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The lower semicontinuity says that begin{aligned} P_n overset{s}{rightarrow } P_infty Rightarrow dim {mathrm{ran}}, P_infty le liminf dim {mathrm{ran}}, P_n end{aligned} (3.31 Kato was well aware that equality might not hold on the right side of (3.31) for examples of relevance to physics—a main example that he mentions is the Stark effect where the right side is infinite.
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It surfaces uncomfortable questions about the present situation – for example, the relevance of paid jobs as a key unit of analysis or the validity of existing macro-economic models that were designed for an era of full employment.
The concept of the metastatic niche is still discussed controversially, reflecting the still limited number of publications in this area to date, as well as uncertainties regarding, for example, the relevance of DTCs to metastasis formation, the role of BMDC in tumor angiogenesis, and the precise definition of CD11b+ subsets.
What is the relevance to justice, for example, of the apparently artificial boundaries demarcating the groups—'America 2,' say (Northland low-income rural whites)—in the 'eight Americas' analysis from which our opening illustration of inequalities in health was drawn?
Nothing in it diminishes, for example, the relevance of the larger Mueller investigation.
Nevertheless, although fat intake during adult life has largely been dismissed as an important risk factor for mammary tumors, fat intake during childhood or adolescence, for example, might be of relevance.
In a related study of the interaction networks of genes (Lezon et al. 2006), larger networks have been studied, but this required that the trade-off between the rigor of analysis, controlling, for example, for the relevance of higher-order correlations, and the size of the treatable network had been biased towards the network size.
In some instances, there may have been flaws in the experimental methodology (for example, relevance and quality of models, incomplete understanding of treatment mechanisms and inadequate elucidation of brain pharmacokinetics of the drug used).
Clinical relevance is still important since if as some argue [ 45] that a generic measure is sufficient to provide both estimates of utilities and a clinical effect size of HRQoL, estimates based on odds ratios are likely to be more easily interpretable: for example the clinical relevance of a mean treatment difference of 0.012 on the EQ-5D-3L is difficult to judge.
The recommendations refer, for example, to the relevance of the diagnosis for the evaluation and to the boundaries of the concept of disease.
Brazil and Korea present seemingly opposite but complementary examples of the relevance of taking both dimensions into account.
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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