Bending of an elastoplastic strip with isotropic and kinematic hardening

Summary  We propose an exact analysis for finite bending of a compressible elastoplastic strip with combined hardening at a given stretch normal to the bending plane. We apply the self-consistent eulerian rate-type elastoplastic model based on the logarithmic rate, in conjunction with a Tresca-type loading function. Utilizing the maximum circumferential stretch at the outer surface as an independent parameter, we derive exact analytic expressions for the bending angle, the bending moment, the outer and inner radii, the radii of the two elastic-plastic interfaces and the circumferential stretches at these two interfaces, as well as the stress distributions in every current cross section. In particular, we establish an explicit relation between the two circumferential stretches at the two elastic-plastic interfaces, and we show that this relation is universal for all cases of hardening. We show also that the maximum and minimum circumferential stretches at the outer and inner surfaces obey a reciprocal relation in the course of both elastic and elastic-plastic deformations. Received 4 June 2002; accepted for publication 14 November 2002 This research was carried out under financial support from the German Science Foundation (DFG) (Contract No.: Br. 580/26-2) and from Alexander von Humboldt Foundation. We wish to express our sincere gratitude to these Foundations.     

Continuity of Bessel potentials

It is shown that certain capacities associated with potentials of functions in Lebesgue classes are non-increasing under orthogonal projection of sets. This inequality is then used to discuss continuity of traces of potentials on subspaces of possibly low dimension. The case of principal interest is the Bessel potential. This research was partially sponsored by the Air Force Office of Scientific Research, Office of Aerospace Research, United States Air Force, under AFOSR Grant No. 883-67.     

On embeddings of gauge groups in Yang-Mills theory

We discuss some group theoretical properties of Yang-Mills theories. We consider conditions necessary and sufficient to decide if the gauge field is reducible and prove some related theorems. We give criteria for embeddings and work out the case of SU (3) explicitly.     

The N-9, C-1 dianion of tetrahydro-β-carbolines. Regioselective alkylation leading to indole alkaloid systems

By treatment of β-carboline formamidine (1) with potassium hydride followed by an alkyl lithium reagent, both the pyrrole proton (N-9) and the proton at C-1 are removed. The resulting dianion (3) alkylates cleanly at C-1 and ultimately at N-9 or N-2.     

A convenient synthesis of 1-azabicycloalkanes and their lactams via cuprates of formamidines

Piperidine and pyrrolidine formamidines, transformed into their α-metalloderivatives are alkylated with bifunctional electrophiles and cyclized, on formamidine removal, to the title compounds.     

Formamidines as α-amino carbanion precursors. The synthesis of 2-arylpiperidines, -pyrrolidines,and nicotine analogs

Metallation of the $\text{t}$-butyl formamidines of benzyl or picolinyl amines followed by alkylation with α,ω -dihaloalkanes gives the title compounds after hydrazinolysis.