Nonlinear programming with cumulatively bounded variables

The problem [maximize f(x), subject to x₁ + … + x_j ? b_j for j = 1, …, N] is solved by a feasible direction method that takes advantage of its special structure. A direction vector that approximates the vector of Lagrange multipliers is used. In the one-dimensional subproblem the direction vector is bent every time a constraint becomes active. Convergence to a K-T point is proven. McCormick has used a similar method for the problem [maximize f(x), subject to x ? 0], with the gradient as direction vector. A computationally implementable algorithm is given, with a finite stepsize procedure and a finite stopping rule. Observations from numerous applications to a recurring banking problem are discussed. Related techniques might be useful in other situations.     

Alkenyl C-H insertion of iodonium ylides into pyrroles: studies toward the total syntheses of tolmetin and amtolmetin guacil

The thermal-catalyzed or photochemical reaction of iodonium ylides with pyrroles yields exclusively alpha-substituted pyrroles in moderate to good yields. [reaction: see text]     

A facile diastereoselective synthesis of functionalized 1,2,3-trisubstituted benzocyclopentenes through the cycloaddition of bis(phenylsulfonyl)iodonium ylides to cyclic alkenes

The thermal cycloaddition of beta-disulfonyl iodonium ylides to cyclic alkenes affords exclusively 1,2,3-trisubstituted cis(1,2)/cis(2,3)-configured benzocyclopentenes by an electrophilic attack of the ylide on the olefinic double bond. This unsual transformation provides a convenient and direct method for the diastereoselective synthesis of functionalized bicyclo[3.3.0]octanes (characteristic structural units contained in polyquinane natural products), when cyclopentenes are used as cycloalkene partner.     

Stability and topology of scale-free networks under attack and defense strategies

We study tolerance and topology of random scale-free networks under attack and defense strategies that depend on the degree k of the nodes. This situation occurs, for example, when the robustness of a node depends on its degree or in an intentional attack with insufficient knowledge of the network. We determine, for all strategies, the critical fraction p(c) of nodes that must be removed for disintegrating the network. We find that, for an intentional attack, little knowledge of the well-connected sites is sufficient to strongly reduce p(c). At criticality, the topology of the network depends on the removal strategy, implying that different strategies may lead to different kinds of percolation transitions.     

Structure-electrical properties relationships of polymer composites filled with Fe-powder

Structure-properties relationships of composite materials, consisting of a polymer matrix and metal inclusions, is very important for designing new materials with desirable properties. In the present work the electrical and dielectric properties of several composites, consisting of a polymer matrix and iron (Fe) particles as filler, were investigated. Broadband dielectric relaxation spectroscopy measurements were carried out. The electrical behaviour of the composites is described in terms of the percolation theory. Percolation threshold values were calculated and the values of the dielectric permittivity critical exponent were found in good agreement with the theoretical ones. The influence of using different polymer matrices on the physical properties of the composites was also of particular interest. The results were related to the microstructure of the composites and a schematic model was proposed.     

Structure and dielectric properties of a thermoplastic blend containing dispersed metal

In the present work broadband dielectric relaxation spectroscopy measurements were employed to investigate the dielectric properties of polymer composites. A polyethylene/polyoxymethylene (PE/POM) thermoplastic blend was used as a matrix, while the inclusions were iron (Fe) particles. For comparison, the two pure polymers- PE and POM- were used as a matrix, too. In the PE/POM-Fe composites, the polymer matrix is two-phase and the filler particles are localized only in the POM phase, resulting in an ordered distribution of the dispersed filler particles within the blend. In PE-Fe and POM-Fe composites, the filler spatial distribution is random. The behaviour of all the composites studied is described in terms of the percolation theory. The PE/POM-Fe composites, based on the PE/POM blend, demonstrate different electrical behaviour compared to that of POM-Fe and PE-Fe systems. The percolation threshold value of the PE/POM-Fe composites was found much lower than that of the other two systems. The results were related to the microstructure of the composites. A schematic model for the morphology of the composites studied has been proposed. This model explains the peculiar behaviour of the PE/POM-Fe composites by taking into account the ordered distribution of the filler particles in a binary polymer matrix. Optical microscopy photographs confirm this model.