2017
DOI: 10.1186/s13660-017-1428-6
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Two S-type Z-eigenvalue inclusion sets for tensors

Abstract: In this paper, we present two S-type Z-eigenvalue inclusion sets involved with a nonempty proper subset S of N for general tensors. It is shown that the new sets are tighter than those provided by Wang et al. (Discrete Contin. Dyn. Syst., Ser. B 22(1):187-198, 2017). Furthermore, we obtain upper bounds for the spectral radius of weakly symmetric nonnegative tensors, which are sharper than existing results.

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Cited by 28 publications
(27 citation statements)
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“…The increased surface hydrophilicity is desirable because not only it is better for water permeation but also it could reduce fouling by various hydrophobic foulant, since water molecules will be adsorbed to a hydrophilic surface through hydrogen bonds and form a thin water boundary layer, which promotes the transport of water across membrane and serves as a barrier to restrain undesirable adhesion of hydrophobic foulant on the membrane surface …”
Section: Resultsmentioning
confidence: 99%
“…The increased surface hydrophilicity is desirable because not only it is better for water permeation but also it could reduce fouling by various hydrophobic foulant, since water molecules will be adsorbed to a hydrophilic surface through hydrogen bonds and form a thin water boundary layer, which promotes the transport of water across membrane and serves as a barrier to restrain undesirable adhesion of hydrophobic foulant on the membrane surface …”
Section: Resultsmentioning
confidence: 99%
“…Physical coating and chemical grafting of zwitterionic materials that possess both negatively and positively charged moieties within the same side chain segment have also been investigated. Surface‐initiated atom‐transfer radical polymerization, initiated chemical vapor deposition, and concentration–polarization‐enhanced graft polymerization are some of the methods that are typically used to coat or graft zwitterionic polymers on the membrane surface . Particularly, owing to strong and stable electrostatic bonds with water, this modification approach is viably used to improve the anti‐biofouling properties of RO TFC membranes .…”
Section: Solutions Towards Energy‐efficient Desalinationmentioning
confidence: 99%
“…Wang et al. have modified a commercial RO membrane with carboxybetaine methacrylate (CBMA) zwitterionic polymer containing quaternary ammonium cations by redox‐initiated graft polymerization of N , N ′‐dimethylaminoethyl methacrylate (DMAEMA), followed by a surface quaternization reaction with 3‐bromopropionic acid (3‐BPA) to improve the water flux and biofouling resistance simultaneously . The water flux recovery of the modified membrane is much higher than that of the unmodified RO membrane, and almost complete removal (99 %) of Gram‐positive and Gram‐negative bacteria by bacteriostasis mechanisms is observed.…”
Section: Solutions Towards Energy‐efficient Desalinationmentioning
confidence: 99%
“…[6][7][8][9][10][11][12] Due to the superior atom efficiency, tunable structures and readily available characterization methods, the transition metal complexes had been explored deeply. Until now, quantities of transition metal catalysts based copper, [13][14][15][16] manganese, [17][18][19] cobalt, [20,21] iron [22,23] and nickel [24,25] have been explored for water oxidation. The catalysts can electrocatalyze water oxidation at a moderate or good turnover frequency (TOF) and a low overpotential.…”
Section: Introductionmentioning
confidence: 99%