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Relating to the work of the mathematician K. G. J. Jacobi.
- ‘He showed how to find integrals of a general system of partial differential equations by using sequential complete systems instead of passing to Jacobian systems.’
- ‘Göpel… finally, after ingenious calculations, obtained the result that the quotients of two theta functions are solutions of the Jacobian problem for p = 2.’
- ‘In order to calculate the inverse Jacobian matrix, we need the following derivatives of the functional response [F.sub.ki] (for all values of k and i).’
- ‘Asymptotic stability of the EP was also determined by computing 14 eigenvalues of a 14 × 14 Jacobian matrix derived from the linearization of the nonlinear system around the EP (for more details, see Vinet and Roberge).’
A determinant whose constituents are the derivatives of a number of functions (u, v, w, …) with respect to each of the same number of variables (x, y, z, …).
- ‘Therefore, the determinants of the set of variable transformations (Jacobians) must be calculated for both states involved: the original and the new one, to properly weigh up each new configuration.’
- ‘He also worked on determinants and studied the functional determinant now called the Jacobian.’
- ‘These problems form the basis of a conjecture: every elliptic curve defined over the rational field is a factor of the Jacobian of a modular function field.’
- ‘In 1889 Poincaré proved that for the restricted three body problem no integrals exist apart from the Jacobian.’
- ‘Advanced calculus gives us a strong tool for finding the change in the area of a given shape under continuously differentiable transformations-namely, the Jacobian.’
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