Infinite free set for small measure set mappings

Infinite Set of Equations

The paper deals with t he relative convergence of a d oubly-infini te set of equations pertaining to a boundary value problem in a waveguide. It is shown that the solution for t he equations converges differently for different choices of the co mbination of t he number of equations from the two sets. This is demonstrated by st udying t he co nvergence proper ties of t he truncated set of equati...

Image Feature Set for Correspondence Mappings

We present a method to automatically construct features capable of putting images in correspondence with each other (i.e., registration) without requiring control points or landmarks on the images in question. Our method is based primarily on Principal Component Analysis (PCA) and a suitable image representation. The feature set is a collection of weight vectors and the correspondence mapping i...

A Sard Theorem for Set-Valued Mappings∗†

If F is a set-valued mapping from IRn into IRm with closed graph, then y ∈ IRm is a critical value of F if for some x with y ∈ F (x), F is not metrically regular at (x, y). We prove that the set of critical values of a set-valued mapping whose graph is a definable (tame) set in an o-minimal structure containing additions and multiplications is a set of dimension not greater than m − 1 (resp. a ...

Fixed Point Theorems for Set-valued Mappings

Number-Set Representations for Infinite-State Verification

In order to compute the reachability set of infinite-state models, one needs a technique for exploring infinite sequences of transitions in finite time, as well as a symbolic representation for the finite and infinite sets of configurations that are to be handled. The representation problem can be solved by automata-based methods, which consist in representing a set by a finite-state machine re...