Reduction of bowl-shaped hydrocarbons: dianions and tetraanions of annelated corannulenes

[structure: see text] The reduction of several annelated corannulene derivatives was undertaken using lithium and potassium metals. It was found that annelation affects the annulenic character of corannulene by changing its charge distribution; the dianions of derivatives that are annelated with six-membered rings have less annulenic character and are less paratropic than corannulene dianion. This effect is even more pronounced in corannulenes that are peri-annelated with five-membered rings. The alkali metal used in the reduction process has a great influence on the outcome, especially on the degree of reduction. Most derivatives get reduced to tetraanions only with potassium, and not with lithium, the exception being systems that can stabilize the tetraanion with lithium by special means, such as aggregation or dimerization. One such system is cyclopenta[bc]corannulene (acecorannulylene), which gives a coordinative dimer that consists of two cyclopentacorannulene tetraanions, bound together in a convex-convex fashion by lithium cations. The points of contact in this dimer are two rehybridized carbons from each cyclopentacorannulene unit, which are bridged together by two lithium cations.     

TURAN'S EXTREMAL PROBLEM FOR POSITIVE DEFINITE FUNCTIONS ON GROUPS

We study the following question: given an open set , symmetricabout 0, and a continuous, integrable, positive definite functionf, supported in and with f(0) = 1, how large can f be? Thisproblem has been studied so far mostly for convex domains inEuclidean space. In this paper we study the question in arbitrarylocally compact abelian groups and for more general domains.Our emphasis is on finite groups as well as Euclidean spacesand ^d. We exhibit upper bounds for f assuming geometric propertiesof of two types: (a) packing properties of and (b) spectralproperties of . Several examples and applications of the maintheorems are shown. In particular, we recover and extend severalknown results concerning convex domains in Euclidean space.Also, we investigate the question of estimating f over possiblydispersed sets solely in dependence of the given measure m :=||of . In this respect we show that in and the integral is maximalfor intervals.     

Periodicity of the Spectrum of a Finite Union of Intervals

A set Ω, of Lebesgue measure 1, in the real line is called spectral if there is a set Λ of real numbers such that the exponential functions e _λ (x)=exp (2πiλx), λ∈Λ, form a complete orthonormal system on L ²(Ω). Such a set Λ is called a spectrum of Ω. In this note we present a simplified proof of the fact that any spectrum Λ of a set Ω which is finite union of intervals must be periodic. The original proof is due to Bose and Madan.     

A short, rigid, structurally pure carbon nanotube by stepwise chemical synthesis

The inaccessibility of uniform-diameter, single-chirality carbon nanotubes (CNTs) in pure form continues to thwart efforts by scientists to use these ultrathin materials in innovative applications that could revolutionize nanoscale electronics. Stimulated by the challenge to address this long-standing problem, we and other organic chemists have envisioned a new production strategy involving the controlled elongation of small hydrocarbon templates, such as hemispherical nanotube end-caps, prepared by bottom-up chemical synthesis; the diameter and rim structure encoded in the template would dictate the diameter and chirality of the resulting CNT. Toward that objective, a short [5,5] CNT has now been synthesized by stepwise chemical methods. This C(50)H(10) geodesic polyarene has been isolated, purified, crystallized, and fully characterized by NMR spectroscopy, UV-vis absorption spectroscopy, high resolution mass spectrometry, and X-ray crystallography.     

Universal mechanism of dissipation in Fermi superfluids at ultralow temperatures

We show that the vortex dynamics in Fermi superfluids at ultralow temperatures is governed by the local heating of the vortex cores creating the heat flux carried by nonequilibrium quasiparticles emitted by moving vortices. This mechanism provides a universal zero temperature limit of dissipation in Fermi superfluids. For the typical experimental conditions realized by the turbulent motion of ^{3}He-B, the temperature of the vortex cores is estimated to be of the order 0.2 T(c). The dispersion of Kelvin waves is derived, and the heat flow generated by Kelvin cascade is shown to have a value close to that experimentally observed.     

An investment model with switching costs and the option to abandon

We develop a complete analysis of a general entry–exit–scrapping model. In particular, we consider an investment project that operates within a random environment and yields a payoff rate that is a function of a stochastic economic indicator such as the price of or the demand for the project’s output commodity. We assume that the investment project can operate in two modes, an “open” one and a “closed” one. The transitions from one operating mode to the other one are costly and immediate, and form a sequence of decisions made by the project’s management. We also assume that the project can be permanently abandoned at a discretionary time and at a constant sunk cost. The objective of the project’s management is to maximise the expected discounted payoff resulting from the project’s management over all switching and abandonment strategies. We derive the explicit solution to this stochastic control problem that involves impulse control as well as discretionary stopping. It turns out that this has a rather rich structure and the optimal strategy can take eight qualitatively different forms, depending on the problems data.     

A primal-dual approximation algorithm for generalized steiner network problems

We present the first polynomial-time approximation algorithm for finding a minimum-cost subgraph having at least a specified number of edges in each cut. This class of problems includes, among others, the generalized Steiner network problem, also called the survivable network design problem. Ifk is the maximum cut requirement of the problem, our solution comes within a factor of 2k of optimal. Our algorithm is primal-dual and shows the importance of this technique in designing approximation algorithms.Research supported by an NSF Graduate Fellowship, DARPA contracts N00014-91-J-1698 and N00014-92-J-1799, and AT&T Bell Laboratories.Research supported in part by Air Force contract F49620-92-J-0125 and DARPA contract N00014-92-J-1799.Part of this work was done while the author was visiting AT&T Bell Laboratories and Bellcore.     

Redox couples in the selective catalytic reduction of NOx with hydrocarbons over Co-ZSM-5 and Ni-ZSM-5 catalysts: an FT-IR study

On the basis of IR spectroscopy studies it is concluded that the redox couples Co(2+)/Co(+) and Ni(2+)/Ni(+) operate in the selective catalytic reduction of nitrogen oxides with hydrocarbons over Co-ZSM-5 and Ni-ZSM-5.     

Etude des reactions des diazoderives avec les cycloimmonium ylures-I : Action des sels de diazonium sur quelques pyridinium - ylures

The synthesis of cycloimmonium salts of the type $\text{7}$, $\text{8}$ and the corresponding cycloimmonium ylides $\text{9}$, $\text{10}$ are reported. In the reaction with diazonium salts $\text{11}$, $\text{12}$ the pyridinium monosubstituted carbanion ylides $\text{9}$, $\text{10}$ give the pyridinium disubstituted carbanion ylides $\text{17}$ – $\text{20}$. These are new types of isolable stable ylides. The synthesis involves the formation “in situ” of ylides $\text{9}$, $\text{10}$ which are bonded by their nucleophile ylide carbon atom to the nitrogen atom in diazonium salts. The intermediat formation of cycloimmonium salts $\text{13}$ – $\text{16}$ must be accepted. The structures of all compounds presented in this paper have been established by using elementary analysis, IR and ¹H-RMN spectra.