Related papers: A concise and universal method for deriving arbitr…
We establish quadratic asymptotics for solutions to special Lagrangian equations with supercritical phases in exterior domains. The method is based on an exterior Liouville type result for general fully nonlinear elliptic equations toward…
We investigate the problem of shaping radially symmetric annular beams into desired intensity patterns along the optical axis. Within the Fresnel approximation, we show that this problem can be expressed in a variational form equivalent to…
We study the problem of recovering a function of the form $f(x) = \sum _{k\in \mathbb{Z} } c_k e^{-(x-k)^2}$ from its phaseless samples $|f(\lambda )|$ on some arbitrary countable set $\Lambda \subseteq \mathbb{R} $. For real-valued…
Paraxial ray tracing procedures have become widely accepted techniques for acoustic models in seismology and underwater acoustics. To date a generic form of these procedures including fluid motion and time dependence has not appeared in the…
Using purely Hamiltonian methods we derive a simple differential equation for the generator of the most general local symmetry transformation of a Lagrangian. The restrictions on the gauge parameters found by earlier approaches are easily…
In this article we consider certain types of weighted generalized functions associated with nondegenerate quadratic forms. Such functions and their derivatives are used for constructing fundamental solutions of iterated ultra-hyperbolic…
We present a new method to study light scattering on non-absorbing spherical particles. This method is based on the Ramsauer approach, a model known in atomic an nuclear physics. Its main advantage is its intuitive understanding of the…
The Gaussian Process Convolution Model (GPCM; Tobar et al., 2015a) is a model for signals with complex spectral structure. A significant limitation of the GPCM is that it assumes a rapidly decaying spectrum: it can only model smooth…
We present a quantum algorithm for efficiently sampling transformed Gaussian random fields on $d$-dimensional domains, based on an enhanced version of the classical moving average method. Pointwise transformations enforcing boundedness are…
We introduce a natural method of computing antiderivatives of a large class of functions which stems from the observation that the series expansion of an antiderivative differs from the series expansion of the corresponding integrand by…
In this paper we discuss a new method which can be used to obtain arbitrarily accurate analytical expressions for the deflection angle of light propagating in a given metric. Our method works by mapping the integral into a rapidly…
We develop a new point of view to introduce families of functions, which can be identified as generalization of the ordinary trigonometric or hyperbolic functions. They are defined using a procedure based on umbral methods, inspired to the…
We describe a generalized formalism, addressing the fundamental problem of reflection and transmission of complex optical waves at a plane dielectric interface. Our formalism involves the application of generalized operator matrices to the…
The transverse field profile of light is being recognized as a resource for classical and quantum communications for which reliable methods of sorting or demultiplexing spatial optical modes are required. Here, we demonstrate,…
We present a new formalism for light beam optics starting with an exact eight-dimensional matrix representation of the Maxwell equations. The Foldy-Wouthuysen iterative diagonalization technique is employed to obtain a Hamiltonian…
In a parametric framework, the paper is devoted to the study of a new estimation procedure for the inverse filter and the level noise in a complex noisy blind discrete deconvolution model. Our estimation method is a consequence of the sharp…
A general explicit form for generating functions for approximating fractional derivatives is derived. To achieve this, an equivalent characterisation for consistency and order of approximations established on a general generating function…
Deformed correlated Gaussian basis functions are introduced and their matrix elements are calculated. These basis functions can be used to solve problems with nonspherical potentials. One example of such potential is the dipole…
We propose a reconstruction of vortex beams based on the implementation of quadratic transformations in the orbital angular momentum. The information is encoded in a superposition of Bessel-like nondiffracting beams. The measurement of the…
Bayesian filtering is a general framework for recursively estimating the state of a dynamical system. Classical solutions such that Kalman filter and Particle filter are introduced in this report. Gaussian processes have been introduced as…