds are calculated from a convex relaxation problem. The numerical results compared with those of COUENNE (http://www.coin-or.org/download/binary/Couenne/), a solver for mixed integer nonconvex programming, show the rapidity and the ?-globality of DCA in almost cases, as well as the efficiency of the combined DCA-Branch and Bound algorithm. We also propose a simple heuristic algorithm which is proved by experimental results to be better than an existing heuristic in the literature for this problem.     

On the commuting probability and supersolvability of finite groups

For a finite group \(G\) , let \(d(G)\) denote the probability that a randomly chosen pair of elements of \(G\) commute. We prove that if \(d(G)>1/s\) for some integer \(s>1\) and \(G\) splits over an abelian normal nontrivial subgroup \(N\) , then \(G\) has a nontrivial conjugacy class inside \(N\) of size at most \(s-1\) . We also extend two results of Barry, MacHale, and Ní Shé on the commuting probability in connection with supersolvability of finite groups. In particular, we prove that if \(d(G)>5/16\) then either \(G\) is supersolvable, or \(G\) isoclinic to \(A_4\) , or \(G/\mathbf{Z}(G)\) is isoclinic to \(A_4\) .     

Raman characterization of localized CdS nanostructures synthesized by UV irradiation in sol–gel silica matrices

A new technique of UV irradiation has been used for the first time to create microstructures of CdS nanoparticles in bulk xerogels. Porous silica matrices, which were first soaked in a solution containing CdS precursors, were subjected to irradiation using a nanopulsed ArF laser with a wavelength of 193 nm and a repetition rate of 10 Hz. Resonant micro‐Raman spectra, recorded using the 325‐nm line of a He‐Cd laser (with a continuous power less than 0.5 mW so as to avoid the thermal formation of nanoparticles) made it possible to identify CdS nanoparticles within the inscribed yellow zones and also to estimate the average particle size (3.6 to 8.0 nm, depending on the number of UV pulses used). The emission of CdS particles embedded in the silica matrix under excitation at 351.1 nm was studied by photoluminescence spectroscopy. It was then possible to show the effect of the number of pulses on the electronic structure of the nanocrystals. Finally, Raman spectra were used to monitor the structural changes in the silica matrix caused by the irradiation. It was found that the pulsed UVirradiation resulted in a local densification of the matrix, which was compensated for by a depolymerization process of the Si O Si network. In spite of this pulsed irradiation and the resulting structural depolymerization, no apparent ablation or cracking of the samples was observed. Copyright © 2010 John Wiley & Sons, Ltd.