Dipartimento di Matematica

3 weeks ago | 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.

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.

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.

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.

May 9, 2023 | link.springer.com | Dipartimento di Matematica

AbstractAfter revisiting the properties of generalized trigonometric functions, i.e., the trigonometric function linked to the planar (Fermat) curve \(x^p+y^p=1\), using the tool of Keplerian trigonometry, introduced in (Gambini et al.: Monatsh. Math. 195, 55–72, 2021), we present the extension to this class of functions of the Wallis product, discovering connections with the representations of ordinary trigonometric functions by means of infinite products.