1H, 13C,and 15N NMR spectra of some pyridazine derivatives

¹H, ¹³C, and ¹⁵N NMR chemical shifts for pyridazines 4–22 were measured using 1D and 2D NMR spectroscopic methods including ¹H? ¹H gDQCOSY, ¹H? ¹³C gHMQC, ¹H? ¹³C gHMBC, and ¹H? ¹⁵N CIGAR–HMBC experiments. Copyright © 2010 John Wiley & Sons, Ltd.     

A Bioinspired Synthesis of Polyfunctional Indoles

Polyfunctional indoles bearing substituents at C5 and C6 are prevalent in natural products, pharmaceuticals, agrochemicals, and materials. Owing to the remoteness of the C5 and C6 positions, indoles of this family can be difficult to prepare, and often require multistep syntheses. Herein, we describe a concise process that converts simple derivatives of tyrosine into 5,6‐difunctionalized indoles by direct oxidation of C?H, N?H, and O?H bonds. Our work draws inspiration from the biosynthetic polymerization of tyrosine to make melanin pigments, but makes an important departure to provide well‐defined indole heterocycles.     

Integral functional equations on locally compact groups with involution

Our main goal is to introduce some integral-type generalizations of the cosine and sine equations for complex-valued functions defined on a group G that need not be abelian. These equations provide a joint generalization of many trigonometric type functional equations such as d’Alembert’s, Cauchy’s, Gajda’s, Kannappan’s and Van Vleck’s equations. We prove that the continuous solutions for the first type and the central continuous solutions for the second one of these equations can be expressed in terms of characters, additive maps and matrix elements of irreducible, 2-dimensional representations of the group G. So the theory is part of harmonic analysis on groups.