New invariants extracted from the topology of complexifications of real algebraic sets classify algebraic vector bundles over sphere products and obstruct weak algebraic approximation, disproving Kucharz-Kurdyka conjecture.
On Homology of Real Algebraic Varieties
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Develops Hamilton-Jacobi theory for non-conservative classical field theories in the k-contact framework, with z-independent and z-dependent approaches, affine/quadratic Hamiltonian cases, and recovery of the k=1 contact theory.
A model-free diffusion test for discrete time series that uses the scaling of excursion counts with quadratic variation to classify signals as stochastic or deterministic.
Quantum channels built from sigma-complete ultrafilters map normal states to singular sigma-additive states on ell_2(kappa) precisely when kappa is Ulam measurable.
Partial advance on the conjecture that a quarter-plane walk's univariate generating function is D-finite precisely when its group is finite, by establishing non-D-finiteness for 21 infinite-group cases and stating a conjecture for 21 others.
Obtains limit formula for observable diameter with non-Euclidean screen and defines error versions for sequences with varying screens.
Gauge-fixed LQG quantization of spherically symmetric gravity plus scalar matter reproduces the Dirac quantization results for vacuum black holes throughout the outer region.
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Hamilton--Jacobi theory for non-conservative field theories in the $k$-contact framework
Develops Hamilton-Jacobi theory for non-conservative classical field theories in the k-contact framework, with z-independent and z-dependent approaches, affine/quadratic Hamiltonian cases, and recovery of the k=1 contact theory.