Global strong pathwise well-posedness established for stochastically forced 2D incompressible Navier-Stokes coupled to 1D damped Kirchhoff plate via velocity continuity and stress balance on fixed interface.
Tohoku Math
8 Pith papers cite this work. Polarity classification is still indexing.
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The authors define divisible weighted projective spaces, give sharp bounds for minimal-degree non-degenerate subvarieties therein, and develop a theory of weighted determinantal scrolls that achieve minimal degree while satisfying weighted N_p properties tied to regularity notions.
Classifies rational (quasi-)elliptic surfaces with global vector fields in char p ≠ 2, determining fibers, automorphism schemes, moduli, and Jacobian property except for p=3,5.
Determines the GL(n,R)-invariant and Isom-invariant statistical connections on the centered Gaussian model and describes the corresponding moduli spaces under two categorical equivalence relations.
Under a codimension assumption on the singular locus, isomorphism of the m-th differential sheaf implies isomorphisms for all lower i on complex hypersurfaces, with a positive characteristic analogue discussed.
Establishes geodesic connectedness from completeness for affine connections on statistical manifolds with divisible cubic forms, producing a Cartan-Hadamard theorem.
No complete non-orientable minimal surfaces of finite total curvature in R^3 with one end foliated by closed curvature lines exist.
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Stochastically forced Navier-Stokes equations interacting with an elastic structure
Global strong pathwise well-posedness established for stochastically forced 2D incompressible Navier-Stokes coupled to 1D damped Kirchhoff plate via velocity continuity and stress balance on fixed interface.
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Varieties of minimal degree in weighted projective space
The authors define divisible weighted projective spaces, give sharp bounds for minimal-degree non-degenerate subvarieties therein, and develop a theory of weighted determinantal scrolls that achieve minimal degree while satisfying weighted N_p properties tied to regularity notions.
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Rational (quasi-)elliptic surfaces with global vector fields in odd characteristic
Classifies rational (quasi-)elliptic surfaces with global vector fields in char p ≠ 2, determining fibers, automorphism schemes, moduli, and Jacobian property except for p=3,5.
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Invariant statistical connections on the multivariate centered Gaussian model and their moduli spaces
Determines the GL(n,R)-invariant and Isom-invariant statistical connections on the centered Gaussian model and describes the corresponding moduli spaces under two categorical equivalence relations.
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Higher singularities for hypersurfaces
Under a codimension assumption on the singular locus, isomorphism of the m-th differential sheaf implies isomorphisms for all lower i on complex hypersurfaces, with a positive characteristic analogue discussed.
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Geodesic Connectedness on Statistical Manifolds with Divisible Cubic Forms
Establishes geodesic connectedness from completeness for affine connections on statistical manifolds with divisible cubic forms, producing a Cartan-Hadamard theorem.
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Minimal surfaces with closed curvature lines
No complete non-orientable minimal surfaces of finite total curvature in R^3 with one end foliated by closed curvature lines exist.
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