Optimization on Stiefel manifolds was discussed by Rapcsák in earlier papers. There, some numerical methods of global optimization are dealt with and tested on Stiefel manifolds. In the paper the structure of the optimizer points is given in some particular problem instances and for a special form of a quadratic problem defined on a Stiefel manifold. Some reduction tricks and results are obtain...

Article history: Received 13 June 2008 Received in revised form 29 May 2009 Accepted 2 June 2009 Available online 6 June 2009 Extending a geometric construction due to Sederberg and to Bajaj, Holt, and Netravali, an algorithm is presented for parameterizing a nonsingular cubic surface by polynomials of degree three. The fact that such a parametrization exists is classical. The present algorithm...

We prove a novel unique continuation result for weak bisolutions to the massive Klein–Gordon equation on a 2-dimensional cylinder M. Namely, if such a bisolu-tion vanishes in a neighbourhood of a 'sufficiently large' portion of a 2-dimensional surface lying parallel to the diagonal in M ×M , then it is (globally) translationally invariant. The proof makes use of methods drawn from Beurling's th...

Experience shows that there is a strong parallel between metrization theory for compact spaces and for linearly ordered spaces in terms of diagonal conditions. Recent theorems of Gruenhage, Pelant, Kombarov, and Stepanova have described metrizability of compact (and related) spaces in terms of the offdiagonal behavior of those spaces, i.e., in terms of properties of X −∆. In this paper, we show...

We present the basic elements of a generalization of symmetric function theory involving functions of commuting and anticommuting (Grassmannian) variables. These new functions, called symmetric functions in superspace, are invariant under the diagonal action of the symmetric group on the sets of commuting and anticommuting variables. In this work, we present the superspace extension of the clas...

We tested whether analogical processes can be harnessed to help children learn in a complex, naturalistic learning situation. Specifically, we asked whether a brief analogical training experience could help children learn a key principle of stable construction— namely, the idea of using a diagonal brace to stabilize a structure. The context for this learning was a free construction activity in ...