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An addendum and corrigendum to "Almost free splitters" (Colloq. Math. 81 (1999), 193-221)

Rüdiger Göbel, Saharon Shelah (2001)

Colloquium Mathematicae

Let R be a subring of the rational numbers ℚ. We recall from [3] that an R-module G is a splitter if E x t ¹ R ( G , G ) = 0 . In this note we correct the statement of Main Theorem 1.5 in [3] and discuss the existence of non-free splitters of cardinality ℵ₁ under the negation of the special continuum hypothesis CH.

An algebraic framework for linear identification

Michel Fliess, Hebertt Sira-Ramírez (2003)

ESAIM: Control, Optimisation and Calculus of Variations

A closed loop parametrical identification procedure for continuous-time constant linear systems is introduced. This approach which exhibits good robustness properties with respect to a large variety of additive perturbations is based on the following mathematical tools: (1) module theory; (2) differential algebra; (3) operational calculus. Several concrete case-studies with computer simulations demonstrate the efficiency of our on-line identification scheme.

An algebraic framework for linear identification

Michel Fliess, Hebertt Sira–Ramírez (2010)

ESAIM: Control, Optimisation and Calculus of Variations

A closed loop parametrical identification procedure for continuous-time constant linear systems is introduced. This approach which exhibits good robustness properties with respect to a large variety of additive perturbations is based on the following mathematical tools: (1) module theory; (2) differential algebra; (3) operational calculus. Several concrete case-studies with computer simulations demonstrate the efficiency of our on-line identification scheme.

Associated primes and primal decomposition of modules over commutative rings

Ahmad Khojali, Reza Naghipour (2009)

Colloquium Mathematicae

Let R be a commutative ring and let M be an R-module. The aim of this paper is to establish an efficient decomposition of a proper submodule N of M as an intersection of primal submodules. We prove the existence of a canonical primal decomposition, N = N ( ) , where the intersection is taken over the isolated components N ( ) of N that are primal submodules having distinct and incomparable adjoint prime ideals . Using this decomposition, we prove that for ∈ Supp(M/N), the submodule N is an intersection of -primal...

Bifurcations in symplectic space

G. Ishikawa, S. Janeczko (2008)

Banach Center Publications

In this paper we take new steps in the theory of symplectic and isotropic bifurcations, by solving the classification problem under a natural equivalence in several typical cases. Moreover we define the notion of coisotropic varieties and formulate also the coisotropic bifurcation problem. We consider several symplectic invariants of isotropic and coisotropic varieties, providing illustrative examples in the simplest non-trivial cases.

Biliaisons élémentaires en codimension 2

Mireille Martin-Deschamps (2006)

Annales de la faculté des sciences de Toulouse Mathématiques

Un théorème de Strano montre que si une courbe gauche localement Cohen-Macaulay n’est pas minimale dans sa classe de biliaison, elle admet une biliaison élémentaire strictement décroissante. R. Hartshorne a récemment donné une nouvelle preuve de ce résultat en le plaçant dans un contexte plus général. Dans cet article on apporte une précision, en utilisant les techniques introduites par Hartshorne : on montre que si un sous-schéma de codimension 2 localement Cohen-Macaulay de N n’est pas minimal...

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