In this study,the removal of monovalent and divalent cations,Nat,Kt,Mg2t,and Ca2t,in a diluted solution from Chott-El Jerid Lake,Tunisia,was investigated with the electrodialysis technique.The process was tested using...In this study,the removal of monovalent and divalent cations,Nat,Kt,Mg2t,and Ca2t,in a diluted solution from Chott-El Jerid Lake,Tunisia,was investigated with the electrodialysis technique.The process was tested using two cation-exchange membranes:sulfonated polyether sulfone cross-linked with 10%hexamethylenediamine(HEXCl)and sulfonated polyether sulfone grafted with octylamine(S-PESOS).The commercially available membrane Nafion®was used for comparison.The results showed that Nafion®and S-PESOS membranes had similar removal behaviors,and the investigated cations were ranked in the following descending order in terms of their demineralization rates:Nat>Ca2t>Mg2t>Kt.Divalent cations were more effectively removed by HEXCl than by monovalent cations.The plots based on the WebereMorris model showed a strong linearity.This reveals that intra-particle diffusion was not the removal rate-determining step,and the removal process was controlled by two or more concurrent mechanisms.The Boyd plots did not pass through their origin,and the sole controlling step was determined by film-diffusion resistance,especially after a long period of electrodialysis.Additionally,a semi-empirical model was established to simulate the temporal variation of the treatment process,and the physical significance and values of model parameters were compared for the three membranes.The findings of this study indicate that HEXCl and S-PESOS membranes can be efficiently utilized for water softening,especially when effluents are highly loaded with calcium and magnesium ions.展开更多
In this paper the operator-valued martingale transform inequalities in rearrangement invariant function spaces are proved.Some well-known results are generalized and unified.Applications are given to classical operato...In this paper the operator-valued martingale transform inequalities in rearrangement invariant function spaces are proved.Some well-known results are generalized and unified.Applications are given to classical operators such as the maximal operator and the p-variation operator of vector-valued martingales,then we can very easily obtain some new vector-valued martingale inequalities in rearrangement invariant function spaces.These inequalities are closely related to both the geometrical properties of the underlying Banach spaces and the Boyd indices of the rearrangement invariant function spaces.Finally we give an equivalent characterization of UMD Banach lattices,and also prove the Fefferman-Stein theorem in the rearrangement invariant function spaces setting.展开更多
This paper is concerned with the existence theory of a semilinear elliptic system. In particular, we will prove that the system has a nontrivial positive solution in some appropriate solution spaces.
文摘In this study,the removal of monovalent and divalent cations,Nat,Kt,Mg2t,and Ca2t,in a diluted solution from Chott-El Jerid Lake,Tunisia,was investigated with the electrodialysis technique.The process was tested using two cation-exchange membranes:sulfonated polyether sulfone cross-linked with 10%hexamethylenediamine(HEXCl)and sulfonated polyether sulfone grafted with octylamine(S-PESOS).The commercially available membrane Nafion®was used for comparison.The results showed that Nafion®and S-PESOS membranes had similar removal behaviors,and the investigated cations were ranked in the following descending order in terms of their demineralization rates:Nat>Ca2t>Mg2t>Kt.Divalent cations were more effectively removed by HEXCl than by monovalent cations.The plots based on the WebereMorris model showed a strong linearity.This reveals that intra-particle diffusion was not the removal rate-determining step,and the removal process was controlled by two or more concurrent mechanisms.The Boyd plots did not pass through their origin,and the sole controlling step was determined by film-diffusion resistance,especially after a long period of electrodialysis.Additionally,a semi-empirical model was established to simulate the temporal variation of the treatment process,and the physical significance and values of model parameters were compared for the three membranes.The findings of this study indicate that HEXCl and S-PESOS membranes can be efficiently utilized for water softening,especially when effluents are highly loaded with calcium and magnesium ions.
基金supported by National Natural Science Foundation of China (GrantNo. 11001273)Research Fund for International Young Scientists (Grant No. 11150110456)+1 种基金Research Fundfor the Doctoral Program of Higher Education of China (Grant No. 20100162120035)Postdoctoral Science Foundation of China and Central South University
文摘In this paper the operator-valued martingale transform inequalities in rearrangement invariant function spaces are proved.Some well-known results are generalized and unified.Applications are given to classical operators such as the maximal operator and the p-variation operator of vector-valued martingales,then we can very easily obtain some new vector-valued martingale inequalities in rearrangement invariant function spaces.These inequalities are closely related to both the geometrical properties of the underlying Banach spaces and the Boyd indices of the rearrangement invariant function spaces.Finally we give an equivalent characterization of UMD Banach lattices,and also prove the Fefferman-Stein theorem in the rearrangement invariant function spaces setting.
文摘This paper is concerned with the existence theory of a semilinear elliptic system. In particular, we will prove that the system has a nontrivial positive solution in some appropriate solution spaces.
