Riemann-Hilbert problems for poly-Hardy space on the unit ball

In this paper, we focus on a Riemann–Hilbert boundary value problem (BVP) with a constant coefficients for the poly-Hardy space on the real unit ball in higher dimensions. We first discuss the boundary behaviour of functions in the poly-Hardy class. Then we construct the Schwarz kernel and the higher order Schwarz operator to study Riemann–Hilbert BVPs over the unit ball for the poly- Hardy class. Finally, we obtain explicit integral expressions for their solutions. As a special case, monogenic signals as elements in the Hardy space over the unit sphere will be reconstructed in the case of boundary data given in terms of functions having values in a Clifford subalgebra. Such monogenic signals represent the generalization of analytic signals as elements of the Hardy space over the unit circle of the complex plane.

Problems of optimal transportation on the circle and their mechanical applications

We consider a mechanical problem concerning a 2D axisymmetric body moving forward on the plane and making slow turns of fixed magnitude about its axis of symmetry. The body moves through a medium of non-interacting particles at rest, and collisions of particles with the body's boundary are perfectly elastic (billiard-like). The body has a blunt nose: a line segment orthogonal to the symmetry axis. It is required to make small cavities with special shape on the nose so as to minimize its aerodynamic resistance. This problem of optimizing the shape of the cavities amounts to a special case of the optimal mass transfer problem on the circle with the transportation cost being the squared Euclidean distance. We find the exact solution for this problem when the amplitude of rotation is smaller than a fixed critical value, and give a numerical solution otherwise. As a by-product, we get explicit description of the solution for a class of optimal transfer problems on the circle.

The Riemann-Hilbert method applied to the theory of orthogonal polynomials

Doutoramento em Matemática

Geometric Hamiltonian formulation of a variational problem depending on the covariant acceleration

We consider a second-order variational problem depending on the covariant acceleration, which is related to the notion of Riemannian cubic polynomials. This problem and the corresponding optimal control problem are described in the context of higher order tangent bundles using geometric tools. The main tool, a presymplectic variant of Pontryagin’s maximum principle, allows us to study the dynamics of the control problem.

On the application of contextual IoT service discovery in Information Centric Networks

The continuous flow of technological developments in communications and electronic industries has led to the growing expansion of the Internet of Things (IoT). By leveraging the capabilities of smart networked devices and integrating them into existing industrial, leisure and communication applications, the IoT is expected to positively impact both economy and society, reducing the gap between the physical and digital worlds. Therefore, several efforts have been dedicated to the development of networking solutions addressing the diversity of challenges associated with such a vision. In this context, the integration of Information Centric Networking (ICN) concepts into the core of IoT is a research area gaining momentum and involving both research and industry actors. The massive amount of heterogeneous devices, as well as the data they produce, is a significant challenge for a wide-scale adoption of the IoT. In this paper we propose a service discovery mechanism, based on Named Data Networking (NDN), that leverages the use of a semantic matching mechanism for achieving a flexible discovery process. The development of appropriate service discovery mechanisms enriched with semantic capabilities for understanding and processing context information is a key feature for turning raw data into useful knowledge and ensuring the interoperability among different devices and applications. We assessed the performance of our solution through the implementation and deployment of a proof-of-concept prototype. Obtained results illustrate the potential of integrating semantic and ICN mechanisms to enable a flexible service discovery in IoT scenarios.