Related papers: On solenoidal-injective and injective ray transfor…
We present a versatile method for full-field, X-ray scattering tensor tomography that is based on energy conservation and is applicable to data obtained using different wavefront modulators. Using this algorithm, we pave the way for…
An overview is given on those theoretical gravitational lensing results that can be formulated in a spacetime setting, without assuming that the gravitational fields are weak and that the bending angles are small. The first part is devoted…
The analysis of contours of scalar fields plays an important role in visualization. For example the contour tree and contour statistics can be used as a means for interaction and filtering or as signatures. In the context of tensor field…
We show that an invariant surface allows to construct the Jacobi vector field along a geodesic and construct the formula for the normal component of the Jacobi field. If a geodesic is the transversal intersection of two invariant surfaces…
Observer-invariance is regarded as a minimum requirement for an appropriate definition of time derivatives. We systematically discuss such time derivatives for surface tensor field and provide explicit formulations for material,…
We present a comprehensive method for the evaluation of a vast class of integrals representing 3-point functions of conformal field theories in momentum space. The method leads to analytic, closed-form expressions for all scalar and…
We reformulate the abelian tensor multiplet on a curved spacetime with at least two supercharges in a cohomological form where all the bosonic and fermionic fields become tensor fields. These tensor fields are rewritten as fields in loop…
Tensor diagrams are a handy way to depict complicated relationships between objects in projective geometry. One of the simpler ones takes two copies of a $3\times 3$ matrix and computes its adjugate. In this paper, we give a geometric…
Relativistic field theory for a vector field on a curved space-time is considered assuming that the Lagrangian field density is quadratic and contains field derivatives of first order at most. By applying standard variational calculus, the…
We prove a sufficient condition for the existence of explicit first integrals for vector fields which admit an integrating factor. This theorem recovers and extends previous results in the literature on the integrability of vector fields…
In this paper we investigate injective generation for graded rings. We first examine the relation between injective generation and graded injective generation for graded rings. We then reduce the study of injective generation for graded…
The goal of inversion is to estimate the model which generates the data of observations with a specific modeling equation. One general approach to inversion is to use optimization methods which are algebraic in nature to define an objective…
Radio-frequency (RF) tomographic imaging is a promising technique for inferring multi-dimensional physical space by processing RF signals traversed across a region of interest. However, conventional RF tomography schemes are generally based…
We reduce boundary determination of an unknown function and its normal derivatives from the (possibly weighted and attenuated) broken ray data to the injectivity of certain geodesic ray transforms on the boundary. For determination of the…
For the coherently driven \Lambda-type three-level systems the general ready-to-calculate expression for the susceptibility tensor at the frequency of the weak probe field is obtained for the arbitrary polarization of the strong coupling…
Higher order tensor inversion is possible for even order. We have shown that a tensor group endowed with the Einstein (contracted) product is isomorphic to the general linear group of degree $n$. With the isomorphic group structures, we…
In this note, we give a generalization of the inversion formulas of Pestov-Uhlmann for the geodesic ray transform of functions and vector fields on simple 2-dimensional manifolds of constant curvature. The inversion formulas given here hold…
We present a reconstruction method that stably recovers the real valued, symmetric tensors compactly supported in the Euclidean plane, from knowledge of their attenuated momenta ray transform. The problem is recast as an inverse boundary…
Waveform inversion is theoretically a powerful tool to reconstruct subsurface structures, but a usually encountered problem is that accurate sources are very rare, causing the computation unstable and divergent. This challenging problem,…
Seismic surface wave tomography uses surface wave information to obtain velocity structures in the subsurface. Due to data noise and nonlinearity of the problem, surface wave tomography often has non-unique solutions. It is therefore…