Exact solutions for the agricultural and the two-dimensional packing problems

Objectives and study method: The objective of this study is to develop exact algorithms that can be used as management tools for the agricultural production planning and to obtain exact solutions for two of the most well known twodimensional packing problems: the strip packing problem and the bin packing problem. For the agricultural production planning problem we propose a new hierarchical scheme of three stages to improve the current agricultural practices. The objective of the first stage is to delineate rectangular and homogeneous management zones into the farmer’s plots considering the physical and chemical soil properties. This is an important task because the soil properties directly affect the agricultural production planning. The methodology for this stage is based on a new method called “Positions and Covering” that first generates all the possible positions in which the plot can be delineated. Then, we use a mathematical model of linear programming to obtain the optimal physical and chemical management zone delineation of the plot. In the second stage the objective is to determine the optimal crop pattern that maximizes the farmer’s profit taken into account the previous management zones delineation. In this case, the crop pattern is affected by both management zones delineation, physical and chemical. A mixed integer linear programming is used to solve this stage. The objective of the last stage is to determine in real-time the amount of water to irrigate in each crop. This stage takes as input the solution of the crop planning stage, the atmospheric conditions (temperature, radiation, etc.), the humidity level in plots, and the physical management zones of plots, just to name a few. This procedure is made in real-time during each irrigation period. A linear programming is used to solve this problem. A breakthrough happen when we realize that we could propose some adaptations of the P&C methodology to obtain optimal solutions for the two-dimensional packing problem and the strip packing. We empirically show that our methodologies are efficient on instances based on real data for both problems: agricultural and two-dimensional packing problems. Contributions and conclusions: The exact algorithms showed in this study can be used in the making-decision support for agricultural planning and twodimensional packing problems. For the agricultural planning problem, we show that the implementation of the new hierarchical approach can improve the farmer profit between 5.27% until 8.21% through the optimization of the natural resources. An important characteristic of this problem is that the soil properties (physical and chemical) and the real-time factors (climate, humidity level, evapotranspiration, etc.) are incorporated. With respect to the two-dimensional packing problems, one of the main contributions of this study is the fact that we have demonstrate that many of the best solutions founded in literature by others approaches (heuristics approaches) are the optimal solutions. This is very important because some of these solutions were up to now not guarantee to be the optimal solutions.

Ligand effects on the optical and chiroptical properties of the thiolated Au18cluster

The effect of chiral and achiral ligands protecting the inner Au9 core of the Au18(SR)14 cluster is studied based on density functional theory (DFT) and its corrected long-range interaction (DFT-D) approach. It was found that the electronic properties (energy levels) depend on the specific ligands, which induce distinct distortions on the Au–S framework. However, the substitution of S-c-C6H11 as SCH3 ligands may be considered to be correct given the obtained resemblance to the displayed bonding, optical and chiroptical properties. A further comparison of the CD and UV spectra displayed by the Au18 cluster protected by chiral and achiral ligands attests that more intense profiles are featured by ligands including phenyl rings and/or oxygen atoms such that the Au18 cluster protected by either achiral metamercaptobenzoic acid (m-MBA) or achiral SPh ligands displays more intense UV and CD signals. These results provide new insight into the effect of ligands on thiolated gold clusters

Thiolated Au18cluster: preferred Ag sites for doping, structures, and optical and chiroptical properties

Recently, the X-ray determined structure of the thiolated Au18 cluster has been reported. In this communication, we addressed a study of structures and chiroptical properties of thiolated Au18 cluster doped with up to ten Ag atoms, which have been calculated by Time Dependent Density Functional Theory (TD-DFT). The number of Ag atoms was steadily varied and more stable isomers showed optical and Circular Dichroism (CD) spectra distinct from that found for the parent Au18 cluster. Doping with more than four Ag atoms results in enhancement of the oscillator strength of the HOMO–LUMO peak and it is expected that this feature can be exploited for photoluminescence applications.