114 research outputs found

    Graphene transistors are insensitive to pH changes in solution

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    We observe very small gate-voltage shifts in the transfer characteristic of as-prepared graphene field-effect transistors (GFETs) when the pH of the buffer is changed. This observation is in strong contrast to Si-based ion-sensitive FETs. The low gate-shift of a GFET can be further reduced if the graphene surface is covered with a hydrophobic fluorobenzene layer. If a thin Al-oxide layer is applied instead, the opposite happens. This suggests that clean graphene does not sense the chemical potential of protons. A GFET can therefore be used as a reference electrode in an aqueous electrolyte. Our finding sheds light on the large variety of pH-induced gate shifts that have been published for GFETs in the recent literature

    Trees with Given Stability Number and Minimum Number of Stable Sets

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    We study the structure of trees minimizing their number of stable sets for given order nn and stability number α\alpha. Our main result is that the edges of a non-trivial extremal tree can be partitioned into n−αn-\alpha stars, each of size ⌈n−1n−α⌉\lceil \frac{n-1}{n-\alpha} \rceil or ⌊n−1n−α⌋\lfloor \frac{n-1}{n-\alpha}\rfloor, so that every vertex is included in at most two distinct stars, and the centers of these stars form a stable set of the tree.Comment: v2: Referees' comments incorporate

    Data-Driven Induction of Shadowed Sets Based on Grade of Fuzziness

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    We propose a procedure devoted to the induction of a shadowed set through the post-processing of a fuzzy set, which in turn is learned from labeled data. More precisely, the fuzzy set is inferred using a modified support vector clustering algorithm, enriched in order to optimize the fuzziness grade. Finally, the fuzzy set is transformed into a shadowed set through application of an optimal alpha-cut. The procedure is tested on synthetic and real-world datasets

    On Lie algebra obstructions

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    Some homological formulae

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