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

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

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

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