The phrase "analytical relations between" is correct and usable in written English.
It can be used when discussing the connections or interactions between different analytical concepts, variables, or entities in a study or analysis.
Example: "The research focused on the analytical relations between economic growth and environmental sustainability."
Alternatives: "analytical connections among" or "analytical links between".
Finally, analytical relations between the thermodynamic and phase field parameters are found and verified for these simulations.
Analytical relations between the isentropic efficiency and the flow coefficient, the work coefficient, the flow angles and the degree of reaction of the compressor stage are obtained.
We determine analytical relations between fracture toughness and the parameters governing bulk hysteresis, and quantitatively predict the reduction in fracture toughness due to pre-stretch.
Finally, analytical relations between the sink and source terms of the breakage or aggregation of the PBE were derived and discussed, highlighting interesting features of the PBE model.
An approximate analysis of the system of differential equations describing the process enabled us to establish analytical relations between the parameters of the system, which determine the limits of oscillatory instability (Hopf bifurcation), the limits of saddle-type instability and an approximate formula to determine the critical value of the Lewis number.
Analytical relations between the critical buckling load of a functionally graded material (FGM) Timoshenko beam and that of the corresponding homogeneous Euler Bernoulli beam subjected to axial compressive load have been derived for clamped clamped (C C), simply supported simply supported (S S) and clamped free (C F) edges.
We applied this analytical strategy to investigate the relations between stochastic epigenetic alteration and aging.
In this study we applied a new analytical strategy to investigate the relations between stochastic epigenetic mutations (SEMs) and aging.
Based on analytical relations, a design concept is generated that provides a mass reduction of 25% and a fluid channel structure with minimal required pumping power.
After verification of analytical relations, the filtration efficiency of the analytical criterion is reported to be as high as 82%.
