An early demonstration of the strength of Gauss'Method came when it was used to predict the future location of the newly discovered asteroid Kepler's complicated nonlinear equations of planetary motion.
42.
In those limits, the number of equations usually decreases, their order reduces, nonlinear equations can be replaced by linear ones, the initial system becomes averaged in a certain sense, and so on.
43.
In fact, virtually all oscillators become anharmonic when their pump amplitude increases beyond some threshold, and as a result it is necessary to use nonlinear equations of motion to describe their behavior.
44.
The degree of abstraction, combined with a relative lack of good mathematical tools for analyzing nonlinear equation systems, make it hard to connect such theories with the physical phenomena that they might describe.
45.
Gluons therefore participate in the strong interaction in addition to mediating it, making QCD significantly harder to analyze than QED ( quantum electrodynamics ) as it deals with nonlinear equations to characterize such interactions.
46.
During the last few decades fresh approaches have revealed general laws applicable to non-equilibrium system which are described by nonlinear equations, pushing the range of exact thermodynamic statements beyond the realm of traditional linear solutions.
47.
These developments began with a pioneering computer simulation by Kruskal and Norman Zabusky ( with some assistance from Gary Deem ) of a nonlinear equation known as the Korteweg de Vries equation ( KdV ).
48.
Following this intuition, the goal is to find a parameterization that captures the mean and covariance information while at the same time permitting the direct propagation of the information through an arbitrary set of nonlinear equations.
49.
Many times, without using auxiliary variables, there is no known way to get the power series for the solution to a system, hence the power series method alone is difficult to apply to most nonlinear equations.
50.
V SC is the self-consistent voltage that illustrates that the CNT energy is affected by external terminal voltages and is implicitly related to the device terminal voltages and charges at terminal capacitances by the following nonlinear equation:
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