J ‘ edrzejewicz showed that a polynomial map over a field of characteristic zero is invertible, if and only if the corresponding endomorphism maps irreducible polynomials to irreducible polynomials. Furthermore, he showed that a polynomial map over a field of characteristic zero is a Keller map, if and only if the corresponding endomorphism maps irreducible polynomials to square-free polynomial...

Abstract: This paper presents a performance metric for the manipulability of constrained serial manipulators. The manipulability measure and manipulability ellipsoid are found from the manipulability Jacobian, which is easily found for serial manipulators as the standard Jacobian matrix, or for parallel manipulators as the Jacobian that gives the mapping from the active joint velocities to the ...

Many scientific applications benefit from the accurate and efficient computation of derivatives. Automatically generating these derivative computations from an applications source code offers a competitive alternative to other approaches, such as less accurate numerical approximations or labor-intensive analytical implementations. ADIC2 is a source transformation tool for generating code for co...

We present a newly developed Fluid-Structure Interaction coupling algorithm to simulate Bileaflet Mechanical Heart Valves dynamics in a partitioned way. The coupling iterations between the flow solver and the leaflet motion solver are accelerated by using the Jacobian with the derivatives of the pressure and viscous moments acting on the leaflets with respect to the leaflet acceleration. This J...

We explicitly construct the algebraic model of affine Jacobian of a generic algebraic curve of high genus and use it to compute the Euler characteristic of the Jacobian and investigate its structure.

relative to a hereditary torsion theory $tau$ we introduce a dimension for a module $m$, called {em $tau$-rank of} $m$, which coincides with the reduced rank of $m$ whenever $tau$ is the goldie torsion theory. it is shown that the $tau$-rank of $m$ is measured by the length of certain decompositions of the $tau$-injective hull of $m$. moreover, some relations between the $tau$-rank of $m$ and c...