1 IntroductionLet R<sup>n×n</sup> be the set of all n×n real matrices.R<sup>n</sup>=R<sup>n×1</sup>.C<sup>n×n</sup>denotes the set of all n×n co...1 IntroductionLet R<sup>n×n</sup> be the set of all n×n real matrices.R<sup>n</sup>=R<sup>n×1</sup>.C<sup>n×n</sup>denotes the set of all n×n complex matrices.We are interested in solving the following inverse eigenvalue prob-lems:Problem A （Additive inverse eigenvalue problem） Given an n×n real matrix A=(a<sub>ij</sub>),and n distinct real numbers λ<sub>1</sub>,λ<sub>2</sub>,…,λ<sub>n</sub>,find a real n×n diagonal matrix展开更多
Four common types of additives for polymer membrane preparation including organic macromolecule and micromolecule additives, inorganic salts and acids, and the strong non-solvent H2 O were used to prepare poly（vinyli...Four common types of additives for polymer membrane preparation including organic macromolecule and micromolecule additives, inorganic salts and acids, and the strong non-solvent H2 O were used to prepare poly（vinylidene fluoride-co-chlorotrifluoroethylene）（PVDF-CTFE） hydrophobic flat-sheet membranes. Membrane properties including morphology, porosity, hydrophobicity, pore size and pore distribution were investigated, and the permeability was evaluated via direct contact membrane distillation（DCMD） of 3.5 g/L Na Cl solution in a DCMD configuration. Both inorganic and organic micromolecule additives were found to slightly influence membrane hydrophobicity. Polyethylene glycol（PEG）,organic acids, Li Cl, Mg Cl2, and Li Cl/H2 O mixtures were proved to be effective additives to PVDF-CTFE membranes due to their pore-controlling effects and the capacity to improve the properties and performance of the resultant membranes. The occurrence of a pre-gelation process showed that when organic and inorganic micromolecules were added to PVDF-CTFE solution, the resultant membranes presented a high interconnectivity structure. The membrane prepared with dibutyl phthalate（DBP） showed a nonporous surface and symmetrical cross-section. When H2 O and Li Cl/H2 O mixtures were also used as additives, they were beneficial for solid–liquid demixing, especially when Li Cl/H2 O mixed additives were used. The membrane prepared with 5% Li Cl ＋ 2% H2 O achieved a flux of24.53 kg/（m2·hr） with 99.98% salt rejection. This study is expected to offer a reference not only for PVDF-CTFE membrane preparation but also for other polymer membranes.展开更多
文摘1 IntroductionLet R<sup>n×n</sup> be the set of all n×n real matrices.R<sup>n</sup>=R<sup>n×1</sup>.C<sup>n×n</sup>denotes the set of all n×n complex matrices.We are interested in solving the following inverse eigenvalue prob-lems:Problem A （Additive inverse eigenvalue problem） Given an n×n real matrix A=(a<sub>ij</sub>),and n distinct real numbers λ<sub>1</sub>,λ<sub>2</sub>,…,λ<sub>n</sub>,find a real n×n diagonal matrix
基金Financial support by the National Natural Science Foundation of China (Nos. 51378491, 51578533, 21307149) is also gratefully acknowledged
文摘Four common types of additives for polymer membrane preparation including organic macromolecule and micromolecule additives, inorganic salts and acids, and the strong non-solvent H2 O were used to prepare poly（vinylidene fluoride-co-chlorotrifluoroethylene）（PVDF-CTFE） hydrophobic flat-sheet membranes. Membrane properties including morphology, porosity, hydrophobicity, pore size and pore distribution were investigated, and the permeability was evaluated via direct contact membrane distillation（DCMD） of 3.5 g/L Na Cl solution in a DCMD configuration. Both inorganic and organic micromolecule additives were found to slightly influence membrane hydrophobicity. Polyethylene glycol（PEG）,organic acids, Li Cl, Mg Cl2, and Li Cl/H2 O mixtures were proved to be effective additives to PVDF-CTFE membranes due to their pore-controlling effects and the capacity to improve the properties and performance of the resultant membranes. The occurrence of a pre-gelation process showed that when organic and inorganic micromolecules were added to PVDF-CTFE solution, the resultant membranes presented a high interconnectivity structure. The membrane prepared with dibutyl phthalate（DBP） showed a nonporous surface and symmetrical cross-section. When H2 O and Li Cl/H2 O mixtures were also used as additives, they were beneficial for solid–liquid demixing, especially when Li Cl/H2 O mixed additives were used. The membrane prepared with 5% Li Cl ＋ 2% H2 O achieved a flux of24.53 kg/（m2·hr） with 99.98% salt rejection. This study is expected to offer a reference not only for PVDF-CTFE membrane preparation but also for other polymer membranes.
