The Crystal Structure of N-(2-Hydroxyethyl)taurine, HOCH2CH2NHCH2CH2SOJH

The crystals of N-(2-hydroxyethyl)taur~ne are orthorhombic; a= 9.666 (4), b = 11.681 (6), c = 12.754 (8) A; space group is Pbca with eight formula units in the unit cell. A three-dimensional X-ray crystal structure analysis has shown that the compound crystallizes as zwitterion, formula HOCH2CH2NH2•CH2CH2S03-. Dihedral aingle S- C- C- N = 175.60, and N- C- C-0 = - 59.8°. Zwitterions are connected by hydrogen bonds into a three-dimensional network

Rolling balls and Octonions

In this semi-expository paper we disclose hidden symmetries of a classical nonholonomic kinematic model and try to explain geometric meaning of basic invariants of vector distributions

Genetic homogenisation of two major orchid viruses through global trade‐based dispersal of their hosts

Orchid viruses are capable of causing flower deformities and death, which can se‐ verely impact the horticultural industry and wild orchid conservation. Here we show how two of these quickly evolving viruses display few genetic differences since their first emergence, across countries and host plants. This is concerning as, despite bios‐ ecurity regulations to control the movement of orchids and their related pathogens, these patterns are suggestive of rapid and regular international movement of horti‐ cultural material. Poor biosecurity practices could threaten the orchid horticultural industry and result in the accidental translocation or reintroduction of infected plant material intended to recover wild populations

Classification of integrable discrete Klein-Gordon models

The Lie algebraic integrability test is applied to the problem of classification of integrable Klein-Gordon type equations on quad-graphs. The list of equations passing the test is presented containing several well-known integrable models. A new integrable example is found, its higher symmetry is presented.Comment: 12 pages, submitted to Physica Script

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