Related papers: Inversion Problems for Fourier Transforms of Parti…
The collective absorption and emission of light by an ensemble of atoms is at the heart of many fundamental quantum optical effects and the basis for numerous applications. However, beyond weak excitation, both experiment and theory become…
The well-known discrete Fourier transform (DFT) can easily be generalized to arbitrary nodes in the spatial domain. The fast procedure for this generalization is referred to as nonequispaced fast Fourier transform (NFFT). Various…
The present manuscript consists of inverse problems for a coupled system of wave equations with potential in $\mathbb{R}^3$. By establishing the fundamental solution to the aforementioned operator, we study the uniqueness aspects of the…
The notion of Fourier transform is among the more important tools in analysis, which has been generalized in abstract harmonic analysis to the level of abelian locally compact groups. The aim of this paper is to further generalize the…
Recently, Malik and Ferreyra introduced the $m$-weak core inverse for complex square matrices which generalizes the core-EP inverse, the WC inverse, and therefore the core inverse. The main aim of this paper is to extend the concept of…
While colloids are promising building blocks for the self-assembly of materials with novel microstructures, their numerous tunable parameters inhibit brute force searching for appropriate parameter combinations that yield self-assembly of a…
Over the last decade, the light microscope has become increasingly useful as a quantitative tool for studying colloidal systems. The ability to obtain particle coordinates in bulk samples from micrographs is particularly appealing. In this…
We provide a rigorous convergence proof demonstrating that the well-known semi-analytical Fourier cosine (COS) formula for the inverse Fourier transform of continuous probability distributions can be extended to discrete probability…
If a collection of identical particles is poured into a container, different shapes will fill to different densities. But what is the shape that fills a container as close as possible to a pre-specified, desired density? We demonstrate a…
The coherent process of particle deflection by aligned atomic strings and planes of oriented crystals is accompanied by incoherent scattering by atomic cores. While the coherent particle deflection, described by the axial or planar averaged…
Fourier transforms are ubiquitous mathematical tools in basic and applied sciences. We here report classical and quantum optical realizations of the discrete fractional Fourier transform, a generalization of the Fourier transform. In the…
Inversion of potential field data is a central technique of remote sensing in physics, geophysics, neuroscience and medical imaging. In spite of intense research, uniqueness theorems for potential-field inversion are scarce. Applied studies…
In machine learning and molecular design, there exist two approaches: discriminative and generative. In the discriminative approach dubbed forward design, the goal is to map a set of features/molecules to their respective electronics…
We establish a novel convergent iteration framework for a weak approximation of general switching diffusion. The key theoretical basis of the proposed approach is a restriction of the maximum number of switching so as to untangle and…
We consider the integrable family of symmetric boundary-driven interacting particle systems that arise from the non-compact XXX Heisenberg model in one dimension with open boundaries. In contrast to the well-known symmetric exclusion…
Inverse spectral problems are studied for first-order integro-differential operators on a finite interval. These problems consist in recovering some components of the kernel from one or multiple spectra. Uniqueness theorems are proved for…
Inverse scattering and spectral one-dimensional problems are discussed systematically in a self-contained way. Many novel results, due to the author are presented. The classical results are often presented in a new way. Several highlights…
Many applications require recovering the geometry information of multiple elastic particles based on the scattering information. In this paper, we consider the inverse time-harmonic elastic scattering of multiple rigid particles in three…
We introduce a technique for recovering a sufficiently smooth function from its ray transform over a wide class of curves in a general region of Euclidean space. The method is based on a complexification of the underlying vector fields…
We extend the theory of fast Fourier transforms on finite groups to finite inverse semigroups. We use a general method for constructing the irreducible representations of a finite inverse semigroup to reduce the problem of computing its…