ON ASYMPTOTIC UNIFORM SMOOTHNESS AND NONLINEAR GEOMETRY OF BANACH SPACES

These notes concern the nonlinear geometry of Banach spaces, asymptotic uniform smoothness and several Banach–Saks-like properties. We study the existence of certain concentration inequalities in asymptotically uniformly smooth Banach spaces as well as weakly sequentially continuous coarse (Lipschitz) embeddings into those spaces. Some results concerning the descriptive set theoretical complexity of those properties are also obtained. We finish the paper with a list of open problem.

Failure Modes of American Petroleum Institute 12F Tanks With a Rectangular Cleanout and Stepped Shell Design

The design and fabrication of shop-welded and prefabricated relatively small tanks, when compared to field-welded tanks, used in the upstream segment of the oil and gas industry is governed by the American Petroleum Institute specification 12F (API 12F). This study explores the changing designs of API 12F tanks to include a new rectangular cleanout design with reinforcement as shell extension internally of cleanout frame and a stepped shell design. This study also investigated the introduction of two additional tank sizes in addition to existing eleven tank sizes in the current 12th edition of API 12F. The adequacy of the new design changes and proposed tank designs were verified by elastic stress analysis with nonlinear geometry, elastic–plastic stress analysis with nonlinear geometry, and elastic buckling analysis to verify their ability to operate at a design internal pressure of 16 oz/in2 (6.9 kPa) and maximum pressure during emergency venting of 24 oz/in2 (10.3 kPa). A vacuum pressure of 1.5 oz/in2 (0.43 kPa) was also investigated using the elastic buckling analysis. The stress levels and uplift of the tanks are reported in this report to provide insights into the behavior of proposed API 12F tanks exposed to higher internal pressure and vacuum pressure.