41. In 1772 the Jacobian line of the Waldburgs died out with Count Francis Charles Eusebius. 42. The Jacobian and its determinant is given by 43. In 1429, the Trauchburg went to the Jacobian line of the House of Waldburg. 44. Diffeomorphisms of or Jacobian , are also classified to orientation-preserving and orientation-reversing. 45. Specifically, the eigenvalues of the Jacobian are indicative of the center manifold's existence. 46. By the previous example, having non-zero Jacobian is the same as being �tale. 47. This incorporates the Abel Jacobi map from cycles homologically equivalent to zero to the intermediate Jacobian . 48. A regular solution is a solution at which the Jacobian is full rank ( n ). 49. Kontsevich in 2007, showed that the Dixmier conjecture is stably equivalent to the Jacobian conjecture. 50. Where, stands for the Jacobian matrix of, and the clear circle denotes function composition.
