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The phrase "a variational upper bound on" is correct and usable in written English.
It can be used in mathematical or statistical contexts, particularly in optimization problems or theoretical discussions.
Example: "We established a variational upper bound on the expected value of the function to improve our estimates."
Alternatives: "a variational limit on" or "an upper estimate for".
Exact(1)
A variational upper bound on the effective diffusion coefficient for a porous slab of arbitrary pore geometry is derived for liquid or gas phase Fickia bulk diffusion in the void and Fickian surface diffusion on the pore walls.
Similar(59)
The free energy here is a variational free energy that provides a computationally tractable upper bound on the negative logarithm of Bayesian model evidence (see Appendix 1).
Variational free energy provides an upper bound on surprise (i.e., free energy is always greater than surprise).
Although Equation (25) shows a tight upper bound on the channel capacity, in some regions, there are bounds that are a bit tighter than the above bound.
Secondly, it provides a minimized upper bound on the output.
These constraints limit possible peak regrowth and place a tight upper bound on the problem formulation.
A natural upper bound on the achievable rates of chunked codes is established as follows.
The primary benefit of 3D CNOC is scalability and a clear upper bound on power dissipation.
This is significant because it represents a theoretical upper bound on loading rate for wetlands design.
A sharper upper bound on the determinant of the related matrix is derived.
Using the bound, Corollary 3 presents a further upper bound on the success probability of the SAMD, which is straightforward from Theorems 3 and 4 with μ(H =1.
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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