Biquandles are algebraic objects with two binary operations whose axioms encode the generalized Reidemeister moves for virtual knots and links. These objects also provide set theoretic solutions of the well-known Yang-Baxter equation. The first half of this paper proposes some natural constructions of biquandles from groups and from their simpler counterparts, namely, quandles. We completely determine all words in the free group on two generators that give rise to (bi)quandle structures on all groups. We give some novel constructions of biquandles on unions and products of quandles, including what we refer as the holomorph biquandle of a quandle. These constructions give a wealth of solutions of the Yang-Baxter equation. We also show that for nice quandle coverings a biquandle structure on the base can be lifted to a biquandle structure on the covering. In the second half of the paper, we determine automorphism groups of these biquandles in terms of associated quandles showing elegant relationships between the symmetries of the underlying structures. 相似文献
Acta Mathematicae Applicatae Sinica, English Series - Joint analysis of multiple phenotypes can have better interpretation of complex diseases and increase statistical power to detect more... 相似文献
This paper focus on the event-triggered sliding mode controller design for discrete-time switched genetic regulatory networks (GRNs) with persistent dwell time (PDT) switching. Firstly, the observation error dynamics of switched GRNs with PDT is constructed in the light of event-triggered sliding mode control (SMC) scheme. Next, sufficient conditions are derived to ensure the exponential stability of the augmented plant. Moreover, an event-triggered SMC law is synthesized to impel the system trajectories onto the sliding surface in a finite time. Finally, a verification example is provided to illustrate the effectiveness and potential of the proposed method. 相似文献
Small molecules are difficult to detect by conventional surface plasmon resonance (SPR) spectroscopy due to the fact that the changes in the refractive index resulted from the binding process of small biomolecules are quite small. Here, we report a simple and effective method to detect small biomolecule using SPR spectroscopy and electrochemistry by catalyzed deposition of metal ions on SPR gold film. As an example, the ascorbic acid-mediated deposition of Ag on gold film was monitored by in situ SPR spectrum. The deposition of Ag atom on gold film resulted in an obvious decrease of depth in SPR angular scan curves of reflectance intensity and minimum reflectivity angle. The depth change of the SPR reflectance intensity and minimum reflectivity angle curves mainly relied on the amount of Ag atom deposited on gold film that can be controlled by the concentration of ascorbic acid. By monitoring the deposition of Ag atom on gold film, ascorbic acid was detected in the concentration range of 2 × 10−5 M to 1 × 10−3 M. After each of detections, the SPR sensor surface was completely regenerated by a potential step that stripped off the Ag atom. Furthermore, the regeneration process of the sensor surface provides the feasibility for detecting the concentration of ascorbic acid by electrochemical method. 相似文献
Photoresists are essential for the fabrication of flexible electronics through all-photolithographic processes. Single component semiconducting photoresist exhibits both semiconducting and photo-patterning properties, and as a result, the device fabrication process can be simplified. However, the design of semiconducting polymeric photoresist with ambipolar semiconducting property remains challenging. In this paper, we report a single component semiconducting photoresist (PFDPPF4T-N3) by incorporating azide groups and noncovalent conformation locks into the side alkyl chains and conjugated backbones of a diketopyrrolopyrrole-based conjugated polymer, respectively. The results reveal that PFDPP4FT-N3 exhibits ambipolar semiconducting property with hole and electron mobilities up to 1.12 and 1.17 cm2 V?1 s?1, respectively. Moreover, field effect transistors with the individual photo-patterned thin films of PFDPPF4T-N3 also show ambipolar semiconducting behavior with hole and electron mobilities up to 0.66 and 0.80 cm2 V?1 s?1, respectively. These results offer a simple yet effective design strategy for high-performance single component semiconducting photoresists, which hold great potential for flexible electronics processed by all photolithography.
The dirhodium-catalyzed aziridination of olefins with chiral sulfonimidamides as iminoiodane precursors has been investigated under stoichiometric conditions. Diastereoisomeric excesses of up to 82% have been achieved using [Rh2{(S)-nttl}4] as catalyst. Matching and mismatching effects were observed upon use of chiral rhodium(II) carboxylate catalysts. 相似文献