The phrase "analytical roots" is correct and usable in written English.
It can be used when discussing the foundational or underlying principles of analytical thinking or methods in various contexts, such as mathematics, science, or philosophy.
Example: "To fully understand the theory, we must explore its analytical roots and how they influence current practices."
Alternatives: "foundational analysis" or "underlying principles of analysis".
But (35) is a transcendental equation, which is hard to obtain the analytical root.
Adjusted pseudo-time and adjusted pseudo-pressure were used instead of real time and real pressure in the analytical solution for Warren and Root's model.
The analytical solution requires the determination of roots of the characteristic equations, which is cumbersome for spherical particles.
An analytical solution for the stress field exhibits a square root singularity near the free edges.
For larger d n, we can see the appearance of an additional hump structure (Fig. 1, dotted curve) above V = V Δ which reminds about the presence of a non-analytical square-root dependence of Andreev-reflection amplitudes (3).
" Computing with Classical Soliton Collisions", M.H. Jakubowski, K. Steiglitz, R. Squier, Chapter 12 in Advances in Unconventional Computing, Volume 2: Prototypes, Models and Algorithms, pp. 261-295, Adamatzkyzky (ed)., Springer, 2017. 1. " An Analytical Approach to Root Loci," IRE Trans.
The response time history simulations also provide a bases for assessing the performance of analytical predictions of root-mean-square (RMS) response using crosswind loading spectrum and equivalent aerodynamic damping models.
Based on the technique of D-decomposition, the analytical boundaries of root invariant regions are derived and the admissible H∞ region in the parameter space is the intersection of the admissible sets, and it can be drawn and identified immediately, not to be computed mathematically.
After running simulation on RTC software, a heuristic (analytical) method, called root cause analysis (RCA), was applied to evaluate the simulation output.
