Synthesis of Novel 2-Aminothiophene-3-carboxylates by Variations of the Gewald Reaction

Summary.  The synthesis of the title compounds through variations of the Gewald reaction is presented. Knoevenagel condensation of methylketone derivatives with methyl cyanoacetate and subsequent treatment of the α,β-unsaturated nitriles with sulfur and amine resulted in the corresponding 2-aminothiophenes 5 or isomers 9 and 10. Reaction of methylketone derivatives bearing a leaving group at the methyl group under modified Gewald conditions selectively led to the formation of 4-substituted 2-aminothiophenes 9a and 12. The introduction of the sulfur atom occurs through nucleophilic displacement with sodium sulfide. Received July 5, 2000. Accepted (revised) August 23, 2000     

A regular space without a uniformly regular quasi-uniformity

We point out that a construction due to J. Vaughan yields an example of a regularT ₁-space that does not admit a uniformly regular quasi-uniformity.     

Existence and bifurcation theorems for nonlinear elliptic eigenvalue problems on unbounded domains

We consider nonlinear elliptic eigenvalue problems on unbounded domains G?$\text{R}$ⁿ. Using an extended Ljusternik-Schnirelman theory we prove the existence of infinitely many eigenfunctions on every sphere in L²(G). Moreover, we establish that the infimum λ1 of the spectrum of the linearized problem L is always a bifurcation point. In addition, there is an infinity of branches emanating at λ1 from the trivial line of solutions if λ1 belongs to the essential spectrum of L.