Efficient syntheses of 5-brominated and 5,5'-dibrominated 2,2'-bipyridines and 2,2'-bipyrimidines, useful for the preparation of metal-complexing molecular rods, have been developed. 5-Bromo-2,2'-bipyridine, 5-bromo-5'-n-butyl-2,2'-bipyridine, and 5-bromo-5'-n-hexyl-2,2'-bipyridine were obtained by Stille coupling of 2,5-dibromopyridine with 2-trimethylstannylpyridine or the requisite 5-alkyl-2-trimethylstannylpyridine, obtained via regioselective zincation of a 3-alkylpyridine.BF(3) complex in the less hindered of the two reactive positions with lithium di-tert-butyl-(2,2,6,6-tetramethylpiperidino)zincate. 5,5'-Dibromo-2,2'-bipyridine was obtained by the reductive symmetric coupling of 2,5-dibromopyridine with hexa-n-butyldistannane. The yields of these coupling reactions ranged from 70 to 90%. 5-Bromo- and 5,5'-dibromo-2,2'-bipyrimidines were obtained in yields of 30 and 15%, respectively, by bromination of 2,2'-bipyrimidine, prepared from 2-chloropyrimidine in 80% yield by an improved reductive symmetric coupling procedure.

A synthetic approach to a two-dimensional grid polymer is proposed and the execution of initial steps is described. Pd-catalyzed coupling of (1,12-dicarba-closo-dodecaboran-1-yl)copper ( 10) with iodobenzene, mdiiodobenzene, and 1,3,5-triiodobenzene yielded the known 1,12-dicarba-closo-dodecaboran-1-ylbenzene (3) and the new m-bis(1,12-dicarba-closo-dodecaboran-1-yl)benzene (4) and 1,3,5-tris(1,12-dicarba-closo-dodecaboran-1yl)benzene (1), respectively. Each arm of the trigonal connector 1 was provided with one or two sticky tentacles by conversion to 1,3,5-tris [12-((3-(ethylthio)propyl)dimethylsilyl)-1,12-dicarba-closo-dodecaboran-1-yl]benzene (7) and 1,3,5-tris [12-(bis(3-(ethylthio)propyl)methylsilyl)-1,12-dicarba-closo-dodecaboran-1-yl]benzene (8). Linear coupling of carboranyl CH terminals through a mercury atom produced very stable dimeric structures from 3 and 4. The carborane 3, its mercury-linked dimer 13, the 1:1 complex of 13 with 2,2′-bipyridyl, and the 2:1 complex of 13 with 2,2′-bipyrimidyl have been structurally characterized by single-crystal X-ray crystallography, but crystals of 1 showed an intriguing disorder and could not be used for molecular structure determination. Grazing incidence IR spectra show that the tentacled species 7 and 8 adsorb firmly on the surface of gold, apparently without a strong preference for a particular orientation. At room temperature, the tritentacled species 7 can be removed readily and the hexatentacled species 8 more slowly by treatment with a THF solution containing fluoride, which severs the tentacles.

We propose a mathematical model to describe the microstructure of the gas diffusion layer ͑GDL͒ in proton exchange membrane fuel cells ͑PEMFCs͒ based on tools from stochastic geometry. The GDL is considered as a stack of thin sections. This assumption is motivated by the production process and the visual appearance of relevant microscopic images. The thin sections are modeled as planar ͓two-dimensional ͑2D͔͒ random line tessellations which are dilated with respect to three dimensions. Our 3D model for the GDL consists of several layers of these dilated line tessellations. We also describe a method to fit the proposed model to given GDL data provided by scanning electron microscopy images which can be seen as 2D projections of the 3D morphology. In connection with this, we develop an algorithm for the segmentation of such images which is necessary to obtain the required structural information from the given grayscale images.

Among the surrogate endpoints for overall survival (OS) in oncology trials, progression-free survival (PFS) is more and more taking the leading role. Although there have been some empirical investigations on the dependence structure between OS and PFS (in particular between the median OS and the median PFS), statistical models are almost non-existing. This paper aims at filling this gap by introducing an easy-to-handle model based on exponential time-to-event distributions that describe the dependence structure between OS and PFS. Based on this model, explicit formulae for individual correlations are derived together with a lower bound for the correlation of OS and PFS, which is given by the fraction of the two medians for OS and PFS. Two methods on how to estimate the parameter of the model from real data are discussed. One method is based on a maximum-likelihood estimator whereas the other method uses a plug-in approach. Three examples from non-small cell lung cancer are considered. In the first example, the parameters of the model are determined and the estimated survival curce is compared with the observed one. The second example explains how to obtain sample size estimates for OS based on assumptions on median PFS and OS. Finally, the third example provides a way of modelling and quantifying confounding effects that might explain a levelling of differences in OS although a difference in PFS is observed.

than multiple t-tests. The functional value of the first maximum of the reduced g-function and a global statistical parameter of short-range ordering was significantly reduced in the carcinoma group. Prostate cancer tissue is more densely supplied with capillaries than normal prostate tissue and the threedimensional arrangement of the vessels differs with respect to interaction at various distance ranges. In the local approach used here, bootstrap methods can be used as a robust statistical tool for the computation of confidence intervals and group comparisons of mean reduced g-functions at specific ranges of interaction.