The Routh reduction of cyclic variables in the Lagrange function and the Jacobi-Maupertuis principle of constant energy systems are generalized. The article deals with one-dimensional variational integral subject to differential constraints, the Lagrange variational problem, that admits the Lie group of symmetries. Reduction to the orbit space is investigated in the absolute sense relieved of all accidental structures. In particular, the widest possible coordinate-free approach to the underdetermined systems of ordinary differential equations, Poincaré-Cartan forms, variations and extremals is involved for the preparation of the main task. The self-contained exposition differs from the common actual theories and rests only on the most fundamental tools of classical mathematical analysis, however, they are applied in infinite-dimensional spaces. The article may be of a certain interest for nonspecialists since all concepts of the calculus of variations undergo a deep reconstruction.
Some open problems appearing in the primary article on the symmetry reduction are solved. A new and quite simple coordinate-free definition of Poincaré-Cartan forms and the substance of divergence symmetries (quasisymmetries) are clarified. The unbeliavable uniqueness and therefore the global existence of Poincaré-Cartan forms without any uncertain multipliers for the Lagrange variational problems are worth extra mentioning.
Like the classical Gram-Schmidt theorem for symplectic vector spaces, the sheaf-theoretic version (in which the coefficient algebra sheaf $\mathcal A$ is appropriately chosen) shows that symplectic $\mathcal A$-morphisms on free $\mathcal A$-modules of finite rank, defined on a topological space $X$, induce canonical bases (Theorem 1.1), called symplectic bases. Moreover (Theorem 2.1), if $(\mathcal {E}, \phi )$ is an $\mathcal A$-module (with respect to a $\mathbb C$-algebra sheaf $\mathcal A$ without zero divisors) equipped with an orthosymmetric $\mathcal A$-morphism, we show, like in the classical situation, that “componentwise” $\phi $ is either symmetric (the (local) geometry is orthogonal) or skew-symmetric (the (local) geometry is symplectic). Theorem 2.1 reduces to the classical case for any free $\mathcal A$-module of finite rank.
For companies doing business in mining mineral deposits, ensuring safe work is one of the key tasks (Safety First!). One of the important trends in this area is prevention and endeavour to forestall risk situations. Risks need to be searched, technically described, spatially defined, evaluated and categorized by degree of risk. Complex geological and stability conditions can be one of the sources of persistent and significant risks, which are mainly landslides and rockslides threatening both mining equipment and employees. The problem described in this article and its solution concerns the Most Basin (formerly the North Bohemian Lignite Basin). This is a tertiary basin that was founded in the Oligocene. The main mineral is lignite and mining takes place on the surface. The main excavating machinery in the surface lignite quarries in Europe (Czech Republic, Germany, Poland) is the bucket wheel excavator., Roman Kapica, Dana Vrublová and Martin Vrubel., and Obsahuje bibliografii
The Tachyusa coarctata species group is revised. The species group is defined on the basis of the distinctly asperate punctation on elytra, the dense punctation on tergites III-V with interstices between punctures 1.5-2.0 times their diameter, and the dense, subrecumbent pubescence on the abdomen. The T. coarctata species group is composed of twenty three species restricted in occurrence to the Holarctic and Africa, including one new species described from Iran: Tachyusa frischi sp.n. A revised key to the species in this group is provided. An analysis of the phylogeny of the Tachyusa coarctata species group based on cladistic methods is presented and the phylogenetic relationships among species are discussed.
The present study analysed the taxonomic status and phylogenetic relationships of two species of xiphidiocercariae of the ʻmicrocotylaeʼ group, Cercaria pugnax La Valette St. George, 1855, from Viviparus viviparus (Linnaeus) in the Ukraine and Cercaria helvetica XII Dubois, 1928 from Bithynia tentaculata (Linnaeus) in Lithuania. Molecular phylogenetic analyses based on sequences of the ITS2 region and partial 28S gene of the nuclear rDNA revealed that both these xiphidiocercariae belong to the Lecithodendriidae Lühe, 1901 and represent larval stages of lecithodendriids parasitic in bats. Cercaria helvetica XII clustered with the typical representatives of the genus Lecithodendrium Looss, 1896, being very close, but not identical, to Lecithodendrium linstowi Dollfus, 1931. Sequences of C. pugnax matched exactly the sequences of adult Paralecithodendrium chilostomum (Mehlis, 1831). Morphological descriptions of the cercariae are included; these represent the first report of non-virgulate xiphidiocercariae belonging to the family Lecithodendriidae. Until now, the presence of glandular virgula organ in the region of the oral sucker was considered a robust synapomorphy for the Lecithodendriidae and several closely related families. Our results have shown that the relative importance of this character is in need of a re-assessment., Olena Kudlai, Virmantas Stunžėnas, Vasyl Tkach., and Obsahuje bibliografii
Globalization – multifactor phenomenon. Dimensions of globalization. The erosion of state power,global integration of the world and of most states result in the removal of barriers between national and internationalpolicies. The theory of governance: public power is no longer exercised exclusively by state, but its exerciseis participated in significantly by private supranational corporations and nongovernmental organizations. Onstate and global level governance includes the process of participation, negotiation and co-ordination. Its keyinstruments are projects, partnership and consensus – in the first place the knowledge of the process leading tothe achievement of consensus. There are know founding conditions within the existing international order thatrepresent something like a global constitution. Contemporary transition stage to it is global governance.
Agrimonia eupatoria L. is an herb of the Rosaceae family, widely used in traditional (folk) medicine for its beneficial effects. Its water extracts (infusions and decoctions) are used in the treatment of airway and urinary system diseases, digestive tract diseases, and chronic wounds. Phytochemical analyses of Agrimonia eupatoria L. identified a variety of bioactive compounds including tannins, flavonoids, phenolic acids, triterpenoids and volatile oils possessing antioxidant, immunomodulatory and antimicrobial activities. The authors review the available literature sources examining and discussing the therapeutic and pharmacological effects of Agrimonia eupatoria L. at the molecular level in vitro and in vivo.