Function spaces for decoupling
Journal of the London Mathematical Society, Volume 113, Issue 4, April 2026.Abstract We introduce new function spaces LW,sq,p(Rn)$\mathcal {L}_{W,s}^{q,p}(\mathbb {R}^{n})$ that yield a natural reformulation of the ℓqLp$\ell ^{q}L^{p}$ decoupling inequalities for the sphere and the light cone. These spaces are invariant under the Euclidean half‐wave propagators, but not under all Fourier integral operators unless p=q$p=q$, in ...
Andrew Hassell +3 more
wiley +1 more source
A Miyaoka–Yau inequality for hyperplane arrangements in CPn$\mathbb {CP}^n$
Journal of the London Mathematical Society, Volume 113, Issue 4, April 2026.Abstract Let H$\mathcal {H}$ be a hyperplane arrangement in CPn$\mathbb {CP}^n$. We define a quadratic form Q$Q$ on RH$\mathbb {R}^{\mathcal {H}}$ that is entirely determined by the intersection poset of H$\mathcal {H}$. Using the Bogomolov–Gieseker inequality for parabolic bundles, we show that if a∈RH$\mathbf {a}\in \mathbb {R}^{\mathcal {H}}$ is ...
Martin de Borbon, Dmitri Panov
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Unitarily invariant valuations on convex functions
Journal of the London Mathematical Society, Volume 113, Issue 4, April 2026.Abstract Continuous, dually epi‐translation invariant valuations on the space of finite‐valued convex functions on Cn$\mathbb {C}^n$ that are invariant under the unitary group are investigated. It is shown that elements belonging to the dense subspace of smooth valuations admit a unique integral representation in terms of two families of Monge–Ampère ...
Jonas Knoerr
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Stable Symplectic Integrators for Power Systems [PDF]
, 2002 The paper illustrates the application of symplectic integrators obtained by composition for solving power system consisting of several machines. The multi-machine angular swings during and following fault conditions and clearing are investigated. Numerical results obtained using symplectic integrators were found to be comparable to those obtained using
Daniel Okunbor, Emmanuel Akinjide
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Symplectic integrators revisited
Brazilian Journal of Physics, 2002 This paper is a survey on Symplectic Integrator Algorithms (SIA): numerical integrators designed for Hamiltonian systems. As it is well known, n degrees of freedom Hamiltonian systems have an important property: their ows preserve not only the total volume of the phase space, which is only one of the Poincare invariants, but also the volume of sub ...
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Molecular Dynamics of Artificially Pair-Decoupled Systems: An Accurate Tool for Investigating the Importance of Intramolecular Couplings. [PDF]
J Chem Theory Comput, 2023 Gandolfi M, Ceotto M.
europepmc +1 more source
Nearly Periodic Maps and Geometric Integration of Noncanonical Hamiltonian Systems. [PDF]
J Nonlinear Sci, 2023 Burby JW, Hirvijoki E, Leok M.
europepmc +1 more source
A minimal-variable symplectic integrator on spheres
Mathematics of Computation, 2016 We construct a symplectic, globally defined, minimal-variable, equivariant integrator on products of 2-spheres. Examples of corresponding Hamiltonian systems, called spin systems, include the reduced free rigid body, the motion of point vortices on a sphere, and the classical Heisenberg spin chain, a spatial discretisation of the ...
Robert I. McLachlan +2 more
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Lie Group Cohomology and (Multi)Symplectic Integrators: New Geometric Tools for Lie Group Machine Learning Based on Souriau Geometric Statistical Mechanics. [PDF]
Entropy (Basel), 2020 Barbaresco F, Gay-Balmaz F.
europepmc +1 more source
Which Algorithm Best Propagates the Meyer-Miller-Stock-Thoss Mapping Hamiltonian for Non-Adiabatic Dynamics? [PDF]
J Chem Theory Comput, 2023 Cook LE +3 more
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