Usually in the study of limit problems, will encounter more complex problems, in this paper, we discuss how to use the concept of equivalent infinitesimal better limit operation. At the same time, in the process of research, we re-explore the proof of Taylor's formula, and find that some functions have a similar expansion form to Taylor's formula, that is, 'fractional expansion'. It is also found that after the linear combination of Taylor expansion and fractional expansion, the obtained expansion is more accurate, which helps us to have a better understanding of the approximation of function expansion.

Plastic products are items that we use every day around us, and their replacement speed are very fast, so that to recycle waste plastic has become the focus of environmental problems. This study has proposed an optimized circular design for the recycle plant of waste plastic, therefore, and our proposed strategy is to build a new tertiary recycling plant to reduce the total generation amount of the derived solid plastic waste from ordinary and secondary recycling plants and the semi-finished products from secondary recycling plant. Results obtained from a real recycle plant has showed that to recycle the tertiary waste plastic in a tertiary recycling plant, the finished products produced from a secondary recycling plant accounts about 27% of ordinary waste plastic, and the semi-finished products that mainly is scrap hardware accounts about 1% of ordinary waste plastic. Other derived solid plastic waste accounts for 6% of ordinary plastic waste. Therefore, if the ordinary, secondary and tertiary recycle plant can be set all-in-one, it can reduce the total generation amount of derived solid plastic waste from 34% to 6%, without and with a tertiary recycling plant, respectively. It can also increase the operating income of the secondary recycle plant and the investment willingness of the new tertiary recycle plant.

Facing the digital economy era, considerable attention is paid to the importance of understanding the fundamental impact on the information and development of blended teaching methods regarding the higher education. For this reason, the purpose of this study is to answer the challenges brought by the digital economy era, identify the effective teaching methods which would be used in English Correspondence course in the era of digital economy, aiming to form the patterns of learning, provide high motivation, strength and knowledge, and most importantly contribute to the complex competences of future working. For further research, it is expected to be able to prove that using the blended teaching methods will effectively improve students’ communication skills and learning efficiency, enhance students’ learning experience and critical thinking skills.

Lithospermum extract from Lithospermum is a kind of naphthoquinone, which has good anti-ultraviolet and anti-bacterial function. In this paper, the effects of different treatment temperature, time and ratio of liquid to liquid on the UV resistance of Lithospermum erythrorhizon extract were studied. The optimum extraction conditions were as follows: extraction temperature 60 ℃, extraction time 2 h, ratio of liquid to liquid of Lithospermum and ethanol 1:11. In this paper, the anti-UV finishing of cotton fabric was carried out, and the anti-ultraviolet and whiteness of the fabric were taken as the main indexes. The optimum process of the anti-UV finishing was as follows: the impregnation temperature was 70 ℃, the immersion time was 2h, 1:40. Compared with the uncoated cotton fabric, the fabric UPF value of the fabric was improved from 12.31 to 83.25, and the anti-ultraviolet performance was excellent, and it had certain bacteriostatic effect on Bacillus subtilis and Escherichia coli.

Nanotransformations of a blanket at the fair dimensional combined processing with imposing of electric field the tool in the form of untied metal granules are considered. An object of researches are the figurine details applied in aviation, the missile and space equipment and in the oil and gas industry: driving wheels and a flowing part of cases of turbo-pump units, screws, krylchatka where there are sites of variable curvature with limited access of the tool in a processing zone.It is shown that the combination in the combined process of two-component technological environments of current carrying granules and the electroconductive liquid environment given with a high speed to a processing zone allows to receive the required quality of a blanket; action of electric field from a source with the increased tension allows to create at fair dimensional processingthe required peening from blows of firm granules. It gives the chance to raise a resource and durability of responsible knots of the aerospace equipment and oil and gas equipment, to expand the field of use of the combined processing with untied granules on a detailwith the sitesnot available to processing by a profile electrode.