We consider the following problem in the theory of (virtual) species of structures: Given a polynomial species F such that its derivative dF equals 1, will its inverse w.r.t substitution F h?1i also be polynomial species? We shall see that this is in general not the case. From this result it follows that an analogue of the jacobian conjecture in the context of species does not hold.

This paper focuses on Clarke generalized Jacobian of the projection onto symmetric cones. First, we recall some basic concepts. Let ̥ : Ω ⊆ X → Y be a locally Lipschitz function on an open set Ω, where X and Y are two finite dimensional inner product spaces over the field R. Let ∇̥(x) denote the derivative of ̥ at x if ̥ is differentiable at x. The Clarke generalized Jacobian of ̥ at x is defined by...

In this paper we describe some recent developments concerning the Jacobian Conjecture(JC). First we describe Drużkowski’s result in [6] which asserts that it suffices to study the JC for Drużkowski mappings of the form x + (Ax)∗3 with A = 0. Then we describe the authors’ result of [2] which asserts that it suffices to study the JC for so-called gradient mappings i.e. mappings of the form x − ∇f...

In this article, we present a simple direct matrix method for analytically computing the Jacobian of nonlinear algebraic equations that arise from the discretization of nonlinear integrodifferential equations. This method is based on a formulation of the discretized equations in vector form using only matrix-vector products and component-wise operations. By applying simple matrixbased different...

ADIFOR is a source translator that, given a collection of Fortran subroutines for the computation of a \function," produces Fortran code for the computation of the derivatives of this function. More speciically, ADIFOR produces code to compute the matrix-matrix product JS, where J is the Jacobian of the \function" with respect to the user-deened independent variables, and S is the composition o...

Good robot performance often relies upon the selection of design parameters that lead to a well conditioned Jacobian or impedance " design " matrix. In this paper, a new design matrix normalization technique is presented to cope with the problem of non-homogeneous physical units. The technique pre and post-multiplies a design matrix by diagonal scaling matrices corresponding to the range of joi...

Manipulator kinetostatic performances are usually investigated considering only the geometrical structure of the robot, neglecting the effect of the drive system. In some circumstances this approach may leads to errors and mistakes. This may happen if the actuators are not identical to each other or when the employed transmission ratio are not identical and/or not constant. The paper introduces...

Issues of indefinite preconditioning of reduced Newton systems arising in optimization with interior point methods are addressed in this paper. Constraint preconditioners have shown much promise in this context. However, there are situations in which an unfavorable sparsity pattern of Jacobian matrix may adversely affect the preconditioner and make its inverse representation unacceptably dense ...

We first study some properties of images of commuting differential operators of polynomial algebras of order one with constant leading coefficients. We then propose what we call the image conjecture on these differential operators and show that the Jacobian conjecture [BCW], [E] (hence also the Dixmier conjecture [D]) and the vanishing conjecture [Z3] of differential operators with constant coe...

Using a model from a chromatographic separation process in chemical engineering, we demonstrate that large, sparse Jacobians of fairly complex structures can be computed accurately and efficiently by using automatic differentiation (AD) in combination with a four-step procedure involving matrix compression and de-compression. For the detection of sparsity pattern (step 1), we employ a new opera...