[en] An N=1 supersymmetric system is constructed and its integrability is shown by obtaining three soliton solutions for it using the supersymmetric version of Hirota's direct method

[en] Induced variability in green gram genotypes, T-44, AAU-34 and AAU-39 were assessed in the M₂ generation comprising single, combined and recurrent treatments of ethyl methane sulphonate (EMS) and gamma rays. Differential response of the genotypes to the mutagenic treatments was observed for all the characters. The highest range of variability for various characters were induced mostly by the recurrent treatments followed by single and combined treatments. The recurrent treatments were more effective in changing the mean values and inducing additional variability than single and combined treatments. Among the two mutagens gamma rays in general induced higher mean performance and variability than EMS. (author)

[en] We show the complete integrability of N=2 nonstandard KP flows establishing the bi-Hamiltonian structures. One of Hamiltonian structures is shown to be isomorphic to the nonlinear N=2 W_∞ algebra with the bosonic sector having W_1+∞·W_∞ structure. A consistent free field representation of the super conformal algebra is obtained. The bosonic generators are found to be an admixture of free fermions and free complex bosons, unlike the linear one. The fermionic generators become exponential in free fields, in general

[en] We present an axially symmetric, asymptotically flat empty space solution of the Einstein field equations containing a naked singularity. The space-time is regular everywhere except on the symmetry axis where it possesses a true curvature singularity. The space-time is of type D in the Petrov classification scheme and is locally isometric to the metrics of case IV in the Kinnersley classification of type D vacuum metrics. Additionally, the space-time also shows the evolution of closed timelike curves (CTCs) from an initial hypersurface free from CTCs.

[en] Here we present a vacuum spacetime with closed null geodesics (CNGs). These CNGs are obtained by analytically solving the geodesic equations. This spacetime is locally isometric to the plane wave spacetime and has very different global properties from metrics of the latter type. - Highlights: ► Closed null geodesics are found in a vacuum spacetime. ► These are obtained by analytically solving the geodesic equations. ► The nature of the spacetime is fully analysed.

[en] We construct an axially symmetric spacetime admitting, after a certain instant, closed timelike curves (CTCs) indicating that it is a time-machine spacetime. The spacetime, which is locally anti-de Sitter, is a four-dimensional extension of the Misner space with identical causality-violating properties. In this spacetime, CTCs evolve from a casually well-behaved initial hypersurface.