A Relation between Hausdorff Dimension and a Condition on Time Sets for the Image by the Brownian Sheet to Possess Interior Points

We prove that if W_{N, d} is a Brownian sheet mapping to R^d and E is a set in (0, )^N of Hausdorff dimensiongreater than , then for almost every rotation about a point x and translation _x such that _x(E) (0, )^N, the set _x(E) is such that almost surely W(E) containsinterior points. The techniques are adapted from Kahane andRosen and generalize to higher dimensional time and range.     

Preparation, characterization and thermolysis of metal nitrate complexes with 4,4’-bipyridine

Two bis(bipyridine) polymeric metal nitrate complexes with 4,4’-bipyridine of simple formula like [M(bipy)₂](NO₃)2⋅xH₂O (where M=Co, Ni and Cu; x=4, 2 and 0, respectively) have been prepared and characterized. Their thermal decomposition has been undertaken using simultaneous TG-DTG-DTA and DSC in nitrogen atmosphere and non-isothermal TG in air atmosphere. Isothermal TG has been performed at decomposition temperature range of the complexes to evaluate the kinetics of decomposition by applying model-fitting as well as isoconversional method. Possible mechanistic pathways have also been proposed for the thermolysis. Ignition delay measurements have been carried out to investigate the response of these complexes under the condition of rapid heating.     

New diamide-diamine ligands and their zirconium and hafnium dichloride and bis(dimethylamide) complexes

The multigram syntheses of the protio ligands (2-NC(5)H(4))CH(2)N(CH(2)CH(2)NHSiMe(2)R)(2) (R = Me, H(2)N(2)NN' 3; R = (t)Bu, H(2)N(2)NN() 4) are described via reactions of the previously reported (2-NC(5)H(4))CH(2)N(CH(2)CH(2)NH(2))(2) (1). A new synthesis of 1 is reported starting from 2-aminomethylpyridine and N-tosylaziridine, proceeding via (2-NC(5)H(4))CH(2)N(CH(2)CH(2)NHTs)(2) (2). Reaction of H(2)N(2)NN' or H(2)N(2)NN* with (n)BuLi gives good yields of the dilithiated derivatives Li(2)N(2)NN' and Li(2)N(2)NN*. Reaction of H(2)N(2)NN' or H(2)N(2)NN* with [MCl(2)(CH(2)SiMe(3))(2)(Et(2)O)(2)] gives the cis-dichloride complexes [MCl(2)(L)] (L = N(2)NN', M = Zr 7 or Hf 8; L = N(2)NN(), M = Zr 9). The corresponding reactions of H(2)N(2)NN' or H(2)N(2)NN* with [Zr(NMe(2))(4)] afford the bis(dimethylamide) derivatives [Zr(NMe(2))(2)(L)] (L = N(2)NN' 10 or N(2)NN* 11). All of these protonolysis reactions proceed smoothly and in good yields. Attempts to prepare the titanium complexes [Ti(X)(2)(N(2)NN')] (X = Cl or NMe(2)) were unsuccessful. The X-ray crystal structures of (2-NC(5)H(4))CH(2)N(CH(2)CH(2)NHTs)(2).EtOH, [ZrCl(2)(N(2)NN')].0.5C(6)H(6), [Zr(NMe(2))(2)(N(2)NN')], and [Zr(NMe(2))(2)(N(2)NN*)] are reported.     

Lanthanide borohydride complexes supported by diaminobis(phenoxide) ligands for the polymerization of epsilon-caprolactone and L- and rac-lactide

Reaction of Na2O2NN' [H2O2NN' = (2-C5H4N)CH2N[2-HO-3,5-C6H2(t)Bu2]2] with M(BH4)3(THF)3 afforded the dimeric, rare-earth borohydride compounds [M(O2NN')(mu-BH4)(THF)n]2 [M = Y(III), n = 0.5 (1-Y); M = NdIII, n = 1 (1-Nd); M = SmIII, n = 0 (1-Sm)]. For comparison the chloride analogues [M(O2NN')(mu-Cl)(THF)n]2 (2-M; M = La(III) or Sm(III), n = 0; M = Nd(III), n = 1) and the corresponding pyridine adducts [M(O2NN')(mu-X)(py)]2 [X = BH4 (3-M) or Cl (4-M); M = La(III), Nd(III), or Sm(III)] were prepared and structurally characterized for 4-La. Compounds 1-M initiated the ring-opening polymerization of epsilon-caprolactone. The best molecular weight control (suppression of chain transfer) for all three monomers was found for the samarium system 1-Sm. The most effective heterotactic enrichment (Pr) in the polymerization of rac-lactide was found for 1-Y (P(r) = 87%). Compound 1-Nd catalyzed the block copolymerization of epsilon-caprolactone and L- and rac-lactide provided that epsilon-caprolactone was added first. Attempted block polymerization by the addition of L-lactide first, or random copolymerization of a ca. 1:1 mixture of epsilon-caprolactone and L-lactide, gave only a poly(L-lactide) homopolymer.     

Nonclassical titanocene silyl hydrides

The titanocene silyl hydride complexes [Ti(Cp)2(PMe3)(H)(SiR3)] [SiR3=SiMePhCl (6), SiPh2Cl (7), SiMeCl2 (8), SiCl3 (9)] were prepared by HSiR3 addition to [Ti(Cp)2(PMe3)2] and were studied by NMR and IR spectroscopy, X-ray diffraction (for 6, 8, and 9), and DFT calculations. Spectroscopic and structural data established that these complexes exhibit nonclassical Ti-H-Si-Cl interligand hypervalent interactions. In particular, the observation of silicon-hydride coupling constants J(Si,H) in 6-9 in the range 22-40 Hz, the signs of which we found to be negative for 8 and 9, is conclusive evidence of the presence of a direct Si-H bond. The analogous reaction of [Ti(Cp)2(PMe3)2] with HSi(OEt)3 does not afford the expected classical silyl hydride complex [Ti(Cp)2(PMe3)(H)[Si(OEt)3]], and instead NMR-silent titanium (apparently TiIII) complex(es) and the silane redistribution product Si(OEt)4 are formed. The structural data and DFT calculations for the compounds [Ti(Cp)2(PMe3)(H)(SiR3)] show that the strength of interligand hypervalent interactions in the chlorosilyl complexes decreases as the number of chloro groups on silicon increases. However, in the absence of an Si-bound electron-withdrawing group trans to the Si-H moiety, a silane sigma complex is formed, characterized by a long Ti-Si bond of 2.658 A and short Si-H contact of 1.840 A in the model complex [Ti(Cp)2(PMe3)(H)(SiMe3)]. Both the silane sigma complexes and silyl hydride complexes with interligand hypervalent interactions exhibit bond paths between the silicon and hydride atoms in Atoms in Molecules (AIM) studies. To date a classical titanocene phosphane silyl hydride complex without any Si-H interaction has not been observed, and therefore titanocene silyl hydrides are, depending on the nature of the R groups on Si, either silane sigma complexes or compounds with an interligand hypervalent interaction.     

Are J(Si-H) NMR coupling constants really a probe for the existence of nonclassical H-Si interactions?

A series of hydridosilyl complexes of tantalum, Cp(ArN)Ta(PMe3)(H)(SiClnR3-n) (n = 0-3), was prepared and studied by 29Si NMR, X-ray diffraction, and DFT calculations. An unprecedented increase of the J(Si-H) coupling constant between the hydride and silyl ligands from 14 Hz for n = 0 to 50 Hz n = 3 was observed, which however, according to DFT calculations, does not correspond to stronger bonding interaction between silicon and hydride ligands, with the strongest interaction being for n = 1.     

Level Sets of Multiparameter Stable Processes

We establish the correct Hausdorff measure function for the level sets of additive strictly stable processes derived from strictly stable processes satisfying Taylor’s condition (A). This leads naturally to a characterization of local time in terms of the corresponding Hausdorff measure function of the level set.      

直接键连原子间的NMR偶合常数的自然杂化轨道研究V.~(13)C-~(13)C和~(13)C-~(31)P核自旋偶合常数~1J_(CC)和~1J_(CP)

在前文工作的基础上，结合ＭＮＤＯ／ＥＨＭＯ分子轨道方法和自然杂化轨道方法，具体计算了ＣＣ键和ＣＰ键的核自旋偶合常数．计算结果表明，１ＪＣＣ和１ＪＣＰ主要由成键原子的轨道杂化作用和键极性这两种结构因素所决定．为从简单价键理论角度解释和计算１ＪＣＣ和１ＪＣＰ值提供了简便直观的方法．