Virtual University of Pakistan

A Topological Hydrodynamic Framework for High-Rank Elliptic Curves: Geometric Realization of the Birch and Swinnerton-Dyer Invariants up to Rank 5

We introduce a deterministic topological and fluid-mechanical correspondence for rational points on elliptic curves over Q, extending the framework systematically from Rank 1 through Rank 5. By establishing a Bohr-Sommerfeld-type circulation quantization condition (\Gamma_k = n_k...

Responsibility vs. sensationalism: A cross-cultural review of media coverage of sexual violence

In this study, the media coverage of various incidents of sexual violence across the various countries of the world has been analyzed, and to surface that whether the media is responsible, sensational or neutral in coverage of such events. Media Coverage of sexual violence is exa...

Assessing the drivers of green growth: an empirical investigation of green technological innovation, economic complexity, and investments in renewable energy in G20 countries

As the world grapples with the long-term consequences of the changing climate and dreadful ecological conditions, the G20 nations, as the largest and most influential economies, face a particularly daunting challenge: striking the optimal balance between environmental sustainabil...

Prioritizing sustainable practices for decarbonizing construction SMEs: an actionable roadmap for capability development in developing economies

Purpose As the construction sector strives to meet global climate targets, small and medium-sized enterprises (SMEs) in developing economies represent a critical yet often overlooked frontier for decarbonization. Despite their significant role, construction SMEs face barriers suc...