This paper foresees a critical analysis and development of a legislative proposal for the effective implementation of blockchain technology in Civil Mediation in conflicts in condominiums. This paper provides a legal analysis of personal, property rights and condominium disputes, applying blockchain technology for the purpose of self-executing civil mediation. This paper provides several solutions for conflicts in condominiums: Condominium Statute in blockchain, telematic attendance and voting systems, the self-execution of civil mediation agreements in conflicts in condominiums and Tokenization and IoT for property remote control in condominiums. The novelty of this research lies in the fact that, based on the experience of civil mediation in conflicts in condominiums, foreseen in US States and in other States such as Canada, Spain, the regulation is adapted for the correct application of blockchain technology for mediation in conflicts in condominiums.

The relationship between new-quality productivity and educational equity is characterized by close mutual influence and co-evolution. Driven by technological innovation, new-quality productivity is profoundly transforming the economic and social landscape. Educational equity, a crucial component of social justice, is vital for ensuring equal development opportunities for all individuals. The robust growth of new-quality productivity not only optimizes the distribution of educational resources and enhances educational quality but also poses new challenges and demands for equity in education. In turn, the continuous advancement of educational equity provides a solid talent foundation and a conducive environment for innovation to new-quality productivity. These two aspects intertwine and progress together in various domains, including policy systems, cultural values, and educational practices. This interplay highlights the central role of new-quality productivity and educational equity in societal development, while also demonstrating their dynamic and complementary relationship.

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.

In this study, we define the unrestricted Pell and Pell-Lucas quaternions. We give generating functions, Binet formulas and some generalizations of well-known identities such as Vajda’s, Catalan’s, Cassini’s d’Ocagne’s identities.