Equality of P-partition Generating Functions

To every partially ordered set (poset), one can associate a generating function, known as the P-partition generating function. We find necessary conditions and sufficient conditions for two posets to have the same P-partition generating function. We define the notion of a jump sequence for a labeled poset and show that having equal jumpsequences is a necessary condition for generating function equality. We also develop multiple ways of modifying posets that preserve generating function equality. Finally, we are able to give a complete classification of equalities among partially ordered setswith exactly two linear extensions.

Slow Strain Rate Testing and Stress Corrosion Cracking of Ultra-Fine Grained and Conventional Al-Mg Alloy

Stress corrosion cracking susceptibility was investigated for an ultra-fine grained (UFG) AI-7.5Mg alloy and a conventional 5083 H111 alloy in natural seawater using slow strain rate testing (SSRT) at very slow strain rates between 1E(-5) s(-1), 1E(-6) s(-1) and 1E(-7) s(-1). The UFG Al-7.5Mg alloy was produced by cryomilling, while the 5083 H111 alloy is considered as a wrought manufactured product. The response of tensile properties to strain rate was analyzed and compared. Negative strain rate sensitivity was observed for both materials in terms of the elongation to failure. However, the UFG alloy displayed strain rate sensitivity in relation to strength while the conventional alloy was relatively strain rate insensitive. The mechanical behavior of the conventional 5083 alloy was attributed to dynamic strain aging (DSA) and delayed pit propagation while the performance of the UFG alloy was related to a diffusion-mediated stress relaxation mechanism that successfully delayed crack initiation events, counteracted by exfoliation and pitting which enhanced crack initiation. (C) 2014 Elsevier B.V. All rights reserved.