Conservation criteria, canonical transformations, and integral invariants in the field theory of Carathéodory for multiple integral variational problems
Copyright policy )Conservation criteria, canonical transformations, and integral invariants in the field theory of Carathéodory for multiple integral variational problems
A composition of n into s parts is a partition in which the order of the parts is taken into account. For example, the compositions of 4 into two parts are (3, 1), (1, 3), (2, 2). In the above example there is only one composition of 4 into two parts with no part exceeding 2, namely (2, 2). Let c(n, s, r ) be the number of compositions of n into s parts with no part exceeding r, and let c(s, r ) be the maximum of c(n, s, r ) over n for fixed s and r. The following results are established for r ~> 2:
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- University of Arizona United States
510.mathematics, Hamilton-Jacobi theories, Existence theories for problems in abstract spaces, Hamilton-Jacobi equations in mechanics, Article
510.mathematics, Hamilton-Jacobi theories, Existence theories for problems in abstract spaces, Hamilton-Jacobi equations in mechanics, Article
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