Thus the Picard-Lindelöf theorem guarantees the existence and uniqueness of the solution.

In the theory of differential equations, Lipschitz continuity is the central condition of the Picard-Lindelöf theorem which guarantees the existence and uniqueness of the solution to an initial value problem.

The above methods can be combined, hierarchically or singly, to create other generation schemes which guarantee uniqueness.

This guarantees the standardization and uniqueness of access points of catalogues, which makes it easier the exchange and a more efficient communication of bibliographic records and, in the end, enables users to carry out assisted, precise and exhaustive searches.

In mathematics, the Banach fixed-point theorem (also known as the contraction mapping theorem or contraction mapping principle) is an important tool in the theory of metric spaces; it guarantees the existence and uniqueness of fixed points of certain self-maps of metric spaces, and provides a constructive method to find those fixed points.

The signum function does not satisfy the Lipschitz continuity condition required for the usual theorems guaranteeing existence and uniqueness of strong solutions.

In the case of hyperbolic systems, the notion of weak solution based on distributions does not guarantee uniqueness, and it is necessary to supplement it with entropy conditions or some other selection criterion.

In contrast, file fingerprints need to be at least 64-bit long to guarantee virtual uniqueness in large file systems (see birthday attack).

The EPC is designed to meet the needs of various industries, while guaranteeing uniqueness for all EPC-compliant tags.

Often some of the integers are given readily in the table in order to guarantee uniqueness of the solution and/or for making the task easier.