Distribution theory and fundamental solutions of differential operators

The objective of this dissertation is to study the theory of distributions and some of its applications. Certain concepts which we would include in the theory of distributions nowadays have been widely used in several fields of mathematics and physics. It was Dirac who first introduced the delta function as we know it, in an attempt to keep a convenient notation in his works in quantum mechanics. Their work contributed to open a new path in mathematics, as new objects, similar to functions but not of their same nature, were being used systematically. Distributions are believed to have been first formally introduced by the Soviet mathematician Sergei Sobolev and by Laurent Schwartz. The aim of this project is to show how distribution theory can be used to obtain what we call fundamental solutions of partial differential equations.

The Environmental, Social, Governance, and Financial Performance Effects on Companies that Adopt the United Nations Global Compact

This paper aims to investigate companies' environmental, social, governance (ESG), and financial implications of their commitment to the United Nations Global Compact (UNGC). The focus is placed on companies operating in the three countries with the highest number of UNGC participants: Spain, France, and Japan. The results clearly reveal that adoption of the UNGC often requires an organizational change that fosters stakeholder engagement, ultimately resulting in improvements in companies' ESG performance. Additionally, the results reveal that ESG performance has a significant impact on financial performance for companies that adopted the principles of the UNGC. These findings provide both non-financial and financial incentives to companies to commit to this voluntary corporate social responsibility (CSR) initiative, which will have important implications on companies' strategic management policies that aim to foster sustainable businesses and community development. Finally, the linkages between the UNGC-committed companies' ESG and financial performance may be influenced by geographical spread, mainly due to the appearance of differences in the institutional, societal, and cultural settings.