In this note we deal with the problem of force/tracking control of constrained manipulators without velocity measurements interacting with an innnitely stii environment. We use a reduced order model for which the coordinates space is restricted to a subset where the constraints Jacobian is guaranteed to be non singular. In contrast to other similar approaches, we do not assume that the generali...

We give necessary and suucient conditions on the parameters s 1 ; s 2 such that the Jacobian determinant extends to a bounded operator from _ H s1 p1 _ H s2 p2 : : : _ H sm pm into Z 0. Here all spaces are deened on R n and 2 m n. In almost all cases the regularity of the Jacobian determinant is calculated exactly.

This paper generalizes for non-abelian theta functions a number of formulae valid for theta functions of Jacobian varieties. The addition formula, the relation with the Szëgo kernel and with the multicomponent KP hierarchy and the behavior under cyclic coverings are given.

We report experimental results indicating that defensive distillation successfully mitigates adversarial samples crafted using the fast gradient sign method [2], in addition to those crafted using the Jacobian-based iterative attack [5] on which the defense mechanism was originally evaluated.

This article presents a new method for classification of critical points. A vector field is usually classified using only a Jacobian matrix of the approximated vector field. This work shows how an approximation using a second order derivative can be used for more detailed classification. An algorithm for calculation of the curvature of main axes is also presented.

We provide the first explicit construction of genus 2 curves over finite fields whose Jacobians are ordinary, have large prime-order subgroups, and have small embedding degree. Our algorithm works for arbitrary embedding degrees k and prime subgroup orders r. The resulting abelian surfaces are defined over prime fields Fq with q ≈ r. We also provide an algorithm for constructing genus 2 curves ...

The object of this note is to answer this question in the affirmative when F(x) is of class C2. (It can be mentioned that, even if F(x) is analytic, there need not exist such a map R of class C1 with nonvanishing Jacobian; [2].) The mapping (1.3) to be obtained below maps solution paths of (1.1) into those of (1.4) preserving parametrizations. The first part of the paper concerns the linearizat...

The purpose of this note is to define a tri-moment map for certain manifolds with an Sp(1)-action. We show how this map can be used ro reduce such manifolds. The images of such maps for quaternionic flag manifolds, which are defined using the Dieudonné determinant, resemble the polytopes from the complex case.

We present a family of hyperelliptic curves whose Jacobians are suitable for cryptographic use, and whose parameters can be specified in a highly efficient way. This is done via complex multiplication and identity-based parameters. We also present some novel computational shortcuts for these families.

We prove that there are exactly 149 genus two curves C defined over Q such that there exists a nonconstant morphism π : X 1 (N) → C defined over Q and the jacobian of C is Q-isogenous to the abelian variety A f attached by Shimura to a newform f ∈ S 2 (Γ 1 (N)). We determine the corresponding newforms and present equations for all these curves.