Bott periodicity and calculus of Euler classes on spheres

AbstractA variety of computations regarding the Euler class group E(An,An) and the Grothendieck group K0(An) of the algebraic sphere Spec(An) is done. The Euler class of the algebraic tangent bundle on Spec(An) is computed. It is also investigated whether every element in the Euler class group E(An,An) is the Euler class of a projective An module of rank n

The collapse behaviour of tapered steel beams

In this thesis, the collapse mode of failure of tapered steel beams is examined for three different loading cases. Firstly, for the case when the beam is loaded inside the tip; secondly, when the beam is loaded outside the tip, and thirdly, when the beam is loaded at the tip. The theoretical collapse mode of failure presented here provides an identical collapse load whether obtained from lower or upper bound solutions. Fourteen tests on tapered steel beam specimen were carried out to examine the collapse modes of failure and their ultimate strengths for steel tapered beams loaded inside, outside and at the tip. The experimental collapse loads and their collapse modes of failure are compared with theoretically predicted collapse loads and the proposed collapse mechanisms respectively. The first elastic yield load of the tapered web panels is assessed on the basis of 'circular Arc Theory' simplified by Davies et al. (6) and is compared with the predicted theoretical collapse loads. Conclusions are drawn relating to the plastic collapse modes of failure and ultimate strengths of tapered steel beam

The collapse behaviour of tapered steel beams

In this thesis, the collapse mode of failure of tapered steel beams is examined for three different loading cases. Firstly, for the case when the beam is loaded inside the tip; secondly, when the beam is loaded outside the tip, and thirdly, when the beam is loaded at the tip. The theoretical collapse mode of failure presented here provides an identical collapse load whether obtained from lower or upper bound solutions. Fourteen tests on tapered steel beam specimen were carried out to examine the collapse modes of failure and their ultimate strengths for steel tapered beams loaded inside, outside and at the tip. The experimental collapse loads and their collapse modes of failure are compared with theoretically predicted collapse loads and the proposed collapse mechanisms respectively. The first elastic yield load of the tapered web panels is assessed on the basis of 'circular Arc Theory' simplified by Davies et al. (6) and is compared with the predicted theoretical collapse loads. Conclusions are drawn relating to the plastic collapse modes of failure and ultimate strengths of tapered steel beam

Ethyl 3-oxo-2-(2-phenyl­hydrazinyl­idene)butano­ate: a re-determination

The previous crystallographic studies [Wang et al. (2005 ▶). Huaxue Yanjiu 16, 29–32; Wang et al. (2007 ▶). Youji Huaxue, 27, 524] of the title compound, C12H14N2O3, gave only the unit-cell dimensions and an R factor with no other details available: the full structure is presented here. The eth­oxy group is disordered over two orientations with refined occupancies of 0.642 (15):0.358 (15). The nine C atoms and two N atoms of the 1-phenyl-2-(propan-2-yl­idene)hydrazine segment of the mol­ecule are close to being coplanar, with a maximum deviation of 0.0779 (14) Å for the phenyl­amino N atom and an intra­molecular N—H⋯O hydrogen bond generates an S(6) ring. In the crystal, pairs of C—H⋯O hydrogen bonds link mol­ecules into inverson dimers, generating R 2 2(16) loops