相关论文: Inversion of the Momenta Doppler Transform in two …

We propose a numerical method to solve the Monge-Ampere equation which admits a classical convex solution. The Monge-Ampere equation is reformulated into an equivalent first-order system. We adopt a novel reconstructed discontinuous…

Vector calculus in three-dimensional space is ubiquitous in applications of mathematics in physics and engineering. Its two-dimensional version is, however, quite rare. Here we try to provide a pedagogical account of the subject. It is…

We present an original method for reconstructing a three-dimensional object having two spatial dimensions and one spectral dimension from data provided by the infrared slit spectrograph on board the Spitzer Space Telescope. During…

A binary vector of length $N$ has elements that are either 0 or 1. We investigate the question of whether and how a binary vector of known length can be reconstructed from a limited set of its discrete Fourier transform (DFT) coefficients.…

The formula for the relativistic Doppler effect is investigated in the context of two compelling invariance axioms. The axioms are expressed in terms of an abstract operation generalizing the relativistic addition of velocities. We prove…

We introduce the concept of bi-conformal transformation, as a generalization of conformal ones, by allowing two orthogonal parts of a manifold with metric $\G$ to be scaled by different conformal factors. In particular, we study their…

An approximate method is proposed for the recovery of a compactly supported spherically-symmetric potential from the set of fixed-energy phase-shifts known for all angular momenta. The method reduces the inverse scattering problem to a…

Doppler reflectometry is considered in slab plasma model in the frameworks of analytical theory. The diagnostics locality is analyzed for both regimes: linear and nonlinear in turbulence amplitude. The toroidal antenna focusing of probing…

We give a detailed technical report on the implementation of the algorithm presented in Gravin et al. (Discrete & Computational Geometry'12) for reconstructing an $N$-vertex convex polytope $P$ in $\mathbb{R}^d$ from the knowledge of…

This revisit gives a survey on the analytical methods for the inverse exponential Radon transform which has been investigated in the past three decades from both mathematical interests and medical applications such as nuclear medicine…

Integrable systems in low dimensions, constructed through the symmetry reduction method, are studied using phase portrait and variable separation techniques. In particular, invariant quantities and explicit periodic solutions are…

In our article we consider some algebraical methods which may be useful in some inverse spectral problems. The reconstraction of the matrix from its minors is considered.

The inversion of nabla Laplace transform, corresponding to a causal sequence, is considered. Two classical methods, i.e., residual calculation method and partial fraction method are developed to perform the inverse nabla Laplace transform.…

In this paper we obtain an algorithm towards solving the two-dimensional moment problem. This algorithm gives the necessary and sufficient conditions for the solvability of the moment problem. It is shown that all solutions of the moment…

We prove uniqueness and stability for the inverse boundary value problem of the two dimensional Schr\"odinger equation. We do not assume the potentials to be continuous or even bounded. Instead, we assume that some of their positive…

We outline a general methodology to infer the inductive velocity field vector in solar active regions. For the first time, both the field-aligned and the cross-field velocity components are reconstructed. The cross-field velocity solution…

We consider the problem of reconstruction of planar domains from their moments. Specifically, we consider domains with boundary which can be represented by a union of a finite number of pieces whose graphs are solutions of a linear…

This paper deals with the solution of Maxwell's equations to model the electromagnetic fields in the case of a layered earth. The integrals involved in the solution are approximated by means of a novel approach based on the splitting of the…

Moment closure methods appear in myriad scientific disciplines in the modelling of complex systems. The goal is to achieve a closed form of a large, usually even infinite, set of coupled differential (or difference) equations. Each equation…

In this article we present an improved exact inversion formula for the 3D cone beam transform of vector fields. It is well known that only the solenoidal part of a vector field can be determined by the longitudinal ray transform of a vector…