The phrase "a restricted variation of" is correct and usable in written English.
It can be used when discussing a specific subset or limited form of something, often in academic or technical contexts.
Example: "The study focuses on a restricted variation of the original theory, which limits its applicability to certain scenarios."
Alternatives: "a limited version of" or "a constrained form of".
where is a Lagrange multiplier which can be identified optimally via variational theory, is the th approximate solution, and denotes a restricted variation; that is,.
Then, we present an exact dynamic programming algorithm for solving the SNP - M S P problem and also show that the SNP - M S Q problem is NP-hard by a reduction from the restricted variation of the 3-partition problem [ 7, 8].
But, it can be easily done by adding B to each a i and then multiplying B by 4. Theorem 14 The S N P - M S Q problem is NP-hard, even when | ∑ | = 2. Proof: We prove it by a reduction from the above restricted variation of the 3-partition problem.
To compare our model with existing methods and also to evaluate the effect of neglecting variation in infectivity, a restricted version of the model assuming variation only in susceptibility (hereafter denoted the alternative model) was also fitted to the simulated infection data.
Interestingly, this restricted variation of the 3-partition problem remains strongly NP-complete [ 8], just like the general form of the 3-partition problem.
The combination of restricted variation in potentially deleterious directions and feedback between variation and stress, explains how any type of newly-forming random variation can self-organize into emergent physiological adaptations.
Data suggest that swallows occur within a restricted range of lung volumes with variation due to instructions, bolus type and other experimental variables.
A restricted number of genes showed either impaired variation when compared with control cells (clusters b and d) or variation restricted to cells with low levels of HP1γ (Figure 5B, cluster e), but their analysis did not reveal any convergent function.
Factor co-kriging analysis was applied separately to the two data sets to synthesize the complex multivariate variation of the two areas in a restricted number of zones so they could be ranked as at different risks of NO3 N leaching.
By the use of a restricted number of significant PCs, experimental noise and random variations can be eliminated.
