Series representation for semistable laws and their domains of semistable attraction

If the centered and normalized partial sums of an i.i.d. sequence of random variables converge in distribution to a nondegenerate limit then we say that this sequence belongs to the domain of attraction of the necessarily stable limit. If we consider only the partial sums which terminate atk _n wherek _n+1 ck _n then the sequence belongs to the domain of semistable attraction of the necessarily semistable limit. In this paper, we consider the case where the limiting distribution is nonnormal. We obtain a series representation for the partial sums which converges almost surely. This representation is based on the order statistics, and utilizes the Poisson process. Almost sure convergence is a useful technical device, as we illustrate with a number of applications.This research was supported by a research scholarship from the Deutsche Forschungsgemeinschaft (DFG).     

Sur les metriques admettant les plans comme surfaces minimales

We establish the system of partial differential equations satisfied by the riemannian metrics on open subsets of which admit planes as minimal surfaces. This is a nonlinear system of 10 partial differential equations, with the euclidian metric as a particular solution. In a previous work, we solved this system for axially symmetrical metrics. In this paper we linearize the system at the euclidian metric and solve the linear system. We obtain a 20-dimensional space of solutions.

     

Curvature invariants, differential operators and local homogeneity

We first prove that a Riemannian manifold with globally constant additive Weyl invariants is locally homogeneous. Then we use this result to show that a manifold whose Laplacian commutes with all invariant differential operators is a locally homogeneous space.

     

The role of radicals in metal-assisted oxygenation reactions

The oxo-functionalization of organic substrates with the aid of metal oxo moieties is of fundamental importance not only in nature but also in academic and industrial research. Nevertheless the corresponding reaction mechanisms remain among the most enigmatic in chemistry and few of them are understood in detail. Recent research efforts have resulted in significantly improved information: in the cases of many oxygenation reactions evidence has been provided for the occurrence radical intermediates, even though the high selectivity observed suggests to a different mechanism. Examples stem from various areas of chemistry and include processes involving molecular metal oxo complexes, gas-phase and matrix-isolated species, metalloenzymes, and solid-state oxide surfaces. This review treats this seemingly wide variety of systems with the aim of providing an overview of common reactivity patterns and principles, as well as open problems.     

Mechanism of Reppe's nickel-catalyzed ethyne tetramerization to cyclooctatetraene: a DFT study

In this B3 LYP model study, homoleptic nickel(0) ethyne complexes have been predicted as the catalyst resting state for the title reaction. Ethyne ligand coupling of Ni(C(2)H(2))(3) yields monoethyne nickelacyclopentadiene in the rate-determining step. Ethyne coordination is followed by insertion of an ethyne ligand into the Ni--C sigma bond. A highly strained monoethyne trans-nickelacycloheptatriene is formed. This trans intermediate is unable to reductively eliminate benzene without prior isomerization to a cis-structure. Instead, it rapidly collapses to a nickelacyclononatetraene. Ethyne coordination induces reductive elimination to the cyclooctatetraene complex Ni(eta(2)-C(2)H(2))(eta(2)-C(8)H(8)), followed by facile ligand exchange. Other ethyne coupling pathways have been computed to be less favored. The cyclooctatetraene ligand binds significantly weaker to nickel(0) than ethyne, both for mononuclear, and for dinuclear species. For this reason, C--C bond formation steps at Ni(2)(micro-cot) fragments have been predicted to feature prohibitively high overall reaction barriers.     

Corrugated single-layer graphite sheet as a model of stepped surface of a crystal

Electronic structure calculations have been performed for flat graphite sheets and periodically distorted sheets with different values of deformation angle and hydrogen adsorption. These characteristics do not all behave monotonically with increasing deformation angle. At small deformation angles, the electrons pass from the atoms of terraces to those of edges, while at larger angles the reverse pattern is observed. The position of the Fermi level also varies nonmonotonically. The binding energy of hydrogen depends significantly on the adsorption site, and the difference can be doubled. Based on the ata obtained, it was concluded that a priori statements derived from the “general concepts” on the difference in the physicochemical properties of, for example, terrace and edge atoms on high-index facets are unreliable.     

Effect of molecular orientation distribution and crystallinity on the measurement of the crystal lattice modulus of nylon 6 by x-ray diffraction

The crystal lattice modulus of nylon 6 (-type) was measured by x-ray diffraction using nylon 6 films drawn up to five times. The measured crystal lattice modulus was 173–175 GPa for all specimens whose crystallinity and the Young's modulus were beyond 46% and 3.75 GPa, respectively. These results indicate that a state of homogenous stress can be achieved. In contrast, the values were scattered for the speciments whose crystallinity and Young's modulus are less than the above values. To study the origin, a numerical calculation of the crystal lattice modulus, as measured by x-ray diffraction, was carried out by considering effects on the orientation factors of molecular chains and crystallinity. In this calculation, a previously introduced model was employed, in which oriented crystalline layers are surrounded by oriented amorphous phases so that the strains of the two phases at the boundary are identical. The theoretical results calculated by the introduced model indicated that the crystal lattice modulus by x-ray diffraction is almost equal to the intrinsic crystal modulus if the morphology of the test specimen can be represented as a series model. In contrast, if a parallel model is more appropriate, the difference between the measured modulus and the intrinsic value can be pronounced. Such morphological dependence was found to be less pronounced with increasing high degree of molecular orientation and crystallinity.     

Transition metal-catalyzed olefin arylation via C–H bond activation of arenes

In this article, two kinds of our transition metal-catalyzed olefin arylations are summarized and discussed. The first one is Ir-catalyzed novel anti-Markovnikov hydroarylation of olefins with benzene. Using this reaction catalyzed by [Ir(μ-acac-O,O′,C₃)(acac-O,O′)(acac-C₃)]₂ (acac = acetylacetonato), 1, straight-chain alkylarenes, which were not obtainable by the conventional Friedel-Crafts aromatic alkylation with olefins, were able to be successfully synthesized directly from arenes and olefins with the higher selectivity than that of branched alkylarenes. This is the first efficient catalyst which shows the desirable high regioselectivity. The reaction of benzene with propylene gave n-propylbenzene and cumene in 61% and 39% selectivities, respectively, and the reaction of benzene and styrene afforded 1,2-diphenylethane in 98% selectivity. The reaction of alkylarene and olefin showed meta and para orientations. A wide range of olefins and arenes can be employed for the synthesis of alkylarenes. The mechanism of the reaction involves C–H bond activation of benzene by Ir center to form Ir–phenyl species. The second reaction is Rh-catalyzed oxidative arylation of ethylene with benzene to directly produce styrene, namely one-step synthesis of styrene. The reaction of benzene with ethylene catalyzed by Rh(ppy)₂(OAc) (ppyH = 2-phenylpyridine, OAc = acetate), 3 with Cu oxidizing agent gave styrene and vinyl acetate in 77% and 23% selectivities, respectively, in contrast to those by Pd(OAc)₂, 47% of styrene and 53% of vinyl acetate. The mechanism of the reaction involves Rh-mediated C–H bond activation of benzene, which appears to be a rate-determining step. Furthermore, Rh complexes in a Rh(I) oxidation state at the beginning of the reaction work as catalysts for the reaction by addition of acacH and O₂ without any oxidizing agent, like Cu salt.     

微圆盘电极上耦合—级均相反应的稳态电流

在电极袭面反应物浓度均匀的近似假设下,得到了微圆盘电极上暂态可逆反应的一般解.然后利用该一般解得到了微圆盘电极上耦合一级均相反应的可逆电极反应CE、EC、EC′和ECE 的稳态电流计算公式.