Everywhere surjections and related topics. Examples and counterexamples

This paper deals with everywhere surjections, i.e. functions defined on a topological space whose restrictions to any non-empty open subset are surjective. We introduce and discuss several constructions in different contexts; some constructions are easy, while others are more involved. Among other things, we prove that there is a vector space of uncountable dimension whose non-zero elements are everywhere surjections from Q to Q; we give an example of an everywhere surjection whose domain is the set of countably infinite real sequences; we construct an everywhere surjective linear map from the Cantor set into itself. Finally, we prove the existence of functions from R to R which are everywhere surjections in stronger senses

Graphs of real functions with pathological behaviors

This paper deals with constructions and properties of unusual function from R to R, as discontinuous additive functions and everywhere surjections.Comment: Soft Computing, 201

Gli angoli alla base di un triangolo isoscele

This paper deals with the celebrated Euclidean theorem about isosceles triangles, comparing different proofs.Comment: in Italia

Una tentazione affascinante

We discuss some aspects of infinity in the history of mathematics

Un'esperienza di Coordinamento

pp.21-2

Insegnare matematica

Il titolo dell'intervento può sembrare da un lato un po' generico, dall'altro impegnativo e forse anche pretenzioso. La mia intenzione è solo parlare della professione di insegnante e, in particolare, dell'insegnante di matematica. Inevitabilmente mi soffermerò su alcuni aspetti e non su altri; mi scuso, in particolare, se trascurerò aspetti legati alle nuove tecnologie.The title of the contribute may seem a little generic on one hand, but on the other hand demanding and perhaps even pretentious. My intention is only to talk about the profession of a teacher and, in particular, of a math teacher. Of course I will focus on some aspects and not on others; I apologize, in particular, if I neglect aspects related to new technologies

Single-grid spectral collocation for the Navier-Stokes equations

The aim of the paper is to study a collocation spectral method to approximate the Navier-Stokes equations: only one grid is used, which is built from the nodes of a Gauss-Lobatto quadrature formula, either of Legendre or of Chebyshev type. The convergence is proven for the Stokes problem provided with inhomogeneous Dirichlet conditions, then thoroughly analyzed for the Navier-Stokes equations. The practical implementation algorithm is presented, together with numerical results

Agri-Food Traceability Management using a RFID System with Privacy Protection

In this paper an agri-food traceability system based on public key cryptography and Radio Frequency Identification (RFID) technology is proposed. In order to guarantee safety in food, an efficient tracking and tracing system is required. RFID devices allow recording all useful information for traceability directly on the commodity. The security issues are discussed and two different methods based on public cryptography are proposed and evaluated. The first algorithm uses a nested RSA based structure to improve security, while the second also provides authenticity of data. An experimental analysis demonstrated that the proposed system is well suitable on PDAs to