Related papers: Certain inequalities involving prolate spheroidal …
Differentiable programming has facilitated numerous methodological advances in scientific computing. Physics engines supporting automatic differentiation have simpler code, accelerating the development process and reducing the maintenance…
By "surface waves" one means a special kind of waves that propagate at the interface between two different media. There exists a large variety of such waves, which are interesting on their own, and sometimes have also practical importance…
The wave operators $W_\pm(H_1,H_0)$ of two selfadjoint operators $H_0$ and $H_1$ are analyzed at asymptotic spectral values. Sufficient conditions for $\|(W_\pm(H_1,H_0)-P_{1}^\mathrm{ac}P_{0}^\mathrm{ac})f(H_0)\| <\infty$ are given, where…
Predicting ocean wave behavior is challenging due to the difficulty in choosing suitable numerical models among many with varying capabilities. This review examines the development and performance of numerical wave models in coastal…
The discrete prolate spheroidal sequences (DPSS's) provide an efficient representation for discrete signals that are perfectly timelimited and nearly bandlimited. Due to the high computational complexity of projecting onto the DPSS basis -…
The spectral problem for self-adjoint extensions is studied using the machinery of boundary triplets. For a class of symmetric operators having Weyl functions of a special type we calculate explicitly the spectral projections in the form of…
In this paper, the Authors establish a new identity for differentiable functions. By the well-known H\"older and power mean inequality, they obtain some integral inequalities related to the convex functions and apply these inequalities to…
Due to growing interest in quantum measurement, control and feedback, we reproduce a manuscript from 1992, presenting a simple physical and mathematical derivation of stochastic differential equations for wave functions of probed quantum…
Wave packet propagation in the basis of interpolating scaling functions (ISF) is studied. The ISF are well known in the multiresolution analysis based on spline biorthogonal wavelets. The ISF form a cardinal basis set corresponding to an…
The quadratic phase Fourier transform has gained much popularity in recent years because of its applications in image and signal processing. However, the QPFT is inadequate for localizing the quadratic phase spectrum which is required in…
Superoscillations are a phenomenon in physics, where linear combinations of low-frequency plane waves interfere almost destructively in such a way that the resulting wave has a higher frequency than any of the individual waves. The…
The Dirichlet problem for the wave equation is a classical example of a problem which is not well-posed. Nevertheless, it has been used to model internal waves oscillating sinusoidally in time, in various situations, standing internal waves…
Following some strong argumentations of differential geometry in the Landau's book, some corrections about errors in the old literature on scalar gravitational waves (SGWs) are given and discussed. In the analysis of the response ofi…
Commonly used wavefront sensors, the Shack Hartmann wavefront sensor and the pyramid wavefront sensor, for example, have large dynamic range or high sensitivity, trading one regime for the other. A new type of wavefront sensor is being…
Ultrasound imaging systems rely on accurate point spread function (PSF) estimation to support advanced image quality enhancement techniques such as deconvolution and speckle reduction. Phase aberration, caused by sound speed inhomogeneity…
Operator eigenvalue problems play a critical role in various scientific fields and engineering applications, yet numerical methods are hindered by the curse of dimensionality. Recent deep learning methods provide an efficient approach to…
In this paper presents the results obtained in the field of spectral theory operators of fractional differentiation. Proven a number of propositions which represents independent interest in the theory of fractional calculus. Introduced…
Self-potential (SP) data are of interest to vadose zone hydrology because of their direct sensitivity to water flow and ionic transport. There is unfortunately little consensus in the literature about how to best model SP data under…
The similarity between the Schr\"odinger equation and the paraxial wave equation permits numerous analogies linking these fields, which is pivotal in advancing both quantum mechanics and wave optics. In this study, we demonstrate the…
Exact reflection and transmission coefficients for supersymmetric shape-invariant potentials barriers are calculated by an analytical continuation of the asymptotic wave functions obtained via the introduction of new generalized ladder…