The phrase "analytically establish" is correct and usable in written English.
It can be used in contexts where you want to indicate that something is being determined or proven through analysis or logical reasoning.
Example: "In this study, we aim to analytically establish the relationship between diet and health outcomes."
Alternatives: "systematically determine" or "empirically demonstrate".
The objective of this paper is to analytically establish the effects of bidirectional loading on the response of reinforced masonry shear walls.
We also analytically establish the relationship between the mass exchange rates of solutes with different molecular diffusion coefficients, and verify this relationship against the results directly calculated from the pore-scale simulations.
In particular, although we will not specify an optimal β, we will analytically establish some results about how spike times depend on β, including the fact that the number of spikes saturates as β grows, which is consistent with [13] and contrasts with the non-monotone dependence of θ ( P ) on β seen in the previous section.
We analytically establish the conditions for the existence of at least two or three positive solutions in the generalized -point boundary value problem for the -Laplacian dynamic equations on time scales by means of the Avery-Henderson fixed point theorem and the five functionals fixed point theorem.
By virtue of the Avery-Henderson fixed point theorem and the five functionals fixed point theorem, we analytically establish several sufficient criteria for the existence of at least two or three positive solutions in the -Laplacian dynamic equations on time scales with a particular kind of -Laplacian and -point boundary value condition.
Its statistical performances are analytically established; this highlights the impact of quantization on the most powerful steganalyzer.
With the consideration of both longitudinal and hoop deformation behavior of pipeline, a ring-truss theory was analytically established in this study.
Since free-tunable product of two eigenfunctions also controls stability of the model, the validity of the analytically established von Neumann stability diagram is examined in Poiseuille profile.
In this work, the model of eddy current damping for moving Halbach Permanent Magnet (PM) array is analytically established to predict the damping force in operating of the maglev positioning system.
Exploiting the existence of a system of action and angular variables for trapped and circulating particles, a functional, extremum in the turbulent electromagnetic field, is analytically established and implemented in the code TORRID.
To fill this gap, this paper suggests an analytical model of grinding-induced SSD in silicon, where the explicit relationship between SSD and the ground surface roughness Rz is analytically established considering the (i) ductile-regime effect, (ii) crystallographic orientation effect, and (iii) material property degradation due to high grinding temperature.
