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.

Forest ecological benefit compensation plays a promoting role in improving the enthusiasm of forest ecological builders and maintainers, maintaining the legitimate economic interests of forest owners, and coordinating the fairness between the “clear water and green mountains” protectors and the “gold and silver mountains” beneficiaries. Comprehensive combed the domestic forest ecological benefit compensation mechanism, including the compensation scope, compensation subject, compensation object, the research progress of compensation standard, summarized the forest ecosystem benefits measurement, including physical appraisal method, the value evaluation method, energy analysis method and the characteristics and application research progress of ecological model method. This paper discusses the research status and existing problems of the calculation basis of compensation standard, the origin, research emphasis and progress of forest ecological service payment abroad in recent years, and the mechanism of forest ecological service payment in many countries. Finally, some suggestions are put forward to improve the compensation mechanism of forest ecological benefits in China. On the one hand, it is necessary to broaden the source of funds through various ways of marketization and scientifically evaluate the forest ecological benefits. On the other hand, the compensation standard should be established scientifically and reasonably to achieve different compensation levels or compensation intervals.

The present article reports the applications of Caputo-Fabrizio time-fractional derivatives. This article generalizes the idea of unsteady MHD free convective flow in a Walters.-B fluid with heat and mass transfer study over an exponential isothermal vertical plate embedded in a porous medium. The governing equations are converted into dimensionless form and extended to fractional model. The generalized Walters-B fluid model has been solved analytically using the Laplace transform technique. From the general solutions we reduce limiting solutions when to the similar motion for Newtonian fluid. The corresponding expressions for and Nusselt and Sherwood numbers are also assessed. Numerical results for velocity, temperature and concentration are demonstrated graphically for various factors of interest and discussed. As a result, we have plotted the influence of fractional parameter on fluid flow and drawn comparison between fractional Walters’-B and fractional Newtonian fluid and found that fractional Newtonian fluid is faster than fractional Walters’-B fluids.

The Western capitalist system is an important part of the economy and society of the contemporary world, and it has played a huge role in the past few centuries. Nonetheless, with the continuous development of globalization, technological revolution and social change, the Western capitalist system is also facing a series of difficulties and new changes. This paper aims to explore the dilemma facing the Western capitalist system today, and to analyze and discuss the new changes.

This study was conducted to study the growth process of silkworm eggs in a silkworm research center under the condition of no electromagnetic radiation and strong electromagnetic radiation. In the course of the study, the silkworm seeds were randomly divided into two groups. All the mulberry leaves were used to observe and record the time of molting dormancy growth and the related physiological parameters were recorded and recorded. The effect of mobile phone radiation on the growth process of silkworm larvae was analyzed. Based on the experimental results, the microcosmic mechanism of the effects of mobile radiation on organisms and adolescents was analyzed and the preventive measures were put forward. First, for young people as much as possible to reduce the frequency of mobile phone use, thereby reducing the adverse effects of electromagnetic radiation on the growth and development of young people, to develop good habits. Second, the social and electromagnetic wave management departments attach importance to strengthen the rational use of electromagnetic waves.

This paper attempts to shed light on the current role of academia in the context of rural areas of low population density, which are regional interaction models. In this study, we follow a qualitative research methodology of a case study. We found that through the case study applied to a hotel unit, that the Academia can through its third mission, and in the context of regional triple helix dynamics (Academia-Business-government interaction), play an important role in terms of knowledge dissemination, wealth creation and employability. The limitations, which our study presents, are principally related to the measurement of the variables. Some of the characteristics of education should be studied more deeply. In the instance of a case study applied to the hospitality industry, it is important to take as limitations of the study to its direct application to any economic context. This study allowed however, contribute to the enrichment of literature through case studies presented in the hospitality industry.