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This work proposes a framework of benchmark functions designed to facilitate the creation of test cases for numerical optimisation techniques. The framework, written in Python 3, is designed to be easy to install, use, and expand. The collection includes some of the most used multi-modal continuous functions present in literature, which can be instantiated using an arbitrary number of dimensions. Meta-information of each benchmark function, like search boundaries and position of known optima, are included and made easily accessible through class methods. Built-in interactive visualisation capabilities, baseline techniques, and rigorous testing protocols complement the features of the framework. The framework can be found here: \url{https://gitlab.com/luca.baronti/python_benchmark_functions, Comment: 7 pages, 2 figures

The polarimetric Synthetic Aperture Radar (SAR) is a powerful sensor for high resolution ocean and land mapping and particularly for monitoring hydrological parameters in large watersheds. There is currently much research in progress to assess the SAR operational capability as well as to estimate the accuracy achievable in the measurements of geophysical parameters with the presently available airborne and spaceborne sensors. An important goal of this research is to improve our understanding of the basic mechanisms that control the interaction of electro-magnetic waves with soil and vegetation. This can be done both by developing electromagnetic models and by analyzing statistical relations between backscattering and ground truth data. A systematic investigation, which aims at a better understanding of the information obtainable from the multi-frequency polarimetric SAR to be used in agro-hydrology, is in progress by our groups within the framework of SIR-C/X-SAR Project and has achieved a most significant milestone with the NASA/JPL Aircraft Campaign named MAC-91. Indeed this experiment allowed us to collect a large and meaningful data set including multi-temporal multi-frequency polarimetric SAR measurements and ground truth. This paper presents some significant results obtained over an agricultural flat area within the Montespertoli site, where intensive ground measurements were carried out. The results are critically discussed with special regard to the information associated with polarimetric data.

A numerical program has been developed to determine the effects on lift interference of the finite length of the slotted portion of a square tunnel. Also analyzed by the program are the effects produced by small variations of static pressure between upper and lower plenum, and by boundary layer development on upper and lower walls downstream of the slotted section. In the flow model, based on compressible linear theory, the wing is represented by a single vortex and the wall induced perturbations are obtained by superimposing the effects of a series of images of the central vortex and of a distribution of sources and sinks on panels along the tunnel walls. The present results can be indicative of the magnitude and of the trends of the interference patterns associated with slotted test sections of finite length at high subsonic Mach numbers.