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

New records of Dacrymyces ovisporus and Tremella diaporthicola from the Ukraine

The present paper deals with new records of the heterobasidioid fungi Dacrymyces ovisporus Bref. and Tremella diaporthicola Ginns et M.N.L. Lefebvre in Europe. The taxonomical status of these species is considered and detailed descriptions and illustrations of specimens are given

Potentials in N=4 superconformal mechanics

Proceeding from nonlinear realizations of (super)conformal symmetries, we explicitly demonstrate that adding the harmonic oscillator potential to the action of conformal mechanics does not break these symmetries but modifies the transformation properties of the (super)fields. We also analyze the possibility to introduce potentials in N=4 supersymmetric mechanics by coupling it with auxiliary fermionic superfields. The new coupling we considered does not introduce new fermionic degrees of freedom - all our additional fermions are purely auxiliary ones. The new bosonic components have a first order kinetic term and therefore they serve as spin degrees of freedom. The resulting system contains, besides the potential term in the bosonic sector, a non-trivial spin-like interaction in the fermionic sector. The superconformal mechanics we constructed in this paper is invariant under the full $D(2,1;\alpha)$ superconformal group. This invariance is not evident and is achieved within modified (super)conformal transformations of the superfields.Comment: 12 pages, PACS number: 12.60.J

Diffeomorphism, kappa transformations and the theory of non-linear realisations

We will show how the theory of non-linear realisations can be used to naturally incorporate world line diffeomorphisms and kappa transformations for the point particle and superpoint particle respectively. Similar results also hold for a general p-brane and super p-brane, however, we must in these cases include an additional Lorentz transformation.Comment: 19pages, no figure. References are added and typos are correcte

Dynamics of (SUSY) AdS Space Isometry Breaking

Actions governing the dynamics of the Nambu-Goldstone modes resulting from the spontaneous breaking of the SO(4,2) and $SU(2,2|1)$ isometries of five dimensional anti-de Sitter space ($AdS_{5}$) and SUSY $AdS_{5}\times S_1$ spaces respectively due to a restriction of the motion to embedded four dimensional $AdS_{4}$ space and four dimensional Minkowski space ($M_4$) probe branes are presented. The dilatonic Nambu-Goldstone mode governing the motion of the $M_4$ space probe brane into the covolume of the SUSY $AdS_5\times S_1$ space is found to be unstable. No such instablility appears in the other cases. Gauging these symmetries leads to an Einstein-Hilbert action containing, in addition to the gravitational vierbein, a massive Abelian vector field coupled to gravity.Comment: 6 pages, 0 figures, to appear in Proceedings of IRGAC 2006: 2nd International Conference on Quantum Theories and Renormalization Group in Gravity and Cosmology, Barcelon

Chemodivergence in Metal-Catalyzed Cross-Dehydrogenative Coupling Reactions of 2H-imidazole 1-oxides with 1H-pyrrole

This work was supported by the Russian Science Foundation (Project # 18-73-00088)

Superfield equations for the interacting system of D=4 N=1 supermembrane and scalar multiplet

We present the superfield action for the dynamical N=1 D=4 supermembrane in interaction with a dynamical scalar multiplet and use it to derive the superfield equations of motion. These include the supermembrane equations, which formally coincide with equations of supermembrane in a background of the (off-shell) scalar multiplet, and the special chiral superfield equations with supermembrane source. In the case when the scalar supermultiplet part of the action contains only the simplest kinetic term we have also extracted the spacetime component field equations from the superfield equations and solve these in the leading order on supermembrane tension. The inclusion of nontrivial superpotential and relation with known supersymmetric domain wall solutions is briefly discussed.Comment: 26 pages. V2: misprints corrected, references and an acknowledgment added, minor changes, in particular in sec. 4.2.1. V.3. discussion on the relation with known solutions added; to appear in Nucl.Phys. B (2011