Laws of the iterated logarithm for the central part of (semi-)stable measures on the Heisenberg groups

We prove laws of the iterated logarithm for certain symmetric stable and semistable measures on the Heisenberg groups.     

Synthese substituierter Cyclononatetraene

Synthesis of Substituted Cyclononatetraenes In the course of an exploration of possible synthetic pathways to nonafulvenes, a series of 1-substituted cyclononatetraenes (CNT) 4b–1 have been prepared in yields of about 60%. Their structures follow from spectroscopic data as well as from the quantitative valence isomerisation to 1-endo-substituted cis-3a, 7a-dihydroindenes 8 . Both all-cis-CNT⁻ 1 and cis,cis,cis,trans-CNT⁻ 2 have been used as nucleophiles. Whereas 2 is normally more nucleophilic than 1 , the yield of cyclononatetraenes 4 prepared with 2 may be reduced due to by-products such as 9 and 10 .     

Synthese neuer Heptafulvene,Röntgenstrukturanalyse von ‘8,8-(1′,4′-Dioxotetramethylen)heptafulven’(2-(Cyclohepta-2,4,6-trien-1-yliden)cyclopentan-1,3-dion)

Synthesis of New Heptafulvenes; X-Ray Analysis of ‘8,8-(1′,4′-Dioxotetramethylene)heptafulvene’ (2-(Cyclohepta-2,4,6-trien-1-ylidene)cyclopentane-1,3-dione) Experimental procedures for the synthesis of heptafulvene ( 3a ), 8,8-tetramethylene heptafulvene ( 3c ) and ‘8,8-(1′,4′-dioxotetramethylene) heptafulvene’ (2-(cyclohepta-2,4,6-trien-1-ylidene)-cyclopentane-1,3-dion; 3d ) are described. The most important sequences include a low-temperature reaction of tropylium salts with lithium or Grignard carbenoids (Scheme 1) to give 3a and 3b as well as hydride abstraction from substituted cycloheptatrienes followed by deprotonation to give 3c and 3d . Limitations of these sequences are discussed. Two other heptafulvenes 3h and 3i are available by silylation of heptafulvenolates according to well-known procedures. NMR-Spectroscopic evidence as well as an X-ray analysis of 3d are presented. Compound 3d is a relatively polar heptafulvene with a planarised seven-membered ring as well as a partly delocalized π system.     

Effects of trace contaminants on catalytic processing of biomass-derived feedstocks

Model compound testing was conducted in a batch reactor to evaluate the effects of trace contaminant components on catalytic hydrogenation of sugars. Trace components are potential catalyst poisons when processing biomass feedstocks to value-added chemical products. Trace components include inorganic elements such as alkali metals and alkaline earths, phosphorus, sulfur, aluminum, silicon, chloride, or transition metals. Protein components in biomass feedstocks can lead to formation of peptide fractions (from hydrolysis) or ammonium ions (from more severe breakdown), both of which might interfere with catalysis. The batch reactor tests were performed in a 300-mL stirred autoclave, with multiple liquid samples withdrawn over the period of the experiment. Evaluation of these test results suggest that most of the catalyst inhibition is related to nitrogen-containing components.     

Oxidative Coupling Of 2-Alkyl-6,6-dimethylpentafulvenyl Anions

Cucl₂-Induced oxidative coupling of 2-(tert-butyl)-6,6-dimethylpentafulvenyl anion 9 predominantly takes place at C(7) and C(5) to give [7–7] and [7–5] coupling products 15 and 16 in 35 and 47% yields, respectively (Scheme 3) whose structures are elucidated from 1D- and 2D-NMR analysis. Compared with the product distribution observed for 6,6-dimethylpentafulvenyl anion 2 (Scheme 1), no coupling at C(2)/C(3) of 9 is observed. This means that, besides electronic effects, steric effect are also important in oxidative couplings of fulvenyl anions. The same couplings occur in the case of 2,3-bis(6,6-dimethylfulven-2-yl)-2,3-dimethylbutane dianion 10 as well but, due to electronic as well as conformational effects (Scheme 5), intermolecular coupling (to give polymers 17 , Scheme 4) is strongly favored over intermolecular coupling. Mechanisms explaining base-catalyzed isomerization 15a ? 15b ? 15c (Scheme 6) as well as isomerization 16a ? 16b (Scheme 7) are proposed.     

UNUSUAL CRYSTALLIZATION AND MELTING PROCESSES OF AN OPTICALLY ACTIVE POLYOLEFIN： ISOTACTIC POLY（（S）-4-METHYL-HEXENE-1）

Polyolefins that bear a chiral side chain (typically an isobutyl group) experience a so-called macromolecular amplification of chirality: the chiral side-chain induces a slight preference for either tg or tg- main chain conformation. This slight conformational bias is amplified cooperatively along the chain, and results in preferred chirality of the main chain helical conformations. As a result, these polymers display a liquid-crystal (LC) phase both in solution and, in the melt as a transient phase on the way to crystallization. The existence of two processes (melt-LC and LC-crystal transitions) results in unconventional behaviors that were first analyzed by Pino and collaborators back in 1975. These polymers also offer a means to test the structural consequences of recently introduced crystallization schemes. These schemes postulate the formation of a transient liquid-crystal phase as a general scheme for polymer crystallization.     

Acetylene mit Elektronendonator und Elektronenakzeptorgruppen

Acetylenes having both electrondonating and electronaccepting groups ( 1 ) may be obtained in good yield from the correspondingly substituted olefines via bromination and elimination of HBr. The reaction of the acetylene aldehyde 1a with proton acids yields, after rearrangement of the primary adducts, the β-substituted acrylamides. Addition of nucleophiles leads to the β-disubstituted α.β-unsaturated carbonyl compounds. With hydrazines one obtains pyrazoles and pyrazolones. The acetylenes 1 undergo [2+2]-, [2+3]- and [2+4]-cycloaddition reactions.     

1H-and 13C-NMR Investigation of Pentafulvenes

¹H- and ¹³C-NMR spectra of a series of 6-(p-X-phenyl)pentafulvenes 1 – 9 as well as of 6-R-substituted and 6,6-R¹,R²-disubstituted pentafulvenes 10 – 23 have been analysed. It turns out that the π-system of pentafulvenes is an attractive probe for the investigation of electronic substituent effects. Changes of vicinal H,H-coupling constants with increasing electron-donating capacity of the substituents X and R are interpreted in terms of an increasing π delocalisation in the 5-membered ring, and linear correlations of Hammett Substituent constants σ or MNDO-calculated C–C bond lengths and ³J values are observed. On the other hand, a systematic high-field shift of ₁₃C chemical shifts of the ring C-atoms is induced by electron-releasing substituents R and X, which decreases in the series C(5) > C(2)/C(3) > C(1)/C(4), and which mainly reflects changes in π-charge density.     

Uniqueness of Embedding into a Gaussian Semigroup and a Poisson Semigroup with Determinate Jump Law on a Simply Connected Nilpotent Lie Group

Let {μ _t ⁽ⁱ⁾} _t≥0 (i=1,2) be continuous convolution semigroups (c.c.s.) on a simply connected nilpotent Lie group G. Suppose that μ ₁⁽¹⁾=μ ₁⁽²⁾. Assume furthermore that one of the following two conditions holds: