Bismuth(III) Flavonolates: The Impact of Structural Diversity on Antibacterial Activity,Mammalian Cell Viability and Cellular Uptake

A series of homoleptic and heteroleptic bismuth(III) flavonolate complexes derived from six flavonols of varying substitution have been synthesised and structurally characterised. The complexes were evaluated for antibacterial activity towards several problematic Gram-positive (Staphylococcus aureus, methicillin-resistant Staphylococcus aureus (MRSA), and vancomycin-resistant Enterococcus (VRE)) and Gram-negative (Escherichia coli, Pseudomonas aeruginosa) bacteria. The cell viability of COS-7 (monkey kidney) cells treated with the bismuth flavonolates was also studied to determine the effect of the complexes on mammalian cells. The heteroleptic complexes [BiPh(L)₂] (in which L=flavonolate) showed good antibacterial activity towards all of the bacteria but reduced COS-7 cell viability in a concentration-dependent manner. The homoleptic complexes [Bi(L)₃] exhibited activity towards the Gram-positive bacteria and showed low toxicity towards the mammalian cell line. Bismuth uptake studies in VRE and COS-7 cells treated with the bismuth flavonolate complexes indicated that Bi accumulation is influenced by both the substitution of the flavonolate ligands and the degree of substitution at the bismuth centre.     

非交换加权Lorentz空间的对偶空间

设μ是一个半有限von Neumann代数.对于0P∞,0q≤∞,定义了非交换加权Lorentz空间Λ_ω~(p,q)(μ)及其associate空间Λ_ω~(p,q)(μ)',给出了空间Λ_ω~(p,q)(μ)'和Λ_ω~(p,q)(μ)'的一些基本性质.应用这些性质,还给出了非交换加权Lorentz空间Λ_ω~p(μ),0P∞的对偶空间.     

Free cumulants,Schröder trees,and operads

The functional equation defining the free cumulants in free probability is lifted successively to the noncommutative Faà di Bruno algebra, and then to the group of a free operad over Schröder trees. This leads to new combinatorial expressions, which remain valid for operator-valued free probability. Specializations of these expressions give back Speicher's formula in terms of noncrossing partitions, and its interpretation in terms of characters due to Ebrahimi-Fard and Patras.     

Orthonormal bases generated by Cuntz algebras

We show how some orthonormal bases can be generated by representations of the Cuntz algebra; these include Fourier bases on fractal measures, generalized Walsh bases on the unit interval and piecewise exponential bases on the middle third Cantor set.     

Several Jordan-algebraic aspects of optimization†

We describe some concepts from the theory of Euclidean Jordan algebras and their use in optimization theory. This includes: primal-dual algorithms, optimality conditions, convexity of spectral functions, proof of some inequalities and a Jordan-algebraic version of Horn–Schur theorem     

PEG接枝氧化石墨烯的制备与细胞成像

通过酯化反应将不同分子量的聚乙二醇（PEG）接枝到氧化石墨烯（GO）表面,得到系列GO-PEG。利用傅里叶变换红外光谱（FTIR）、拉曼光谱（Raman）、扫描电子显微镜（SEM）对GO-PEG的结构和形貌进行了表征,用热重分析（TGA）测定了GO-PEG中PEG的接枝量。SEM结果表明GO-PEG的剥离程度高于GO。GO-PEG在磷酸盐缓冲溶液中具有良好的分散稳定性,稳定性与接枝量呈正相关。GO-PEG通过非共价键合作用对荧光素（Flu）的负载量可达1.75mg·mg^-1,且负载量受接枝量影响;另外,GO-PEG对Flu的释放行为具有pH值触发药物释放性能。将接枝PEG的端羟基与Flu共价键合,所得GO-PEG₆₀₀₀-Flu荧光探针实现了对HepG₂细胞的成像。     

Factoriality for the reductive Zassenhaus variety and quantum enveloping algebra

Let U(g)$U(\mathfrak{g})$ be the enveloping algebra of a finite dimensional reductive Lie algebra g$\mathfrak{g}$ over an algebraically closed field of prime characteristic. Let _U?,P(s:)$U_{?,P}(\mathfrak{s}:)$ be the simply connected quantum enveloping algebra at the root of unity ?  , of a complex semi-simple finite dimensional Lie algebra s:$\mathfrak{s}:$. We show, by similar proofs, that the centers of both are factorial. While the first result was established by R. Tange [32] (by different methods), the second one confirms a conjecture in [4]. We also provide a general criterion for the factoriality of the centers of enveloping algebras in prime characteristic.