in this paper lie’s formalism is applied to deduce classes of solutions of a nonlinear partialdifferential equation (npde) of second order with quadratic nonlinearity. the equation has themeaning of a field equation appearing in the formulation of kinetic models. similaritysolutions and transformations are given in a most general form derived to the first time interms of reciprocal jacobian ell...

The contact structure of two meromorphic curves gives a factorization of their jacobian. Section 1: Introduction Let J(F,G) = J(X,Y )(F,G) be the jacobian of F = F (X,Y ) and G = G(X,Y ) with respect to X and Y , i.e., let J(F,G) = FXGY − FY GX where subscripts denote partial derivatives. Here, to begin with, F and G are plane curves, i.e., polynomials in X and Y over an algebraically closed gr...

We study Jacobian inverse kinematics algorithms for mobile manipulators composed of a nonholonomic mobile platform and a holonomic onboard manipulator. In general, the Jacobian algorithms converge locally, often producing weird end effector and platform trajectories. In the paper we use the existing theory of Newton algorithms in order to improve the quality of convergence of the Jacobian algor...

This paper addresses the synthesis problem of Jacobian inverse kinematics algorithms for stationary manipulators and mobile robots. Special attention is paid to the design of extended Jacobian algorithms that approximate the Jacobian pseudoinverse algorithm. Two approaches to the approximation problem are developed: one relies on variational calculus, the other is differential geometric. Exampl...

This paper describes a comparative study of performance between the estimated image Jacobian that come from taking into account the geometry epipolar of a system of two cameras, and the well known analytic image Jacobian that is utilized for most applications in visual servoing. Image Based Visual Servoing architecture is used for controlling a 3 d.o.f. articular system using two cameras in eye...

Divisors whose Jacobian ideal is of linear type have received a lot attention recently because its connections with the theory $D$-modules. In this work we are interested on divisors expected type, that is, gradient and relation coincides reduction number respect to plus one. We provide conditions in order be able describe precisely equations Rees algebra ideal. also relate some $D$-module theo...

In this article we provide a stack-theoretic framework to study the universal tropical Jacobian over moduli space of curves. We develop two approaches process tropicalization compactified curves -- one from logarithmic and other non-Archimedean analytic point view. The central result both points view is that maps in each contexts are compatible with tautological morphisms. sequel will use techn...