In this paper we prove two results of nonsmooth analysis involving the Fréchet subdifferential. One of these results provides a necessary optimality condition for an optimization problem which arise naturally from a class of wide studied problems. In the second result we establish a sufficient condition for the metric regularity of a set-valued map without continuity assumptions. 1. Preliminari...

This article is concerned with Alexandroff L-topological spaces and L-co-topological spaces, where L is a commutative, unital quantale. On one hand, an example is given to show that there is a finite strong L-topological space that is not Alexandroff. On the other hand, it is proved that every finite strong L-co-topological space is Alexandroff and that the category of Alexandroff strong L-co-t...

1. Abstract Structural topology optimization often leads to slender structures which are sensitive to geometric imperfections such as the misplacement of material. A robust approach is therefore presented in order to take into account material misplacement in topology optimization problems. A probabilistic approach to robust optimization is followed. Spatially varying geometric imperfections ar...

In this paper we compare the expressive power of elementary representation formats for vague, incomplete or conflicting information. These include Boolean valuation pairs introduced by Lawry and Gonzalez-Rodriguez, orthopairs of sets of variables, Boolean possibility and necessity measures, three-valued valuations, supervaluations. We make explicit their connections with strong Kleene logic and...

The computation of reachable sets of nonlinear dynamic and control systems is an important problem of systems theory. In this paper we consider the computability of reachable sets using Turing machines to perform approximate computations. We use Weihrauch's type-two theory of effectivity for computable analysis and topology, which provides a natural setting for performing computations on sets a...

The set of confidence procedures is identified as a fundamental subset of the set of random sets. This is accomplished by defining a simple a-field on the codomain of a set-valued mapping such that the mapping is a confidence procedure if it is measurable relative to that a-field. The confidence procedure becomes Borei measurable when the a-field is generated by a topology that we also define. ...

Switched-capacitor (SC) signal processing, :ing a sampled-data, analog-circuit technique, has a natural affinity to multiple-valued logic (MVL). Its simplicity in creating and manipulating signedsignals (in the form of voltage or charge) in any desired radix makes the SC topology a unique circuit technique for MVL implementation, especially when the base value is relatively high. In this paper,...

In pointfree topology, a continuous real function on a frame L is a map L(R) → L from the frame of reals into L. The discussion of continuous real functions with possibly infinite values can be easily brought to pointfree topology by replacing the frame L(R) with the frame of extended reals L ( R ) (i.e. the pointfree counterpart of the extended real line R = R ∪ {±∞}). One can even deal with a...

We introduce the point degree spectrum of a represented space as a substructure of the Medvedev degrees, which integrates the notion of Turing degrees, enumeration degrees, continuous degrees, and so on. The notion of point degree spectrum creates a connection among various areas of mathematics including computability theory, descriptive set theory, infinite dimensional topology and Banach spac...