A theoretical investigation of the effect of an inverse parabolic potential on third harmonic generation in cylindrical quantum wires is presented. The wave functions are obtained as solutions to Schrödinger equation solved within the effective mass approximation. It turns out that peaks of the third harmonic generation susceptibility (THGS) associated with nanowires of small radii occur at larger photon energies as compared to those associated with quantum wires of larger radii. The inverse parabolic potential red-shifts peaks of the THGS, and suppresses the amplitude of the THGS. THGS associated with higher radial quantum numbers is diminished in magnitude and blue-shifted, as a function of the photon energy. As a function of the inverse parabolic potential, the THGS still characterized by peaks, and the peaks shift to lower values of the potential as the photon energy increases.

The Lancaster mutual teaching model originated in late 18th century England and quickly spread to the American colonies after receiving positive responses in Europe. In the 1820s, renowned Spanish physician, educator, and publisher Manuel Codorniú Ferreras brought it to Mexico, making outstanding contributions to the newly independent nation in educational philosophy, system, and methods. In the mid-19th century, with the absence of a centralized institution for public education in Mexico, the Lancaster Company took on the significant responsibility of guiding the direction of national public education development. Although this function did not persist for too long due to political changes in Mexico, the educational system continued to play an important role in the Mexican education sector. The Lancaster Company and its teaching system exerted a positive and profound influence on the democratization and secularization of education in Mexico, laying important foundations for the modernization and reform of Mexican education.

Nowadays, finding a suitable solution to the problem of generational change in case of small and medium-size enterprises (SMEs) is becoming increasingly challenging. The aim of this research to investigate whether entering into the stock exchange could be a realistic alternative for Hungarian companies to eliminate this issue. This study reviews the process of Initial Public Offering (IPO) and summarises the advantages and the difficulties of going public. The paper focuses on the opportunities for value creation and saving offered to SMEs by listing on the stock exchange. As primary research on practical experiences, semi-structured in-depth interviews were conducted with the managers of 10 involved companies, and some financial indicators were examined. The research does not cover all relevant companies; however, it is still suitable for drawing a conclusion. The presence on the stock market proved to be useful for the companies and played a significant role in the preservation of the company’s value as well as in financing opportunities. The path demonstrated in this article is suitable for other businesses to follow the pioneers.

The Human Development Index, which accounts for both net foreign income and the total value of goods and services generated domestically, illustrates how income becomes less significant as Gross National Income (GNI) rises by using the logarithm of income. South Africa ranks 109th out of 189 countries in the Human Development Index (HDI) within the Brazil, Russia, India, China and South Africa (BRICS) economic bloc, raising long-term sustainability concerns. The study explores the relationship between economic, demography, policy indicators and human development in South Africa. South Africa’s unique status as a developing country within the BRICS economic group, alongside its lengthy history of racial discrimination, calls for a sophisticated approach to understanding Human Development. Existing research considered economic, demography, policy indicators independently; the gap of understanding their interconnection and long-term effects in the South African contexts exists. The study addresses the gap by using Autoregressive-Distributed Lag (ARDL) approach to investigate the short-term and the long-term relationship between economic, demography, policy indicators and human development in South Africa. By discovering these links, the study hopes to provide useful insights for policymakers seeking to promote sustainable human development in South Africa. The findings indicate that growth in GDP is a key factor in the HDI since it shows that there are more financial resources available for human development. By discovering these links, the study hopes to provide useful insights for policymakers seeking to promote sustainable human development in South Africa.