Sentence examples for analytic transformations from inspiring English sources

According to normal form theory, for system (1.1), we can find analytic transformations in the neighborhood of origin to transform system (1.7) into (1.6).

In Section 3, we recall some formal and analytic transformations such as the formal q-Borel transform of a positive order and the analytic q-Laplace transform of a positive order.

In his study of the rectification of the lemniscate, a ribbon-shaped curve discovered by Jakob Bernoulli in 1694, Giulio Carlo Fagnano (1682 1766) introduced ingenious analytic transformations that laid the foundation for the theory of elliptic integrals.

Furthermore, if condition (1.2) holds, there exist analytic transformations in the neighborhood of origin of (1.3) to make (1.1) be changed into the Liénard equation frac{du}{dtau }=v, qquad frac{dv}{dtau }=alpha u^{2n-1}+v sum_{k=n-1}^{infty }B_{k}u ^{k},qquad B_{n-1}=beta, (1.6) so (B_{2k}) could be thought of as Lyapunov constants of (1.1).

Analytic transformation formulas are derived which describe dispersion effects of resizing the inclusions.

□ Let X and G be, respectively, a real-analytic manifold of dimension n and a Lie group acting freely and properly on X by real-analytic transformations.

Additionally, when assessing the case times on each shift by urgency level, the distributions were severely skewed with different shapes for each period, and no simple analytic function (transformation) provided an adequate fit.

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Analytic algorithms and transformations presupposed a correspondence between local and global change, the basic concern of the calculus.

According to Theorem 2, any function (u(x in L^{2}_{rho}(Lambda )) that is analytic under the transformation (x=-Lln(frac{1-s}{2})) has a superlinear convergence series in the form (16).

Those systems could be changed into analytic systems by two transformations with the help of computer algebra system MATHEMATICA.