A generalized Milne-Thomson theorem

A Note on the Potential Flow past a Lemniscate and a General Method of Milne-thomson*

Basset's (1885) solution for potential flow past a lemniscate is (a) disproved and (b) reproduced by a naive application of "a general method" of MilneThomson. The correct solution is also given. The result is of interest for Rayleigh scattering, as well as for potential theory. 1. Lemniscate in uniform flow. We seek the complex potential associated with uniform, plane, potential flow past a le...

A Fixed Point Theorem in Generalized D-metric Spaces

A Generalized Cantor Theorem

A well known theorem of Cantor asserts that the cardinal of the power-set of a given set always exceeds the cardinal of the original set. An analogous result for sets having additional structure is the well known theorem that the set of initial segments of a well ordered set always has order type greater than the original set. These two theorems suggest that there should be a similar result for...

A Generalized Winternitz Theorem

We prove that, for every simple polygon P having k ≥ 1 reflex vertices, there exists a point q ∈ P such that every half-polygon that contains q contains nearly 1/2(k + 1) times the area of P . We also give a family of examples showing that this result is the best possible. Mathematics Subject Classification (2010). 51E99.

A Generalized Representer Theorem

Wahba’s classical representer theorem states that the solutions of certain risk minimization problems involving an empirical risk term and a quadratic regularizer can be written as expansions in terms of the training examples. We generalize the theorem to a larger class of regularizers and empirical risk terms, and give a self-contained proof utilizing the feature space associated with a kernel...