Related papers: Functions of diffraction correction and analytical…
Ab initio computation of two-dimensional electronic spectra is an expanding field, whose goal is improving upon simple, few-dimensional models often employed to explain experiments. Here, we propose an accurate and computationally…
In this paper, an alternative approximation to the innovation method is introduced for the parameter estimation of diffusion processes from partial and noisy observations. This is based on a convergent approximation to the first two…
We investigate a general system of two coupled harmonic oscillators with cubic nonlinearity. Without damping, the system is Hamiltonian, with the origin as an elliptic equilibrium characterized by two distinct linear frequencies. To…
We present a simple method for calculation of diffraction effects in a beam passing an aperture. It follows the well-known approach of Miyamoto and Wolf, but is simpler and does not lead to singularities. It is thus shown that in the…
Quantum noise in a model of singly resonant frequency doubling including phase mismatch and driving in the harmonic mode is analyzed. The general formulae about the fixed points and their stability as well as the squeezing spectra…
Photoacoustic imaging is the leading technique for deep tissue optical imaging, allowing single-shot imaging at depths. However, its resolution may be limited by acoustic aberrations, caused by natural unknown heterogeneities in the tissue…
Fourier Series is the second of monographs we present on harmonic analysis. Harmonic analysis is one of the most fascinating areas of research in mathematics. Its centrality in the development of many areas of mathematics such as partial…
Accurate fitting formulae to the synchrotron function, $F(x)$, and its complementary function, $G(x)$, are performed and presented. The corresponding relative errors are less than $0.26\%$ and $0.035\%$ for $F(x) $ and $G(x)$, respectively.…
Contactless characterization of mechanical resonances using Fabry-Perot interferometry is a powerful tool to study the mechanical and dynamical properties of atomically thin membranes. However, amplitude calibration is often not performed,…
The common approach to radial distortion is by the means of polynomial approximation, which introduces distortion-specific parameters into the camera model and requires estimation of these distortion parameters. The task of estimating…
This paper is concerned with backward problem for nonlinear space fractional diffusion with additive noise on the right-hand side and the final value. To regularize the instable solution, we develop some new regularized method for solving…
We consider the iterative reconstruction of both the internal geometry and the values of an inhomogeneous acoustic refraction index through a piecewise constant approximation. In this context, we propose two enhancements intended to reduce…
In this paper, we introduce a novel approach for effectively reducing nonlinear distortion in single back-plate condenser microphones, i.e., most MEMS microphones, studio recording condenser microphones, and laboratory measurement…
Spectroscopic measurements can show distorted spectral shapes arising from a mixture of absorbing and scattering contributions. These distortions (or baselines) often manifest themselves as non-constant offsets or low-frequency…
In computational optics, numerical modeling of diffraction between arbitrary planes offers unparalleled flexibility. However, existing methods suffer from the trade-off between computational accuracy and efficiency. To resolve this dilemma,…
In this paper we present a treatment of hypersingular integral equations, which have relevant applications in many problems of wave dynamics, elasticity and fluid mechanics with mixed boundary conditions. The main goal of the present work…
We generalize stochastic resonance to the nonadiabatic limit by treating the double-well potential using two quadratic potentials. We use a singular perturbation method to determine an approximate analytical solution for the probability…
In this paper, it is shown how a combination of approximate symmetries of a nonlinear wave equation with small dissipations and singularity analysis provides exact analytic solutions. We perform the analysis using the Lie symmetry algebra…
On an example of the open nonlinear electrodynamic system - transverse non-homogeneous, isotropic, nonmagnetic, linearly polarized, nonlinear (a Kerr-like dielectric nonlinearity) dielectric layer, the algorithms of solution of the…
The physical interpretation of weak measurements has been the subject of much debate. It is known that anomalous phenomena and results that appear in weak measurements are essentially related to the phase of the quantum system being…