Neue Wege zu 1H- und 2H-Pyrrolen

New Routes to 1H- and 2H-Pyrroles A synthesis of 1H-pyrroles is described starting with pyridine analogues of chalcones and involving the reaction of acetic anhydride with 1-pyrroline-1-oxides. Another route leads from 1-pyrrolines to 2 H-pyrroles via bromination with N-bromosuccinimide and subsequent dehydrobromination in dimethylformamide.     

Synthesis of pyrrolo[1,2-b]cinnolines

The synthesis of the pyrrolo[1,2-b]cinnoline analogs 2 and 4–13 is described. The key step of this synthesis involves an intramolecular aromatic halide displacement on [2-(2-halobenzoyl)pyrrol-1-yl]carbamic acid esters. Several reactions of these cinnoline analogs with electrophilic reagents have been investigated.     

Weak convergence of nonparametric estimators of the multidimensional and multidimensional-multivariate renewal functions on Skorohod topology spaces

Statistical Inference for Stochastic Processes - This paper deals with the weak convergence of nonparametric estimators of the multidimensional and multidimensional-multivariate renewal functions...     

Trace Inequalities,Maximal Inequalities,and Weighted Fourier Transform Estimates

In the spirit of work of Kerman and Sawyer, a condition is given that is necessary and sufficient for the Fourier transform norm inequality $\Big(\int_{{\Bbb R}_d} \vert\hat{f}\vert^q d\mu\Big)^{1/q} \leq C\Big(\int_{{\Bbb R}_d} \vert f\vert^p v\Big)^{1/p}$ provided v is a radial weight for which v^?1/p is convexly decreasing and μ is a suitable measure. We also establish alternative conditions for such inequalities by proving corresponding trace type inequalities and maximal function inequalities that underlie the Fourier transform estimates. Our conditions are relatively simple to compute. Among applications we give extensions of a Sobolev restriction theorem.     

Polarized emission from a rhenium metal-ligand complex

We report the first observation of polarized emission from a rhenium-phenanthroline complex, Re(CO)₃(phen)Cl. Highly luminescent rhenium complexes are known, with quantum yields near 0.5 and lifetimes in excess of 10 s. The detection of polarized emission suggests the use of rhenium complexes as probes of the hydrodynamics of large macromolecular complexes and for use in fluorescence polarization immunoassays with gated detection.     

On the products of cross-ratios on diagonals of polygons

The purpose of this paper is to establish a conjecture of B. Grünbaum, which states that in every n-polygon P in the plane, n 5, some diagonals intersect in a pattern that defines a new n-polygon (P), such that the product of the cross-rations on the diagonals of P is equal to the product of the corresponding cross-ratios on the diagonals of (P).