A quantum simulation of a travelling salesman is described. A vector space for a graph is defined together with a sequence of operators which transform a special initial state into a superposition states representing Hamiltonian tours. The quantum amplitude for any tour is a function of the classical cost of travelling along the edges in that tour. Tours with the largest quantum amplitude may be different than those with the smallest classically-computed cost.

Ravindra N. Rao

Nath and Paul (Linear Algebra Appl.,460(2014),97-110) have shown that the largest distance Laplacian eigenvalue of a path is simple and the corresponding eigenvector has properties similar to the Fiedler vector. We given an alternative proof, establishing a more general result in the process. It is conjectured that a similar phenomenon holds for any tree.

Ravindra B. Bapat

We exhibit a class of extendable codimension $2$ subvarieties in a general hypersurface of dimension at least $4$ in projective space. As a consequence, we prove that a general hypersurface of degree $d$ and dimension at least $4$ does not support globally generated indecomposable ACM bundles of any rank if their first Chern class $e \ll d$.

G. V. Ravindra Debaditya Raychaudhury

We present an analysis of the entanglement characteristics in the Majumdar-Ghosh (MG) or $J_{1}$-$J_{2}$ Heisenberg model. For a system consisting of up to 28 spins, there is a deviation from the scaling behaviour of the entanglement entropy characterizing the unfrustrated Heisenberg chain as soon as $J_{2} >0.25$. This feature can be used as an indicator of the dimer phase transition that occurs at $J_{2} = J_{2}^{*} \approx 0.2411 J_{1}$. Additionally, we also consider entanglement at the MG point $J_{2}=0.5 J_{1}$.

Ravindra W. Chhajlany Piotr Tomczak Antoni Wojcik Johannes Richter

The dynamical properties of Cu in a regime relevant to femtosecond micro machining are obtained on picosecond time scales using pump-probe reflectivity study for 100fs, 1015 W cm-2 laser pulses. The electrical resistivity is obtained by solving Helmoltz equations. The dissipation mechanisms and scaling laws are obtained in high and low temperature limits. The 'resistivity saturation' effect in an unexplored regime intermediate to hot plasma and cold solid is studied in detail. The temperature evolution and thermal conductivity is obtained in the temporal range 0 to 30ps after the interaction of laser pulse with solid Cu.

Arvinder S. Sandhu A. K. Dharmadhikari G. Ravindra Kumar

We study certain moduli spaces of stable vector bundles of rank two on cubic and quartic threefolds. In many cases under consideration, it turns out that the moduli space is complete and irreducible and a general member has vanishing intermediate cohomology. In one case, all except one component of the moduli space has such vector bundles.

Indranil Biswas Jishnu Biswas G. V. Ravindra

Recently it has been proved that any arithmetically Cohen-Macaulay (ACM) bundle of rank two on a general, smooth hypersurface of degree at least three and dimension at least four is a sum of line bundles. When the dimension of the hypersurface is three, a similar result is true provided the degree of the hypersurface is at least six. We extend these results to complete intersection subvarieties by proving that any ACM bundle of rank two on a general, smooth complete intersection subvariety of sufficiently high multi-degree and dimension at least four splits. We also obtain partial results in the case of threefolds.

Jishnu Biswas G. V. Ravindra

We show that for a smooth hypersurface $X\subset \bbP^n$ of degree at least 2, there exist arithmetically Cohen-Macaulay (ACM) codimension two subvarieties $Y\subset X$ which are not an intersection $X\cap{S}$ for a codimension two subvariety $S\subset\bbP^n$. We also show there exist $Y\subset X$ as above for which the normal bundle sequence for the inclusion $Y\subset X\subset\bbP^n$ does not split.

N. Mohan Kumar A. P. Rao G. V. Ravindra

Motivated by rapid advances in plasma based accelerators, we propose a simple mechanism for the production of highly collimated quasi monochromatic electrons beams. By considering Compton scattering of electrons (in the plasma) with virtual photons -- through an effective interaction --- we demonstrate angular collimation with a divergence less than 3 mrad quasi mono-energetic nature of the beam and an energy gain of O (1 GeV/cm), in laser induced accelerators.

Ravindra Kumar V. Ravishankar

Data clustering is a process of arranging similar data into groups. A clustering algorithm partitions a data set into several groups such that the similarity within a group is better than among groups. In this paper a hybrid clustering algorithm based on K-mean and K-harmonic mean (KHM) is described. The proposed algorithm is tested on five different datasets. The research is focused on fast and accurate clustering. Its performance is compared with the traditional K-means & KHM algorithm. The result obtained from proposed hybrid algorithm is much better than the traditional K-mean & KHM algorithm.

Ravindra Jain