We study a class of smooth torus manifolds whose orbit space has the combinatorial structure of a simple polytope with holes. We construct moment angle manifolds for such polytopes with holes and use them to prove that the associated torus manifolds admit stable almost complex structure. We give a combinatorial formula for the Hirzebruch genus of these torus manifolds. We show that they have (invariant) almost complex structure if they admit positive omniorientation. We give examples of almost complex manifolds that do not admit a complex structure. When the dimension is four, we calculate the homology groups and describe a method for computing the cohomology ring.

The G5 geomagnetic storm of May 2024 provided a significant opportunity to investigate global ionospheric disturbances using vertical total electron content (VTEC) data derived from 422 GNSS-IGS stations and GIM. This study presents a comprehensive spatio-temporal analysis of VTEC modulation before, during, and after the storm, focusing on hemispheric asymmetries and longitudinal variations. The primary objective of this study is to analyze the spatial and temporal modulation of VTEC under extreme geomagnetic conditions, assess the hemispheric asymmetry and longitudinal disruptions, and evaluate the influence of geomagnetic indices on storm-time ionospheric variability. The indices examined reveal intense geomagnetic activity, with the dst index plunging to −412 nT, the Kp index reaching 9, and significant fluctuations in the auroral electrojet indices (AE, AL, AU), all indicative of severe space weather conditions. The results highlight storm-induced hemispheric asymmetries, with positive storm effects (VTEC enhancement) in the Northern Hemisphere and negative storm effects (VTEC depletion) in the Southern Hemisphere. These anomalies are primarily attributed to penetration electric fields, neutral wind effects, and composition changes in the ionosphere. The storm’s peak impact on DoY 132 exhibited maximum disturbances at ±90° and ±180° longitudes, emphasizing the role of geomagnetic forces in plasma redistribution. Longitudinal gradients were strongly amplified, disrupting the usual equatorial ionization anomaly structure. Post-storm recovery on DoY 136 demonstrated a gradual return to equilibrium, although lingering effects persisted at mid- and high latitudes. These findings are crucial for understanding space weather-induced ionospheric perturbations, directly impacting GNSS-based navigation, communication systems, and space weather forecasting.

A novel method is proposed to determine the magnetic moment of a magnet by studying its free-falling motion inside a non-ferromagnetic and conducting pipe. The dynamics of a neodymium magnet falling inside a pipe is tracked by using sound waves of a fixed frequency generated by one smartphone and detecting acoustic resonance in the pipe simultaneously by the other. This tracking technique leads to the measurement of the terminal velocity of the falling magnet, as the interaction between the magnet and the conducting pipe produces a force, similar to viscous drag, on the falling magnet. The result obtained is verified by studying torsional oscillations of the suspended magnet and conforms to the reported value in such a low-cost setup. The experiment is designed with concepts integrating the domains of general physics, electromagnetic induction, and acoustics.