Subgroup-Permutability and Affine Planes*

We classify all finite groups whose subgroup-permutability graph is the incidence graph of an affine plain.     

Hybrid Metaheuristics for the Vehicle Routing Problem with Stochastic Demands

This article analyzes the performance of metaheuristics on the vehicle routing problem with stochastic demands (VRPSD). The problem is known to have a computationally demanding objective function, which could turn to be infeasible when large instances are considered. Fast approximations of the objective function are therefore appealing because they would allow for an extended exploration of the search space. We explore the hybridization of the metaheuristic by means of two objective functions which are surrogate measures of the exact solution quality. Particularly helpful for some metaheuristics is the objective function derived from the traveling salesman problem (TSP), a closely related problem. In the light of this observation, we analyze possible extensions of the metaheuristics which take the hybridized solution approach VRPSD-TSP even further and report about experimental results on different types of instances. We show that, for the instances tested, two hybridized versions of iterated local search and evolutionary algorithm attain better solutions than state-of-the-art algorithms.     

Polymeric liquid crystals: cholesteric superstructure from blends of hydroxypropylcellulose esters

n-Butyric, iso-butyric, n-valeric and iso-valeric esters of hydroxypropylcellulose were synthesized. Their behaviors, in terms of cholesteric structure, glass (T_g) and anisotropic-isotropic (T_i) transition temperatures are compared to results in the literature. A 6–8 month time period from sample preparation has no influence on the cholesteric phase characteristics. Six binary blends may be formed from the four esters. They show only a T_g value at each composition, which suggests a good miscibility among the components. However, positive deviation of linearity of T_g vs. composition varies from one pair to another. Analysis of the absorption curves in UV-vis spectra show that three pairs form a single cholesteric helix containing both components while other three give a only nematic phase. Colors changing from red to violet are shown for blends of n-butyric and iso-butyric esters at different weight ratio. Copyright © 2003 John Wiley & Sons, Ltd.     

Existence of equilibria via Ekeland's principle

In the literature, when dealing with equilibrium problems and the existence of their solutions, the most used assumptions are the convexity of the domain and the generalized convexity and monotonicity, together with some weak continuity assumptions, of the function. In this paper, we focus on conditions that do not involve any convexity concept, neither for the domain nor for the function involved. Starting from the well-known Ekeland's theorem for minimization problems, we find a suitable set of conditions on the function f that lead to an Ekeland's variational principle for equilibrium problems. Via the existence of ε-solutions, we are able to show existence of equilibria on general closed sets for equilibrium problems and systems of equilibrium problems.