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We study full exact functors between triangulated categories. With some hypotheses on the source category we prove that it admits an orthogonal decomposition into two pieces such that the functor restricted to one of them is zero while the…

Images generated by a transmission electron microscope (TEM) are blurred by aberrations from the objective lens and can be difficult to interpret correctly. One possible solution to this problem is to reconstruct the so-called exit wave,…

Microwave imaging is commonly based on the solution of linearized inverse scattering problems by matched filtering algorithms, i.e., by applying the adjoint of the forward scattering operator to the observation data. A more rigorous…

It is often said that the fundamental problem of causal inference is a missing data problem -- the comparison of responses to two hypothetical treatment assignments is made difficult because for every experimental unit only one potential…

We proposed a method to achieve superresolved optical imaging without beating the diffraction limit of light. This is achieved by magnifying the ideal optical image of the object through higher-order spatial frequency generation while…

From the fundamental requirement of causality, we derive a rigorous criterion of negative refraction (left-handedness). This criterion imposes the lower limits on the electric and magnetic losses in the region of the negative refraction. If…

We examine the Seidel aberrations of thin spherical lenses composed of media with refractive index not restricted to be positive. We find that consideration of this expanded parameter space allows reduction or elimination of more…

A fundamental problem in computer vision is that of inferring the intrinsic, 3D structure of the world from flat, 2D images of that world. Traditional methods for recovering scene properties such as shape, reflectance, or illumination rely…

When a Monte Carlo algorithm is used to evaluate a physical observable A, it is possible to slightly modify the algorithm so that it evaluates simultaneously A and the derivatives $\partial$ $\varsigma$ A of A with respect to each…

Electron and x-ray microscopes allow one to image the entire, unlabeled structure of hydrated materials at a resolution well beyond what visible light microscopes can achieve. However, both approaches involve ionizing radiation, so that…

We discuss the claims of the comment at arXiv.org:physics/0609234. We show that A.V. Kildishev et al. misread our method of extracting of optical constants of nanostructured films. The theoretical calculations performed in the comment…

A reduction of the Maxwell's system to a Fredholm second-kind integral equation with weakly singular kernel is given for electromagnetic (EM) wave scattering by one and many small bodies. This equation is solved asymptotically as the…

In this article we consider the existence of positive radial solutions for Hessian equations and systems with weights and we give a necessary condition as well as a sufficient condition for a positive radial solution to be large. The method…

This user manual is intended to provide a detailed description on model-based optimization for imaging inverse problem. Theseproblems can be particularly complex and challenging, especially for individuals without prior exposure to convex…

Photonic crystals with a two-dimensional triangular lattice have a conical singularity in the spectrum. Close to this so-called Dirac point, Maxwell's equations reduce to the Dirac equation for an ultrarelativistic spin-1/2 particle. Here…

There exists a class of realizable, active media for which the refractive index cannot be defined as an analytic function in the upper half-plane of complex frequency. The conventional definition of the refractive index based on analyticity…

Coherent diffraction imaging is a high-resolution imaging technique whose potential can be greatly enhanced by applying the extrapolation method presented here. We demonstrate enhancement in resolution of a non-periodical object…

The possibility of an incompletness of the equations of electromagnetism is analyzed using a thought experiment that shows a non-physical behavior according to classical electromagnetism. Basically, from Maxwell equations it is shown that a…

We consider the problem of recovering linear image of unknown signal belonging to a given convex compact signal set from noisy observation of another linear image of the signal. We develop a simple generic efficiently computable nonlinear…

Garay-Avenda\~no \& Zamboni-Rached (2014) defined two classes of axisymmetric solutions of the free Maxwell equations. We prove that the linear combinations of these two classes of solutions cover all totally propagating time-harmonic…