Category: Mathematics
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Analytic equivalence relations arise from loop homotopy in Polish spaces
This research indicates that studying loops in a fixed path-connected Polish space from a descriptive set-theoretic viewpoint yields many analytic equivalence relations, while many others do not arise this way.
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Global regularity and blow-up criteria established for a non-local equation
This research indicates that a non-local integrable evolution equation has global higher-order Sobolev solutions under a natural assumption on the initial momentum, and it also identifies a criterion for blow-up solutions.
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Spatially heterogeneous exposure-lag-response patterns need cluster-aware modeling
This research indicates that accounting for spatially heterogeneous exposure-lag-response associations can improve risk estimation in environmental epidemiology.
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Arithmetic manifolds guide questions on systole and kissing number
This research indicates that arithmetic manifolds are used as a guide to answer two geometric questions about systole and kissing number in hyperbolic manifolds, with detailed answers for dimension 2 and a survey of what is known in higher dimensions and other locally symmetric spaces.
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Subnormalisers of semisimple elements in finite groups are determined
This research indicates that the subnormalisers of semisimple elements of prime power order in finite quasi-simple groups of Lie type are determined, along with the maximal overgroups of normalisers of Sylow tori.
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Moving-potential Klein–Gordon equations satisfy decay and Strichartz estimates
This research indicates that linear Klein–Gordon equations with multiple moving potentials can satisfy local energy decay and Strichartz estimates when the solution is orthogonal to discrete spectral modes.
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Low-precision LP solutions supported fix-and-propagate heuristics
This research indicates that low-accuracy linear programming solutions can still support fix-and-propagate heuristics without reducing solution quality, and can help produce strong solutions for very large mixed-integer problems.
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Synthetic Lorentzian Cartan-Hadamard theorem established
This research indicates that a synthetic Lorentzian Cartan-Hadamard theorem can be proved in the setting of synthetic Lorentzian geometry, with timelike geodesic existence and uniqueness under additional assumptions.
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Uniqueness proven for inverse random source recovery in stochastic equations
This research indicates that the strength of the time-dependent source component can be uniquely recovered from boundary flux in stochastic heat and wave equations.
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Exact residual finiteness growth for some two-step nilpotent groups
This research indicates that the residual finiteness growth of two-step nilpotent groups can be improved, depends only on the complex Mal’cev completion, and is exact when the commutator subgroup is one- or two-dimensional.
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