Definition of Jacobian in English:

Jacobian

adjective dʒəˈkəʊbɪənjəˈkōbēən

Mathematics

Relating to the work of the mathematician K. G. J. Jacobi.
（与）数学家雅可比的理论（有关）的
Example sentencesExamples
- 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).
- Göpel… finally, after ingenious calculations, obtained the result that the quotients of two theta functions are solutions of the Jacobian problem for p = 2.
- 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.

noun dʒəˈkəʊbɪənjəˈkōbēən

Mathematics

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, …).
雅可比行列式，函数行列式
Example sentencesExamples
- 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.
- He also worked on determinants and studied the functional determinant now called the Jacobian.
- 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.
- 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.

Definition of Jacobian in US English:

Jacobian

adjectivejəˈkōbēən

Mathematics

Relating to the work of the mathematician K. G. J. Jacobi.
（与）数学家雅可比的理论（有关）的
Example sentencesExamples
- 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).
- 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).
- Göpel… finally, after ingenious calculations, obtained the result that the quotients of two theta functions are solutions of the Jacobian problem for p = 2.
- 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.

nounjəˈkōbēən

Mathematics

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, …).
雅可比行列式，函数行列式
Example sentencesExamples
- 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.
- 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.
- 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.
- He also worked on determinants and studied the functional determinant now called the Jacobian.

词汇	Jacobian
释义	Definition of Jacobian in English: Jacobian adjective dʒəˈkəʊbɪənjəˈkōbēən Mathematics Relating to the work of the mathematician K. G. J. Jacobi. （与）数学家雅可比的理论（有关）的 Example sentencesExamples 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). Göpel… finally, after ingenious calculations, obtained the result that the quotients of two theta functions are solutions of the Jacobian problem for p = 2. 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. noun dʒəˈkəʊbɪənjəˈkōbēən Mathematics 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, …). 雅可比行列式，函数行列式 Example sentencesExamples 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. He also worked on determinants and studied the functional determinant now called the Jacobian. 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. 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. Definition of Jacobian in US English: Jacobian adjectivejəˈkōbēən Mathematics Relating to the work of the mathematician K. G. J. Jacobi. （与）数学家雅可比的理论（有关）的 Example sentencesExamples 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). 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). Göpel… finally, after ingenious calculations, obtained the result that the quotients of two theta functions are solutions of the Jacobian problem for p = 2. 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. nounjəˈkōbēən Mathematics 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, …). 雅可比行列式，函数行列式 Example sentencesExamples 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. 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. 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. He also worked on determinants and studied the functional determinant now called the Jacobian.
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