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I will discuss our recent work looking at the random behavior of monomial ideals.
We will begin the proof by looking at the random quantity X k,M (t,u).
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He looked at the random collection of items, from the "Love Generator" poster to the barber pole to an Empire-style table with a pedestal base made of a sawed-off porch column.
Running around the landscape, looking at the seemingly random distribution of trees, grass, burned landscapes, and different slopes, I remembered learning about all the ways that landscapes varied in landscape ecology.
For the typical type of paper representative of ~70 80 % of Western library and archival collections, we looked at the 'random failure phase' when material weakens, as well as at the 'wear-out failure phase' during which reduction in DP becomes so pronounced that wear and tear (mechanical failure) becomes increasingly likely.
Kacper's PhD thesis is "looking at the dependence between random processes".
"What's the reason for not changing the bike?" "To see where it goes, who rides it". Kacper's PhD thesis is "looking at the dependence between random processes".
5 There has been an extensive body of empirical research looking at the influence of random sequence generation and allocation concealment on treatment effect estimates of health RCTs.
When looking at the 3% random sample, we found direct treatment costs of approximately €1.99 million which shows, that the treatment costs per case are - on average - rather low.
The significance of the modules found is assessed empirically by looking at the scores of random sets of reactions and metabolites of the same size as the modules found Spuriously routes via highly connected currency metabolites (e.g. water, carbon dioxide or ATP) are minimised by the assignment of connectivity-dependent weights to their nodes in the bipartite network.
You do it on Android and there's a good chance you could end up looking at the middle of a random paragraph.
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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