Sentence examples for both real and complex from inspiring English sources

The cases illustrated include both real and complex wave fields.

Yes, there is a terrorist threat which is both real and complex.

These solutions are valid for both real and complex values of the invariants.

Our investigation of both real and complex (or coupled) van der Pol oscillators enriches the nonlinear dynamical systems.

That is, they can be added, subtracted, multiplied, divided, etc., using exactly the same rules of algebra (since both real and complex numbers are mathematical fields).

Chaos control and nonlinear dynamics of both real and complex nonlinear oscillators constitutes some of the most fascinating developments in applied sciences.

We will use the Hermitian since it will work for both real and complex-valued training matrices.

For this purpose, a complex predictor corrector method is developed, which tracks both real- and complex-valued paths and locates bifurcation points where real-valued paths become complex-valued paths.

Hence, we will jointly use both real- and complex-valued forms in the sequel.

These simulation results indicate that the wire/slurry system consists of both real and paired complex eigenvalues, which correspond to the over-damped modes and other vibration modes of the system.

Throughout this paper, we denote by (L^{2}(mathbb{R}^{n})) both the standard real and complex Hilbert spaces and equip (L^{2}(mathbb{R}^{n})) with the inner product and norm as (u,v =int_{mathbb{R}^{n}}u(x bar{v}(x),dx, qquad |u |^{2}= u,u).