Related papers: Orange Peels and Fresnel Integrals
We consider the Euler system describing a one-dimensional inviscid flows in space along curves of a certain class. Using differential invariants for the Euler system, we obtain its quotient equation. The solutions of the quotient equation…
Auger analysis of high-aspect ratio contact holes of integrated microelectronic devices is a challenging analytical task. Due to geometrical shadowing the primary electron beam and the energy analyser have not the required direct line of…
We seek to complement Nelson's work on the two-slit experiment by showing that the two-slit process, whose density exhibits the characteristic interference pattern, may be obtained as the model after the beam has reached the screen by means…
This paper improves upon existing data pruning methods for image classification by introducing a novel pruning metric and pruning procedure based on importance sampling. The proposed pruning metric explicitly accounts for data separability,…
Ordinary differential equation (ODE) is widely used in modeling biological and physical processes in science. In this article, we propose a new reproducing kernel-based approach for estimation and inference of ODE given noisy observations.…
An edge-unfolding of a polyhedron is produced by cutting along edges and flattening the faces to a *net*, a connected planar piece with no overlaps. A *grid unfolding* allows additional cuts along grid edges induced by coordinate planes…
Whitening, or sphering, is a common preprocessing step in statistical analysis to transform random variables to orthogonality. However, due to rotational freedom there are infinitely many possible whitening procedures. Consequently, there…
Even in two dimensions, the spectrum of the linearized Euler operator is notoriously hard to compute. In this paper we give a new geometric calculation of the essential spectrum for 2D flows. This generalizes existing results---which are…
We study a popular algorithm for fitting polynomial curves to scattered data based on the least squares with gradient weights. We show that sometimes this algorithm admits a substantial reduction of complexity, and, furthermore, find…
We begin by studying the surface area of an ellipsoid in n-dimensional Euclidean space as the function of the lengths of the semi-axes. We write down an explicit formula as an integral over the unit sphere in n-dimensions and use this…
In this article, we briefly describe various tools and approaches that algebraic geometry has to offer to straighten bent objects. Throughout this article we will consider a specific example of a bent or curved piece of paper which in our…
We explore the possibility of retrieving Auger spectra with FEL radiation. Using a laser pulse of 260 eV photon energy, we study the interplay of photo-ionization and Auger processes following the initial formation of a 2p inner-shell hole…
A mechanical beam chopper consists of a rotating disc of regularly spaced wide slits which allow light to pass through them. A continuous light beam, after passing through the rotating disc, is switched-on and switched-off periodically, and…
We consider the problem of minimizing Euler's elastica energy for simple closed curves confined to the unit disk. We approximate a simple closed curve by the zero level set of a function with values +1 on the inside and -1 on the outside of…
Frequency conversion of non-classical light enables robust encoding of quantum information based upon spectral multiplexing that is particularly well-suited to integrated-optics platforms. Here we present an intrinsically deterministic…
For the optical testing of a large mirror with a long radius of curvature, it is generally necessary to use a single-shot phase-shifting interferometer to take several measurements because the influence of air turbulence on air…
It is shown that a classical optical Fourier processor can be used for the shaping of quantum correlations between two or more photons, and the class of Fourier masks applicable in the multiphoton Fourier space is identified. This concept…
We show that strong photoluminescence (PL) can be induced in single-layer graphene on using an oxygen plasma treatment. PL characteristics are spatially uniform across the flakes and connected to elastic scattering spectra distinctly…
Human faces are one interesting object class with numerous applications. While significant progress has been made in the generic deblurring problem, existing methods are less effective for blurry face images. The success of the…
In 1822 A. Fresnel described an experiment to separate a beam of light into its right- and left- circular polarization components using chiral interfaces. Fresnel's experiment combined three crystalline quartz prisms of alternating…