In general, a referring expression ("the president of the United States") in its de dicto reading picks out whoever or whatever may satisfy a certain condition, while in its de re reading it picks out the person or thing that in fact satisfies that condition.
To prove the existence of a fixed point of such mappings, it is essential for mappings to satisfy certain contractive conditions which may involve the Hausdorff metric.
See Social Fund - NI Social Security Agency The social fund includes a regulated scheme which provides entitlement to maternity, funeral and cold weather payments for people who satisfy certain qualifying conditions; and a discretionary scheme under which people may be eligible in certain circumstances for a community care grant or an interest free loan.
It may be the most reliable within a given weight limit, the simplest that will satisfy certain safety requirements, or the most efficient for a given cost.
Specifically, let m satisfy certain conditions.
where,,,,,,, and in satisfy certain conditions.
This route must also satisfy certain bandwidth requirements.
His view implies that democratic legitimacy only obtains if the outcomes themselves satisfy certain quality conditions specifically, he postulated that they should satisfy certain rationality axioms.
The truth predicate has to satisfy certain principles; otherwise the global reflection principle would be vacuous.
The operations of vector addition and scalar multiplication must satisfy certain requirements, called axioms, listed below.
