CO-trapping reaction under thermolysis of alkoxyamines: application to the synthesis of 3,4-cyclopenta-1-tetralones

[reaction: see text] An efficient one-pot sequence comprising a PRE-mediated radical 5-exo-cyclization, a radical carbonylation, a nitroxide trapping reaction, and a subsequent acid-catalyzed Friedel-Craft-type acylation provides a new entry into 3,4-cyclopenta-1-tetralones. Eight examples are presented.     

Synthetic studies of tedanolide, a marine macrolide displaying potent antitumor activity. Stereoselective synthesis of the C13-C23 segment

[structure: see text] A highly stereoselective synthesis of the C13-C23 segment of tedanolide (1), an 18-membered macrolide isolated from the Caribbean sponge Tedania ignis, displaying significant cytotoxicity against KB and PS tumor cell lines, is described which involves two stereoselective epoxidations of regioisomeric trisubstituted double bonds and a stereospecific S(N)2' methylation reaction of a trans-gamma,delta-epoxy-cis-alpha,beta-unsaturated ester as the key steps.     

An Infinite Product Formula for the Elliptic Modular Function λ(τ)

We present an infinite product formula for the elliptic modular function λ(τ) of the following form:

Linear Independence of the Values of <Emphasis Type="Italic">q</Emphasis>-Hypergeometric Series and Related Functions

We give linear independence results for the values of certain entire series and of functions satisfying certain first order q-difference equations. The former generalizes a result of Bézivin, while the latter refines that of the second named author in qualitative form. These results imply linear independence of the values of q-hypergeometric series.Research supported in part by Grant-in-Aid for Scientic Research (No. 13640007), the Ministry of Education, Science, Sports and Culture of Japan.2000 Mathematics Subject Classification: Primary—11J72     

Rational synthesis of a two-dimensional honeycomb structure based on a paramagnetic paddlewheel diruthenium complex

A novel 2-D coordination polymer with honeycomb (6,3) net topology is constructed from a paramagnetic paddlewheel diruthenium tetrabenzoate, [RuII2(O2CPh)4], as a linear linker motif and triazine as a three-connected node; the RuII2 cores are positioned on nodes of a 2-D Kagome lattice.     

Comparison of tails of distributions in models for estimating safe doses

Summary Heaviness of tail of distributions is compared each other analytically and systematically. Distributions under the study are the lognormal, loglogistic, Weibull, gamma, exponential-polynomial distributions. The beta loglogistic, which covers some of these distributions as its limits, is also discussed. Heaviness of tail is an important notion in life-test, robust estimation and rank test. Here the notion is studied to examine models for estimating safe doses. Some results about heaviness of tail are given, and a new notion of heaviness of tail at the origin is defined and discussed.     

Measurements of complex degree of spatial coherence at the end face of an optical fiber

The phase and modulus of the complex degree of spatial coherence at the exit end face of an optical fiber are measured with the help of a real-time data processing computer. Interference fringes produced by superimposing wavefronts of the image of the end cross-section are scanned by a linear photodiode array to calculate the one dimensional value of spatial coherence. Evolution of phase measured at the different positions in the fringe pattern reveals that the phase is intimately related to modal structures of the propagating field in an optical fiber supporting a small number of guided modes.