These results suggest that experimental studies are needed to assess the effects of treatment aimed at increasing ankle power and hip power and at decreasing the stance time on the affected side, and that these studies should be directed at obtaining a larger hip flexion moment and a larger ankle moment range on the unaffected side.

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A family Ω of valuations of the field K is said to be of finite character if only a finite number of valuations are non-zero at any non-zero element of K. If w ∈ Ω has ring and maximal ideal , then A = ∩w∈Ω is said to be defined by Ω and ∩ A is a prime ideal called the centre of w on A and denoted by Z(w). If = Az(w), then w is said to be an essential valuation for A. A domain defined by a family of finite character in which every valuation is essential is called a ring of Krull type.

The principal-component analysis allowed clustering of related variables and simplified the complex picture presented by the large number of variables resulting from gait analysis. Examination of variables closely related to each principal component yielded insight into the nature of the strategies used in walking and their interrelationships. The method has potential for insight into similarities and differences in gait performances arising from different pathologies and for comparing the progress of individuals with similar pathologies.

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The word ring is used to mean commutative ring. Just as valuations on fields are used to study domains, so valuations on rings can be used to study rings; these rings need not have units [12]. We introduce slightly weaker conditions than having identity in order to get a more general theory. A Prufer ring A is one in which every finitely generated regular ideal is invertible. If we replace invertibility in the total quotient ring K, by invertibility in a ring R where A ⊆ R ⊆ K we get an R-Prufer ring. These rings do occur, for example the Witt ring of a non-Pythagorean field or a ring of bounded continuous functions.