A Lesson Plan with an Arc Midpoint

The article introduces an explicit way of locating the arc midpoint in the Cartesian plane, which is consistent for both x- and y-coordinates and is technically accessible for students starting as young as fifteen. The authors give the proof of the statement using two trigonometry identities, and discuss some materials for innovative lessons on the arc midpoint computation that could enrich and enhance curriculum

σ\sigma-models on the quantum group manifolds SLq(2,R)SL_{q}(2,R), SLq(2,R)/Uh(1)SL_{q}(2,R)/U_{h}(1), Cq(2∣0)C_{q}(2|0) and infinitesimal trasformations

The differential and variational calculus on the $SL_{q}(2,R)$ group is constructed. The spontaneous breaking symmetry in the WZNW model with $SL_{q}(2,R)$ quantum group symmetry and in the $\sigma$-models with ${SL_{q}(2,R)/U_{h}(1)}$ ,$C_{q}(2|0)$ quantum group symmetry is considered. The Lagrangian formalism over the quantum group manifolds is discussed. The classical solution of $C_{q}(2|0)$ {$\sigma$}-model is obtained.Comment: LaTex, 7 page

Nilpotent Marsh and SUSY QM

We consider the nilpotent additions to classical trajectories in supersymmetric and nonsupersymmetric theories. The condition of anilpotence of action on some generalized solutions leads to the Witten supersymmetric Lagrangian. The condition of anilpotence of topological charge is the same as one of superpotential with spontaneous broken supersymmetry. We should vanish half of Grassmann constants of integration, because in this case only we obtain the same number of normalized bosonic and fermionic zero modes.Comment: 8 pages, Latex 2.09. Talk given at the conference in memory of V.I. Ogievetski, Dubna, July, 1997. To be published in the Proceeding

Russian & USA health system: the benchmarking research

Population's health is the most important factor of successful social development and main resource for ensuring state stability. By social standard of living and population's health it is possible to judge an efficiency of a state policy in the public health service sphere

The rare fungicolous fungus Pseudotrichia mutabilis (Pers.) Wehm.: new data and a historical perspective

The paper reports two new records of a rare fungicolous fungus Pseudotrichia mutabilis (Melanommataceae, Pleosporales) from Ukraine. Both specimens were collected within protected areas in association with two xylariaceous species, Hypoxylon crocopeplum and Rosellinia corticium. The paper provides descriptions, nomenclatural data, and original illustrations of the reported species. Information on substrate specialization and nutritional strategies of Pseudotrichia mutabilis, as well as general distribution of the species and known localities in Ukraine are specified and summarized

D=10 super-D9-brane

Superfield equations of motion for D=10 type IIB Dirichlet super-9-brane are obtained from the generalized action principle. The geometric equations containing fermionic superembedding equations and constraints on the generalized field strength of Abelian gauge field are separated from the proper dynamical equations and are found to contain these dynamical equations among their consequences. The set of superfield equations thus obtained involves a Spin(1,9) group valued superfield h_\a^{~\b} whose leading component appears in the recently obtained simplified expression for the kappa-symmetry projector of the D9-brane. The Cayley image of this superfield coincides (on the mass shell) with the field strength tensor of the world volume gauge field characteristic for the Dirichlet brane. The superfield description of the super-9-brane obtained in this manner is known to be, on the one hand, the nonlinear (Born-Infeld) generalization of supersymmetric Yang-Mills theory and, on the other hand, the theory of partial spontaneous breaking of D=10, N=IIB supersymmetry down to D=10, N=1.Comment: 34 pages, LATEX. Minor corrections. References adde