Homomorphisms to oriented cycles

We discuss the existence of homomorphisms to oriented cycles and give, for a special class of cyclesC, a characterization of those digraphs that admit, a homomorphism toC. Our result can be used to prove the multiplicativity of a certain class of oriented cycles, (and thus complete the characterization of multiplicative oriented cycles), as well as to prove the membership of the corresponding decision problem in the classNPcoNP. We also mention a conjecture on the existence of homomorphisms to arbitrary oriented cycles.     

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.     

Modular synthesis of chiral homo- and heterotrisoxazolines. Improving the enantioselectivity in the asymmetric Michael addition of indole to benzylidene malonate

A simple approach to a diverse set of chiral trisoxazolines is described. Deprotonation of bisoxazolines 2, followed by treatment of 2-chloromethyloxazolines 3, affords chiral trisoxazolines, including chiral homo- and hetero-trisoxazolines in good to high yields. These trisoxazolines are successfully applied in the asymmetric reaction of indole with benzylidene malonate, and ee's up to 93% were obtained.     

Theoretical Study on the Mass Transfer of Metal Ions in Ion Exchange Process

The kinetics of ion exchange between Ca2 , Mg2 , Co(Ⅱ), Cu(Ⅱ),Ni(Ⅱ), Fe(Ⅲ), y3 or Sm3 , respectively, in 0.50 mol/L HC1 and H on macrorecticular sulfonic ion exchange resin and the kinetics of the same reactions (M -H exchange) when Mn(Ⅱ) coexisted in resin phase as accelerating ion were studied. The accelerating effect manifested and its rule are consistent with the accelerating effect theory based on the concept concerned with adsorption electrical double layer which has been suggested in a previous paper published.     

示波极谱法测定地质样品中痕量氟

提出了地质样品经半熔法分解后,8-羟基喹啉沉淀干扰组分,过量的8-羟基喹啉用四氯化碳萃取分离,在六次甲基四胺缓冲液中测定Ce(Ⅲ)-ALC-F~-络合吸附波。并对标准物质中F~-进行测定,其测定值与推荐值吻合。方法的RSD为5.6％,检出限为0.6μg·g~(-1)。     

稀土元素在LD30铝合金真空钎焊中的作用

研究了添加La和Ce的Al-Si基钎料真空钎焊LD30铝合金接头的力学性能，微观组织形貌和EDS，并与未添加稀土元素的Al-Si基钎料真空钎焊接头进行对比。结果表明，添加稀土元素的LD30铝合金真空钎焊接头抗拉强度为288MPa，达母材抗拉强度的97．6％，明显高于未添加稀土的LD30合金真空钎焊接头。其机制在于La,Ce能够明显提高Al-Si基钎料与LD30铝合金的润湿性能，改善LD30铝合金真空钎焊接头焊缝及其基体中杂质元素的分布，促进钎料和母材中各元素的均匀扩散，从而提高真空钎焊接头的力学性能。