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Let $\mathcal{L}$ be the set of all positive integers $n$ such that the denominator of $1+1/2+\cdots +1/n$ is less than the least common multiple of $1, 2, \dots , n$. In this paper, under a certain assumption on linear independence, we prove that the set $\mathcal{L}$ has the upper asymptotic density $1$. The assumption follows from Schanuel’s conjecture.

Rare earths are a kind of mineral resource with important strategic value, playing an irreplaceable key role in modern high-tech development and other fields. However, how to realize the efficient and green mining of rare earth resources has been a key issue that the rare earth industry has been trying to break through, because the rare earth mining process is prone to pollute ecological environments such as soil and water. Ion adsorption rare earth ore, mainly distributed in the south of China, is one of the rare earths, for which rare earth researchers have developed a new process leaching system with magnesium salt. In this study, the soil environmental problems as well as the microbial community structure underneath this new process heap-leaching demonstration site are evaluated. The results of the study showed that under the new process, there was a significant accumulation of sulfate content in the soil of the heap-leaching site and an imbalance in the soil calcium-magnesium ratio, which may disrupt the soil structure and reduce soil fertility. Meanwhile, the microbial community structure before and after the leaching site showed large differences at different points and depths, but didn't cause ecological risks. This study helps us to understand the environmental problems and impacts that may be caused by the new process of magnesium salt, and also helps to promote the application of the new process of magnesium salt leaching of ion adsorption rare earth ore, which lays the foundation for the exploitation of rare earth resources.

Lithium ion battery is the most widely used and reliable power source for electric vehicles. With the development of electric vehicles, the safety, energy density, life and reliability of lithium ion batteries have been continuously improved. However, in the field of vehicle power battery technology, battery monomers are combined in series and parallel to provide enough energy, but one of the major problems faced by group batteries is the consistency between battery monomers. Taking the capacity increment curve (IC curve) of lithium iron phosphate battery as the analysis tool, it is found that the characteristic peak of IC curve of different monomers in battery pack can reflect the relationship of monomer capacity. On this basis, the mathematical model is established, and the IC curve II peak characteristic point of a single cell are used as the reference to characterize the capacity of the single cell one by one. The results show that the method can be used in the normal charging process of the battery pack, and the capacity of the single cell in the battery pack can be characterized in real time during the whole life of the battery pack. It has certain research value for the ladder utilization and accurate management of battery pack.

The patient was a 56-year-old female. The whole body has brown patches for 16 years. Dermatological examination: brown patches were observed on the trunk and lower limbs, with scattered hypomigmentation patches and symmetrical distribution of skin lesions. Histopathology of the skin showed mild hyperkeratosis in the epidermis, focal liquefaction degeneration in the basal layer, masses of light red stained material in the dermal papilla, scattered or small patches of lymphocytes and tissue cell infiltration around capillaries in the superficial dermis, more pigmentophagocytes and positive methyl violet staining were observed. Diagnosis: cutaneous amyloidosis with abnormal pigmentation. The patient is still being followed up.

Explore the 3R design strategy of straw woven living products from the perspective of green design. By analyzing the characteristics of traditional straw weaving technology, based on the principles of reduction, reuse and recyclability of 3R design, the green design strategy of straw woven living products is put forward, and the product development and life cycle are divided into design stage, use stage and abandoned stage, and the ideas of reduction, reuse and recycling and the implementation strategies of each link are put forward. Traditional straw weaving technology conforms to the idea of green design. The introduction of the 3R design strategy not only opens up the development path for the contemporary inheritance of traditional straw weaving technology, but also provides ideas for the realization of the green design of modern living products. The integration of straw weaving technology and 3R design will have important practical significance for cultural heritage, product development, resource conservation and environmental protection.