Near-net shape rheocasting with the Council for Scientific and Industrial Research Rheo casting system(CSIR-RCS) and a high pressure die casting machine was successfully performed on Al-5Ti-1B grain refined aluminum a...Near-net shape rheocasting with the Council for Scientific and Industrial Research Rheo casting system(CSIR-RCS) and a high pressure die casting machine was successfully performed on Al-5Ti-1B grain refined aluminum alloy 7075.Grain refinement levels used were 0.03% Ti,0.13% Ti and 0.29% Ti(mass fraction).Tensile tests reveal that the ultimate tensile strengths,at all levels of grain refinement,are at least 97% of the specified minimum.Elongation at fracture increases with the increase of level of grain refinement although a maximum elongation is only 76% of the required minimum elongation in the case of 0.29% Ti.Incipient melting,during solution treatment,of the low melting point multinary eutectic causes porosity in the material and accounts for poor elongation results.0.03% Ti has a coarse eutectic structure forming larger pores while 0.29% Ti has a fine structure forming fine pores in the multinary eutectic.The 0.2% offset yield strengths of all the grain refinement levels are at least equal to or above the specified minimum and a decrease is observed with the increase of grain refinement level.There is a clear reduction in grain size from 0.03% Ti to 0.29% Ti in the as-cast condition.An underlying grain structure develops in the T6 condition material which has an inverse size to the as-cast structure;coarse grained as-cast material results in fine grained T6 condition material after solution heat treatment.The decrease in the offset yield strength as grain refinement increases correlates very strongly with the T6 grain sizes according to a Hall-Petch type relationship.展开更多
In this paper, we prove that under the F<sub>4</sub> condition, any L log<sup>+</sup> L bounded two-parameter Banach space valued martingale converges almost surely to an integrable Banach spac...In this paper, we prove that under the F<sub>4</sub> condition, any L log<sup>+</sup> L bounded two-parameter Banach space valued martingale converges almost surely to an integrable Banach space valued random variable if and only if the Banach space has the Radon-Nikodym property. We further prove that the above conclusion remains true if the F<sub>4</sub> condition is replaced by the weaker local F<sub>4</sub> condition.展开更多
Let（X,Y） be a pair of R<sup>d</sup>×R<sup>1</sup>-valued random variables.In thispaper we investigate the asymptotic properties of the L<sub>1</sub>-norm kernel estimator oft...Let（X,Y） be a pair of R<sup>d</sup>×R<sup>1</sup>-valued random variables.In thispaper we investigate the asymptotic properties of the L<sub>1</sub>-norm kernel estimator ofthe conditional median function of Y on X.Under appropriate regularity condi-tions,asymptotic normality and the optimal rates of convergence n<sup>（-1）/（2+d）</sup>and(n<sup>-1</sup>log n)<sup>1/（2+d）</sup> in the L<sup>q</sup>（1（?）q【∞）-and L<sup>∞</sup>-norms restricted to a compactset,respectively,are obtained.Our study shows that this estimator and the well-known Nadaraya-Watson’s kernel estimator of the conditional mean function of Yon X have the same asymptotic properties.展开更多
文摘Near-net shape rheocasting with the Council for Scientific and Industrial Research Rheo casting system(CSIR-RCS) and a high pressure die casting machine was successfully performed on Al-5Ti-1B grain refined aluminum alloy 7075.Grain refinement levels used were 0.03% Ti,0.13% Ti and 0.29% Ti(mass fraction).Tensile tests reveal that the ultimate tensile strengths,at all levels of grain refinement,are at least 97% of the specified minimum.Elongation at fracture increases with the increase of level of grain refinement although a maximum elongation is only 76% of the required minimum elongation in the case of 0.29% Ti.Incipient melting,during solution treatment,of the low melting point multinary eutectic causes porosity in the material and accounts for poor elongation results.0.03% Ti has a coarse eutectic structure forming larger pores while 0.29% Ti has a fine structure forming fine pores in the multinary eutectic.The 0.2% offset yield strengths of all the grain refinement levels are at least equal to or above the specified minimum and a decrease is observed with the increase of grain refinement level.There is a clear reduction in grain size from 0.03% Ti to 0.29% Ti in the as-cast condition.An underlying grain structure develops in the T6 condition material which has an inverse size to the as-cast structure;coarse grained as-cast material results in fine grained T6 condition material after solution heat treatment.The decrease in the offset yield strength as grain refinement increases correlates very strongly with the T6 grain sizes according to a Hall-Petch type relationship.
基金Project supported by the National Natural Science Foundation of Chinathe State Education Commission Ph. D. Station Foundation
文摘In this paper, we prove that under the F<sub>4</sub> condition, any L log<sup>+</sup> L bounded two-parameter Banach space valued martingale converges almost surely to an integrable Banach space valued random variable if and only if the Banach space has the Radon-Nikodym property. We further prove that the above conclusion remains true if the F<sub>4</sub> condition is replaced by the weaker local F<sub>4</sub> condition.
基金Research supported by National Natural Science Foundation of China
文摘Let（X,Y） be a pair of R<sup>d</sup>×R<sup>1</sup>-valued random variables.In thispaper we investigate the asymptotic properties of the L<sub>1</sub>-norm kernel estimator ofthe conditional median function of Y on X.Under appropriate regularity condi-tions,asymptotic normality and the optimal rates of convergence n<sup>（-1）/（2+d）</sup>and(n<sup>-1</sup>log n)<sup>1/（2+d）</sup> in the L<sup>q</sup>（1（?）q【∞）-and L<sup>∞</sup>-norms restricted to a compactset,respectively,are obtained.Our study shows that this estimator and the well-known Nadaraya-Watson’s kernel estimator of the conditional mean function of Yon X have the same asymptotic properties.
