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.     

Weighted Composition Operators from the Bloch Spaces to Weighted Hardy Spaces on Bounded Symmetric Domains*

Let B_E be a bounded symmetric domain realized as the unit open ball of JB*-triples.The authors will characterize the bounded weighted composition operator from the Bloch space B(BE) to weighted Hardy space H_v^∞ in terms of Kobayashi distance.The authors also give a sufficient condition for the compactness,and also give the upper bound of its essential norm.As a corollary,they show that the boundedness and compactness are equivalent for composition operator fromB(B...     

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.     

Search of truncation of (N−1) electron basis containing full connected triple excitations in computing main and satellite ionization potentials via Fock‐space coupled cluster approach

A valence‐universal multireference coupled cluster (VUMRCC) theory, realized via the eigenvalue independent partitioning (EIP) route, has been implemented with full inclusion of triples excitations for computing and analyzing the entire main and several satellite peaks in the ionization potential spectra of several molecules. The EIP‐VUMRCC method, unlike the traditional VUMRCC theory, allows divergence‐free homing‐in to satellite roots which would otherwise have been plagued by intruders, and is thus numerically more robust to obtain more efficient and dependable computational schemes allowing more extensive use of the approach. The computed ionization potentials (IPs) as a result of truncation of the (N−1) electron basis manifold involving virtual functions such as 2h‐p and 3h‐2p by different energy thresholds varying from 5 to 15 a.u. with 1 a.u. intervals as well as thresholds such as 20, 25, and 30 a.u. have been carefully looked into. Cutoff at around 25 a.u. turns out to be an optimal threshold. Molecules such as C₂H₄ and C₂H₂ (X = D,T), and N₂ and CO (X = D,T,Q) with Dunning's cc‐pVXZ bases have been investigated to determine all main and 2h‐p shake‐up and 3h‐2p double shake‐up satellite IPs. We believe that the present work will pave the way to a wider application of the method by providing main and satellite IPs for some problematic N‐electron closed shell systems. © 2013 Wiley Periodicals, Inc.     

Ultrasound-assisted synthesis of Li-rich mesoporous LiMn2O4 nanospheres for enhancing the electrochemical performance in Li-ion secondary batteries

The hierarchically structured mesoporous LiMn₂O₄ (LMO) nanospheres were synthesized using a template-free self-assembly process that was coupled with ultrasound (U). The ultrasound technique suggested here is very powerful for controlling an ordered nanostructure and improving crystallinity with large single-crystalline domains. Owing to the hierarchical mesoporous structure and high crystallinity, U-LMO provides an excellent rate capability and cycle stability with a capacity retention of more than 98% up to 50 cycles at a 0.2 C rate. Here, we demonstrate that mesoporous U-LMO nanospheres were fabricated to enhance the electrochemical performance and protect it from structurally significant collapsing because of high crystallinity.     

Interpolatory Hermite splines on rectangular domains

Based on Bittner and Urban’s construction of interpolatory multiwavelets [Kai Bittner, Karsten Urban, On interpolatory divergence-free wavelets, Math. Comput. 76 (258) (2007) 903-929], we use the truncation method to obtain interpolatory multiwavelets on rectangular domains in this paper. In addition, the characterization for the corresponding functional spaces is given.     

泛Clifford分析中无界域上的Cauchy积分公式和Cauchy-Pompeiu公式

本文研究了泛Clifford分析中的Cauchy积分公式和Cauchy-Pompeiu公式.通过引入修正的Cauchy核,得出了取值在泛Clifford代数上的两公式在无界域上的表达式.此两公式是有界域上的相应结果的推广,并为研究无界域上的边值问题打下了基础.     

对偶导集及其应用

借助对偶范畴的思想和方法在点集拓扑学中引入了对偶导集概念,讨论了对偶导集和对偶导集运算的相关性质.并以此为基础引入了对偶连通空间的概念,讨论了对偶连通空间和连通空间之间的关系,借此给出了不连通空间的几个等价刻画.为拓扑空间的研究提供了新的途径.     

On locally convex hypersurfaces in Hadamard manifolds

Locally convex compact hypersurfaces immersed in a hollow simply connected Riemannian space of nonpositive sectional curvature are considered. They are proved to be convex hypersurfaces homeomorphic to the sphere. A similar result for immersed hypersurfaces with nonpositive definite second quadratic form of rank no smaller than one is obtained. Translated fromMatematicheskie Zametki, Vol. 67, No. 4, pp. 498–507, April, 2000.