Five Rare μ4‐O‐Centered Ln6 Clusters with Single‐Molecule Magnet Behavior for Dy6

Five hexanuclear lanthanide clusters of composition [Ln₆(μ₄‐O)₂(HCOO)₂L₄(HL′)₂(dmf)₂] [Ln=Dy ( 1 ), Er ( 2 ), Ho ( 3 ), Tb ( 4 ), Gd ( 5 ); H₂L=2‐{[2‐(hydroxymethyl)phenylimino]methyl}‐6‐methoxyphenol; H₃L′=3‐{[2‐(hydroxymethyl)phenylimino]methyl}benzene‐1,2‐diol; H₃L′ was derived in situ from the H₂L ligand] were prepared under solvothermal conditions. The [Ln₆] cores of 1 – 5 possess an unprecedented motif, namely, two tetrahedron Ln₄ units sharing an edge and two vertices. The six Ln^III ions of 1 – 5 are connected through two μ₄‐O anions. Magnetic susceptibility studies reveal that complex 1 exhibits frequency dependence of the alternating current susceptibility typical of single‐molecule magnets. Complex 1 possesses a relatively large energy barrier of 85 K among all of the reported Dy₆ single‐molecule magnets.     

一种由1,4,7-三氮杂环壬烷形成的三脚架配体及其与高氯酸钠组装的含[Na4(ClO4)4]四面体晶体结构

合成了一种多齿的三脚架配体：三（2-（4,7-二甲磺酸基-1,4,7-三氮杂环壬烷基）甲基苄基）胺,即N（CH₂-o-C₆H₄-CH₂-tacnTs₂）₃（L）,其中Ts=tosyl。它包含3个1,4,7-三氮杂环壬烷连接在三苄基胺的邻位。该配体在高氯酸钠存在情况下结晶,自组装得到4个钠离子形成的四面体结构晶体：[Na₄（L）（CH₃CN）（ClO₄）₄（H₂O）₃]_n。该晶体结构用X射线单晶衍射、粉末衍射、红外光谱和热重分析表征,并用紫外吸收和荧光对其光学性质进行表征。     

细胞膜锚定DNA四面体传感器实时监测外泌体的分泌

外泌体是细胞主动分泌的一种纳米级双层膜结构的小囊泡,能够直接反映分泌细胞的生理和功能状态,进行细胞间的物质运输和信息通讯,并参与多种生理及病理过程.本文针对细胞分泌外泌体的动态过程,以DNA四面体为基础,结合细胞膜修饰技术和荧光成像技术,构建了一种易操作、高稳定性的细胞膜表面DNA四面体传感器,应用于不同细胞类型分泌外泌体的实时监测. DNA四面体传感器通过脚支链与疏水性胆固醇探针的杂交互补作用锚定于细胞膜表面,利用四跨膜蛋白CD63核酸适配体序列特异性捕获细胞膜表面释放的外泌体,通过监测细胞膜表面荧光的变化,实时测定外泌体的分泌情况.     

一种具有化学发光性能的锆基金属有机四面体

利用二氯二茂锆与4,4′-(蒽-9,10-二基)二苯甲酸自组装制备了一种锆基金属有机四面体(ZrT-6), 并将其应用于过氧草酸酯类化学发光的研究, 发现其在发光强度和寿命方面均优于所使用的配体. 更重要的是, ZrT-6在化学发光过程中保持了良好的稳定性, 为其进一步的实际应用打下了坚实的基础. 该工作对过氧草酸酯类化学发光系统的设计具有借鉴意义.     

Is There a “Most Chiral Tetrahedron”?

A degree of chirality is a function that purports to measure the amount of chirality of an object: it is equal for enantiomers, vanishes only for achiral or degenerate objects and is similarity invariant, dimensionless and normalisable to the interval [0,1]. For a tetrahedron of non-zero three-dimensional volume, achirality is synonymous with the presence of a mirror plane containing one edge and bisecting its opposite, and hence it is easy to design degree-of-chirality functions based on edge length that incorporate all constraints. It is shown that such functions can have largest maxima at widely different points in the tetrahedral shape space, and by incorporation of appropriate factors, the maxima can be pushed to any point in the space. Thus the phrase "most chiral tetrahedron" has no general meaning: any chiral tetrahedron is the most chiral for some legitimate choice of degree of chirality.     

不包含｛4，5，7｝-圈平面图的结构性质

根据每个不包含｛4,5,6,7｝‐圈的平面图是3‐可染的定理,研究不包含｛4,5,7｝‐圈平面图是3‐可染极小反例的几个性质,为研究每个不包含｛4,5,7｝‐圈平面图是3‐可染的观点做了辅垫。     

A Lobatto interpolation grid in the tetrahedron

A sequence of increasingly refined interpolation grids insidethe tetrahedron is proposed with the goal of achieving uniformconvergence and ensuring high interpolation accuracy. The numberof interpolation nodes, N, corresponds to the number of termsin the complete mth-order polynomial expansion with respectto the three tetrahedral barycentric coordinates. The proposedgrid is constructed by deploying Lobatto interpolation nodesover the faces of the tetrahedron, and then computing interiornodes using a simple formula that involves the zeros of theLobatto polynomials. Numerical computations show that the Lebesgueconstant and interpolation accuracy of the proposed grid comparefavourably with those of alternative grids constructed by solvingoptimization problems. The condition number of the mass matrixis significantly lower than that of the uniform grid and comparableto that of optimal grids proposed by previous authors.     

关于四面体的一个向量恒等式及其推论

利用解析法,给出空间任意一点与四面体体积有关的一个向量恒等式,并给出若干推论.     

正四面体生成的Sierpinski块的Hausdorff测度

构造了正四面体生成的一般Sierpinski块,通过构造其覆盖序列,得到了一般Sierpinski块的Hausdorff测度的上界,即ss1a22,　　Hs(V)≤61 34-2a 1657a2-121-a39a2　　(0.32≤a≤0.5).