Condensation reactions of 3-oxo-2-arylhydrazonopropanals with active methylene reagents: formation of 2-hydroxy- and 2-amino-6-substituted-5-arylazonicotinates and pyrido[3,2-c]cinnolines via 6π-electrocyclization reactions

3-Oxo-3-phenyl-2-(p-tolylhydrazono)propanal (1a) undergoes condensation with ethyl cyanoacetate in acetic acid in the presence of ammonium acetate to yield either 2-hydroxy-6-phenyl-5-p-tolylazonicotinic acid ethyl ester (6a) or 2-amino-6-phenyl-5-ptolyl-azonicotinic acid ethyl ester (8), depending on the reaction conditions. Similarly, other 3-oxo-3-aryl-2-arylhydrazonopropanals 1a,b condense with active methylene nitriles 2c,d to yield arylazonicotinates 6b,c. In contrast, 2-[(4-nitrophenyl)-hydrazono]-3-oxo-3-phenyl-propanal (1c) reacts with ethyl cyanoacetate to yield ethyl 6-(4-nitrophenyl)-2-oxo-2,6-dihydropyrido[3,2–c]cinnoline-3-carboxylate (11), via a novel 6π-electrocyclization pathway. Finally, 3-oxo-2-(phenylhydrazono)-3-p-tolylpropanal (1d) condenses with 2a-c to yield pyridazinones 13a-c.     

Reassignment of the structures of products produced by reactions of the product believed to be 2-(1-phenyl-2-thiocyanatoethylidene)-malononitrile with electrophiles

The reactivity of the product believed to be 2-(1-phenyl-2-thiocyanato-ethylidene)malononitrile toward a variety of electrophilic and nucleophilic reagents is reported.     

A Microwave Assisted Diazo Coupling Reaction: The Synthesis of Alkylazines and Thienopyridazines

Heating diazoaminobenzene with active methylene compounds 1–3 in microwave oven in acetic acid, in the presence of hydrochloric acid, afforded the corresponding arylhydrazones 5–7. These reaction products were condensed with ethyl cyanoacetate in a domestic microwave oven after 1–2 minutes heating to yield the pyridazinones 8–12. Compounds 8c and 12 reacted with sulfur in basic DMF solution, in microwave oven using MORE technology to yield the thienopyridazinone 14 and 16 respectively. While 17 was produced when 8b was treated like wise with sulfur and DMF in the presence of piperidine. Compounds 16 coupled with aromatic diazonium salts to yield arylazo derivatives 21a–c.     

Simple Zeros of the Riemann Zeta-Function

Assuming the Riemann Hypothesis, Montgomery showed by meansof his pair correlation method that at least two-thirds of thezeros of Riemann's zeta-function are simple. Later he and Taylorimproved this to 67.25 percent and, more recently, Cheer andGoldston increased the percentage to 67.2753. Here we proveby a new method that if the Riemann and Generalized LindelöofHypotheses hold, then at least 70.3704 percent of the zerosare simple and at least 84.5679 percent are distinct. Our methoduses mean value estimates for various functions defined by Dirichletseries sampled at the zeros of the Riemann zeta-function. 1991Mathematics Subject Classification: 11M26.     

Reassignment of the structures of condensation products of α-keto α′-formylarylhydrazones with ethyl cyanoacetate: a novel route to ethyl 5-arylazo-2-hydroxynicotinates

The condensation of α-keto α′-formylarylhydrazones with ethyl cyanoacetate afforded ethyl 5-arylazo-2-hydroxy-6-aryl (or alkyl) nicotinates. The structures of the reaction products could be established based on X-ray crystal structure determination.