This article investigates the income and expenditure patterns of individuals, with a specific focus on investments in luxury items, real estate, and expensive modes of transportation. Using global databases such as “Luxury Goods—Worldwide/Statista Market Forecast” and “Data—WID—World Inequality Database”, the authors explore the correlation between high demand for luxury items and economic inequality. The study emphasizes the role of luxury tax as essential for implementing a progressive personal income tax system in Russia. By examining country-specific factors, particularly in China and Russia, and conducting a comparative analysis of progressive tax systems globally, the research highlights the potential of luxury tax to enhance the efficacy of income tax in reducing inequality.

As China’s urbanization process accelerates, it has become common for rural men to go out to work and women to stay at home. The implementation of China’s rural revitalization strategy is in dire need of a large amount of high-quality human capital, and education and training are an important way to improve human capital and empower left-behind women. Starting from the background of China’s rural revitalization, this study focuses on the education and training of rural left-behind women, a topic that has received less attention. Through in-depth interviews and participatory observation, we analyzed the factors affecting rural left-behind women’s participation in education and training, as well as the problems that exist in China’s rural education and training process, and proposed strategies to solve them. The study found that education level, traditional attitudes, economic income, knowledge of education and training, and mental health are important factors affecting the participation of left-behind women in education and training in rural China. At the same time, there are some problems in the process of education and training, such as a single main body of supply and training methods, a lack of teachers, and a lack of management, etc., which affect the development of education and training, and thus also the promotion of rural revitalization.

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.

A theory of many-body wave scattering is developed under the assumption a << d << λ, where a is the characteristic size of the small body, d is the distance between neighboring bodies and λ is the wave-length in the medium in which the bodies are embedded. The multiple scattering is essential under these assumptions. The author’s theory is used for creating materials with a desired refraction coefficient. This theory can be used in practice. A recipe for creating materials with a desired refraction coefficient is formulated. Materials with a desired radiation pattern, for example, wave-focusing materials, can be created.