Superhydrophobic surfaces on engineering materials are prepared via a convenient solution‐immersion method. The binary geometric structures at the micro‐ and nanometer scale bestow superhydrophobic properties on the surfaces. The surfaces show stable superhydrophobicity even in many corrosive solutions, such as acidic or basic solutions over a wide pH range, and also in salt solutions. The procedure is time‐saving, inexpensive, and fairly facile to carry out. It is expected that this facile technique will accelerate the large‐scale production of superhydrophobic engineering materials with new industrial applications.
In a shortest path improvement problem under unit Hamming distance (denoted by SPIUH), an edge weighted graph with a set of source-terminal pairs is given; we need to modify the lengths of edges by a minimum cost under unit Hamming distance such that the modified distances of the shortest paths are upper bounded by given values. The SPIUH problem on arborescent network is formulated as a 0-1 integer programming model. Some strongly polynomial time algorithms are designed for the problems on some special arborescent networks. Firstly, two greedy algorithms are proposed for problems on chain networks and special star-tree networks, respectively. Secondly, a strongly polynomial time algorithm is presented for the problem with a single source and constrained paths. Finally, a heuristic algorithm and its computational experiments are given for the SPIUH problem on general graphs.
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