The presence of symplectic strata improves the Gevrey regularity for sums of squares

We consider a class of operators of the type sum of squares of real analytic vector fields satisfying the Hörmander bracket condition. The Poisson-Treves stratification is associated to the vector fields. We show that if the deepest stratum in the stratification, i.e., the stratum associated to the longest commutators, is symplectic, then the Gevrey regularity of the solution is better than the minimal Gevrey regularity given by the Derridj-Zuily theorem.     

The shape of planar smooth gestures and the convergence of a gesture recognizer

Aequationes mathematicae - In this work we provide the mathematical framework of !FTL, a new gesture recognition algorithm. This allows us to algebraically quantify the notion of shape for a smooth...     

On the norms of quaternionic harmonic projection operators

As a consequence of integral bounds for three classes of quaternionic spherical harmonics, we prove some bounds from below for the $(L^p,L^2)$ norm of quaternionic harmonic projectors, for $p\in [1,2]$.     

Parabolic quasi‐concavity for solutions to parabolic problems in convex rings

We investigate some geometric properties of level sets of the solutions of parabolic problems in convex rings. We introduce the notion of parabolic quasi‐concavity, which involves time and space jointly and is a stronger property than the spatial quasi‐concavity, and study the convexity of superlevel sets of the solutions (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Probing electron transfer dynamics at MgO surfaces by Mg-atom desorption

Ultraviolet excitation of high surface area MgO films using 4.7 eV femtosecond pulses results in neutral Mg-atom desorption with hyperthermal kinetic energies in the range 0.1-0.4 eV. The Mg-atom hyperthermal energies and power dependences are similar to those previously observed using nanosecond pulsed excitation. Femtosecond two-pulse correlation measurements reveal the existence of different dynamical paths for Mg-atom desorption. One mechanism displays a sub-150 fs time scale and involves the simultaneous or near-simultaneous transition of two electrons to a 3-coordinated Mg(2+) site. Other paths display picosecond time scales that we associate with dynamics following electron trapping at 3-coordinated Mg(2+) surface sites.     

Experimental test of two-way quantum key distribution in the presence of controlled noise

We describe the experimental test of a quantum key distribution performed with a two-way protocol without using entanglement. An individual incoherent eavesdropping is simulated and induces a variable amount of noise on the communication channel. This allows a direct verification of the agreement between theory and practice.     

On a spatial Solow model with technological diffusion and nonconcave production function

In this paper the classical Solow model is extended, by considering spatial dependence of the physical capital and technological progress, and by introducing a nonconcave production function. The physical capital and technological progress accumulation equations are governed by semilinear parabolic differential equations which describe their evolution over time and space. The convergence to a steady state according to different hypotheses on the production function is discussed. The analysis is focused on an S-shaped production function, which allows the existence of saddle points and poverty traps. The evolution of this system over time, and its convergence to the steady state is described mainly through numerical simulations.