On convergent sequences in dual groups

Let X = (X, p) be a seminormed complex linear space with zero θ. Natural definitions of convergent sequence, Cauchy sequence, absolutely convergent series, etc., can be given in terms of the seminorm p. Let us write C = C(X) for the set of all convergent sequences for the set of Cauchy sequences; and L∞ for the set of all bounded sequences.

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Synergistic effect of carboxyl and sulfate groups for effective removal of radioactive strontium ion in a Zr-metal-organic framework

Water Science & Technology ◽

10.2166/wst.2021.103 ◽

2021 ◽

Author(s):

Lin Ren ◽

Xudong Zhao ◽

Baosheng Liu ◽

Hongliang Huang

Keyword(s):

Adsorption Capacity ◽

High Efficiency ◽

Metal Organic Framework ◽

Maximum Adsorption Capacity ◽

Potential Candidate ◽

Dual Groups ◽

Metal Organic ◽

Strontium Ion ◽

Rapid Adsorption ◽

Organic Framework

Abstract Rapid removal of radioactive strontium from nuclear wastewater is of great significance for environment safety and human health. This work reported the effective adsorption of strontium ion in a stable dual-group metal-organic framework, Zr6(OH)14(BDC-(COOH)2)4(SO4)0.75 (Zr-BDC-COOH-SO4), which contains strontium-chelating groups (-COOH and SO4) and strongly ionizable group (-COOH). Zr-BDC-COOH-SO4 exhibits very rapid adsorption kinetics (<5 min) and a maximum adsorption capacity of 67.5 mg g−1. The adsorption behaviors can be well evaluated by pseudo-second-order model and Langmuir isotherm model. Further investigations indicate that the adsorption of Sr2+ in Zr-BDC-COOH-SO4 would not be interfered by solution pH and adsorption temperature obviously. Feasible regeneration of the adsorbent was also demonstrated through a simple elution method. Mechanism investigation suggests that free -COOH contributes to the rapid adsorption based on electrostatic interaction while introduction of -SO4 can enhance the adsorption capacity largely. Thus, these results suggest that Zr-BDC-COOH-SO4 might be a potential candidate for Sr2+ removal and introducing dual groups is an effective strategy for designing high-efficiency adsorbents.

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Matrix transformations related to I-convergent sequences

Acta et Commentationes Universitatis Tartuensis de Mathematica ◽

10.12697/acutm.2018.22.16 ◽

2019 ◽

Vol 22 (2) ◽

pp. 191-200

Author(s):

Enno Kolk

Keyword(s):

Linear Operators ◽

Matrix Transformations ◽

Infinite Matrices ◽

Bounded Linear Operators ◽

Bounded Linear ◽

Convergent Sequences

Characterized are matrix transformations related to certain subsets of the space of ideal convergent sequences. Obtained here results are connected with the previous investigations of the author on some transformations defined by infinite matrices of bounded linear operators.

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