This is a complementary document to the paper presented in [1], where more detailed proofs are provided for some results. The main paper addresses the problem of trajectory tracking control of autonomous rotorcraft in operation scenarios where only relative position measurements obtained from LiDAR sensors are possible. The proposed approach defines an alternative kinematic model, directly base...

The splitting of invariant manifolds of whiskered (hyperbolic) tori with two frequencies in a nearly-integrable Hamiltonian system, whose hyperbolic part is given by a pendulum, is studied. We consider a torus with a fast frequency vector ω/ √ ε, with ω = (1,Ω) where the frequency ratio Ω is a quadratic irrational number. Applying the Poincaré-Melnikov method, we carry out a careful study of th...

We study the splitting of invariant manifolds of whiskered tori with two or three frequencies in nearly-integrable Hamiltonian systems, such that the hyperbolic part is given by a pendulum. We consider a 2-dimensional torus with a frequency vector ω = (1,Ω), where Ω is a quadratic irrational number, or a 3-dimensional torus with a frequency vector ω = (1,Ω,Ω2), where Ω is a cubic irrational num...

We present a theoretical study of the emission from a superluminal polarization current whose distribution pattern rotates (with an angular frequency ω) and oscillates (with a frequency Ω) at the same time, and which comprises both poloidal and toroidal components. This type of polarization current is found in recent practical machines designed to investigate superluminal emission. We find that...

This paper proposes and validates a novel simulation for thermal non-destructive characterization. An electro-thermal modelling of the sample is adapted for MATLAB-SIMULINK simulation. Though the technique is capable of considering any heat stimuli on an arbitrary sample, the special case of lock-in thermography (LT) with periodic heating is taken up for illustration. A mild-steel sample having...

the tenacity of a graph g, t(g), is de ned by t(g) = min{[|s|+τ(g-s)]/[ω(g-s)]}, where the minimum is taken over all vertex cutsets s of g. we de ne τ(g - s) to be the number of the vertices in the largest component of the graph g - s, and ω(g - s) be the number of components of g - s.in this paper a lower bound for the tenacity t(g) of a graph with genus γ(g) is obtained using the graph's...

In the framework of the paraxial and of the slowly varying envelope approximations, with reference to a normally dispersive medium or to vacuum, I report a new approach to field quantization. The electromagnetic field is given as a continuous superposition of non-dispersive and non-diffracting wave-packets (namely X-waves). This enables a new representation of a pulsed beam as a quantum fluid. ...

We introduce bicircular high-harmonic spectroscopy as a new method to probe dynamical symmetries of atoms and molecules and their evolution in time. Our approach is based on combining a circularly polarized femtosecond fundamental field of frequency ω with its counterrotating second harmonic 2ω. We demonstrate the ability of bicircular high-harmonic spectroscopy to characterize the orbital angu...

In the framework of the paraxial and of the slowly varying envelope approximations, with reference to a normally dispersive medium or to vacuum, I report a new approach to field quantization. The electromagnetic field is given as a continuous superposition of non-dispersive and non-diffracting wave-packets (namely X-waves). This enables a new representation of a pulsed beam as a quantum fluid. ...

BACKGROUND Despite the use of low-osmolar contrast media that have significantly reduced the occurrence of severe adverse reactions, contrast-induced (CI) acute kidney injury (AKI) remains the third cause of AKI in hospitals. We sought to estimate the frequency of CI-AKI among hospitalized patients undergoing image-guided cardiovascular procedures, to quantify the effect of risk factors on the ...