相关论文: Inversion of the Momenta Doppler Transform in two …
A real vector space combined with an inverse for vectors is sufficient to define a vector continued fraction whose parameters consist of vector shifts and changes of scale. The choice of sign for different components of the vector inverse…
The equation of the Doppler shift of two bodies in inertial motion in a reference frame at rest (i.e., stationary reference frame) is derived. In this derivation, the wave-particle duality of photons in the theory of special relativity is…
We present a novel numerical method to the time-harmonic inverse medium scattering problem of recovering the refractive index from near-field scattered data. The approach consists of two stages, one pruning step of detecting the scatterer…
In the paper a two-dimensional integro-differential system is considered. Using some variational methods we give sufficient conditions for the existence and uniqueness of a solution to the considered system. Moreover, we show that the…
In this article, we study Momentum Light Ray Transform (MLRT) on symmetric tensor fields. MLRT is an integral transform in time-space domain ($(t,x)\in \mathbb{R}^{1+n}$), which integrates a scalar function or a tensor field along the light…
Electromagnetic induction methods are a common means for geophysical survey. For soil structures that are invariant in one spatial dimension such as trench structures, we propose a fast forward model based on a 2D response function, taking…
For the first time, a versatile, eyesafe, compact and direct detection Doppler lidar is developed using upconversion single-photon detection method. An all-fiber and polarization maintaining architecture is realized to guarantee the high…
The first part of this paper is devoted to an analysis of moment problems in R^n with supports contained in a closed set defined by finitely many polynomial inequalities. The second part of the paper uses the representation results of…
Determining accurate plasma Doppler (line-of-sight) velocities from spectroscopic measurements is a challenging endeavour, especially when weak chromospheric absorption lines are often rapidly evolving and, hence, contain multiple spectral…
Deterministic two-way transducers with pebbles (aka pebble transducers) capture the class of polyregular functions, which extend the string-to-string regular functions allowing polynomial growth instead of linear growth. One of the most…
We discuss various aspects concerning transformations of local analytic, or formal, vector fields to Poincare-Dulac normal form, and the convergence of such transformations. We first review A.D. Bruno's approach to formal normalization, as…
The retarded vector potential of a point magnetic dipole with an arbitrary time dependence undergoing accelerated relativistic motions is derived. A novel expression for the angular distribution of the radiated power of an arbitrary moving…
By means of the Helmholtz theorem on the decomposition of vector fields, the angular momentum of the classical electromagnetic field is decomposed, in a general and manifestly gauge invariant manner, into a spin component and an orbital…
The accuracy of wavefront reconstruction from discrete slope measurements depends on the sampling geometry, coherence length of the incoming wavefronts, wavefront sensor specifications and the accuracy of the reconstruction algorithm. Monte…
We propose an interferometric method to investigate the non-locality of high-dimensional two-photon orbital angular momentum states generated by spontaneous parametric down conversion. We incorporate two half-integer spiral phase plates and…
The results on the inversion of convolution operators as well as Toeplitz (and block Toeplitz) matrices in the $1$-D (one-dimensional) case are classical and have numerous applications. Last year, we considered the $2$-D case of…
It is found what part of the fixed-energy phase shifts allows one to recover uniquely a compactly supported potential. For example, the knowledge of all phase shifts with even angular momenta is sufficient to recover the above potential.
We theoretically describe the optical computation of the divergence of a two-dimensional vector field, which is composed by the transverse electric field components of an incident light beam. The divergence is computed in reflection at…
A two-fold singularity is a point on a discontinuity surface of a piecewise-smooth vector field at which the vector field is tangent to the surface on both sides. Due to the double tangency, forward evolution from a two-fold is typically…
The vector transform operators are investigated; these operators are used at the solution of boundary value problems in piecewise homogeneous spherically symmetric areas. In particular, examples of transformation operators for vector…