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
The inexact Rayleigh quotient iteration (RQI) is used for computing the smallest eigenpair of a large Hermitian matrix. Under certain condition, the method was proved to converge quadratically in literature. However, ...The inexact Rayleigh quotient iteration (RQI) is used for computing the smallest eigenpair of a large Hermitian matrix. Under certain condition, the method was proved to converge quadratically in literature. However, it is shown in this paper that under the original given condition the inexact RQI may not quadratically converge to the desired eigenpair and even may misconverge to some other undesired eigenpair. A new condition, called the uniform positiveness condition, is given that can fix misconvergence problem and ensure the quadratic convergence of the inexact RQI. An alternative to the inexact RQI is the Jacobi-Davidson (JD) method without subspace acceleration. A new proof of its linear convergence is presented and a sharper bound is established in the paper. All the results are verified and analyzed by numerical experiments.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supported by the National Natural Science Foundation of China (Grant Nos. 10471074, 10771116)the Doctoral Program of the Ministry of Education of China (Grant No. 20060003003)
文摘The inexact Rayleigh quotient iteration (RQI) is used for computing the smallest eigenpair of a large Hermitian matrix. Under certain condition, the method was proved to converge quadratically in literature. However, it is shown in this paper that under the original given condition the inexact RQI may not quadratically converge to the desired eigenpair and even may misconverge to some other undesired eigenpair. A new condition, called the uniform positiveness condition, is given that can fix misconvergence problem and ensure the quadratic convergence of the inexact RQI. An alternative to the inexact RQI is the Jacobi-Davidson (JD) method without subspace acceleration. A new proof of its linear convergence is presented and a sharper bound is established in the paper. All the results are verified and analyzed by numerical experiments.
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.
