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Trust region methods are robust optimisation methods with strong convergence properties.
Results show that methods with strong difference between biological and seepage source CO2, such as Δ14C signatures in this study, have the best overall SNR values.
Since we don't know whether the mapping, where is a strong pseudo-contraction, has a unique fixed point or not, we can not get the desired results from Theorem S. Next, we give the second convergence theorem for the non-expansive semigroup by Moudafi's viscosity approximation methods with strong pseudo-contractions.
It is non-unique in nature; however, the strength of our EHVR inversion lies in its capability to obtain both S-wave velocities and the thicknesses of the layers down to the bedrock at the same time, unlike the other methods with strong trade-offs between them, because we use both amplitudes and peak/trough frequencies of EHVR to constrain the velocity profile.
Physical therapists (PTs) use treatment methods with strong or moderate evidence of effect, but also methods with limited or no effect [ 6- 9].
Moreover, the power values collapsed in this situation (around 4% for both methods with strong selection and around 13% for both methods with light selection).
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We employ either the standard fourth-order Runge-Kutta method (RK4) or a third-order (RK3, see Gottlieb et al. 2009) method with strong stability preserving (SSP) properties.
In particular, for advection term, we use the positivity-preserving DG method with strong stability preserving (SSP) high order time discretizations.
A novel and efficient Ti-Ce-Si ternary nanocomposite was prepared by SCFD method with strong thermal stability and high photoactivity in the photodegratation of phenol.
Random walk algorithm with compulsive evolution is a novel stochastic method with strong global search ability for heat exchanger network synthesis; however, its mutation behavior of accepting bad solutions might substitute excellent solutions with bad ones and consequently cost-optimal structures cannot be guaranteed.
Each of these results was robust to the selection of source-apportionment method, with strong agreement between the RR estimates from the PMF and CMB-LGO models, as well as with results from models using single-species tracers as surrogates of the source-apportioned PM2.5 values.
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