Generating functions for volume-preserving transformations

Generating functions for volume-preserving transformations

A general implicit solution for determining volume-preserving transformations in the ndimensional Euclidean space is obtained in terms of a set of 2n generating functions in mixed coordinates. For n = 2, the proposed representation corresponds to the classical definition of a potential stream function in a canonical transformation. For n = 3, the given solution defines a more general class of i...

Generating Dense Subgroups of Measure Preserving Transformations

Except for a set of first category, all pairs of measure preserving transformations generate a dense subgroup of G, the group of all invertible measure preserving transformations of the unit interval when G has the weak topology. Consider G the group of invertible (Lebesgue) measure preserving transformations of the unit interval onto itself. On G, we put the weak topology (Halmos [2, pp. 61-67...

Tractability-preserving transformations of global cost functions

Graphical model processing is a central problem in artificial intelligence. The optimization of the combined cost of a network of local cost functions federates a variety of famous problems including CSP, SAT and Max-SAT but also optimization in stochastic variants such as Markov Random Fields and Bayesian networks. Exact solving methods for these problems typically include branch and bound and...

Probability Generating Functions for Sattolo’s Algorithm

In 1986 S. Sattolo introduced a simple algorithm for uniform random generation of cyclic permutations on a fixed number of symbols. Recently, H. Prodinger analysed two important random variables associated with the algorithm, and found their mean and variance. H. Mahmoud extended Prodinger’s analysis by finding limit laws for the same two random variables.The present article, starting from the ...

Generating Forms for Exa t Volume-Preserving Maps