Geometric Approach to Pontryagin's Maximum Principle

Since the second half of the 20th century, Pontryagin's Maximum Principle has been widely discussed and used as a method to solve optimal control problems in medicine, robotics, finance, engineering, astronomy. Here, we focus on the proof and on the understanding of this Principle, using as much geometric ideas and geometric tools as possible. This approach provides a better and clearer understanding of the Principle and, in particular, of the role of the abnormal extremals. These extremals are interesting because they do not depend on the cost function, but only on the control system. Moreover, they were discarded as solutions until the nineties, when examples of strict abnormal optimal curves were found. In order to give a detailed exposition of the proof, the paper is mostly self\textendash{}contained, which forces us to consider different areas in mathematics such as algebra, analysis, geometry.Comment: Final version. Minors changes have been made. 56 page

General models in min-max continous location

In this paper, a class of min-max continuous location problems is discussed. After giving a complete characterization of th stationary points, we propose a simple central and deep-cut ellipsoid algorithm to solve these problems for the quasiconvex case. Moreover, an elementary convergence proof of this algorithm and some computational results are presented

The investigation and provenance of glass vessel fragments attributed to the tomb of Amenhotep II, KV35, Valley of the Kings

Four polychrome glass fragments, excavated from tomb KV35 in the Valley of the Kings, attributed to Amenhotep II, were analysed to further investigate the composition and provenance of early Late Bronze Age glasses. An additional fragment, EA64163, cited by the British Museum as being stylistically analogous to the fragments from KV35, although with a findspot simply recorded as "Thebes", was also analysed. LA-ICP-MS analysis was used to analyse multiple colours on the fragments to determine the major element composition, the colouring strategies and establish provenance using trace element analysis. The resulting data obtained was compared with four polychrome fragments of standard LBA Egyptian composition, excavated from the palace of Amenhotep III at Malkata, previously analysed by SEM-WDS. Analysis showed that the glasses excavated from KV35 are standard LBA glass of Egyptian composition and were most likely produced in Egypt in the 18th Dynasty. The fragment EA64163 is a low magnesia, low potash glass, comparable with Iron Age composition, therefore should be reconsidered as a later glass. The analysis of glasses, excavated from a reliable, early Egyptian context supports the proposition that glass technology for multiple colours was established in Egypt at least as early as 1400 BCE

High Resolution Spectroscopy of CoH and CoD

Author Institution: Department of Chemistry, Massachusetts Institute of TechnologyFive new bands in the spectrum of gas phase CoH, with band heads near 5650, 5710, 6093, 6446 and 6586 {\AA}, as well as three bands in CoD, have been observed via laser excitation spectroscopy with a cw dye laser. Two of the CoH bands, at 5710 and 6093 A, have been rotationally analyzed and identified as $\Omega =4 \leftarrow \Omega =4$, where the lower state for both transitions is the previously characterized $X \Omega =4 (v=0)$ ground state. The two upper states, with approximate molecular constants $T_{v} = 18360 cm^{-1}, Bv = 4,7 cm^{-1}$ and $T_{v} = 17260 cm^{-1}, Bv = 4.9 cm^{-1}$, display strong perturbations characteristic of open-shell, transition-metal containing diatomics. A preliminary analysis of these perturbations will be presented