Related papers: Transformation of a wavefunction under changes of …
We revisit the standard representation of the (inverse) Radon transform which is well-known in the mathematical literature. We extend this representation to the case involving the parton distributions. We have found the new additional…
The author proposes the methodology of transformation optics in orthogonal coordinates to obtain the material parameters of the transformation media from the mapping in orthogonal coordinates. Several examples are given to show the…
Image registration is the process of transforming different sets of data into one coordinate system and is required for various remote sensing applications like change detection, image fusion, and other related areas. The effect of…
We discuss the notion of the orbifold transform, and illustrate it on simple examples. The basic properties of the transform are presented, including transitivity and the exponential formula for symmetric products. The connection with the…
A method for the calculation of translationally invariant wave functions for systems of identical fermions with arbitrary potential of pair interaction is developed. It is based on the well-known result that the essential dynamic part of…
We find a formula that relates the Fourier transform of a radial function on $\mathbf{R}^n$ with the Fourier transform of the same function defined on $\mathbf{R}^{n+2}$. This formula enables one to explicitly calculate the Fourier…
The increasing demand for Fourier transforms on geometric algebras has resulted in a large variety. Here we introduce one single straight forward definition of a general geometric Fourier transform covering most versions in the literature.…
At a fundamental level the notion of particle (quantum) comes from quantum field theory. From this point of view we estimate corrections to the free particle wave function due to minimum-length deformed quantum mechanics to the first order…
We study the structure of differential equations of one-dimensional dispersive flows into compact Riemann surfaces. These equations geometrically generalize two-sphere valued systems modeling the motion of vortex filament. We define a…
This paper presents a comprehensive review of the wave-function approach for derivation of the number-resolved Master equations, used for description of transport and measurement in mesoscopic systems. The review contains important…
It is mandatory to know how to operationally define and translate a reference frame into mathematics, in order that a physical interpretation of theory calculations in terms of observational data is possible. The situation is particularly…
In this note we present a description of wave front evolving from an algebraic hypersurface by means of a pull-back of the discriminantal loci of a tame polynomial via a polynomial mapping. As an application we give examples of wave fronts…
Wavefunction collapse is usually seen as a discontinuous violation of the unitary evolution of a quantum system, caused by the observation. Moreover, the collapse appears to be nonlocal in a sense which seems at odds with General…
It is shown that any convolution operator in the time domain can be represented exactly as a multiplication operator in the time-scale (wavelet) domain. The Mellin transform gives a one-to-one correspondence between frequency filters…
The purpose is to study qualitative and quantitative rates of image compression by using different Haar wavelet banks. The experimental results of adaptive compression are provided. The paper deals with specific examples of orthogonal Haar…
In this paper, we construct framelets associated with a sequence of quadrature rules on the simplex $T^{2}$ in $\mathbb{R}^{2}$. We give the framelet transforms -- decomposition and reconstruction of the coefficients for framelets of a…
The windowed ray transform is a natural generalization of the "Analytic-Signal Transform" which is developed to extend arbitrary functions from $\RR^n$ to $\CC^n$. We present several inversion formulas here.
The dynamics of time-dependent coupled oscillator model for the charged particle motion subjected to a time-dependent external magnetic field is investigated. We used canonical transformation approach for the classical treatment of the…
We describe a new wavelet transform, for use on hierarchies or binary rooted trees. The theoretical framework of this approach to data analysis is described. Case studies are used to further exemplify this approach. A first set of…
In this paper Fourier transform of multivariate orthogonal polynomials on the simplex is presented. A new family of multivariate orthogonal functions is obtained by using the Parseval's identity and several recurrence relations are derived.