Thepaper ismainly devoted to the studyof implicitmultifunction theorems in terms of Fréchet coderivative inAsplund spaces. It sharpens thewell-known implicit multifunction theorem of Ledyaev and Zhu (Set Valued Anal., 7, 209–238, 1999) as well as many recent publications about this significant area.

We prove the existence of viable solutions for an autonomous second-order functional differential inclusions in the case when the multifunction that define the inclusion is upper semicontinuous compact valued and contained in the subdifferential of a proper lower semicontinuous convex function.

The existence of monotone solutions for a second-order functional differential inclusion is obtained in the case when the multifunction that define the inclusion is upper semicontinuous compact valued and contained in the Fréchet subdifferential of a φ-convex function of order two.

In this paper, we further a previous study concerning convergences and pseudo-convergences of sequences of measurable functions on monotone set multifunction spaces. Various considerations concerning operations and the uniqueness of the limit with respect to such convergences are given and several asymptotic structural properties of certain set multifunctions are, in this way, characterized. Ma...

The purpose of this paper is to describe three techniques that are useful for the investigation of monotone sets and multifunctions, and give two applications of them. The three techniques use the “fg–theorem”, the “big convexification” of a subset of E × E∗ or a multifunction E 7→ 2E (we suppose throughout that E is a nontrivial real Banach space with dual E∗), and the “convex function associa...

A new robotic platform for natural orifice surgery is described. The robot is designed to carry multiple tool tips in a single end-effector arm. Design and experimental validation are presented. Although the design is still being improved, results suggest that the new robotic tool will enable dexterous abdominal surgery with improved force transmission capability.

This article presents a non linear multifunction filter design; this design, with minor changes performs as a Media, Median Minimum or Maximum Filter. The analog design block system is based on an ideal macromodel, consisting of VCCS elements, resistances and diodes. The analysis, control variables and limitations are presented. Simulated results in SPICE are presented. Key-Words: Non linear fi...

We introduce multifunction algebras Bτ i where τ is a set of 0 or 1-ary terms used to bound recursion lengths. We show that if for all ` ∈ τ we have ` ∈ O(|x|) then Bτ i = FP p i−1(wit, τ̇), those multifunctions computable in polynomial time with at most O(p(`(x))) queries to a Σpi−1 witness oracle for ` ∈ τ and p a polynomial. We use our algebras to obtain independence results in bounded arithm...