A Generalized Version of Polynomial Convex Functions and Some Interesting Inequalities with Applications

In this article, we introduce a general class of convex functions and proved some of its basic properties. We establish Hermite-Hadamard type inequalities as well as fractional version of Hermite-Hadamard type inequalities by using Riemann-Liouville integral operator. At the end, some application to special means of real numbers are also given. It can be observed from the remarks given in this paper that several exiting results of ligature can be obtained immediacy from our results by taking suitable involved parameters

Microbial Communities Shaped by Treatment Processes in a Drinking Water Treatment Plant and Their Contribution and Threat to Drinking Water Safety

Bacteria play an important role in water purification in drinking water treatment systems. On one hand, bacteria present in the untreated water may help in its purification through biodegradation of the contaminants. On the other hand, some bacteria may be human pathogens and pose a threat to consumers. The present study investigated bacterial communities using Illumina MiSeq sequencing of 16S rRNA genes and their functions were predicted using PICRUSt in a treatment system, including the biofilms on sand filters and biological activated carbon (BAC) filters, in 4 months. In addition, quantitative analyses of specific bacterial populations were performed by real-time quantitative polymerase chain reaction (qPCR). The bacterial community composition of post-ozonation effluent, BAC effluent and disinfected water varied with sampling time. However, the bacterial community structures at other treatment steps were relatively stable, despite great variations of source water quality, resulting in stable treatment performance. Illumina MiSeq sequencing illustrated that Proteobacteria was dominant bacterial phylum. Chlorine disinfection significantly influenced the microbial community structure, while other treatment processes were synergetic. Bacterial communities in water and biofilms were distinct, and distinctions of bacterial communities also existed between different biofilms. By contrast, the functional composition of biofilms on different filters were similar. Some functional genes related to pollutant degradation were found widely distributed throughout the treatment processes. The distributions of Mycobacterium spp. and Legionella spp. in water and biofilms were revealed by real-time quantitative polymerase chain reaction (qPCR). Most bacteria, including potential pathogens, could be effectively removed by chlorine disinfection. However, some bacteria presented great resistance to chlorine. qPCRs showed that Mycobacterium spp. could not be effectively removed by chlorine. These resistant bacteria and, especially potential pathogens should receive more attention. Redundancy analysis (RDA) showed that turbidity, ammonia nitrogen and total organic carbon (TOC) exerted significant effects on community profiles. Overall, this study provides insight into variations of microbial communities in the treatment processes and aids the optimization of drinking water treatment plant design and operation for public health

Kinetics and Interfacial Thermodynamics of the pH-Related Sorption of Tetrabromobisphenol A onto Multiwalled Carbon Nanotubes

Surface functionalization of multiwalled carbon nanotubes (MWCNTs) was performed using mixed acid and ethylenediamine. The materials were characterized by electron microscope, X-ray diffraction, Raman spectra, Fourier transform infrared, N₂ adsorption–desorption, and X-ray photoelectron spectroscopy. The pH-dependent sorption of tetrabromobisphenol A (TBBPA) onto raw and functionalized MWCNTs was investigated. A decrease in TBBPA uptake was found to be dependent on the adsorptive p<i>K</i>_a in alkaline conditions. Two types of MWCNTs exhibited rapid binding kinetics for TBBPA sorption within 20 min. The kinetics of TBBPA sorption onto MWCNTs were analyzed using a pseudo-second-order model, an intraparticle diffusion model and Boyd model. The results showed that TBBPA sorption on MWCNTs and N-MWCNTs could be well described by the pseudo-second-order model, and the external diffusion (boundary layer diffusion) was the rate-limiting step. The extended Derjaguin–Landau–Verwey–Overbeek (XDLVO) theory was applied to calculate interfacial free energies and to explain the sorption characteristics between the sorbent and solute. This analysis revealed that hydrophobic attractive interactions (i.e., interfacial AB interactions) were dominant in TBBPA sorption onto MWCNTs