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Then, we consider the composite operator with a singular factor.
We also have estimates of those integrals with a singular factor.
Next, we prove the imbedding inequality with a singular factor in the John domain.
We also obtain a similar version of the Poincaré type inequality with a singular factor for the norm.
We extend Theorem 3.1 to the Lipschitz norm with a singular factor and have the following result.
We also consider the integrals of this composition operator with a singular factor because of their broad applications in solving differential and integral equations; see [4].
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A quick heuristic that is often used (but not always true) is "one gene, one protein" meaning a singular gene codes for a singular protein type in a cell (enzyme, transcription factor, etc).
Thus, we draw largely upon work examining singular risk factors and vulnerability, assuming that characteristics affecting vulnerability to a singular risk factor likely will alter vulnerability to cumulative risks.
There is no evidence that aluminum may be a singular causative factor for Alzheimer's disease, but may act as a co-factor that can abet the development of the disease [22].
These results suggest that, whereas combined reductions of contrast and complexity in cartoon images result in a smaller P1, neither is a singular driving factor in cortical facilitation by iconic images.
Idiopathic autisms are diagnosed 4 5 times more often in boys than girls and frequently involve a wide range of genes that confer susceptibility as opposed to a singular heritable factor (Geschwind 2011).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com