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The Steiner (k , k ′) -eccentricity of a given k ′ -subset of a graph G is the maximum Steiner distance over all k -subsets of V (G) which contain the given k ′ -subset, an extension of standard Steiner k -eccentricity. In this paper, we mainly study the Steiner (3 , 2) -eccentricity of trees. The σ -transformation which does not increase the average Steiner (3 , 2) -eccentricity is depicted. Using σ -transformation, several lower and upper bounds for the average Steiner (3 , 2) -eccentricity of trees are given. [ABSTRACT FROM AUTHOR]

Chemical stability assessment of biochar has been universally used to indicate its potential of long-term carbon sequestration. The comparative study on oxidation resistance of biochars from diverse series of feedstock is relatively limited, as well as the effects of endogenous minerals on biochar stability. Herein, oxidation resistance of biochars from peanut shell, bamboo, saw dust, reed stalk, furfural residues, seaweed degumming residues and Enteromorpha prolifera at 500 °C (PS500, BB500, SD500, RS500, FR500, SR500 and EP500) was examined by the treatments of H 2 O 2 , K 2 Cr 2 O 7 and thermogravimetric analysis (TGA). Under H 2 O 2 or K 2 Cr 2 O 7 condition, C loss of algae-derived biochars (SR500 and EP500) was extremely greater than that of other biochars due to higher content of labile carbon components. PS500, BB500, SD500, RS500 and FR500 characterized with similar properties in carbon fraction, but they exhibited different ability to resist oxidation. The mineral fraction of biochars (e.g., content and species) varied with the feedstock, which played complex effects on the oxidation resistance. The mineral decomposition (e.g., CaCO 3) in EP500 and SR500 above 500 °C influenced the analysis of biochar stability by TGA. After acid-washing, EP500 and SR500 showed weaker thermal oxidation resistance, agreed with the results of H 2 O 2 and K 2 Cr 2 O 7 oxidation. The oxidation resistance of biochars was correlated better with O/C ratio, implying that O/C ratio was more robust indicator than other indexes (e.g., H/C ratio and the ratio of D band to G band of Raman). The FTIR, Raman and XPS results further demonstrated the elimination of aliphatics and amorphous aromatics and/or the carboxylation/carbonylation of aromatic structures by H 2 O 2 and K 2 Cr 2 O 7. These findings are useful for better understanding the impacts of feedstock and inherent minerals on the oxidation resistance of biochars. Unlabelled Image • Oxidation resistance of biochars from diverse series of feedstock was examined. • C loss of algae-derived biochars was extremely higher in H 2 O 2 /K 2 Cr 2 O 7 oxidation. • Mineral decomposition above 500 °C influenced biochar stability assessment by TGA. • The minerals derived from feedstock showed different effects on biochar stability. • O/C ratio was more robust indicator for biochar stability than H/C and ID/IG ratio. [ABSTRACT FROM AUTHOR]

Halogenated benzoquinones (HBQs) are frequently detected in tap water. HBQ levels are correlated with water age. As the water–transmission distance (water age) increases, the levels of bromo-benzoquinones (Br-BQs) decreased and those of chloro-benzoquinones (Cl-BQs) remained relatively stable in drinking water–distribution system in the presence of residual chlorine. 2,3,5,6-Tetrachloro-1,4-benzoquinone (TCBQ) and 2,6-dibromo-1,4-benzoquinone (DBBQ) were the most abundant Cl-BQ and Br-BQ, with maximum concentrations of 60.2 and 181.4 ng/L, respectively. TCBQ and DBBQ were chosen as representatives of HBQs to investigate their reactions with chlorine, including kinetics, pathways, and changes in toxicity. The hydrolysis and chlorination rates of HBQs were significantly pH-dependent, and the kinetic rates of DBBQ were faster than TCBQ in the pH range of 5–10. Chlorination converted highly toxic TCBQ and DBBQ to less-toxic chlorinated/brominated aliphatic disinfection by-products (DBPs), thereby reducing the overall toxicity of water bodies. This study provides comprehensive insights into the distinct life cycles of TCBQ and DBBQ in drinking water, covering formation, transformation, and toxicity. These findings provide a nuanced understanding of the risks posed by HBQs at various locations within the drinking water distribution system, offering valuable guidance for improving the control of DBPs in drinking water. [Display omitted] • Evolution of HBQs and aliphatic DBPs with age of drinking water was investigated. • Uncovering the reasons for the differ trends in the conversion of Cl-BQs and Br-BQs. • Formation and transformation mechanisms of HBQs were studied. • Chlorine conversion of HBQs reduced the toxicity of water samples. [ABSTRACT FROM AUTHOR]

The dual-chamber photoelectrocatalytic (PEC) system possess advantages in the degradation efficiency and processing cost of organic contaminants. In this study, TiO 2 nanotube arrays modified by rGO and g-C 3 N 4 (rGO/g-C 3 N 4 /TNAs) photoelectrodes were successfully prepared. The surface micromorphology, chemical structure, crystal structure, and basic element composition of rGO/g-C 3 N 4 /TNAs photoelectrodes were studied by SEM, FTIR, XRD, Raman, and XPS. UV–vis absorption, photoluminescence (PL) spectra, and photoelectrochemical (PECH) tests were used to explore the photoelectrochemical characteristics of rGO/g-C 3 N 4 /TNAs photoelectrodes. Under simulated sunlight illumination, the dual-chamber PEC system with external bias voltage was used to investigate the degradation of oxytetracycline (OTC) on rGO/g-C 3 N 4 /TNAs photoelectrodes. The results showed that rGO and g-C 3 N 4 were successfully loaded on TNAs, and the separation efficiency of electrons and holes at rGO/g-C 3 N 4 /TNAs photoelectrodes was improved. The light absorption range of rGO/g-C 3 N 4 /TNAs photoelectrodes extends to the visible light region and has better light absorption performance. Compared with the photocatalytic process, when 1.2 V bias voltage was applied, the degradation efficiency of OTC in anode and cathode chambers in PEC were increased by 3.28% and 44.01% within 60 min, respectively. In addition, the anode and cathode chambers have different degradation effects on OTC. Both the external bias voltage and initial pH have significant effects in cathode chamber, but have little effect in photoanode chamber. The fluorescence excitation-emission matrix spectra and liquid chromatography-tandem mass spectrometry showed that there were different intermediates in the degradation process of OTC. This study indicated that for the dual-chamber PEC system, rGO/g-C 3 N 4 /TNAs photoelectrodes exhibited excellent photocatalytic performance and have potential application prospects in water environmental remediation. [Display omitted] • The novel ternary rGO/g-C 3 N 4 /TNAs photoelectrodes were prepared. • The photoelectrodes showed superior photoelectrocatalytic activity. • Oxytetracycline can be efficiently degraded by rGO/g-C 3 N 4 /TNAs photoelectrodes. • Degradation of oxytetracycline was enhanced in the dual-chamber system. [ABSTRACT FROM AUTHOR]