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