Sentence examples for provided in the preceding from inspiring English sources

Then we define a set-valued mapping T : S → 2 S ∖ by T ( x ) = T 1 ( x ) × T 2 ( x ) × ⋯ × T n ( x ) for all  x ∈ S. Now we prove that the mapping T satisfies all conditions A1, A2 and A3 in the first extension of the Abian-Brown fixed point theorem in a chain-complete preordered set provided in the preceding section.

Hopefully, information provided in the preceding sections has transformed this view into the recognition that marketing is essential for success - no matter what the product or cause.

Hopefully, information provided in the preceding sections has transformed this view into the recognition that marketing is essential for success - no matter what the product.

Given the clues provided in the preceding paragraphs, a framework mechanism for the radical SAM enzymes has been proposed.

Hegel makes reference to contracts in regard to possession of property, but an extension of this thinking, as is provided in the preceding paragraph, can be recognized in American courts today as a contract.

Individuals reporting frequent, compared to infrequent, use of sterile cookers (AOR 3.92 (1.58 - 9.70)) and water (AOR 2.93 (1.12 - 7.68)), but not filters (AOR not provided), in the preceding month were significantly more likely to be self-reported HCV-negative.

Feedback is provided in the practice sessions that precede each test, but not during the actual tests.

The sentence completion task showed that participants used pronouns provided in the prompts to reference elements in preceding subject positions at a rate of nearly 80%%, and linked pronouns to non-subjects much less frequently.

In addition, the PTO tasks did not provide information on the preceding duration of illness of hypothetical patients.

17,450 boys and girls aged 0 17 years provided information on drug use in the preceding seven days.

Attrition of subjects because of loss of health insurance may also affect a study like the present one, that is based on claims data, but some reassurance about this possible source of bias is provided by the finding doses in the preceding six months were similar for subjects who left the cohort and those who remained in it.