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Sub-Pfaffian sets and a generalization of Wilkie's theorem

100%

Hajto Z.

2001

tom Vol. 49, no 2

181-189

We prove an analytic generalization of A. Wilkie's well-known theorem on the model completeness of the theory of the real field with exponentiation.

Lemmass A and B for sub-Pfaffian sets

100%

Hajto Z.

1999

tom Vol. 47, no 4

325--336

In this paper we prove two fundamental lemmas of sub-Pfaffian geometry which are counterparts of Lemmas A and B for subanalytic sets [4]. We use a generalized version of the Tangent Mapping Theorem [2], following our program announced in [11].

Finite linear groups as differential Galois groups

63%

Crespo T. , Hajto Z.

2001

tom Vol. 49, no 4

361--373

An effective construction of linear differential equations with Galois group a given finite group is presented.

An effective approach to Picard-Vessiot theory and the Jacobian Conjecture

51%

Bogdan P. , Hajto Z. , Adamus E.

tom Vol. 26

49--59

In this paper we present a theorem concerning an equivalent statement of the Jacobian Conjecture in terms of Picard-Vessiot extensions. Our theorem completes the earlier work of T. Crespo and Z. Hajto which suggested an effective criterion for detecting polynomial automorphisms of affine spaces. We show a simplified criterion and give a bound on the number of wronskians determinants which we need to consider in order to check if a given polynomial mapping with non-zero constant Jacobian determinant is a polynomial automorphism. Our method is specially efficient with cubic homogeneous mappings introduced and studied in fundamental papers by H. Bass, E. Connell, D.Wright and L. Drużkowski.