We show that a weak sense stationary stochastic process can be approximated by local averages. Explicit error bounds are given. Our result improves an early one from Splettst?sser.
A novel stationary phase for weak cation exchange （WCX） chromatography was prepared by ＂grafting from＂ strategy. Surface initiated atom transfer radical polymerization （ATRP） of acrylic acid （AA） was conducted...A novel stationary phase for weak cation exchange （WCX） chromatography was prepared by ＂grafting from＂ strategy. Surface initiated atom transfer radical polymerization （ATRP） of acrylic acid （AA） was conducted in toluene medium, starting from the macromolecule initiators of poly（4-vinylbenzyl chloride-co-divinylbenzene） （PcMs/DvB） beads, The amounts of poly（acrylic acid） grafted chains with different ATRP formulations were calculated based on the elemental analyses. The poly（acrylic acid） grafted beads obtained with different ATRP formula- tions were tried as chromatographic packings in the separation of proteins by ion-exchange chromatography. The effect of the poly（acrylic acid） grafted chain lengths on PCMS/DVB beads for the separation of proteins was investigated in details. Simultaneously, characterization of the column was investigated as ion chromatographic stationary phase for the separation of inorganic cations. The results show that poly（acrylic acid） grafted columns had excellent performance for separation of proteins and inorganic cations. The highest of the dynamic capacity of the column was 35.55 mg/mL. The columns were provided with high column efficiency.展开更多
In this paper, we propose a Sample Average Approximation （SAA） method for a class of Stochastic Mathematical Programs with Complementarity Constraints （SMPCC） recently considered by Birbil, G/irkan and Listes [3]....In this paper, we propose a Sample Average Approximation （SAA） method for a class of Stochastic Mathematical Programs with Complementarity Constraints （SMPCC） recently considered by Birbil, G/irkan and Listes [3]. We study the statistical properties of obtained SAA estimators. In particular we show that under moderate conditions a sequence of weak stationary points of SAA programs converge to a weak stationary point of the true problem with probability approaching one at exponential rate as the sample size tends to infinity. To implement the SAA method more efficiently, we incorporate the method with some techniques such as Scholtes＇ regularization method and the well known smoothing NCP method. Some preliminary numerical results are reported.展开更多
基金This work was supported partially by the National Natural Science Foundation of China (Grant Nos. 60472042,10571089 and 60572113),the Liuhui Center for Applied Mathematics, the Program for New Century Excellent Talents in Universitiesthe Research Fund for the Doctoral Program of Higher Educationthe Scientific Research Foundation for the Returned Overseas Chinese Scholars, Ministry of Education of China
文摘We show that a weak sense stationary stochastic process can be approximated by local averages. Explicit error bounds are given. Our result improves an early one from Splettst?sser.
基金Project supported by the Foundation of the Ministery of Science and Technology of China （No. 2009CB626608） and the National Natural Science Foundation of China （No. 201065008）.
文摘A novel stationary phase for weak cation exchange （WCX） chromatography was prepared by ＂grafting from＂ strategy. Surface initiated atom transfer radical polymerization （ATRP） of acrylic acid （AA） was conducted in toluene medium, starting from the macromolecule initiators of poly（4-vinylbenzyl chloride-co-divinylbenzene） （PcMs/DvB） beads, The amounts of poly（acrylic acid） grafted chains with different ATRP formulations were calculated based on the elemental analyses. The poly（acrylic acid） grafted beads obtained with different ATRP formula- tions were tried as chromatographic packings in the separation of proteins by ion-exchange chromatography. The effect of the poly（acrylic acid） grafted chain lengths on PCMS/DVB beads for the separation of proteins was investigated in details. Simultaneously, characterization of the column was investigated as ion chromatographic stationary phase for the separation of inorganic cations. The results show that poly（acrylic acid） grafted columns had excellent performance for separation of proteins and inorganic cations. The highest of the dynamic capacity of the column was 35.55 mg/mL. The columns were provided with high column efficiency.
文摘In this paper, we propose a Sample Average Approximation （SAA） method for a class of Stochastic Mathematical Programs with Complementarity Constraints （SMPCC） recently considered by Birbil, G/irkan and Listes [3]. We study the statistical properties of obtained SAA estimators. In particular we show that under moderate conditions a sequence of weak stationary points of SAA programs converge to a weak stationary point of the true problem with probability approaching one at exponential rate as the sample size tends to infinity. To implement the SAA method more efficiently, we incorporate the method with some techniques such as Scholtes＇ regularization method and the well known smoothing NCP method. Some preliminary numerical results are reported.
