Approximate Euclidean shortest paths in polygonal domains

Given a set $\mathcal{P}$ of $h$ pairwise disjoint simple polygonal obstacles in $\mathbb{R}^2$ defined with $n$ vertices, we compute a sketch $\Omega$ of $\mathcal{P}$ whose size is independent of $n$, depending only on $h$ and the input parameter $\epsilon$. We utilize $\Omega$ to compute a $(1+\epsilon)$-approximate geodesic shortest path between the two given points in $O(n + h((\lg{n}) + (\lg{h})^{1+\delta} + (\frac{1}{\epsilon}\lg{\frac{h}{\epsilon}})))$ time. Here, $\epsilon$ is a user parameter, and $\delta$ is a small positive constant (resulting from the time for triangulating the free space of $\cal P$ using the algorithm in \cite{journals/ijcga/Bar-YehudaC94}). Moreover, we devise a $(2+\epsilon)$-approximation algorithm to answer two-point Euclidean distance queries for the case of convex polygonal obstacles.Comment: a few updates; accepted to ISAAC 201

Energy Eigenvalues For Supersymmetric Potentials via Quantum Hamilton-Jacobi Formalism

Using quantum Hamilton-Jacobi formalism of Leacock and Padgett, we show how to obtain the exact eigenvalues for supersymmetric (SUSY) potentials.Comment: 15 pages Latex Compile twice to get cross references correct. 2 Figures not included. Requests for figures should be sent to [email protected]

The stimulating impact of elevated temperatures on growth and productivity of Parthenium hysterophorus L.

Invasive alien weeds pose a great threat to biodiversity by suppressing the native flora and causing negative impacts on crop yields. Parthenium hysterophorus is an exotic weed that causes nuisance and health hazard to mankind and animals, and is a danger to the environment. Experiments were conducted during summer and winter to understand the impact of different temperature conditions on the growth of Parthenium. Pot studies conducted at 22-300°C temperature conditions were considered as control. During summer at 35-450°C, various growth parameters significantly increased in comparison to the 7-150°C temperature regime in winter. Different biochemical constituents were also higher in the leaves during summer than in winter season. The present investigation clearly indicates that growth and productivity of Parthenium was directly proportional to the increase in atmospheric temperature, indicating the possibility of the influence of rising temperature on its invasiveness.Keywords: Climate chang