A framework for a physical interpretation of quantum cosmology appropriate to a nonperturbative hamiltonian formulation is proposed. It is based on the use of matter fields to define a physical reference frame. In the case of the loop representation it is convenient to use a spatial reference frame that picks out the faces of a fixed simplicial complex and a clock built with a free scalar field...

Fourier Integral Operators appear naturally in a variety of problems related to hyperbolic partial differential equations. While wavelets and other traditional time-frequency methods have been successfully employed for representing many classes of singular integral operators, these methods are not equally effective in dealing with Fourier Integral Operators. In this paper, we show that the shea...

in this paper we study properties of symbols such that these belong to class of symbols sitting insidesm ρ,φ that we shall introduce as the following. so for because hypoelliptic pseudodifferential operatorsplays a key role in quantum mechanics we will investigate some properties of m−hypoelliptic pseudodifferential operators for which define base on this class of symbols. also we consider maxi...

this paper presents characterizations of m-fuzzifying matroids bymeans of two kinds of fuzzy operators, called m-fuzzifying derived operatorsand m-fuzzifying difference derived operators.

in this paper, we consider weighted composition operators betweenmeasurable differential forms and then some classic properties of these operators are characterized.

The Schrödinger operators on the Newtonian space-time are defined in a way which make them independent on the class of inertial observers. In this picture the Schrödinger operators act not on functions on the space-time but on sections of certain one-dimensional complex vector bundle – the Schrödinger line bundle. This line bundle has trivializations indexed by inertial observers and is associa...

Preface Application-oriented mathematics develops theoretical results and new mathematical concepts, motivated by application, in contrast to " applied mathematics " focusing just on providing and applying mathematical tools for the applied sciences. The application-oriented approach produces results significant both for mathematics and the applied sciences. In this context we developed new con...

Since their discovery in 1927, the Heisenberg Inequalities have become an icon of quantum mechanics [1]. Often inappropriately referred to as the Uncertainty Principle, these inequalities relating the standard deviations of the position and momentum observables to Planck’s constant are one of the cornerstones of the quantum formalism even if the physical interpretation of quantum mechanics rema...