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.
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On Homology of Real Algebraic Varieties
13 Pith papers cite this work. Polarity classification is still indexing.
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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.
Derives three closed-form basis sets using a single Jacobi polynomial in prolate spheroidal and cylindrical coordinates and shows transformations between spherical, prolate spheroidal, bispherical, and toroidal systems.
Authors derive combinatorial descriptions for the number of inequivalent irreducible rational representations of GL_2(q) by degree and an explicit q-dependent formula for the Wedderburn decomposition of its rational group algebra.
Proves sup pd(Flat_R) = sup Gpd(GFlat_R) for arbitrary rings, giving Gorenstein-based characterizations of n-perfect and weakly n-Σ-cotorsion rings.
The paper gives a sufficient condition, relying on Ulam measurable cardinals, for the existence of quantum channels that turn normal states into singular yet strictly σ-additive states via Yosida-Hewitt decomposition.
Derives a second-order sum rule for eigenvalues of abstract Hamiltonian families and applies it to Lieb-Thirring bounds, Bessel zeros, and trace inequalities.
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.
Establishes boundedness of singular integral operators and commutators in Orlicz spaces L^Φ under Δ2 and ∇2 conditions on the Young function, providing foundation for interior regularity of higher-order elliptic operators.
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