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In the article, we establish some monotonicity and convexity (concavity) properties for certain combinations of polynomials and the Ramanujan R-function by use of the monotone form of L’Hôpital’s rule and present serval new asymptotically sharp bounds for the Ramanujan R-function that improve some previously known results.

High specific capacity and long cycle life are the key to high-performance lithium–sulfur (Li–S) batteries, but they are hard to achieve simultaneously due to the notorious polysulfide shuttle effect. Transition metal oxide nanocatalysts are expected to help address the above issue, but their low conductivity and cumbersome synthesis process limit their application. Here, we propose a defect engineering strategy to induce electron rearrangement by heteroatom doping. Boron-doped spinel-type oxide (B-ZnCo2O4‑x) is synthesized by a two-step hydrothermal method for separator modification. The boron-produced oxygen vacancy (OV) increases unsaturated sites by changing the electron cloud density, and therefore, the B-ZnCo2O4‑x nanocatalyst can reduce the reaction energy barrier and accelerate the nucleation and activation rate of Li2S. Meanwhile, the unique pore defects effectively increase the Li+ flux and ensure battery performance at a high rate and high sulfur loading. The battery equipped with a B-ZnCo2O4‑x-modified separator delivered an initial specific capacity of 1108 mAh g–1 at 0.2 C and a capacity retention rate of 80.4% at 0.5 C after 200 cycles. In particular, at a high sulfur loading of 10.0 mg cm–2, the battery yielded a first-cycle capacity of 1321.9 mAh g–1. This work demonstrates that boron-doping-enabled defect engineering is an effective strategy to improve the catalytic activity of transition metal oxides for application in Li–S batteries. [ABSTRACT FROM AUTHOR]

Shale oil yield, movability, and reservoir brittleness are three factors that must be focused on for shale oil exploration and development. The yield and composition of hydrocarbons and mineral composition have changed significantly during diagenesis, affecting the yield and movability of shale oil and the brittleness of the rock. In this study, the source rocks at different depths in the Dongying Sag were subjected to hydrous pyrolysis, and the yield and composition of pyrolyzed hydrocarbons and mineral composition were systematically analyzed. The brittleness index (BEI), weighted average specific surface area (SSAWA), and polarity index (PI) have been established to quantitatively characterize the brittleness and adsorption capacity of rock as well as the mobility of shale oil. The results suggest that diagenetic evolution controls rocks' brittleness and adsorption capacity by changing their mineral composition. In the low-temperature stage, the mineral transformation is not obvious, and the BEI and SSAWA fluctuate in a small range. In the high-temperature stage, the rapid smectite illitization leads to an increase in the brittleness and a decrease in the adsorption capacity. In addition, the nonpolar components such as saturates and aromatics in the pyrolyzed hydrocarbons gradually increased with the increasing temperature, enhancing the mobility of the shale oil. Based on the three evaluation indexes of BEI, PI, and SSAWA, and combined with the changes in hydrocarbon yields during hydrous pyrolysis, we comparatively analyzed the differences in the mobility and yields of original soluble organic matter as well as pyrolyzed hydrocarbons of the source rocks at different depths. Based on the above results, it can be concluded that the shale in the depth range of 3300–3795 m is a favorable area for shale oil exploration and development in the study area. This work suggests that predicting the sweet spot for shale oil exploration and development requires more attention to the impact of diagenetic evolution on the composition of minerals and hydrocarbons. [ABSTRACT FROM AUTHOR]