Generalized Wasserstein barycenters on Riemannian manifolds are absolutely continuous when all input measures are absolutely continuous, for strictly convex cost profiles h with singularity at zero, via a geometric approximation approach.
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The rational characteristic class ring for oriented S^n x S^n-fibrations injects into smooth bundle cohomology, producing non-trivial classes in all degrees detected by bundles from cyclic subgroups of a finite-index subgroup of SL_2(Z).
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A generalized zeroth-order method samples random directions on the sphere to optimize quotients of quadratics, estimates Riemannian derivatives with surrogates, and yields an accelerated algorithm outperforming prior work.
Blend-to-zero operators are formalized for smooth transitions, with polynomial interpolants represented via the regularized incomplete Beta function and explicit trigonometric smooth step functions linked to higher-order boundary value problems.
Necessary and sufficient conditions for controllability of generic reconfigurable EM devices are derived as a function of geometry and mutual coupling between elements.
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