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Bounds for the mean-square performance are established on the basis of upper bounds for the solution of the relevant Riccati equation.
A conjugate gradient method supplemented by the adjoint variable method is adopted in the solution of the relevant inverse problem to reduce the computational burden.
Tables have been created summarizing the solution of the relevant equations for certain probability distributions, but application of these is awkward.
It should be noted that the character of the resulting algorithm is similar to the FEM if special macro-elements provided by direct solution of the relevant differential system are used.
By building the nominal error system and modifying its cost function, the solution of the relevant HJB equation can be contributed to the adaptive tracking control of the continuous-time uncertain nonlinear system.
Typically, a plant extract-mediated bioreduction involves mixing aqueous extract with an aqueous solution of the relevant metal salt.
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Numerical solutions of the relevant conservation equations have been obtained for various channel shapes, dimensions, vapor-to-surface temperature differences and vapor mass fluxes.
Analytical solutions of the relevant governing equations are proposed and closed-form expressions for simple cases, involving pure mode I and mode II components, are provided.
Adding to the existing numerical solutions of the relevant partial differential equations, the effective particle model provides physical insights into the relationships of the parameters that govern sedimentation patterns.
This is built on the identification and subsequent proposal of solutions of the relevant market failures, i.e. situations in which the allocation of goods and services on a market is not efficient.
The need for an accurate (better than 10 significant digits) and fast algorithm for calculating the Chandrasekhar function, H, has stimulated the present analysis of different solutions of the relevant integral equation.
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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