We present a technique to verify safety properties of linear systems (possibly time varying) using very few simulations. For a linear system of dimension n, our technique needs n+ 1 simulation runs. This is in contrast to current simulation based approaches, where the number of simulations either depends upon the number of vertices in the convex polyhedral initial set, or on the proximity of th...

Very broadly speaking, the Fourier transform is a systematic way to decompose “generic” functions into a superposition of “symmetric” functions. These symmetric functions are usually quite explicit (such as a trigonometric function sin(nx) or cos(nx)), and are often associated with physical concepts such as frequency or energy. What “symmetric” means here will be left vague, but it will usually...

Many works can be found in the literature concerning the vibroacoustic modelling of submerged stiffened cylindrical shells, because of high interest in the industrial domain, in particular for aeronautical or naval applications. However, only a few of them take into account non-axisymmetric internal frames, as for instance engine foundations or floor partitions, that can play a role on the vibr...

Intracerebral hemorrhages (ICHs) occur in 24 out of 100,000 people annually and have high morbidity and mortality rates. The standard treatment is conservative. We hypothesize that a patient-specific, mechanical model coupled with a robotic steerable needle, used to aspirate a hematoma, would result in a minimally invasive approach to ICH management that will improve outcomes. As a preliminary ...

In this paper we study symmetry reductions and exact solutions of the shallow water wave (SWW) equation uxxxt + αuxuxt + βutuxx − uxt − uxx = 0, (1) where α and β are arbitrary, nonzero, constants, which is derivable using the so-called Boussinesq approximation. Two special cases of this equation, or the equivalent nonlocal equation obtained by setting ux = U , have been discussed in the litera...

We propose a quantum-classical hybrid algorithm of the power method, here dubbed as quantum to evaluate H^n|?? with computers, where n is non-negative integer, H^ time-independent Hamiltonian interest, and |?? state. show that number gates required for approximating H^n scales linearly in qubits, making it promising application near-term computers. Using numerical simulation, we method can cont...

All beams are a superposition of plane waves, which carry linear momentum in the direction of propagation with no net azimuthal component. However, plane waves incident on a hologram can produce a vortex beam carrying orbital angular momentum that seems to require an azimuthal linear momentum, which presents a paradox. We resolve this by showing that the azimuthal momentum is not a true linear ...