Sharp upper bounds on the second largest eigenvalues of connected graphs

AbstractLet λ2 be the second largest eigenvalue of a graph. Powers (1988) [4] gave some upper bounds of λ2 for general graphs and bipartite graphs, respectively. Considering that these bounds are not always attainable for connected graphs, we present sharp upper bounds of λ2 for connected graphs and connected bipartite graphs in this paper. Moreover, the extremal graphs are completely characterized

Sustainable Approaches to Incorporate Plant-Based Biomaterials in Power Generation

Biomass-derived materials have traditionally been used to generate electrical energy through the combustion of their organic components. However, within the past few years, certain common biomass compounds, especially plant-based products such as cellulose and lignin, have drawn attention in the energy field due to their wide availability, low cost, and chemical versatility. In the case of cellulose, the combination of crystalline and amorphous domains, along with the high surface area and abundance of hydroxyl groups, has allowed for its application in multiple devices to harvest energy from the environment. However, to date, there are no reviews focusing on the different approaches that have been developed to implement these sustainable materials in the generation of renewable energies and the desirable material properties for these applications. This manuscript reviews alternative ways that have been developed to exploit biomass compounds in power generation, especially cellulose and lignin. Three different types of energy harvesting are discussed: mechanical, osmotic, and thermal energy. In the case of mechanical energy, the application of plant-derived materials in piezoelectric and triboelectric generators is described. In both cases, approaches where the biomass material has an active role in power generation instead of acting as a mechanical support are reported. For osmotic energy, the performance of inverse electrodialysis systems and the use of plant-derived materials, including the chemical modifications carried out to allow for their use for energy generation, was reviewed. Finally, for thermal energy generation, the reported work on biopolymer-based devices that work using thermoelectricity has been summarised. In each case, the latest advances in the field from the materials science perspective and the reported performance were described. Hybrid approaches involving the combination of biomass materials with other components have also been considered and compared with the performance obtained using biopolymers alone. Current limitations and opportunities are, finally, discussed to offer an overview of the current landscape and indicate future directions of the field

Effects of magnesium supplementation on improving hyperglycemia, hypercholesterolemia, and hypertension in type 2 diabetes: A pooled analysis of 24 randomized controlled trials

BackgroundPrevious studies have demonstrated that diabetes is often accompanied with lower magnesium status. However, practical details regarding the influences of magnesium intervention on hyperglycemia, hypercholesterolemia, and hypertension in type 2 diabetes (T2D) need to be further investigated.MethodsWeb of Science, ScienceDirect, and PubMed were searched for relevant literatures published through April 30, 2022, and high-quality data were pooled to evaluate the effects of magnesium supplementation on glycemic, circulating lipids, and blood pressure control in T2D, and to explore the associated practical details.ResultsPooled analyses of 24 randomized controlled trials with 1,325 T2D individuals revealed that subjects who received magnesium supplementation had statistically significant reductions in fasting plasma glucose, glycated hemoglobin, systolic blood pressure and diastolic blood pressure, with WMD values of –0.20 mM (95% CI: –0.30, –0.09), –0.22% (95% CI: –0.41, –0.03), –7.69 mmHg (95% CI: –11.71, –3.66) and –2.71 mmHg (95% CI: –4.02, –1.40), respectively. Detailed subgroup analyses demonstrated that health status of participants including age, body mass index, country, duration of disease, baseline magnesium level and baseline glycemic control condition as well as magnesium formulation, dosage and duration of intervention influenced the effects of magnesium addition. Dose-effect analysis showed that 279 mg/d for 116 d, 429 mg/d for 88 d and 300 mg/d for 120 d are the average optimal dosages and durations for improving glycemic, circulating lipids, and blood pressure controls, respectively.ConclusionOur findings provide clinically relevant information on the adjuvant therapy of magnesium for improving hyperglycemia, hypercholesterolemia, and hypertension in T2D

Environmental taxes and the effects of partial privatization on environmental R&D, environment and welfare

This paper considers environmental R&D (ER&D) of clean technology for reducing pollutant emissions in a polluting mixed duopoly and analyzes partial privatization’s impacts on ER&D, environment and welfare. In the situation that environmental taxes are exogenously given, it finds that the impacts of privatization policy on ER&D and environment critically depend on the level of environmental damage. However, regardless of the marginal damage, an appropriate partial-privatization policy can increase social welfare. In addition, it also considers an endogenously determined optimal environmental tax and shows that if the marginal damage is high, partial privatization’s impacts on ER&D, environment and social welfare may be not the same as the exogenous environmental tax situatio

Environmental R&D subsidy, spillovers and privatization in a mixed duopoly

The study considers an environmental R&D subsidy in a mixed duopoly with spillovers. Public and private firms compete in environmental R&D investments and the government sets the subsidy to environmental R&D. This study examines three cases: (a) the public firm cares for the environment and maximises the welfare; (b) it does not care for the environment and maximises the sum of consumer and producer surpluses net of subsidy; and (c) it is privatised and maximises its own profit. The main findings are as follows: 1) the optimal subsidies are positive in all three cases; 2) the optimal subsidy always increases with spillovers in case (a), but it may decrease with spillovers in cases (b) and (c); 3) the optimal subsidy is higher in case (a) than in case (b) if the seriousness of environmental damage generated by pollution is small, however the opposite case may be the case if it is large; 4) the use of subsidy results in higher total R&D and lower environmental damage in all three cases; 5) privatisation lowers optimal subsidy (or environmental damage) no matter whether the public firm cares for the environment or not; and 6) privatisation reduces welfare if the public firm cares for the environment, but may raise welfare if it does not care for the environment

Surface Modification of Hetero-phase Nanoparticles for Low-Cost Solution-Processable High-k Dielectric Polymer Nanocomposites

The surface modification of nanoparticles (NPs) is crucial for fabricating polymer nanocomposites (NCs) with high dielectric permittivity. Here, we systematically studied the effect of surface functionalization of TiO2 and BaTiO3 NPs to enhance the dielectric permittivity of polyvinylidene fluoride (PVDF) NCs by 23 and 74%, respectively, measured at a frequency of 1 kHz. To further increase the dielectric permittivity of PVDF/NPs-based NCs, we developed a new hetero-phase filler-based approach that is cost-effective and easy to implement. At a 1:3 mixing ratio of TiO2:BaTiO3 NPs, the dielectric constant of the ensuing NC is found to be 50.2, which is comparable with the functionalized BaTiO3-based NC. The highest dielectric constant value of 76.1 measured at 1 kHz was achieved using the (3-aminopropyl)triethoxysilane (APTES)-modified hetero-phase-based PVDF composite at a volume concentration of 5%. This work is an important step toward inexpensive and easy-to-process high-k nanocomposite dielectrics