The articulated arm coordinate measuring machine (AACMM) is a kind of new coordinate measuring device based on non-Cartesian system. The measuring accuracy of the AACMM can be effectively improved by parameter identification. However, some of the structural parameters are coupling (linearly related), so the structural parameters usually cannot be identified correctly. The Jacobian matrix was ob...

We apply concepts of covariant and contravariant vector space in differential geometry and general relativity to derive new, general, exact relations between potential of mean force and free-energy profile. These relations are immensely practical in free-energy simulations because a full Jacobian transformation (which is usually unknown) is not required; rather, only knowledge of the (constrain...

1 Ergodic theory References for this section: CFS]. 1. The basic setting of ergodic theory: a measure-preserving transformation T of a probability space (X; B; m). Usually we assume T is invertible. (More generally, measure-preserving means R f T = R f; equivalently, m(T ?1 (A)) = mA.) How many measure spaces are there? Standard Borel spaces: any Borel subset of a complete, separable metric spa...

The mapping between the Cartesian space and joint space of robot manipulators has long been a difficult task for redundant robots. Two main methods are used in the classical approach. One is by using direct kinematic inversion in the position regime; the other is to use Jacobian Transformation in the velocity regime. However, for a redundant robot, a non-squared Jacobian matrix is resulted when...

The mapping between the Cartesian space and joint space of robot manipulators has long been a difficult task for redundant robots. Two main methods are used in the classical approach. One is by using direct kinematic inversion in the position regime; the other is to use Jacobian Transformation in the velocity regime. However, for a redundant robot, a non-squared Jacobian matrix is resulted when...

In this work are studied the Jacobians of certain singular transformations and the corresponding measures which support the jacobian computations.

Adaptive grid generation is an active research topic for numerical solution of differential equations. In this paper, we propose a variational method which generates transformations with prescribed Jacobian determinant and curl. Then we use this transformation to achieve adaptive grid generation task.

This paper shows graph similarities between Brusselator and Oregonator reaction mechanisms, using the jacobian matrix in convex coordinates as an adjacency matrix which defines a weighted directed pseudograph. A linear transformation is defined for the task of mapping the weights of the three dimensional system onto a two dimensional one where the Oregonator’s pseudograph is isomorphic to Bruss...

Let F (z) = z−H(z) with order o(H(z)) ≥ 1 be a formal map from C to C and G(z) the formal inverse map of F (z). We first study the deformation Ft(z) = z − tH(z) of F (z) and its formal inverse Gt(z) = z + tNt(z). (Note that Gt=1(z) = G(z) when o(H(z)) ≥ 2.) We show that Nt(z) is the unique power series solution of a Cauchy problem of a PDE, from which we derive a recurrent formula for Gt(z). Se...

Let F (z) = z−H(z) with order o(H(z)) ≥ 1 be a formal map from C to C and G(z) the formal inverse map of F (z). We first study the deformation Ft(z) = z − tH(z) of F (z) and its formal inverse Gt(z) = z + tNt(z). (Note that Gt=1(z) = G(z) when o(H(z)) ≥ 2.) We show that Nt(z) is the unique power series solution of a Cauchy problem of a PDE, from which we derive a recurrent formula for Gt(z). Se...