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《Discrete Mathematics》2022,345(4):112767
Let R be a finite commutative chain ring, be the dihedral group of size 2n and be the dihedral group ring. In this paper, we completely characterize left ideals of (called left -codes) when . In this way, we explore the structure of some skew-cyclic codes of length 2 over R and also over , where S is an isomorphic copy of R. As a particular result, we give the structure of cyclic codes of length 2 over R. In the case where is a Galois field, we give a classification for left -codes over , for any positive integer N. In both cases we determine dual codes and identify self-dual ones. 相似文献
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In this paper, we study the local linear convergence properties of a versatile class of Primal–Dual splitting methods for minimizing composite non-smooth convex optimization problems. Under the assumption that the non-smooth components of the problem are partly smooth relative to smooth manifolds, we present a unified local convergence analysis framework for these methods. More precisely, in our framework, we first show that (i) the sequences generated by Primal–Dual splitting methods identify a pair of primal and dual smooth manifolds in a finite number of iterations, and then (ii) enter a local linear convergence regime, which is characterized based on the structure of the underlying active smooth manifolds. We also show how our results for Primal–Dual splitting can be specialized to cover existing ones on Forward–Backward splitting and Douglas–Rachford splitting/ADMM (alternating direction methods of multipliers). Moreover, based on these obtained local convergence analysis result, several practical acceleration techniques are discussed. To exemplify the usefulness of the obtained result, we consider several concrete numerical experiments arising from fields including signal/image processing, inverse problems and machine learning. The demonstration not only verifies the local linear convergence behaviour of Primal–Dual splitting methods, but also the insights on how to accelerate them in practice. 相似文献
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Let be a finite field of cardinality , which is a finite chain ring, and is an odd positive integer. For any , an explicit representation for the dual code of any -constacyclic code over of length is given. And some dual codes of -constacyclic codes over of length 14 are constructed. For the case of , all distinct self-dual -constacyclic codes over of length are determined. 相似文献
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Jose Gracia Mauro Fianchini Chiara Biz Victor Polo Roberto Gómez 《Current Opinion in Electrochemistry》2021
Strongly correlated catalysts can be understood from precise quantum approximations. Incorporating properly electronic correlations thus let’s define Spin rules in catalysis, opening a new door towards optimum compositions for the most important reactions for a sustainable future. 相似文献
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Junki Ochi Kazuhiro Yuhara Prof. Kazuo Tanaka Prof. Yoshiki Chujo 《Chemistry (Weinheim an der Bergstrasse, Germany)》2022,28(20):e202200155
It is still challenging to realize a dual-emission system, in which two luminescent bands simultaneously appear by photoexcitation, in solid with organic dyes due to the difficulty in regulation of electronic properties in the excited state and concentration quenching. o-Carborane is known to be a versatile platform for constructing solid-state emitters since the sphere boron cluster is favorable for suppressing intermolecular interactions and subsequently concentration quenching. Here, we show solid-state dual-emissive o-carborane derivatives. We prepared 4 types of o-carborane derivatives and found dual-emission behaviors both in solution and solid states. By regulating the rotation at the o-carborane unit with the intramolecular CcageH⋅⋅⋅O interaction, the dual-emission intensity ratios were changed. Finally, it was demonstrated that the overall photoluminescence spectra can be estimated using the binding energy of intramolecular interactions. 相似文献