On metric relations of transversals. [I.]

Definable Transversals of Analytic Equivalence Relations

We examine the circumstances under which certain analytic equivalence relations on Polish spaces have definable transversals.

On the design of metric relations

Metric distances and the more general concept of dissimilarities are widely used tools in instance-based learning methods and very especially in the nearestneighbor classification technique. This paper contributes to the design of general dissimilarity measures to increase their utility. The ability to understand the main properties of a hand-crafted dissimilarity measure and to alter them if n...

Notes on Convex Transversals

In this paper, we prove the problem of stabbing a set of disjoint bends by a convex stabber to be NP-hard. We also consider the optimization version of the convex stabber problem and prove this problem to be APX-hard for sets of line segments.

On the relations between the point spectrum of A and invertibility of I + f(A)B

Let A be a bounded linear operator on a Banach space X. We investigate the conditions of existing rank-one operator B such that I+f(A)B is invertible for every analytic function f on sigma(A). Also we compare the invariant subspaces of f(A)B and B. This work is motivated by an operator method on the Banach space ell^2 for solving some PDEs which is extended to general operator space under some ...

Metric Relations among Analog Computers