I have tried to follow closely the organization, the material, and even the wording[1] of that paper wherever possible, though further developments have made many of the conclusions reached here quite different from those in QPR 84. Major points of departure in the present paper are in the graphical notation, which makes the ordering of the elements of a triada much more visible and manipulable...

We study a version of the inverse problem of Calculus of Variations in the context of Vakonomic Mechanics.

We analyse the issue of uniqueness of solutions of the static vacuum Einstein equations with prescribed ‘geometric’ or Bartnik boundary data. Large classes of examples are constructed where uniqueness fails. We then discuss the implications of this behavior for the Bartnik quasi-local mass. A variational characterization of Bartnik boundary data is also given.

A triangulated piecewise-linear minimal surface in Euclidean 3space 3 defined using a variational characterization is critical for area amongst all continuous piecewise-linear variations with compact support that preserve the simplicial structure. We explicitly construct examples of such surfaces that are embedded and are periodic in three independent directions of . Department of Mathematics, ...

:= F̂ − KL (q(X|Z) ‖ p(X)) . At this point, our variational bound is similar to the one of equation (7), but the first term, here denoted as F̂ , refers to the expanded probability space and, thus, involves the inducing inputs and the additional variational distribution q(U). Since the second term (the KL term) is tractable (because it only involves Gaussian distributions), we are now going to fo...

We show that the Lavrentiev phenomenon does not occurr for a class of variational functionals on a multi-dimensional domain. Joint work with G. Bonfanti.

The theory of imprecise previsions admits the use of a wide variety of statistical evidence. Nevertheless, some existing evidence, for example, in reliability applications, cannot be utilized by models developed within its framework. In the pursuit of reducing imprecision, any available evidence should become an input to modeling. It is suggested to take a different look at the natural extensio...