Connectedness of the invertibles in certain nest algebras of order type ω

We solve the connectedness problem for a class of nests of order type ω with finite dimensional atoms.     

A Disulfide Switch Providing Absolute Handedness Control in Double Helices via Conversion from the Antiparallel to Parallel Helical Pattern

A strategy to reversibly switch the parallel/antiparallel helical conformation of aromatic double helices through the formation/breakage of a disulfide bond is presented. Single-crystal X-ray structures, NMR, and circular dichroism spectroscopy demonstrate that the double helices with terminal thiol groups favor an antiparallel helical arrangement both in the solid state and in solution, while the P/M bias of helicity induced by chiral segments from another extremity of the sequence is weak in this structural motif. The antiparallel helices can be rearranged to parallel helices through the disulfide connection of the sequences. This change enhances the bias of helical handedness and results in absolute chirality control of the double helices. The handedness-mediated process can be governed by the oxidation-reduction cycle, thereby switching the structural arrangement and the enhancement of chiral bias. In addition, we find that the sequences can dimerize into an intermolecular double helix with the disulfide connection. And the helical handedness is also fully controlled due to the head-to-head structural motif.     

An improved watermarking method based on double random phase encoding technique

An improved watermarking method, based on the double random phase encoding technique and the cascaded-phases iterative algorithm and random-phase-shift algorithm, is proposed. This method can significantly reduce the needs of watermarking information storage for different multimedia products, and provide a reasonable criterion of determining the authenticity of a product for the copyright owner. This method can also be applied to track the source of copies. The effectiveness of this method was verified through numerical simulations.     

Collective dynamics of genetic oscillators with cell-to-cell communication: a study case of signal integration

This paper investigates the effect of integration of intracellular and extracellular signals on collective dynamics based on a multicellular system with cell-to-cell communication. Using a mathematical model of genetic repressilators coupled to quorum sensing, we show that the changes in parameters of a certain kind of cis-regulatory input function that quantifies the signal integration can lead to the change of coupling type from phase-attractive to phase-repulsive coupling or vice versa. Consequently, the multicellular system can exhibit, in both coupling cases, different collective behaviors in terms of synchronization and clustering. We give a general method of determining coupling type, elucidate the mechanism of generating these phenomena and present a criterion for stability of cluster states, mainly by analyzing phase interaction functions.     

Successive stepwise evolution of host layer‐stacking framework upon the intercalation of mobile vapor guests within side‐chain layers

For the ordered phases of hairy‐rod semiconductive poly(2,5‐bis(3‐tetradecylthiophene‐2‐yl)thieno[3,2‐b]thiophene) (PBTTT) sandwiched in between crystalline platelets of hexamethylbenzene, the successive stepwise evolution of layer‐stacking framework upon guest intercalation has been studied in this research. The direct consequence of the guest intercalation into side‐chain layers is evaluated to cause the lateral shift of thiophene backbones along π–π stacking, resulting in stepwise shift of ultraviolet absorption wavelength. The thermal motions of vapor guests within disordering side‐chain layers subsequently cause progressive expansion of host stacking framework. With the increase in side‐chain length, thicker layers of disordering side chains in liquid crystals (LCs) accommodate additional vapor guests and larger amplitudes of thermal motions of guests, hence promoting the level of reversible d‐spacing change. The mixing between mobile vapor guests and aliphatic side chains is clarified as the mechanism of guest intercalation, which rationalizes successive guest intercalation during heating and the contribution of disordering side‐chain layers. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017 , 55, 1448–1456