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Vengono descritte le gare a squadre delle Olimpiadi della Matematica, una competizione annuale molto seguita dagli studenti delle scuole superiori in Italia. Le squadre, composte da sette membri, si allenano durante tutto l'anno e si sfidano con spirito agonistico. Le gare a squadre stimolano la collaborazione alla risoluzione dei problemi e l'aspetto ludico aiuta a rendere la matematica meno temuta., The paper describes the team competitions of the Mathematical Olympiad, an annual competition much awaited by students in Italy. The teams are composed of seven members and they train throughout the year and challenge each other with a competitive spirit. Mathematical team competitions stimulate collaboration in problemsolving and the playful aspect helps to fight the fear of mathematics.

We study the continuous version of a hyperbolic rescaling of a discrete game, called open mancala. The resulting PDE turns out to be a singular transport equation, with a forcing term taking values in , and discontinuous in the solution itself. We prove existence and uniqueness of a certain formulation of the problem, based on a nonlocal equation satisfied by the free boundary dividing the region where the forcing is one (active region) and the region where there is no forcing (tail region). Several examples, most notably the Riemann problem, are provided, related to singularity formation. Interestingly, the solution can be obtained by a suitable vertical rearrangement of a multi-function. Furthermore, the PDE admits a Lyapunov functional.

A handlebody link is a union of handlebodies of positive genus embedded in 3-space, which generalises the notion of links in classical knot theory. In this paper, we consider handlebody links with a genus two handlebody and n-1 solid tori, n > 1. Our main result is the classification of such handlebody links with six crossings or less, up to ambient isotopy.

X-ray crystallography is a powerful method that has significantly contributed to our understanding of the biological function of proteins and other molecules. This method relies on the production of crystals that, however, are usually a bottleneck in the process. For some molecules, no crystallization has been achieved or insufficient crystals were obtained. Some other systems do not crystallize at all, such as nanoparticles which, because of their dimensions, cannot be treated by the usual crystallographic methods. To solve this, whole pair distribution function has been proposed to bridge the gap between Bragg and Debye scattering theories. To execute a fitting, the spectra of several different constructs, composed of millions of particles each, should be computed using a particle–pair or particle–particle (pp) distance algorithm. Using this computation as a test bench for current field-programmable gate array (FPGA) technology, we evaluate how the parallel computation capability of FPGAs can be exploited to reduce the computation time. We present two different solutions to the problem using two state-of-the-art FPGA technologies. In the first one, the main C program uses OmpSs (a high-level programming model developed at the Barcelona Supercomputing Center, that enables task offload to different high-performance computing devices) for task invocation, and kernels are built with OpenCL using reduced data sizes to save transmission time. The second approach uses task and data parallelism to operate on data locally and update data globally in a decoupled task. Benchmarks have been evaluated over an Intel D5005 Programmable Acceleration Card, computing a model of 2 million particles in 81.57 s – 24.5 billion atom pairs per second (bapps)– and over a ZU102 in 115.31 s. In our last test, over an up-to-date Alveo U200 board, the computation lasted for 34.68 s (57.67 bapps). In this study, we analyze the results in relation to the classic terms of speed-up and efficiency, This work was partially supported by the Spanish Government (AEI) and European Union (FEDER) (projects CTQ2017-88948-P, PID2021-124848OB-I00, RTI2018-095232-B-C21, SEV-2015-0493 and TIN2015-65316-P, grant BES-2016-078046) and by the Generalitat de Catalunya (contracts 2017-SGR-1742, 2017-SGR-1414, 2017-SGR-670 and 2017-SGR-1328)., Peer Reviewed, Postprint (published version)

A handlebody link is a union of handlebodies of positive genus embedded in 3-space, which generalises the notion of links in classical knot theory. In this paper, we consider handlebody links with a genus two handlebody and n - 1 solid tori, n > 1. Our main result is the classification of such handlebody links with six crossings or less, up to ambient isotopy.

X-ray crystallography is a powerful method that has significantly contributed to our understanding of the biological function of proteins and other molecules. This method relies on the production of crystals that, however, are usually a bottleneck in the process. For some molecules, no crystallization has been achieved or insufficient crystals were obtained. Some other systems do not crystallize at all, such as nanoparticles which, because of their dimensions, cannot be treated by the usual crystallographic methods. To solve this, whole pair distribution function has been proposed to bridge the gap between Bragg and Debye scattering theories. To execute a fitting, the spectra of several different constructs, composed of millions of particles each, should be computed using a particle-pair or particle-particle (pp) distance algorithm. Using this computation as a test bench for current field-programmable gate array (FPGA) technology, we evaluate how the parallel computation capability of FPGAs can be exploited to reduce the computation time. We present two different solutions to the problem using two state-of-the-art FPGA technologies. In the first one, the main C program uses OmpSs (a high-level programming model developed at the Barcelona Supercomputing Center, that enables task offload to different high-performance computing devices) for task invocation, and kernels are built with OpenCL using reduced data sizes to save transmission time. The second approach uses task and data parallelism to operate on data locally and update data globally in a decoupled task. Benchmarks have been evaluated over an Intel D5005 Programmable Acceleration Card, computing a model of 2 million particles in 81.57 s - 24.5 billion atom pairs per second (bapps)- and over a ZU102 in 115.31 s. In our last test, over an up-to-date Alveo U200 board, the computation lasted for 34.68 s (57.67 bapps). In this study, we analyze the results in relation to the classic terms of speed-up and efficiency

Associated to an embedded surface in the three-sphere, we construct a diagram of fundamental groups, and prove that it is a complete invariant, whereform we deduce complete invariants of handlebody links, tunnels of handlebody links, and spatial graphs. The main ingredients in the proof of the completeness include a generalization of the Kneser conjecture for three-manifolds with boundary proved here, and extensions of Waldhausen's theorem by Evans, Tucker and Swarup. Computable invariants of handlebody links derived therefrom are calculated.

In this paper we first review the covering space method with constrained BV functions for solving the classical Plateau's problem. Next, we carefully analyze some interesting examples of soap films compatible with the covering space method: in particular, the case of a soap film only partially wetting a space curve, a soap film spanning a cubical frame but having a large tunnel, aa soap film that retracts onto its boundary, hence not modelable with the Reifenberg method, and various soap films spanning an octahedral frame.

In this paper, we study the diffusion of a water release into an important real water basin, Lake Garda in northern Italy, coupling a variety of models from hydrodynamics (full Navier-Stokes for the motion of water) to statistics (for the modelling of rain inflow and the time-periodic wind motion on the surface). Using a recent digital bathymetry, we are able to present some novel forecasts of water dynamics, in the presence of an uncommon water release by river Adige into Lake Garda, necessary to prevent flood situations in case of heavy rainfall, and taking into account common inflows, wind speed on the surface and friction on the bottom. The output shows the trajectories of the released particles, which are typically much colder than the existing ones, and may help to individuate critical sites and shores.

We construct a complete invariant of oriented connected closed surfaces in 3, which generalizes the notion of peripheral system of a knot group. As an application, we define two computable invariants to investigate handlebody knots and bi-knotted surfaces with homeomorphic complements. In particular, we obtain an alternative proof of inequivalence of Ishii, Kishimoto, Moriuchi and Suzuki's handlebody knots 51 and 64.