Sentence examples for following for each from inspiring English sources

In [6], Kada et al. introduced the concept of -distance on a metric space as follows: A function is called - on if it satisfies the following for each : a map is lower semicontinuous; that is, if a sequence in with, then ; for any there exists such that and imply.

For each, let Then By induction, we can obtain the following: for each, (211).

How you choose to keep track of everything is up to you, but I'd strongly suggest the following for each set of demos.

(2) To prove [1, Theorem  3.2] and [1, Theorem  2.9], it is sufficient that satisfy the following: for each sequence (4).

The design displacement profile is developed using the various values obtained as the following for each of the systems, together with the design story drift using Eqs.

The course offerings include the following for each school: Harvard, entrepreneurial opportunities and business management; Kellogg, developing and selling a brand and evaluating franchise opportunities; Stanford, evaluating business opportunities in the sports industry; Wharton, financial analysis, real-estate development, negotiations.

Then for all We now consider the following estimates for each such that and for any : (36).

Bonferroni's correction was applied for multiple comparisons, following ANOVA for each single time point.

For these analyses, APDC records were extracted for the 12 months following recruitment for each participant.

In ORD, each node maintains the following information for each forwarder.

(i) satisfies the following condition; for each and, there exists such that, (ii) is compact for each, (iii).