This paper introduces a possible alternative model of gravity based on the theory of fractional-dimension spaces and its applications to Newtonian gravity. In particular, Gauss’s law for gravity as well as other fundamental classical laws are extended to a D-dimensional metric space, where D can be a non-integer dimension. We show a possible connection between this Newtonian Fractional-Dimension Gravity (NFDG) and Modified Newtonian Dynamics (MOND), a leading alternative gravity model which accounts for the observed properties of galaxies and other astrophysical (...) structures without requiring the dark matter hypothesis. The MOND acceleration constant $${a_{0}} \simeq 1.2 \times 10^{-10} \text {m}\, \text{s}^{-2}$$ can be related to a natural scale length $$l_{0}$$ in NFDG, i.e., $$a_{0} \approx GM/l_{0}^{2}$$, for astrophysical structures of mass M, and the deep-MOND regime is present in regions of space where the dimension is reduced to $$D \approx 2$$. For several fundamental spherically-symmetric structures, we compare MOND results, such as the empirical Radial Acceleration Relation (RAR), circular speed plots, and logarithmic plots of the observed radial acceleration $$g_{obs}$$ vs. the baryonic radial acceleration $$g_{bar}$$, with NFDG results. We show that our model is capable of reproducing these results using a variable local dimension $$D\left( w\right)$$, where $$w =r/l_{0}$$ is a dimensionless radial coordinate. At the moment, we are unable to derive explicitly this dimension function $$D\left( w\right)$$ from first principles, but it can be obtained empirically in each case from the general RAR. Additional work on the subject, including studies of axially-symmetric structures, detailed galactic rotation curves fitting, and a possible relativistic extension, will be needed to establish NFDG as a viable alternative model of gravity. (shrink)

This paper offers a comprehensive discussion on the concept of Africa and freedom, freedoms in indigenous Africa, literacy and freedom from external forces, freedom under colonial rule, the role of World War II, decolonization and the Independence Movement in Africa, independent African and new challenges for freedom and finally a way forward.

LANGUAGE NOTE | Document text in Chinese; abstract also in English. 本文回顧及討論2021年1月至2022年4月COVID-19疫情期間香港抗疫中曾在公共領域提出或引起關注的倫理問題。新型的傳染病是複雜和具有不確定的挑戰，COVID-19全球大流行引起的倫理問題有普世 的性質，但亦必須結合本地具體的情況討論。作者對其中的倫理焦點提出觀察分析，包括接種COVID-19疫苗的知情同意程序及其局限性，以及為精神上無行為能力的老年人接種疫苗決定的特殊挑戰。 This article reviews and discusses ethical issues that emerged in the public realm in the first two years of the COVID-19 pandemic in Hong Kong, between January 2021 and March 2022. Emerging infectious diseases are complex and bring about uncertain challenges. Although many of the ethical issues during the pandemic were universally experienced, it is important to understand them within the local contexts in which they arose. The paper (...) reports on observations related to some of these ethical issues, namely, the process of informed consent for COVID-19 vaccination and its limitations, and the challenge of arriving at vaccination decisions for mentally incapacitated elders. (shrink)