Hausdorff measure of the level sets of multi-parameter wiener processes in one dimension

LetZ _N (t) be anN-parameter Wiener process in one dimension, and $$E(x,T) = \left\{ {t = (t_1 , \cdot \cdot \cdot ,t_N ):Z_N (t) = x,0 \leqslant t_1 , \cdot \cdot \cdot ,t_N \leqslant T} \right\}$$ . Then we obtain that with probability one, the Hausdorff measure function ofE(x,T) is $$\psi _N (r) = r^{N - \tfrac{1}{2}} (\log \log r^{ - 1} )^{\tfrac{1}{2}} ,\forall r \in (0,\frac{1}{4})$$ for anyx∈R ¹ andT>0.     

Study of cross-conjugated iso-polytriacetylenes and related oligoenynes

Two series of monodisperse cross-conjugated oligomers based on enyne repeat units have been realized. The first class of molecules, iso-polytriacetylenes (iso-PTAs, 2), was divergently synthesized using an iterative sequence of palladium-catalyzed cross-coupling reactions of vinyl triflate 5 with terminal alkynes. The second series of oligoenynes (17-20) are based on an octatetrayne backbone, and result from homocoupling of the differentially protected iso-PTA oligomers 8-11. The longest member of this series, 20, spans ca. 5.6 nm from Si atom to Si atom and is composed of a contiguous sequence of 44 sp and sp(2) carbons. The lowest energy electronic absorption band for iso-PTA dimers in the progression 13 --> 9 --> 16 is consistently red-shifted as a result of extending the cross-conjugated structure. A similar comparison within each series (i.e., 16, 6-7, or 17-20), however, suggests little effect on the electronic characteristics of these molecules as oligomer length is increased. The solid-state properties of one derivative, 17, are also described.     

合成香料β-大马酮的高效液相色谱分析

本文提出了用分析型HPLC仪器制备β-大马酮标准品的方法及用HPLC测定β-大马酮含量的方法。制备色谱柱为Zorbax SIL 9.4 mmφ×25cm,流动相为石油醚(30～60℃)/乙醚98.5/1.5。分析用色谱柱为Shim CLC SIL 6 mmφ×15cm(岛津全多孔硅胶柱),流动相为石油醚(60—90℃)/无水乙醇99.88/0.12,检测器为紫外可见分光光度检测器。波长253nm或302nm,标准曲线的线性范围0～1.4mg/ml。峰高或峰面积均可用于测定,回收率100.7%。