We have combined inverse kinematics learned by LWPR with visual servoing to correct for inaccuracies in a low cost robotic arm. By low cost we mean weak inaccurate servos and no available joint-feedback. We show that from the trained LWPR model the Jacobian can be estimated. The Jacobian maps wanted changes in position to corresponding changes in control signals. Estimating the Jacobian for the...

The sine-Gordon equation has hyperelliptic al function solutions over a hyperelliptic Jacobian for y = f(x) of arbitrary genus g. This article gives an extension of the sine-Gordon equation to that over subvarieties of the hyperelliptic Jacobian. We also obtain the condition that the sine-Gordon equation in a proper subvariety of the Jacobian is defined.

Any endomorphism of Cn defined by n polynomials with everywhere non-vanishing Jacobian is an automorphism. The Jacobian conjecture originated fromKeller ([5]). Let F1, . . . , Fn ∈ C[x1, . . . , xn] be a set of n polynomials in n variables with n ≥ 1 such that the Jacobian of these polynomials is a nonzero constant. The Jacobian conjecture says that the subalgebra C[F1, . . . , Fn] of C[x1, . ....

Counting the order of the Jacobian group of a hyperelliptic curve over a nite eld is very important for constructing a hyperelliptic curve cryptosystem (HECC), but known algorithms to compute the order of a Jacobian group over a given large prime eld need very long running times. In this note, we propose a practical polynomial-time algorithm to compute the order of the Jacobian group for a hype...