Observations of Plasma Upflow in a Warm Loop with Hinode/EIS

A complete understanding of Doppler shift in active region loops can help probe the basic physical mechanism involved into the heating of those loops. Here we present observations of upflows in coronal loops detected in a range of temperature temperatures (log T=5.8 - 6.2). The loop was not discernible above these temperatures. The speed of upflow was strongest at the footpoint and decreased with height. The upflow speed at the footpoint was about 20 km/s in Fe VIII which decreased with temperature being about 13 km/s in Fe X, about 8 km/s in Fe XII and about 4 km/s in FeXIII. To the best of our knowledge this is the first observation providing evidence of upflow of plasma in coronal loop structures at these temperatures. We interpret these observations as evidence of chromospheric evaporation in quasi-static coronal loops.Comment: 14 pages, 5 figures, Accepted for Publication in The Astrophysical Journal Letter

A Deterministic Algorithm for the Vertex Connectivity Survivable Network Design Problem

In the vertex connectivity survivable network design problem we are given an undirected graph G = (V,E) and connectivity requirement r(u,v) for each pair of vertices u,v. We are also given a cost function on the set of edges. Our goal is to find the minimum cost subset of edges such that for every pair (u,v) of vertices we have r(u,v) vertex disjoint paths in the graph induced by the chosen edges. Recently, Chuzhoy and Khanna presented a randomized algorithm that achieves a factor of O(k^3 log n) for this problem where k is the maximum connectivity requirement. In this paper we derandomize their algorithm to get a deterministic O(k^3 log n) factor algorithm. Another problem of interest is the single source version of the problem, where there is a special vertex s and all non-zero connectivity requirements must involve s. We also give a deterministic O(k^2 log n) algorithm for this problem

Improved Chen-Ricci inequality for curvature-like tensors and its applications

We present Chen-Ricci inequality and improved Chen-Ricci inequality for curvature like tensors. Applying our improved Chen-Ricci inequality we study Lagrangian and Kaehlerian slant submanifolds of complex space forms and C-totally real submanifolds of Sasakian space forms