Search results for " Fisica Matematica"

Analytic solutions of the diffusion-deposition equation for fluids heavir than atmospheric air

2008

A steady-state bi-dimensional turbulent diffusion equation was studied to find the concentration distribution of a pollutant near the ground. We have considered the air pollutant emitted from an elevated point source in the lower atmosphere in adiabatic conditions. The wind velocity and diffusion coefficient are given by power laws. We have found analytical solutions using or the Lie Group Analysis or the Method of Separation of Variables. The classical diffusion equation has been modified introducing the falling term with non-zero deposition velocity. Analytical solutions are essential to test numerical models for the great difficulty in validating with experiments.

CQ*-algebras: Structure properties

1996

Some structure properties of CQ*-algebras are investigated. The usual multiplication of a quasi *-algebra is generalized by introducing a weak- and strong product. The *-semisemplicity is defined via a suitable family of positive sesquilinear forms and some consequences of this notion are derived. The basic elements of a functional calculus on these partial algebraic structures are discussed.

Projector operators in clustering

2016

In a recent paper the notion of {\em quantum perceptron} has been introduced in connection with projection operators. Here we extend this idea, using these kind of operators to produce a {\em clustering machine}, i.e. a framework which generates different clusters from a set of input data. Also, we consider what happens when the orthonormal bases first used in the definition of the projectors are replaced by frames, and how these can be useful when trying to connect some noised signal to a given cluster.

Some Results about Frames

1997

In this paper we discuss some topics related to the general theory of frames. In particular we focus our attention to the existence of different 'reconstruction formulas' for a given vector of a certain Hilbert space and to some refinement of the perturbative approach for the computation of the dual frame.

Multi-resolution analysis in arbitrary Hilbert spaces

1997

We discuss the possibility of introducing a multi-resolution in a Hilbert space which is not necessarily a space of functions. We investigate which of the classical properties can be translated to this more general framework and the way in which this can be done. We comment on the procedure proposed by means of many examples.

Some perturbation results for quasi-bases and other sequences of vectors

2023

We discuss some perturbation results concerning certain pairs of sequences of vectors in a Hilbert space $\Hil$ and producing new sequences which share, with the original ones, { reconstruction formulas on a dense subspace of $\Hil$ or on the whole space}. We also propose some preliminary results on the same issue, but in a distributional settings.

A Formal Passage From a System of Boltzmann Equations for Mixtures Towards a Vlasov-Euler System of Compressible Fluids

2019

A formal asymptotics leading from a system of Boltzmann equations for mixtures towards either Vlasov-Navier-Stokes or Vlasov-Stokes equations of incompressible fluids was established by the same authors and Etienne Bernard in: A Derivation of the Vlasov-Navier-Stokes Model for Aerosol Flows from Kinetic Theory Commun. Math. Sci., 15: 1703–1741 (2017) and A Derivation of the Vlasov-Stokes System for Aerosol Flows from the Kinetic Theory of Binary Gas Mixtures. KRM, 11: 43–69 (2018). With the same starting point but with a different scaling, we establish here a formal asymptotics leading to the Vlasov-Euler system of compressible fluids. Explicit formulas for the coupling terms are obtained i…

Multi-resolution analysis generated by a seed function

2009

In this paper we use the equivalence result originally proved by the author, which relates a multiresolution analysis (MRA) of ℒ2(R) and an orthonormal set of single electron wave functions in the lowest Landau level, to build up a procedure which produces, starting with a certain square-integrable function, a MRA of ℒ2(R). © 2003 American Institute of Physics.

Meccanica Razionale per l'ingegneria

2011

Validation of models for sprays

2016

We consider complex fluids consisting of a dispersed phase (solid particles or liquid droplets) immersed in a gas. A class of models describing the dynamics of such a kind of systems is given by a system of partial differential equations where a kinetic equation, describing the dispersed phase, is coupled to a fluid equation for the background gas. The coupling is given by the drag force exerted by the gas on the dispersed phase. Within this class, we shall analyse the case where the kinetic equation is a Vlasov-type equation and the fluid equation are of Stokes or Navier-Stokes type. We shall discuss the validation problem for this class of models, i.e. the derivation of the equations of t…