Rupture of unsymmetrical beam.

Coherent beam-beam tune shift of unsymmetrical beam-beam interactions with large beam-beam parameter.

Coherent beam-beam tune shift of unsymmetrical beam-beam interactions was studied experimentally and numerically in HERA, where the lepton beam has such a large beam-beam parameter (up to xi(y) = 0.272 ) that the single-particle motion is locally unstable at the origin (closed orbit). Unlike the symmetrical case of beam-beam interactions, the ratio of the coherent beam-beam tune shift and the b...

Unsymmetrical Approximation of Irrational Numbers

1 A 1 < £ < , 5B B SB so that we have the classical theorem of Hurwitz. For other values of r, approximations from both sides are permitted, but the errors allowed on the two sides are different; hence the term unsymmetrical approximation. The result here was new, and is so related to Hurwitz's inequality that one side is strengthened and the other weakened. Notice that the result for r > l is ...

Efficient synthesis of unsymmetrical disulfides

A novel way of synthesizing unsymmetrical disulfides from thiols with DDQ is presented here. This procedure ran in a straightforward manner to give high product yields. Unsymmetrical disulfides were directly synthesized from the corresponding mixture of thiols in equimolar amounts under mild conditions. 2011 Elsevier Ltd. All rights reserved.

Parallel Synthesis of Unsymmetrical trans-Stilbenes

New unsymmetrical trans-stilbenes have been prepared by the sequential coupling reactions of bromobenzenesulfonate with formylarylboronic acids, benzylphosphonates and arylmagnesium bromides and characterized. The nickel-catalyzed reactions of stilbenesulfonates with aryl Grignard reagents produced the corresponding stilbenes via the nucleophilic aromatic substitution of the neopentyloxysulfony...

Bending of Beams with Unsymmetrical Sections