In this paper the concept of soft fuzzy filter on X, soft fuzzy prime filter on X, soft fuzzy ultrafilter on X, soft fuzzy minimal prime filter collections are introduced. The concept of soft fuzzy limit space (X, ltτ ) and the related properties are discussed. The functor ι from the collection of soft fuzzy filters F(X) to the collection of filters on X and the functor ω defined from the colle...

Defining the observable φ canonically conjugate to the number observable N has long been an open problem in quantum theory. Here we show how to define the absolute phase observable Φ ≡ |φ| by suitably restricting the Hilbert space of x and p like variables. This Φ is actually the absolute value of the phase and has the correct classical limit. A correction to the " cosine " C and " sine " S ope...

In this contribution we go through the developments that in the years from 1968 to about 1974 led from the Veneziano model to the bosonic string theory. They include the construction of the N -point amplitude for scalar particles, its factorization through the introduction of an infinite number of oscillators and the proof that the physical subspace was a positive-definite Hilbert space. We als...

In [1], a new state sum model (the “balanced” model) was suggested as a quantum theory of gravity. In [2], a proposal was made to construct a geometrical interpretation of it, and to demonstrate that it gives general relativity in the classical limit. The purpose of this note is to make several advances in the interpretation of the balanced model. First, we outline a shortcoming of the definiti...

A switched sliding mode control strategy for a class of nonlinear uncertain systems is presented in this paper. It is characterized by an event– driven gain reduction mechanism which relies on a decomposition of the system state into regions. By enforcing sliding mode behaviors on a suitable set of sliding manifolds, while avoiding the generation of limit cycles, the proposed strategy proves to...