Riemannian preconditioned algorithms for tensor completion via tensor ring decomposition

We propose Riemannian preconditioned algorithms for the tensor completion problem via tensor ring decomposition. A new Riemannian metric is developed on the product space of the mode-2 unfolding matrices of the core tensors in tensor ring decomposition. The construction of this metric aims to approximate the Hessian of the cost function by its diagonal blocks, paving the way for various Riemannian optimization methods. Specifically, we propose the Riemannian gradient descent and Riemannian conjugate gradient algorithms. We prove that both algorithms globally converge to a stationary point. In the implementation, we exploit the tensor structure and adopt an economical procedure to avoid large matrix formulation and computation in gradients, which significantly reduces the computational cost. Numerical experiments on various synthetic and real-world datasets -- movie ratings, hyperspectral images, and high-dimensional functions -- suggest that the proposed algorithms are more efficient and have better reconstruction ability than other candidates.Comment: 25 pages, 7 figures, 5 table

Novel Hydrophobically Modified Ethoxylated Urethanes End-Capped by Percec-Type Alkyl Substituted Benzyl Alcohol Dendrons: Synthesis, Characterization, and Rheological Behavior

Novel dendron hydrophobically modified ethoxylated urethanes (DHEUR) with almost the same molecular weights, molecular weight distributions, and identical hydrophilic portion but different terminal hydrophobic group numbers were prepared by using Percec-type alkyl substituted benzyl alcohol dendrons as new end-cappers. These DHEUR polymers in solution possess interesting associative and rheological behavior. For <b>DHEUR-1</b> with 4-mono­(decyloxy)­benzyl alcohol (<b>2</b>), the solutions are dominantly composed of the isolated and separated micelles and exhibit Newtonian behavior in a wide shear rate range accompanied by shear thinning at high shear rate region. <b>DHEUR-2</b> with 3,5-di­(decyloxy)­benzyl alcohol (<b>4</b>) in solutions form a relatively more complete network through dominant micellar junctions and process a relatively higher solution viscosity and similar solution viscosity behavior to <b>DHEUR-1</b>. However, shear thinning behavior shifts to a lower shear rate region due to a relatively longer relaxation time. Interestingly, the solutions of <b>DHEUR-3</b> with 3,4,5-tri­(decyloxy)­benzyl alcohol (<b>6</b>) have developed a complete physical network and show pronounced shear thinning behavior over the whole shear rate range. The oscillatory measurements further confirm that a gradually developing associative network leads to their different solution rheological behavior, i.e., viscous fluid (<b>DHEUR-1</b>), viscoelastic fluid (<b>DHEUR-2</b>), and elastic body (<b>DHEUR-3</b>) with increasing the hydrophobic tail number of dendrons. Furthermore, the rheological activation energy of these DHEUR polymers increases with the increase of terminal hydrophobic group numbers, indicating that DHEUR polymers with more hydrophobic tail chains need more energy potential barrier for the disengagement of hydrophobes from micelles due to stronger association strength. In general, the results demonstrate that the terminal hydrophobic tail number of dendrons plays a key role in determining the associative and rheological behavior of DHEUR in solutions. This work opens a new perspective for more efficient thickeners and also promises the potential of these DHEUR polymers in waterborne coating, cosmetics, dyestuff, medicines, and so on for the first time

Activation of peroxymonosulfate by MnO2 with oxygen vacancies: Degradation of organic compounds by electron transfer nonradical mechanism

Recently, ecofriendly and low toxicity manganese-based materials are receiving increased attention for the activation of peroxymonosulfate (PMS). The surface property of manganese-based materials has strong effect on its activation performance. In this study, MnO2 with differing levels of oxygen vacancies (Vo-MnO2) were prepared and used for PMS activation. The effects of oxygen vacancies (Vo), activator dosage, PMS concentration, and the initial pH on para-chloroaniline (PCA) degradation were studied. In these studies, Vo-MnO2 showed good stability and reusability for PMS activation. In addition, a series of experiments revealed the PMS activation mechanism. Interestingly, •OH, SO4•- and 1O2 were not primarily responsible for PCA degradation. PCA was degraded by the reactive complex formed by PMS and Vo-MnO2. Based on the characterization results and DFT calculations, the introduction of Vo in MnO2 changed the charge distribution of Mn atoms and enhanced PMS adsorption. This is more favorable to form the reactive complex in electron transfer mechanism. Besides, Vo increases the Mn3+ content in MnO2, which enhances oxidation ability of reactive complex and the efficiency of electron transfer. The degradation efficiency of pollutants in the Vo-MnO2/PMS system has been improved significantly. This study highlights the pivotal roles of Vo in electron transfer mechanism and provides a new method for the practical application in wastewater treatment

Aggregation and Rheology of an Azobenzene-Functionalized Hydrophobically Modified Ethoxylated Urethane in Aqueous Solution

Hydrophobically modified ethoxylated urethanes (HEURs) belong to an important class of telechelic associative polymers for improving solution rheological properties. We designed and prepared a novel azobenzene end-functionalized HEUR polymer (AzoHEUR), which was used to investigate the effects of hydrophobicity change of end hydrophobes induced by photoisomerization of azobenzene on the solution aggregation and rheological properties. The concentrated AzoHEUR solutions show a reversible rheological property change upon alternative exposure to UV and visible light. We have demonstrated that a reversible change in hydrophilic–lipophilic balance of polymer followed by photoisomerization of azobenzene induces a reversible rearrangement of micellar junctions through loop–bridge or bridge–loop transitions, which reversibly changes not only the network connectivity but also the solution relaxation behavior. Moreover, a structural model is proposed to describe the rearrangement of micellar junctions induced by photoisomerization of azobenzene. The work will not only provide new insights into the effect of hydrophobicity change of stimuli-responsive end groups on the aggregation and rheological behavior of HEUR aqueous solutions but also open a new perspective for development of some special applications of HEURs in fabrication and transmission of soft materials, medicines, cosmetics, inks for inkjet printers, and flow rate controlling systems

Novel Ferrocenyl-Terminated Linear–Dendritic Amphiphilic Block Copolymers: Synthesis, Redox-Controlled Reversible Self-Assembly, and Oxidation-Controlled Release

Novel linear–dendritic amphiphilic block copolymers with hydrophilic poly­(ethylene glycol) (PEG) block and hydrophobic Percec-type dendrons containing ferrocenyl terminals were synthesized by the esterification reaction of poly­(ethylene glycol) methyl ether with ferrocenyl-terminated alkyl-substituted benzoic acid dendrons. On the basis of the results that the critical aggregation concentration (CAC_ox) of the oxidation state polymer is much higher than CAC_red of the corresponding reduction state, these polymers can reversibly self-assemble into various aggregates, such as spherical, wormlike micelles, and vesicles, and also disassemble into irregular fragments in aqueous solution by redox reaction when changing the polymer concentrations. Copolymer PEG₄₅-<i>b</i>-Fc₃ (<b>3</b>) with 3,4,5-tris­(11-ferrocenylundecyloxy) benzoic acid (<b>2</b>) can self-assemble into nanoscale wormlike micelles when the polymer concentration in aqueous solution is above its CAC_ox. These wormlike micelles can be transformed into nanosized vesicles by Fe₂(SO₄)₃ and regained by vitamin C. Interestingly, copolymer PEG₄₅-<i>b</i>-Fc₂ (<b>5</b>) with 3,5-bis­(11-ferrocenylundecyloxy) benzoic acid (<b>4</b>) can reversibly self-assemble into spherical micelles with two different sizes by redox reaction above the CAC_ox, indicating that the terminal hydrophobic tail number of dendrons plays a key role in determining the self-assembled structures. Furthermore, rhodamine 6G (R6G)-loaded polymer aggregates have been successfully used for the oxidation-controlled release of loaded molecules, and the release rate can be mediated by the concentrations of oxidant and copolymers. The results provide an effective approach to the reversible self-assembly of linear–dendritic amphiphilic block copolymers and also promise the potential of these novel redox-responsive amphiphilic block copolymers in drug delivery systems, catalyst supports, and other research fields

Regulating Crystal Facets of MnO2 for Enhancing Peroxymonosulfate Activation to Degrade Pollutants: Performance and Mechanism

On the catalyst surface, crystal facets with different surface atom arrangements and diverse physicochemical properties lead to distinct catalytic activity. Acquiring a highly reactive facet through surface regulation is an efficient strategy to promote the oxidative decomposition of wastewater organic pollutants via peroxymonosulfate (PMS) activation. However, the mechanism through which crystal facets affect PMS activation is still unclear. In this study, three facet-engineered α-MnO2 with different exposed facets were prepared via a facile hydrothermal route. The prepared 310-MnO2 exhibited superior PMS activation performance to 100-MnO2 and 110-MnO2. Moreover, the 310-MnO2/PMS oxidative system was active over a wide pH range and highly resistant to interfering substances from wastewater. These advantages of the 310-MnO2/PMS system make it highly promising for practical wastewater treatment. Based on quenching experiments, electron paramagnetic resonance (EPR) analysis, solvent exchange, and electrochemical measurements, mediated electron transfer was found to be the dominant nonradical pathway for p-chloroaniline (PCA) degradation. A sulfhydryl group (-SH) masking experiment showed that the highly exposed Mn atoms on the 310-MnO2 surface were sites of PMS activation. In addition, density functional theory (DFT) calculations confirmed that the dominant {310} facet promoted adsorption/activation of PMS, which favored the formation of more metastable complexes on the α-MnO2 surface. The reaction mechanism obtained here clarifies the relationship between PMS activation and crystal facets. This study provides significant insights into the rational design of high-performance catalysts for efficient water remediation