Morphismes de Sturm
نویسندگان
چکیده
منابع مشابه
Approximation De Artin Cylindrique Et Morphismes D’algèbres Analytiques
Nous désignerons toujours par k un corps, x = (x1, ..., xn) et y = (y1, ..., ym). Nous noterons k〈x〉, l’anneau des séries formelles algébriques sur k[x](x), c’est-à-dire l’hensélisé de k[x](x), k{x} l’anneau des séries convergentes à coefficients dans k (quand k est un corps valué), et k[[x]] l’anneau des séries formelles. Si A est un anneau local, on notera  son complété. Si φ : A −→ B est un...
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Regular and singular Sturm-Liouville problems (SLP) are studied including the continuous and differentiable dependence of eigenvalues on the problem. Also initial value problems (IVP) are considered for the SL equation and for general first order systems.
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We have formalized the Sturm-Tarski theorem (also referred as the Tarski theorem): ∑ x∈(a,b),P (x)=0 sign(Q(x)) = Var(SRemS(P, P ′Q; a, b)) where a < b are elements of R ∪ {−∞,∞} that are not roots of P , with P,Q ∈ R[x]. Note, the usual Sturm theorem is an instance of the Sturm-Tarski theorem with Q = 1. The proof is based on [1] and Cyril Cohen’s work in Coq [2]. With the Sturm-Tarki theorem,...
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We study the relationship between the eigenvalues of separated self-adjoint boundary conditions and coupled self-adjoint conditions. Given an arbitrary real coupled boundary condition determined by a coupling matrix K we construct a one parameter family of separated conditions and show that all the eigenvalues for K and −K are extrema of the eigencurves of this family. This characterization mak...
متن کاملThe Sturm-Tarski Theorem
We have formalised the Sturm-Tarski theorem (also referred as the Tarski theorem): Given polynomials p, q ∈ R[x], the Sturm-Tarski theorem computes the sum of the signs of q over the roots of p by calculating some remainder sequences. Note, the better-known Sturm theorem is an instance of the Sturm-Tarski theorem when q = 1. The proof follows the classic book by Basu et al. [1] and Cyril Cohen’...
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ژورنال
عنوان ژورنال: Bulletin of the Belgian Mathematical Society - Simon Stevin
سال: 1994
ISSN: 1370-1444
DOI: 10.36045/bbms/1103408546