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Tensor analysis has received enormous attention as the increasing prevalence of high-dimensional data in science research and engineering application. Tensor recovery is an important and meaningful problem for tensor analysis. It aims to complete a tensor from an observed subset of its entries disturbed by noise. However, classical methods either develop on the second-order statistics or Lasso-type penalty, leading to them not effectively dealing with gross or dense noise effectively. To address such issues, we propose a robust tensor recovery model for simultaneously completing a low tubal rank tensor with complex noise and missing data. Based on tensor–tensor product (t-product), we first develop a tensor factor Frobenius norm to exploit the low tubal rank property which is closely related to tensor nuclear norm and tubal rank. By utilizing the robust L 2 criterion, we derive the nonconvex objective function to accommodate the low tubal rank tensor. An implementable alternating minimization algorithm has been developed to estimate the low tubal rank tensor. It is worth noting that our method is able to jointly estimate the precision parameter to capture the hidden complex noise pattern. Furthermore, some convergence properties of the proposed algorithm are presented. A series of numerical experiments are conducted on both synthetic and real-world data to demonstrate the effectiveness and robustness of the proposed approach in comparison with the state-of-the-art methods. • A robust tensor recovery model is proposed for completing a low tubal rank tensor with complex noise and missing data. • Based on t-product, we develop a tensor factor Frobenius norm to exploit the low tubal rank property. • By utilizing the robust L 2 criteria, we derive the nonconvex objective function and obtain robust estimation algorithm. • Our method is able to jointly estimate the precision parameter to capture the hidden complex noise pattern. • The global convergence property is established for the nonconvex loss function. [ABSTRACT FROM AUTHOR]

The biconjugate gradients (BiCG) and biconjugate residual (BiCR) methods are attractive ways for solving nonsymmetric linear system A x = b. In this paper, the BiCG and BiCR methods are extended to solve the high order Stein tensor equation. The convergent properties of the developed iterative algorithms are studied. Numerical examples are provided to confirm the theoretical results, which demonstrate that the proposed algorithms are effective and feasible for solving the Stein tensor equation. [ABSTRACT FROM AUTHOR]

Ferrate (Fe(VI)) salts are commonly regarded as green and high efficient oxidants to eliminate organic contaminants. Current studies mainly focused on develop homogeneous activation technology or heterogeneous catalysts to promote Fe(VI) performances in contaminants degradation. Interestingly, this study disclosed that the degradation performance of tetracycline hydrochloride (TC) was enhanced by using in situ prepared ferrate supernatant (Fe(VI)s), and the oxidation performance and degradation mechanism were systematically explored by comparing with the ferrate precipitation (Fe(VI)p) and the commercial ferrate (Fe(VI)c). Results showed that the degradation rate of TC by Fe(VI)s reached to 98.5 % within 5 min, while the degradation rate of Fe(VI)p and Fe(VI)c were obtained less than 20 % in 30 min. Although degradation process of TC in these three system were all conformed to the pseudo-first-order reaction kinetic, the rate of degradation (Kobs) obtained in Fe(VI)s was 5.30 and 37.2 times higher than that in Fe(VI)c and Fe(VI)p, respectively. Electron paramagnetic resonance (EPR), radical quenching and PMSO probe experiments proved that Fe(IV)/Fe(V) were the main active species for TC degradation with Fe(VI)s, while ∙ OH and ⋅ O 2 − were the main active substance of Fe(VI)c. On the basis of the intermediates detected by LC-MS/MS analysis, a pathway for TC degradation was proposed. In addition, the toxicity of TC and its degradation products was evaluated by using the toxicity evaluation software tool. This study demonstrated efficient organic contaminant oxidation with in situ prepared ferrate solution (Fe(VI)s) and provided a comprehensive understanding of degradation process for pollutants removal. • Fe(VI)s was prepared and compared with Fe(VI)p and Fe(VI)c. • The Fe(VI)s realized rapid and efficient degradation of TC. • Mechanism and pathways for TC degradation were examined and proposed. • Fe(IV)/Fe(V) was the main reactive species leading to the degradation of TC. • The toxicity evaluations manifested the oxidant has a certain degree of environmental safety. [ABSTRACT FROM AUTHOR]

• A doubly robust classification method is proposed by TRPCA and minimum distance criterion. • We apply the TRPCA of third-order tensor to the input by the low tubal rank with its tensor nuclear norm. • Our procedure is a data driven and adaptive supervised learning method. The growing prevalence of image data in engineering and medical applications motivates the need for classification performance that are robust against outliers. To facilitate efficient and data-driven classification and recovery method, in this paper, we propose a novel supervised learning strategy based on the robust principal component analysis for third-order tensor and minimum distance criterion L 2 E for logistic regression, which is named as doubly robust logistic regression. Our work applies the ADMM method to obtain updating algorithm, and its global convergence is established even though L 2 E loss function is non-convex. We also extend the estimation procedure to the case of incomplete observation in input matrix. The numerical experiments demonstrate the advantages of combining the logistic L 2 E with tensor robust principal component analysis which can not only increase the accuracy of classification but also improve the recovery accuracy of noisy image. Three real data analysis are further used to examine the outperformance of our proposed method over the stat-of-art. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we present a fast algorithm for solving Symmetric penta-diagonal systems. We give the feasibility and Stability analysis of the algorithm. Moreover, parallel computations can be implemented in the algorithm. The numerical examples verify the efficiency of the algorithm. [ABSTRACT FROM AUTHOR]

• Microplastics (MPs) affected soil physicochemical properties and enzyme activities. • Response sensitivities of bacteria and fungi to MPs were inconsistent. • Soil aggregates size governed the response sensitivities of bacteria and fungi to MPs. • MPs altered microbial community structures through the direct and indirect pathways. Microplastics (MPs) alter soil aggregation stability. However, studies have yet to determine whether these alterations further affect microbial community structures and diversities within different soil aggregates and whether they influence the responses of soil microbial structures and diversities to MPs in different aggregate fractions. In this study, long-term soil incubation experiments and soil fractionation were combined to investigate the effects of polyethylene microplastics (PE-MPs) on soil aggregate properties and microbial communities in soil aggregates with different particle sizes. Results showed that the existence of PE-MPs significantly reduced the physicochemical properties of soil aggregates, inhibited the activities of soil enzymes, and changed the richness and diversity of bacterial and fungal communities. Such variations exerted notable differences in soil aggregate levels. The response sensitivity of bacteria in the silt and clay fraction was higher than that in the macroaggregate fraction, but the response sensitivity of fungi in the macroaggregate fraction was higher than that in the silt and clay fraction. Relationships and path analysis between soil aggregate properties and microbial communities after PE-MPs addition were proposed. PE-MPs affected microbial community structures by directly and indirectly influencing soil microenvironmental conditions. The relative abundances of Acidobacteria , Gemmatimonadetes , Bacteroides , Basidiomycota , Chtridiomyota , and Glomeromycota were significantly correlated with physicochemical properties and soil enzyme activities. Enzyme activities were direct factors influencing soil microbial community structures, and physicochemical properties (i.e., dissolved organic carbon, soil available phosphorus) could indirectly affect these structures by acting on soil enzyme activities. Our findings helped improve our understanding of the responses of soil microbial structures and diversities to MPs through the perspective of different soil aggregates. [ABSTRACT FROM AUTHOR]

In this study, scrap irons (SI)/granular activated carbons (GAC) micro-electrolysis treatment and persulfate-releasing materials (PRM) treatment were employed to construct the combination reduction and oxidation system to treat 2,4-dinitrotoluene (2,4-DNT) contaminated groundwater. The 2,4-DNT treatment efficiencies in the PRM pre-treatment before SI/GAC micro-electrolysis treatment (FM-1 = PRM + SI/GAC) and SI/GAC micro-electrolysis pre-treatment before the PRM treatment (FM-3 = SI/GAC + PRM) were investigated in two separated columns. As control groups, the separated SI and GAC instead of the SI/GAC mixture were used in another two separated columns (FM-2 = PRM + SI + GAC; FM-4 = SI + GAC + PRM). The highest treatment efficiencies of 2,4-DNT in the FM-1 and FM-3 systems reached 79% and 93% during 5 PV, respectively. We found that the filling position of SI, GAC and PRM significantly affected the variations of pH, oxidation-reduction potential, Fe2+ and S 2 O 8 2− concentrations in the combined systems. These results indicated that the SI/GAC micro-electrolysis pre-treatment of 2,4-DNT before the PRM treatment (FM-3) is more beneficial. The fifteen main intermediates in the combined system were identified by the detection of liquid chromatograph mass spectrometer. Furthermore, the possible treatment pathways of 2.4-DNT were proposed on the basis of identified intermediates. The treatment mechanisms in the FM-1 and FM-3 systems were proposed with the reduction mechanism in the SI/GAC micro-electrolysis system and the oxidation mechanism in the PRM treatment. Therefore, the combination of the reduction pre-treatment with the SI/GAC micro-electrolysis system and the oxidation post-treatment with persulfate can effectively treat the nitroaromatic compounds contaminated groundwater. Unlabelled Image • The performances of the combination of reduction and oxidation treatment of 2,4-dinitrotoluene contaminated groundwater were investigated; • The scrap irons/granular activated carbons micro-electrolysis pre-treatment of 2,4-dinitrotoluene before persulfate treatment is more beneficial in the combined system; • The fifteen main intermediates in the combined systems were identified; • The reduction in the micro-electrolysis system and the oxidation in the persulfate treatment were the main treatment mechanism. [ABSTRACT FROM AUTHOR]

High-precision displacement platforms are of great significance in micro/nanoscale manipulation, ultraprecision manufacturing, biological manipulation, and scanning probe microscopes. This paper presents a novel compliant planar parallelogram mechanism (CPPM) for high-precision translational motion utilizing 8 flexible initially curved beams (ICBs). Compared with the existing high-precision displacement platforms for traditional motion, CPPM combines the characteristics of large motion ranges, bidirectional anti-buckling and high load-bearing. Moreover, this new mechanism introduces more design parameters compared to traditional parallelogram mechanisms, thus generating other desired characteristics by optimizing these parameters. In this paper, a general mathematical model is first derived for quick design and model-based optimization, followed by nonlinear finite element method (FEM) validation. Three desired performance characteristics in compliant translational mechanisms are proposed thereafter to obtain three optimized designs through global optimization of the preset geometric parameters. Experimental results verify the accuracy of the mathematical model and demonstrate centimeter-level high-precision positioning within a large motion range. Finally, a comparative discussion of the anti-buckling mechanisms for translation is presented. • We present a compliant planar parallelogram mechanism with desired performances. • We use general tensural–compresural initially curved beams. • We develop and validate the mathematical model. • We optimize geometric parameters globally for three desired performance characteristics. [ABSTRACT FROM AUTHOR]

Mercury (Hg2+) contamination in water is associated with potential toxicity to human health and ecosystems. Many research studies have been ongoing to develop new materials for the remediation of Hg2+ pollution in water. In this study, a novel thiol- and amino-containing fibrous adsorbent was prepared by grafting 2-amino-5-mercapto-1,3,4-thiadiazol (AMTD) onto PAN fiber through a microwave-assisted method. The synthesized functional fiber was characterized by FTIR, SEM, and elemental analysis. Adsorption tests depicted that for mercury uptake, PAN MW -AMTD fiber exhibited enhanced adsorption capacity compared with other fibrous adsorbents and selective adsorption feature under the interference of other metal ions, including Pb2+, Cu2+, Cd2+, and Zn2+. The influence of pH on the adsorption process was investigated and the effect of temperature revealed that the adsorption sorption process was endothermic and the adsorption performance of PAN MW -AMTD was elevated with the increase of temperature. Kinetic studies of PAN MW -AMTD fiber followed the pseudo-second-order and the adsorption isotherm of Hg2+ was well fitted by Sips and Langmuir equations, given the maximum adsorption amount of 332.9 mg/g. XPS results suggested that a synergetic coordination effect of sulfur and nitrogen in functional fiber with mercury took responsibility for the adsorption mechanism in the uptake process. In addition, the prepared PAN MW -AMTD fiber could easily be regenerated with 0.1 M HCl for five times without significant reduction of mercury removal efficiency. Thus, this study will facilitate the research on novel functional material for the removal of mercury from water. • An AMTD-modified PAN fiber was efficiently prepared with MW-assisted method. • PAN MW -AMTD fiber displays excellent removal efficiency and selective ability for Hg2+. • Maximum adsorption capacity of PAN MW -AMTD fiber for mercury was obtained at 332.9 mg/g. • Adsorption mechanism is chemisorption and N and S coordinated with Hg2+. • PAN MW -AMTD fiber remained as a cost-effective and reusable chelating adsorbent. [ABSTRACT FROM AUTHOR]