The constrained compartmentalized knapsack problem: mathematical models and solution methods

The constrained compartmentalized knapsack problem can be seen as an extension of the constrained knapsack problem. However, the items are grouped into different classes so that the overall knapsack has to be divided into compartments, and each compartment is loaded with items from the same class. Moreover, building a compartment incurs a fixed cost and a fixed loss of the capacity in the original knapsack, and the compartments are lower and upper bounded. The objective is to maximize the total value of the items loaded in the overall knapsack minus the cost of the compartments. This problem has been formulated as an integer non-linear program, and in this paper, we reformulate the non-linear model as an integer linear master problem with a large number of variables. Some heuristics based on the solution of the restricted master problem are investigated. A new and more compact integer linear model is also presented, which can be solved by a branch-and-bound commercial solver that found most of the optimal solutions for the constrained compartmentalized knapsack problem. On the other hand, heuristics provide good solutions with low computational effort. (C) 2011 Elsevier BM. All rights reserved.

Deterpenation of Bergamot Essential Oil Using Liquid-Liquid Extraction: Equilibrium Data of Model Systems at 298.2 K

The deterpenation of bergamot essential oil can be performed by liquid liquid extraction using hydrous ethanol as the solvent. A ternary mixture composed of 1-methyl-4-prop-1-en-2-yl-cydohexene (limonene), 3,7-dimethylocta-1,6-dien-3-yl-acetate (linalyl acetate), and 3,7-dimethylocta-1,6-dien-3-ol (linalool), three major compounds commonly found in bergamot oil, was used to simulate this essential oil. Liquid liquid equilibrium data were experimentally determined for systems containing essential oil compounds, ethanol, and water at 298.2 K and are reported in this paper. The experimental data were correlated using the NRTL and UNIQUAC models, and the mean deviations between calculated and experimental data were lower than 0.0062 in all systems, indicating the good descriptive quality of the molecular models. To verify the effect of the water mass fraction in the solvent and the linalool mass fraction in the terpene phase on the distribution coefficients of the essential oil compounds, nonlinear regression analyses were performed, obtaining mathematical models with correlation coefficient values higher than 0.99. The results show that as the water content in the solvent phase increased, the kappa value decreased, regardless of the type of compound studied. Conversely, as the linalool content increased, the distribution coefficients of hydrocarbon terpene and ester also increased. However, the linalool distribution coefficient values were negatively affected when the terpene alcohol content increased in the terpene phase.

A statistical evaluation of the field emission for copper oxide nanostructures

A statistical data analysis methodology was developed to evaluate the field emission properties of many samples of copper oxide nanostructured field emitters. This analysis was largely done in terms of Seppen-Katamuki (SK) charts, field strength and emission current. Some physical and mathematical models were derived to describe the effect of small electric field perturbations in the Fowler-Nordheim (F-N) equation, and then to explain the trend of the data represented in the SK charts. The field enhancement factor and the emission area parameters showed to be very sensitive to variations in the electric field for most of the samples. We have found that the anode-cathode distance is critical in the field emission characterization of samples having a non-rigid nanostructure. (C) 2007 Elsevier B.V. All rights reserved.

Symmetry in biology: from genetic code to stochastic gene regulation

Mathematical models, as instruments for understanding the workings of nature, are a traditional tool of physics, but they also play an ever increasing role in biology - in the description of fundamental processes as well as that of complex systems. In this review, the authors discuss two examples of the application of group theoretical methods, which constitute the mathematical discipline for a quantitative description of the idea of symmetry, to genetics. The first one appears, in the form of a pseudo-orthogonal (Lorentz like) symmetry, in the stochastic modelling of what may be regarded as the simplest possible example of a genetic network and, hopefully, a building block for more complicated ones: a single self-interacting or externally regulated gene with only two possible states: ` on` and ` off`. The second is the algebraic approach to the evolution of the genetic code, according to which the current code results from a dynamical symmetry breaking process, starting out from an initial state of complete symmetry and ending in the presently observed final state of low symmetry. In both cases, symmetry plays a decisive role: in the first, it is a characteristic feature of the dynamics of the gene switch and its decay to equilibrium, whereas in the second, it provides the guidelines for the evolution of the coding rules.