Total torsion of 3D lines of curvature is an integer multiple of 2π.
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The appeal of metric evaluation of research impact has attracted considerable interest in recent times. Although the public at large and administrative bodies are much interested in the idea, scientists and other researchers are much more cautious, insisting that metrics are but an auxiliary instrument to the qualitati…
Roads are critically important infrastructure to societal and economic development, with huge investments made by governments every year. However, methods for monitoring those investments tend to be time-consuming, laborious, and expensive, placing them out of reach for many developing regions. In this work, we develop…
Let be an oriented 3-manifold. We investigate when one of the fibers or a combination of fiber components, , of a \emph{harmonic} map with Morse-type singularities delivers the Thurston norm of its homology class . In particular, for a map …
Deep learning excels in AI but struggles with causal physics.