Global Solution of Optimization Problems with Parameter-Embedded Linear Dynamic Systems

This paper develops a theory for the global solution of nonconvex optimization problems with parameter-embedded linear dynamic systems. A quite general problem formulation is introduced and a solution is shown to exists. A convexity theory for integrals is then developed to construct convex relaxations for utilization in a branch-and-bound framework to calculate a global minimum. Interval analysis is employed to generate bounds on the state variables implied by the bounds on the embedded parameters. These bounds, along with basic integration theory, are used to prove convergence of the branch-and-bound algorithm to the global minimum of the optimization problem. The implementation of the algorithm is then considered and several numerical case studies are examined thoroughly     

Fleet configuration subject to stochastic demand: an application in the distribution of liquefied petroleum gas

We study the problem of configuring a fleet, in which vehicles receive information on-line about the demand that they should fulfil while they are on the road. In each district it must be decided the number of vehicles and their capacity. The objective function is to minimise the operational cost subject to constraints for the minimum delivery capacity, the maximum vehicle size and the average waiting time for customers. The last constraint is modelled as a queuing system that is adjusted according to the simulation of the delivery process of a Chilean company that distributes liquefied petroleum gas in portable cylinders. We provide the analytical form of all the components of the model, so it can be solved using a standard non-linear programming package. We show that the fleet may increase its sales by 3% and reduce the waiting time of customers 10% by allowing a set of vehicles to share the buffer of orders rather than having vehicles to exclusively serve smaller sectors.     

New disc-shaped mesogens based on pentakis(phenylethynyl)benzene derivatives

First examples of amphiphilic alkyl pentakis(phenylethynyl)benzene ethers containing functional groups at the terminal position of their alkoxy chains were synthesized by etherification of pentabromophenol with 11-bromoundecan-1-ol and 11-bromoundecanoic acid ethyl ester, respectively, and subsequent palladium catalyzed, fivefold coupling reactions with the substituted phenylacetylene. Two undecanoic acid derivatives with different pentakis(phenylethynyl)phenoxy substituents in the ω-position were prepared by ester cleavage from the corresponding ethyl esters. The thermal behaviours of five penta-alkynes in their pure states, as well as of their charge transfer complexes formed from mixtures with 2,4,7-tri-nitrofluorenone, were examined.     

High-energy gamma-rays accompanying the spontaneous fission of 252Cf

The γ-ray spectrum of ²⁵²Cf(sf) was measured in the Darmstadt-Heidelberg Crystal Ball spectrometer, with a double ionization chamber mounted inside to detect the fission fragments. The measurement was aimed at a better understanding of an unusual component found in the high-energy region between 3 and 8 MeV, with fragment mass splits near symmetry. This component was proved to be predominantly emitted by the heavier fragment, to reach its highest intensity at a fragment mass split of 132:120, and to have an almost isotropic angular distribution. Calculations with the statistical code CASCADE could reproduce the main features.     

Harmonic Algebraic Curves and Noncrossing Partitions

Motivated by Gauss's first proof of the Fundamental Theorem of Algebra, we study the topology of harmonic algebraic curves. By the maximum principle, a harmonic curve has no bounded components; its topology is determined by the combinatorial data of a noncrossing matching. Similarly, every complex polynomial gives rise to a related combinatorial object that we call a basketball, consisting of a pair of noncrossing matchings satisfying one additional constraint. We prove that every noncrossing matching arises from some harmonic curve, and deduce from this that every basketball arises from some polynomial.     

Silylstannation of terminal alkynes using a recyclable palladium(0) catalyst immobilised in an ionic liquid

Silylstannanes can be regioselectively added across terminal alkynes in a quantitative fashion in the presence of a palladium(0) catalyst immobilised in the [bmim]PF6 ionic liquid which can be recycled without loss of activity.