For the inflaton field we determine a new exact solution by using Lie symmetry analysis. Specifically, construct second-order differential master equation for arbitrary scalar potential assuming that spectral index density perturbations $n_{s}$ and to tensor ratio $r$ are related as $n_{s}-1=h\left( r\right) $. Function $h\left( $ is classified according admitted symmetries equation. The possib...

In this paper we propose semi-explicit schemes based on Taylor methods for the solution of the isospectral equation L 0 = B; L] for d d real matrices L, while reproducing the isospectrality of the exact equation. Although the theoretical solution may be symmetric, the proposed schemes usually do not retain symmetry of the underlying ow. We present techniques that allow us to decrease the breakd...

In this paper we propose semi-explicit schemes based on Taylor methods for the solution of the isospectral equation L′ = [B,L] for d × d real matrices L, while reproducing the isospectrality of the exact equation. Although the theoretical solution may be symmetric, the proposed schemes usually do not retain symmetry of the underlying flow. We present techniques that allow us to decrease the bre...

We present an exact solution for the distribution of sample averaged monomer to monomer distance of ring polymers. For non-interacting and local-interaction models these distributions correspond to the distribution of the area under the reflected Bessel bridge and the Bessel excursion respectively, and are shown to be identical in dimension d ≥ 2, albeit with pronounced finite size effects at t...

We present a methodology for characterization and an approach for computing the solutions of fuzzy linear systems with LR fuzzy variables. As solutions, notions of exact and approximate solutions are considered. We transform the fuzzy linear system into a corresponding linear crisp system and a constrained least squares problem. If the corresponding crisp system is incompatible, then the fuzzy ...

In this paper we give an exact analytic solution for tachyon condensation in the modified (picture 0) cubic superstring field theory. We prove the absence of cohomology and, crucially, reproduce the correct value for the D-brane tension. The solution is surprising for two reasons: First, the existence of a tachyon vacuum in this theory has not been definitively established in the level expansio...