An explicitly solvable kinetic model for semiconductors

We consider a simple model for the electron Boltzmann equation in a semiconductor and show that specific boundary value problems can be explicitly solved. Cases of both homogeneous and inhomogeneous electric fields are considered.     

Remarks on the modular operator and local observables

In this paper we give a characterization of the modular group of a von Neumann algebra , with a cyclic and separating vector, which provides at the same time a necessary and sufficient condition so that two von Neumann algebras ₁ and ₂, such that ₁₂, are the mutual commutants, i.e. ₁=₂.An application is made to the duality property in Quantum Field Theory, and we give a sufficient condition for PCT invariance in a theory of local observables.Partially supported by C.N.R.     

The torsion-free part of the Ziegler spectrum of orders over Dedekind domains

We study the R-torsion-free part of the Ziegler spectrum of an order Λ over a Dedekind domain R. We underline and comment on the role of lattices over Λ. We describe the torsion-free part of the spectrum when Λ is of finite lattice representation type.     

A generalization of local divergence measures

In this paper we propose a generalization of the concept of the local property for divergence measures. These new measures will be called g-local divergence measures, and we study some of their properties. Once this family is defined, a characterization based on Ling’s theorem is given. From this result, we obtain the general form of g-local divergence measures as a function of the divergence in each element of the reference set; this study is divided in three parts according to the cardinality of the reference set: finite, infinite countable or non-countable. Finally, we study the problem of componible divergence measures as a dual concept of g-local divergence measures.     

A Talenti Comparison Result for Solutions to Elliptic Problems with Robin Boundary Conditions

Comparison results of Talenti type for elliptic problems with Dirichlet boundary conditions have been widely investigated in recent decades. In this paper, we deal with Robin boundary conditions. Surprisingly, contrary to the Dirichlet case, Robin boundary conditions make the comparison sensitive to the dimension, and while the planar case seems to be completely settled, in higher dimensions some open problems are yet unsolved. © 2023 The Authors. Communications on Pure and Applied Mathematics published by Wiley Periodicals LLC.     

Small values of signed harmonic sums

For every $\tau \in \mathbb{R}$ and every integer N, let ${\mathfrak{m}}_N(\tau )$ be the minimum of the distance of τ from the sums ${\sum }_{n=1}^N{s}_n/n$, where $s_1,\dots ,s_n\in \{?1,+1\}$. We prove that ${\mathfrak{m}}_N(\tau )<\exp ?(?C{(\log ?N)}^2)$, for all sufficiently large positive integers N (depending on C and τ), where C is any positive constant less than $1/\log ?4$.     

Modelling pedestrian dynamics into a metro station by thermostatted kinetic theory methods

This paper deals with the modelling of pedestrian dynamics at the entry of a metro station by means of the thermostatted kinetic theory framework. Specifically, the model depicts the time evolution of the pedestrian dynamics at the turnstiles under no panic conditions. The modelling of the microscopic interactions is based on the stochastic game theory and reflects the decision dynamics of the turnstiles pursued by pedestrians. A qualitative analysis is addressed to the equilibrium solutions by means of the classical stability theory of perturbations. Numerical simulations aim at showing the emerging behaviours captured by the model. In particular the model validation is obtained by performing a sensitivity analysis on the parameters and on the initial conditions. Further refinements and research perspective, including the modelling under panic conditions, are discussed in the last section of the paper.     

On the convergence toward nonequilibrium stationary states in thermostatted kinetic models

A differential equation‐based framework is suitable for the modeling of nonequilibrium complex systems if its solution is able to reach, as time goes to infinity, the related nonequilibrium steady states. The thermostatted kinetic theory framework has been recently proposed for the modeling of complex systems subjected to an external force field. The present paper is devoted to the mathematical proof of the convergence of the solutions of the thermostatted kinetic framework towards the related nonequilibrium stationary states. The proof of the main result is gained by employing the Fourier transform and distribution theory arguments.     

Notes on local o‐minimality

We introduce and study some local versions of o‐minimality, requiring that every definable set decomposes as the union of finitely many isolated points and intervals in a suitable neighbourhood of every point. Motivating examples are the expansions of the ordered reals by sine, cosine and other periodic functions (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)