弱Orlicz鞅空间的弱原子分解及其应用

对3类由凹函数生成的弱Orlicz鞅空间建立了相应的弱原子分解.作为应用,首先给出了这些弱Orlicz鞅空间上次线性算子有界的一个充分条件,并在此基础上证明了一些弱型鞅不等式,然后证明了关于这些弱Orlicz鞅空间的Marcinkiewicz型插值定理.     

Photoinduced alignment of polymer liquid crystals containing azobenzene moieties in the side group VII. On He-Ne laser beam irradiation

Photoinduced alignment in a polymer liquid crystal prepared from 6-{1-[4-(2-cyano-4-nitrophenylazo)phenyl]piperazino}hexyl acrylate and 4'-[6-(methacryloyloxy)hexyloxy]-4-cyanobiphenyl was investigated for the first time on irradiation with a polarized He-Ne laser beam at 633 nm. The azobenzene moieties as well as the inert cyanobiphenyl mesogenic units were aligned with the molecular long axis perpendicular to the polarization direction of the irradiation light. Alignment induced on short irradiation was reversible, while that induced under prolonged irradiation was irreversible due to the occurrence of crosslinking which might be caused by photoinduced decomposition of the azobenzene moieties during the photoirradiation process.     

Photo-induced control of bubble domains in chiral–nematic liquid crystal by a violet laser beam

The stable bubble domains generated by mixing 10% of chiral molecules into an azobenzene liquid crystal (LC)-doped nematic host can be optically controlled by a violet laser beam (415 nm). The photon-induced reversible trans–cis photo-isomerisation of azobenzene changes the helical twisting power (HTP) of LC mixtures in which the HTP of cis-azobenzene LC is lower than trans-azobenzene LC. Under the irradiation of an optical field (>20 mW cm^???2), the helical pitch distance, which is inverted proportional to the HTP, increases and the bubble domains disappear. Immediate obstruction of laser light irradiation initiates cholesteric nucleation, merging of domains and the subsequent generation of stably dispersed bubble domains.     

Fine singularity analysis of solutions to the Laplace equation

We present here a fine singularity analysis of solutions to the Laplace equation in special polygonal domains in the plane. We assume piecewise constant Neumann data on one component of the boundary. Our motivation is to study the so‐called Berg effect, which is explained in the introduction. Copyright © 2014 John Wiley & Sons, Ltd.     

等维Cartan-Hartogs域双全纯映射的特征

本文考虑了等维Cartan-Hartogs域之间的全纯映射.如果Cartan-Hartogs域Ω^Bm(μ)不是球,则它上面存在一函数X使得它在Ω^Bm(μ)的任一全纯自同构作用下不变.通过直接计算得到:如果等维Cartan-Hartogs域间的全纯映射F保持函数X不变,则F必是双全纯映射.由此可得如果Cartan-Hartogs域Ω^Bm(μ)不是球,Ω^Bm(μ)的全纯自映射是自同构的充要条件是F保持函数X不变.     

Incommensurate Phase in Λ-cobalt (III) Sepulchrate Trinitrate Governed by Highly Competitive N−H⋅⋅⋅O and C−H⋅⋅⋅O Hydrogen Bond Networks**

Phase transitions in molecular crystals are often determined by intermolecular interactions. The cage complex of [Co(C₁₂H₃₀N₈)]³⁺ ⋅ 3 NO₃⁻ is reported to undergo a disorder-order phase transition at T_c1 ≈133 K upon cooling. Temperature-dependent neutron and synchrotron diffraction experiments revealed satellite reflections in addition to main reflections in the diffraction patterns below T_c1. The modulation wave vector varies as function of temperature and locks in at T_c3≈98 K. Here, we demonstrate that the crystal symmetry lowers from hexagonal to monoclinic in the incommensurately modulated phases in T_c1<T<T_c3. Distinctive levels of competitions: trade-off between longer N−H⋅⋅⋅O and shorter C−H⋅⋅⋅O hydrogen bonds; steric constraints to dense C−H⋅⋅⋅O bonds give rise to pronounced modulation of the basic structure. Severely frustrated crystal packing in the incommensurate phase is precursor to optimal balance of intermolecular interactions in the lock-in phase.     

Reachable set bounding for nonlinear perturbed time-delay systems: The smallest bound

In this letter, we propose a new approach to obtain the smallest box which bounds all reachable sets of a class of nonlinear time-delay systems with bounded disturbances. A numerical example is studied to illustrate the obtained result.     

Artificial Splitting of a Non‐Ribosomal Peptide Synthetase by Inserting Natural Docking Domains

The interaction in multisubunit non‐ribosomal peptide synthetases (NRPSs) is mediated by docking domains that ensure the correct subunit‐to‐subunit interaction. We introduced natural docking domains into the three‐module xefoampeptide synthetase (XfpS) to create two to three artificial NRPS XfpS subunits. The enzymatic performance of the split biosynthesis was measured by absolute quantification of the products by HPLC‐ESI‐MS. The connecting role of the docking domains was probed by deleting integral parts of them. The peptide production data was compared to soluble protein amounts of the NRPS using SDS‐PAGE. Reduced peptide synthesis was not a result of reduced soluble NRPS concentration but a consequence of the deletion of vital docking domain parts. Splitting the xefoampeptide biosynthesis polypeptide by introducing docking domains was feasible and resulted in higher amounts of product in one of the two tested split‐module cases compared to the full‐length wild‐type enzyme.