To describe accurately the electronic structures of carbon nanotubes, a semi-empirical tight-binding approach is presented in which the main intrinsic curvatures have been fully taken into account. The calculated electronic structures and band gaps are consistent with experimental measurements. Studies of the relative importance of various intrinsic curvatures show that each curvature has a contribution of varying importance to the curvature-induced band gap. Additionally, under both uniaxial and torsional strain, semiconductor–metal–semiconductor phase transitions have been observed for primary metallic carbon nanotubes. The critical stress of the transition and the gap’s sensitivity with stress are dependent on both the diameter and chirality of nanotubes, which is at variance with previous predictions.

Automated program repair (APR) aims to find an automatic solution to program language bugs without human intervention, and it can potentially reduce debugging costs and improve software quality.Conventional approaches adopt learning-based methods such as sequence-to-sequence models for the patches generation. However, they tend to ignore the code structure information and suffer from grammar and syntax errors. To consider the grammar and syntax information, in this paper, we propose a grammar-based ruleto-rule model, which regards the repair process as the transformation of grammar rules, and leverages two encoders modeling both the original token sequence and the grammar rules, enhanced with a new tree-based self-attention. Besides, to guarantee grammar correctness, we employ a grammatically restricted inference method to generate each grammar rule in a legally constrained sub-search-space considering the generated previous rules. Experimental evaluations on a Java dataset demonstrate that the proposed approach significantly outperforms the state-of-the-art baselines in terms of generated code accuracy.

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