By using simultaneous triangularization technique, similarity for operator weighted shifts with finite multiplicity is characterized in terms of K0-group of commutant algebra. The result supports the conjecture posed ...By using simultaneous triangularization technique, similarity for operator weighted shifts with finite multiplicity is characterized in terms of K0-group of commutant algebra. The result supports the conjecture posed by Cao et al. in 1999. Moreover, we discuss the relations between similarity and quasi-similarity for operator weighted shifts.展开更多
DNA computing, currently a hot research field in information processing, has the advantages of parallelism, low energy consumption, and high storability, therefore, it has been applied to a variety of complicated comp...DNA computing, currently a hot research field in information processing, has the advantages of parallelism, low energy consumption, and high storability, therefore, it has been applied to a variety of complicated computational problems. The emerging field of DNA nanotechnology has also developed quickly; within it, the method of DNA strand displacement has drawn great attention because it is self-induced, sensitive, accurate, and operationally simple. This article summarizes five aspects of the recent developments of DNA-strand displacement in DNA computing:(1) cascading circuits;(2) catalyzed reaction;(3) logic computation;(4) DNA computing on surfaces; and(5) logic computing based on nanoparticles guided by strand displacement. The applications and mechanisms of strand displacement in DNA computing are discussed and possible future developments are presented.展开更多
基金supported by National Natural Science Foundation of China (Grant No.10971079)Liaoning Province Education Department (Grant No. L2011001)
文摘By using simultaneous triangularization technique, similarity for operator weighted shifts with finite multiplicity is characterized in terms of K0-group of commutant algebra. The result supports the conjecture posed by Cao et al. in 1999. Moreover, we discuss the relations between similarity and quasi-similarity for operator weighted shifts.
基金supported by the National Natural Science Foundation of China(61272246,61370099,61272161,61127005,61133010,61425002,61320106005)the Graduate Education in Shaanxi Normal University Innovation Fund
文摘DNA computing, currently a hot research field in information processing, has the advantages of parallelism, low energy consumption, and high storability, therefore, it has been applied to a variety of complicated computational problems. The emerging field of DNA nanotechnology has also developed quickly; within it, the method of DNA strand displacement has drawn great attention because it is self-induced, sensitive, accurate, and operationally simple. This article summarizes five aspects of the recent developments of DNA-strand displacement in DNA computing:(1) cascading circuits;(2) catalyzed reaction;(3) logic computation;(4) DNA computing on surfaces; and(5) logic computing based on nanoparticles guided by strand displacement. The applications and mechanisms of strand displacement in DNA computing are discussed and possible future developments are presented.
