
Dipartimento di Matematica
Articles
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Mar 30, 2025 |
link.springer.com | Anna Maria |Dipartimento di Matematica |Northern Arizona
AbstractA comprehensive Gröbner system for a parametric ideal I in K(A)[X] represents the collection of all Gröbner bases of the ideals I′ in K[X] obtained as the values of the parameters A vary in K. The recent algorithms for computing them consider the corresponding ideal J in K[A, X], and are based on stability of Gröbner bases of ideals under specializations of the parameters A.
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Jan 23, 2025 |
link.springer.com | Dipartimento di Matematica
AbstractGiven an open bounded subset Ω of ℝn we consider the eigenvalue problem$$\left\{{\matrix{{\Delta u - \left\langle {\nabla u,\nabla V} \right\rangle = - {\lambda _V}u,} & {u > 0\,{\text{in}}\,\Omega,} \cr {u = 0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,} & {\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{on}}\,\partial \Omega,\,\,} \cr}} \right.$$where V is a given function defined in Ω and λV is the relevant eigenvalue.
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Apr 28, 2024 |
academic.oup.com | Dipartimento di Matematica |Politecnico di Milano
We investigate existence and qualitative properties of globally defined and positive radial solutions of the Lane-Emden system, posed on a Cartan-Hadamard model manifold . We prove that, for critical or supercritical exponents, there exists at least a one-parameter family of such solutions. Depending on the stochastic completeness or incompleteness of , we show that the existence region stays one dimensional in the former case, whereas it becomes two dimensional in the latter.
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Aug 26, 2023 |
academic.oup.com | Claverton Down |Dipartimento di Matematica
This work proposes a nonlinear finite element method whose nodal values preserve bounds known for the exact solution. The discrete problem involves a nonlinear projection operator mapping arbitrary nodal values into bound-preserving ones and seeks the numerical solution in the range of this projection. As the projection is not injective, a stabilisation based upon the complementary projection is added in order to restore well-posedness.
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