Copper-containing dendromesogens: the influence of the metal on the mesomorphism

The synthesis and liquid crystalline behaviour of the first and second generations of a dendrimeric structure based on poly(propyleneimine)(DAB-dendr(NH₂)_x) are reported. 4-(4-n-Alkoxybenzoyloxy)salicylaldehydes are used as mesogenic moieties attached at the peripheral amino groups of the dendrimers giving rise to dendromesogens with four and eight mesogenic branches. From these dendromesogens, considered as organic ligands, were prepared six metal-containing dendrimers which incorporate two or four copper atoms in their structures. All the dendrimeric ligands and three of the metal-containing dendrimers exhibit liquid crystalline properties which were studied by optical microscopy, DSC, X-ray diffraction and EPR spectroscopy.     

On Nash approximation of complex analytic sets in Runge domains

We prove that every complex analytic set X in a Runge domain Ω   can be approximated by Nash sets on any relatively compact subdomain _Ω0${\Omega }_0$ of Ω. Moreover, for every Nash subset Y of Ω   with Y⊂X$Y\subset X$, the approximating sets can be chosen so that they contain Y∩_Ω0$Y\cap {\Omega }_0$. As a consequence, we derive a necessary and sufficient condition for a complex analytic set X to admit a Nash approximation which coincides with X along its arbitrary given subset.     

A uniqueness theorem of radially symmetric positive stationary solutions for a competition–diffusion system

In this paper, as a first step to study the global structure of solution, we treat a class of reaction–diffusion systems with competitive interaction, and discuss a uniqueness theorem of radially symmetric solutions for the system. To do this, the comparison principle and the shooting method are employed, and the spatial profile is investigated.     

Korn inequality on irregular domains

In this paper, we study the weighted Korn inequality on some irregular domains, e.g., s-John domains and domains satisfying quasihyperbolic boundary conditions. Examples regarding sharpness of the Korn inequality on these domains are presented. Moreover, we show that Korn inequalities imply certain Poincaré inequality.     

A blow‐up criterion to the 2D full compressible magnetohydrodynamic equations

We establish a new regularity criterion for the 2D full compressible magnetohydrodynamic system in a bounded domain. 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.     

实对称五对角矩阵Procrustes问题

本文研究了实对称五对角矩阵Procrustes.利用矩阵的奇异值分解简化问题,得到了实对称五对角矩阵X极小化,最后给出数值算例说明方法的有效性.     

Universal C*-algebras defined by completely bounded unital homomorphisms

Suppose A is a unital C*-algebra and r 1.In this paper,we define a unital C*-algebra C_(cb)*(A,r) and a completely bounded unital homomorphism α_r:A → C_(cb)*(A,r)with the property that C_(cb)*(A,r)=C*(α_r(A))and,for every unital C*-algebra B and every unital completely bounded homomorphism φ:A→ B,there is a(unique)unital *-homomorphism π:C_(cb)*(A,r)→B such thatφ=πoα_r.We prove that,if A is generated by a normal set {t_λ:λ∈Λ},then C_(cb)*(A,r)is generated by the set {α_r(t_λ):λ∈Λ}.By proving an equation of the norms of elements in a dense subset of C_(cb)*(A,r)we obtain that,if Β is a unital C*-algebra that can be embedded into A,then C_(cb)*(B,r)can be naturally embedded into C(cb)*(A,r).We give characterizations of C_(cb)*(A,r)for some special situations and we conclude that C_(cb)*(A,r)will be "nice" when dim(A)≤ 2 and "quite complicated" when dim(A)≥ 3.We give a characterization of the relation between K-groups of A and K-groups of C_(cb)*(A,r).We also define and study some analogous of C_(cb)*(A,r).     

Plasmonic Pollen Grain Nanostructures: A Three-Dimensional Surface-Enhanced Raman Scattering (SERS)-Active Substrate

A new route has been developed to design plasmonic pollen grain-like nanostructures (PGNSs) as surface-enhanced Raman scattering (SERS)-active substrate. The nanostructures consisting of silver (Ag) and gold (Au) nanoparticles along with zinc oxide (ZnO) nanoclusters as spacers were found highly SERS-active. The morphology of PGNSs and those obtained in the intermediate stage along with each elemental evolution has been investigated by a high-resolution field emission scanning electron microscopy. The optical band gaps and crystal structure have been identified by UV-vis absorption and X-ray powder diffraction (XRD) measurements, respectively. For PGNSs specimen, three distinct absorption bands related to constituent elements Ag, Au, and ZnO were observed, whereas XRD peaks confirmed the existence of Ag, Au, and ZnO within the composition of PGNSs. SERS-activity of PGNSs was confirmed using Rhodamine 6G (R6G) as Raman-active dyes. Air-cooled solid-state laser kits of 532 nm were used as excitation sources in SERS measurements. SERS enhancement factor was estimated for PGNSs specimen and was found as high as 3.5×10⁶. Finite difference time domain analysis was carried out to correlate the electromagnetic (EM) near-field distributions with the experiment results achieved under this investigation. EM near-field distributions at different planes were extracted for s-, p- and 45° of incident polarizations. EM near-field distributions for such nanostructures as well as current density distributions under different circumstances were demonstrated and plausible scenarios were elucidated given SERS enhancements. Such generic fabrication route as well as correlated investigation is not only indispensable to realize the potential of SERS applications but also unveil the underneath plasmonic characteristics of complex SERS-active nanostructures.