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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]

This new series of Fungal Biodiversity Profiles presents ten new taxa in the genus Russula, including subgenus Crassotunicata subg. nov. In subg. Malodora, sect Edules sect. nov. is described for a number of African species and a first detailed description is given for the type species, while R. pseudocompacta sp. nov. and R. compactoides sp.nov. are described in the new section Pseudocompactae sect. nov. of the same subgenus; in subg. Compactae the new sect. Polyphyllae is described, in subg. Russula, R. kewzingensis sp. nov. is described in subsect. Roseinae, as well as the new section Flavisiccantes, and the new subsect. Tricholomopsidae. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the problem of robust absolute stability of Lurie system with probabilistic time-varying delay and norm-bounded parametric uncertainty is considered. The time delay variation range is divided into two subintervals. By considering the probability distribution of the time-varying delay between the two subintervals and the knowledge of the delay variation range, a novel linear matrix inequalities (LMIs) based stability condition is derived by defining a Lyapunov Krasovskii functional. It is illustrated with the help of numerical examples that the derived stability criteria can lead to less conservative results as compared to the results obtained by the traditional method of using the delay variation range information only. [Copyright &y& Elsevier]