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Two types of cubic oscillators have been used as examples: the linear damped oscillator f x, xdot) = xdot, and the van der Pol oscillator f x, xdot) = (α − βx2)xdot.
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In the third example, the linear design technique involved an optimal control scheme with an integrator.
In this example, the linear scalar conservation law has the following form: v_{t}+v_{x}=0.
For example, the linear polarizations for 13 comets reported by Chernova et al. (1993) were obtained using a 1-m telescope.
To be sure, there were also certain ideas about the nature of the gene, some of which highly speculative, others well established by experiments (for example, the linear arrangement on the chromosome, see Weber 1998b).
The high performance was indicated by some of the key parameters, for example the linear H2O2 concentration response range (1 30 μM), the detection limit (100 nM), and the high amperometric sensitivity (5 A cm− 2 M− 1).
For example, the linear stability and zero Liapunov exponents are obtained and the existence results allow one to construct a local normal form in a neighborhood of the obtained solutions, which is useful for better understanding of the dynamics.
We have chosen the cubic interpolation because for some BS the missing values are situated on the first/last position of the vector and this fact forbids us to use, for example, the linear interpolation.
For example, the linear viscoelastic regime of the HSA organogel, an indicator of the strength of the gel, extends by a factor of four with the incorporation of 0.2 wt% of the carboxylated nanotubes.
Taking the bistatic range history of the scene center as an example, the linear RCM and the high-order one in (5) can be expressed as begin{array}{l}{R}_Wleft( t;{theta}_Rright)={A}_0left {theta}_Rright) t {R}_Cleft( t;{theta}_Rright)={R}_{mathrm{total}}left( t;{theta}_Rright -{A}_0left {theta}_Rright) t-{theta}_Rright -{A}_0left {theta}_Rright
Primal and dual interior-point methods (IPMs) have been well known as the most effective methods for solving wide classes of optimization problems, for example, the linear optimization (LO) problem, the quadratic optimization problem (QOP), the semidefinite optimization (SDO) problem, the second-order cone optimization (SOCO) problem, and the convex optimization problem (CP).
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.
Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com