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We consider an ldquon-graph of treesrdquo whose nodes are the set of trees of fixed order n, and in which two nodes are adjacent if one tree can be derived from the other through a single application of a local edge transformation rule. We derive an exact formula for the length of the shortest path from any node to any ldquocanonicalrdquo node in the n-graph of trees. We use this result to derive...
The need for magnetostrictive materials is growing for applications in microelectromechanical systems (MEMS) and microelectronic devices due to their ability to enable remote control via magnetic fields. This work studies an alloy of iron and gallium, Galfenol (thin films), and its magnetostrictive properties on a nano scale, finding approaches to increase the magnetostriction coefficient of thin-film...
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