On a family of integrable systems on S2S^2 with a cubic integral of motion

We discuss a family of integrable systems on the sphere $S^2$ with an additional integral of third order in momenta. This family contains the Coryachev-Chaplygin top, the Goryachev system, the system recently discovered by Dullin and Matveev and two new integrable systems. On the non-physical sphere with zero radius all these systems are isomorphic to each other.Comment: LaTeX, 8 page

On integrable system on S2S^2 with the second integral quartic in the momenta

We consider integrable system on the sphere $S^2$ with an additional integral of fourth order in the momenta. At the special values of parameters this system coincides with the Kowalevski-Goryachev-Chaplygin system.Comment: LaTeX, 6 page

On bi-hamiltonian geometry of some integrable systems on the sphere with cubic integral of motion

We obtain bi-Hamiltonian structure for a family of integrable systems on the sphere S with an additional integral of third order in momenta. These results are applied to the Goryachev system and Goryachev-Chaplygin top for which we give an explicit procedure to find the separated coordinates and the separated relations.Comment: 11 pages, LaTeX with AMS fonts, corrected typo

Current Approaches to Demonstration of Therapeutic Equivalence of Locally-Acting Gastrointestinal Drugs

Evolution of knowledge about pharmacokinetics and pharmacodynamics of locally acting products, and an increase in the number of generics and medicines under development have laid the ground for the development of new scientific approaches to planning and conducting of therapeutic equivalence studies of medicinal products acting locally in the gastrointestinal (GI) tract. To date, many international guidelines on planning and conducting of bioequivalence (BE) studies of locally acting GI products have been updated, however, there are still no such guidelines in the Russian Federation and the Eurasian Economic Union (EAEU). Therefore, elaboration of common methodological approaches to the planning of clinical studies of these products is of particular relevance for the EAEU. The aim of the study was to analyse foreign approaches to planning, conducting, and evaluation of therapeutic equivalence studies of locally acting GI products. The paper analyses the guidelines of the European Medicines Agency and the US Food and Drug Administration on the planning, conduct, and evaluation of BE studies of locally acting GI products. The analysis demonstrated that BE clinical trials are giving way to in vitro studies providing a sensitive and accurate assessment of the differences between a locally acting GI product and the reference product, based on careful consideration of the medicine’s mechanism of action, dosage form, and site of action. The paper gives examples of test methods applied to medicinal products with a complex biopharmaceutical profile whose bioequivalence assessment is challenging, with a special focus on mesalazine products. The results of the analysis may be used for elaboration of a harmonised methodological approach to planning and conducting therapeutic equivalence studies of locally acting GI products in the Russian Federation and EAEU