Sentence examples for nonlinear modified from inspiring English sources

end{aligned} (52) When we take (G_{n}^{(j)}=H_{n}^{(j)}=0), (j=1,ldots,K) in (49 - 52 49 - 52onlinear modified the-dimenonlinearoda lattice with self-consistent sources (49)-(52) is reduced to the nonlinear modified two-dimensional Toda lattice (6)-(7) with (lambda=1), (nu=mu=0).

The proposed attitude control is based on nonlinear modified Rodrigues parameters feedback control in the presence of unknown terms like external disturbances and actuator faults.

A nonlinear, modified factor is proposed to characterize the difference of the honeycomb's shear modulus under large and small deformation, revealing its independence from the honeycomb's relative density.

end{aligned} (66) Substituting functions (63 - 66 63 - 66he dependent varintoe thensformations (48), we obtain two-soliton solution of the nonlinear modependento-dimensional Toda lattice with self-consistent sources (49)-(52).

end{aligned} end{aligned} (100) We rederive the two-soliton solution of the nonlinear modified two-dimensional Toda lattice with self-consistent sources (49 - 52 49 - 52ed in Sectiobtainedbstinuting the above functionSectionuations (97)-(100) into the dependent variable transformation (48).

However, quantifying climate impacts on populations in order to derive generally applicable predictions is often hampered by strongly nonlinear responses modified by species-specific life histories [ 2] and/or ecosystem complexity [ 3, 4].

Fig. 7 Difference between two nonlinear window functions with various values of control parameter 'p', ​a nonlinear window function, b modified nonlinear window function Fig. 8 a c Simulation of memristor device with modified nonlinear window function at control parameter p = 30 and state variable x = 0.3, 0.5 and 0.7 respectively.

This new truncation on the boundary conditions must satisfy similar properties to the ones of the nonlinear part of the equation, that is, the modified nonlinear boundary value conditions must be bounded, the modified nonlinear boundary value conditions coincide with the nonmodified ones in.

The main achievement of the present manuscript is the modified nonlinear window function which accurately models the nonlinearity of memristor device.

Secondly, considering nonlinear characteristic of the vehicle model and the efficiency of regenerative braking system, the particle swarm optimization algorithm within the modified nonlinear model predictive control is adopted to optimize the torque distribution between regenerative braking system and pneumatic braking system at the wheels.

This section also deals with the modified nonlinear window function.