## About

41

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## Publications

Publications (41)

Il Laboratorio per la Ricerca e la Sperimentazione di Nuove Tecnologie Assistive per le STEM "S. Polin" fa parte del Dipartimento di Matematica “G.Peano” dell’Università di Torino e opera nell'ambito della ricerca e della sperimentazione di nuove tecnologie assistive per lo studio delle STEM (Science, Technology, Engineering and Mathematics). Prend...

We present AudioFunctions.web, a web app that uses sonification, earcons and speech synthesis to enable blind people to explore mathematical function graphs. The system is designed for personalized access through different interfaces (touchscreen, keyboard, touchpad and mouse) on both mobile and traditional devices, in order to better adapt to diff...

AudioFunctions.web is a web-based system that enables blind people to explore mathematical function graphs. It uses sonification, earcons and speech synthesis to convey the overall shape of a function graph, its key points of interest, and accurate quantitative information at any given point. The system can be directly linked from digital documents...

In this paper we study the accessibility by visually impaired people of the learning management system (LMS) Moodle 2. The study is conducted by testing four different visually impaired subjects, with different degrees of disability and performing different tasks connected to different roles in the LMS. A peculiar focus is given to the accessibilit...

Accessing mathematical formulae within digital documents is challenging for blind people. In particular, document formats designed for printing, such as PDF, structure math content for visual access only. While accessibility features exist to present PDF content non-visually, formulae support is limited to providing replacement text that can be rea...

Assistive technologies for visually impaired people (screen readers and braille displays) perform satisfactorily with regard to digital documents containing alphabet characters, but they still have a long way to go as far as formulae and graphs are concerned. In general, the most spread digital documents are in PDF format. However, in the case of m...

Optical Character Recognition software (OCR) are important tools for obtaining accessible texts. We propose the use of artificial neural networks (ANN) in order to develop pattern recognition algorithms capable of recognizing both normal texts and formulae. We present an original improvement of the backpropagation algorithm. Moreover, we describe a...

Si descrivono due esperienze formative (una in contesto scolastico, l'altra rivolta al mondo del lavoro) nelle quali la matematica, se presentata e utilizzata secondo criteri di accessibilità, rappresenta un significativo strumento di inclusione
.

We provide a brief overview on the most common systems used to deal with university teaching
materials (UTM) with mathematical contents, highlighting their problems in terms of accessibility. We
shall describe some instruments and methods that universities could offer to visually impaired students
for reading UTM and we shall point out software ena...

We first study the linear eigenvalue problem for a planar Dirac system in the
open half-line and describe the nodal properties of its solution by means of
the rotation number. We then give a global bifurcation result for a planar
nonlinear Dirac system in the open half-line. As an application, we provide a
global continuum of solutions of the nonli...

In this paper we deal with the existence of unbounded orbits of the map {θ1 = θ + 1/ρ[μ(θ)]-l1(ρ)] + h1 (ρ, θ), ρ1 = ρ - μ'(θ) + l2(ρ) + h2(ρ, θ) where μ is continuous and 2π-periodic, l1, l2 are continuous and bounded, h1(ρ, θ) = o(ρ-1), h2(ρ, θ) = o(1), for ρ → +∞. We prove that every orbit of the map tends to infinity in the future or in the pas...

Dedicated, with gratefulness and friendship, to Professor Fabio Zanolin on the occasion of his 60th birthday Abstract. We deal with a boundary value problem associated to a second order singular equation in the open interval (0, 1]. We first study the eigenvalue problem in the linear case and discuss the nodal properties of the eigenfunctions. We t...

We prove a multiplicity result for a class of strongly indefinite nonlinear second order asymptotically linear systems with Dirichlet boundary conditions. The key idea for the proof is to bring together the classical shooting method and the Maslov index of the linear Hamiltonian systems associated to the asymptotic limits of the given nonlinearity.

We deal with a boundary value problem on the half-line for planar systems of Dirac type. We first study the eigenvalue problem in the linear case and define an index for nontrivial solutions. We then give a global bifurcation result for nonlinear problems.

We study a second order scalar equation of the form x′′+V′(x) = p(t), where p is a π-perodic function and V is a singular potential. We give sufficient conditions on V, p ensuring that all solutions are bounded; we prove the existence of Aubry–Mather sets as well.

We prove the existence of quasi-periodic solutions and of Aubry-Mather sets for a resonant reversible equation of the form x00 +ax+ bx +'(x) +f(x;x0;t) = p(t); the functions p and f are 2 -periodic in t and the perturbation ' is bounded.

We prove a multiplicity result for the two-point boundary value problem associated to a second order equation of the form
¶¶¶¶ where satisfies a sublinear condition at x = 0 and no assumption at infinity is required. We use a topological degree method based on a continuation theorem and on
the performance of a time-map technique for an autonomous p...

In this paper it is studied the Dirichlet problem associated to the planar system z0 = JrF(t,z). We consider the situation where the Hamiltonian F satisfies a superquadratic-type condition at infinity. By means of a bifurcation argument we prove the existence of infinitely many solutions. These solutions are distinguished by the Maslov index of an...

In this paper, we are concerned with the existence of unbounded orbits of the mapping θ1 = θ + 2π + 1/ρ μ(θ) + o(ρ-1), ρ1 = ρ + c - μ′(θ) + o(1), ρ→∞, where c is a constant and μ(θ) is 2π-periodic. Assume that c≠0, that μ(θ) is non-negative (or non-positive) and that μ(θ) has finitely many degenerate zeros in [0,2π]. We prove that every orbit of th...

In this paper we study bifurcation from simple eigenvalues for systems of differential equations; we prove the existence of global bifurcating branches of solutions on which the Maslov index of suitable associated linear systems is preserved.

In this paper we are concerned with a system of second-order differential equations of
the form $x''+A(t,x)x=0$, $t\in [0,\pi]$, $x\in {{\bf R}}^N$, where $A(t,x)$ is a
symmetric $N\times N$ matrix. We concentrate on an asymptotically linear situation and we
prove the existence of multiple solutions to the Dirichlet problem associated to the
system...

It is proved the existence of Aubry-Mather sets and infinitely many subharmonic solutions to an equation of the form u″+au+−bu−+φ(u)=p(t), where u+=max{u,0}, u−=max{−u,0}, is continuous, is continuous and 2π-periodic. We deal with the situation when a≠b are two positive constants satisfying .

The existence of 2π-periodic solutions of the second-order differential equation x″ + f(x)x′ + ax+ - bx- + g(x) = p(t), n ∈ ℕ, where a, b satisfy 1/ √a + 1/ √b = 2/n and p(t) = p(t + 2π), t ∈ ℝ, is examined. Assume that limits lim x→±∞F(x) = F(±∞) (F(x) = ∫ 0x f(u)du) and limx→±∞ g(x) = g(±∞) exist and are finite. It is proved that the equation has...

We prove the existence and multiplicity of solutions, with prescribed nodal properties, for a BVP associated with a system of asymptotically linear second order equations. The applicability of an abstract continuation theorem is ensured by upper and lower bounds on the number of zeros of each component of a solution.

In this paper we are concerned with a differential equation of the form, (x) double over dot + c(x) over dot + q(t)g(x) = 0, t epsilon (a, b), where -infinity less than or equal to a < b less than or equal to + infinity, q has infinitely many zeros in (a, b), and g is superlinear. We prove the existence of solutions with prescribed nodal properties...

In this paper we are concerned with the existence and multiplicity of radial solutions to the BVP
whereB is an open ball in ℝK and u↦∇·(a(|∇u|)∇u) is a nonlinear differential operator (e.g. the plaplacian or the mean curvature operator). The function f is defined in a neighborhood of u=0 and satisfies a «sublinear»-type growth condition for u→0. We...

In this paper we study the existence of radial solutions to sublinear systems of elliptic equations. We first give a multiplicity result on solutions with prescribed nodal properties; then we show the existence of positive solutions. The proofs are based on topological degree arguments.

An ordinary differential equation with a two-point boundary condition is considered. The asymptotically linear case of this equation is analyzed. Existence results for this equation and boundary condition with such a nonlinearity are obtained by a condition which expresses a `non-resonant' behaviour of f with respect to the classical Fucik spectrum...

Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. The JSTOR Archive is a trusted digital repository providing for long-term preservation and access to leading academic journals and scholarly literature from around the world. The Archive is supported...

We show how topological degree techniques can be used to prove the existence of periodic solutions for some superlinear functional differential equations. A continuation theorem particularly suitable when no a priori bounds exist is stated. Applications are then given to the periodic solutions of a planar system of the form z ' (t)=JH ' (z(t)) + p...

The problem of the existence of T-periodic solutions for the differential system x ' =F(t,x), where F: [0,T]×ℝ m ×ℝ m ↦ℝ m is a Carathéodory function, is considered. There are established solvability results of the periodic BVP in the special case of even space dimension. Comparison with existing results in the literature and many applications are...

We prove the existence of multiple solutions to the Dirichlet problem associated to an asymptotically linear Hamiltonian system in ℝ 2N ,N≥1. Solutions are distinguished by means the Maslov index of suitable auxiliary linear systems.

## Projects

Project (1)

The project originates from the necessity of the deployment and use of new technologies for access to higher scientific education by young people with disabilities (both sensorial and motor).
The project, developed in its technological aspects in the Department of Mathematics "G. Peano", University of Turin, is in collaboration with the Office of Disabled Students and the Department of Philosophy and Educational Sciences.