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Usually, in mechanics, we obtain the trajectory of a particle in a given force field by solving Newton's second law with chosen initial conditions. In contrast, through our work here, we first demonstrate how one may analyze the behaviour of a suitably defined family of trajectories of a given mechanical system. Such an approach leads us to develop a mechanics analogue following the well-known Raychaudhuri equation largely studied in Riemannian geometry and general relativity. The idea of geodesic focusing, which is more familiar to a relativist, appears to be analogous to the meeting of trajectories of a mechanical system within a finite time. Applying our general results to the case of simple pendula, we obtain relevant quantitative consequences. Thereafter, we set up and perform a straightforward experiment based on a system with two pendula. The experimental results of this system are found to tally well with our proposed theoretical model. In summary, the simple theory and the related experiment provide us with a way to understand the essence of a fairly involved concept in advanced physics from an elementary standpoint. [ABSTRACT FROM AUTHOR]

Summary: Amanita pseudorufobrunnescens is described as a new species in the subgenus Amanitina section Amidella of family Amanitaceae from north-western Himalaya, India. Distinct morphological characters, odour and molecular phylogenetic analysis based on the large subunit of nuclear ribosomal DNA (nrLSU) data revealed that the present species differs from other members of sect. Amidella. This species is characterised by its whitish basidiomata that turn brownish orange with age, its whitish to cinnamon brown, floccose to radially fibrillose universal veil remnants on the pileus, its close lamellae becoming brownish orange on exposure, its elongate basidiospores and its association with Quercus oblongata (syn. Q. leucotrichophora). A detailed morphological description, line drawings, colour photographs and Maximum Likelihood (ML) phylogenetic placement of the new species are provided. [ABSTRACT FROM AUTHOR]

Since 2007, the quality of Russula descriptions has improved and the use of molecular support for species delimitation and the number of published new species has increased. However, the description style is not consistent and has regional or author-specific patterns. Most recent publications still favour descriptions of spores compared to hymenium and pileipellis elements, and usually only the spore size is provided with statistical support. This study proposes standards for descriptions of the microscopic structure of Russula species (Russulaceae, Agaricomycetes). We present the description template, the template measurements table, the specific terminology and the essential chemical reagents. The proposed standards were tested by mycologists from 11 countries who met at the Russula Microscopy Workshop in Slovakia. Descriptions of 26 species from 9 countries and four continents were prepared, among them R. amarissima, R. castanopsidis, R. seperina and R. subtilis are re-described and 15 species are introduced as new: R. abietiphila, R. amerorecondita, R. aurantioflava, R. echidna, R. flavobrunnescens, R. fluvialis, R. fortunae, R. garyensis, R. gemmata, R. laevis, R. madrensis, R. olivaceohimalayensis, R. purpureogracilis, R. sancti-pauli and R. wielangtae. Seven descriptions for candidate new species are provided without a formal name assignment. Pairwise comparison of species described in this study with available similar descriptions of related species suggests that microscopic characters from all parts of the basidiomata can be equally important for species recognition and they deserve the same treatment including number of measurements and statistics. The majority of recent studies does not recognise differences between the pileus margin and centre, but more than one-third of the species described in this study show distinct differences between the pileus areas, emphasizing the importance to specify the origin of pileipellis observations. This study proved that there is frequently insufficient difference in the ITS barcode between closely related species and that it is necessary to use more genetic markers combined with ecological and geographical data. [ABSTRACT FROM AUTHOR]