Singularity of the potential function makes quantum tunneling, the case 0 () / V x V x of which is the subject of this article, mathematically underdetermined. To circumvent the difficulties it introduced in physics, a potential singularity cutoff is often used, followed by a reverse limit transition, or is a suitable self-adjoint extension of the Hamiltonian along the entire coordinate axis made. However, both of them somehow affect the singular nature of the problem, and so I discuss here how quantum tunneling will behave if the original singular nature of the Schrodinger equation left untouched. To do this, I use the property of the probability density current that the singularities are mutually destroyed in it. It is found that the mildly singular potential with 01 has a finite, but unusual tunnelling transparency, in particular, a non-zero value at zero energy of the incident particle. Тhe tunneling of 1D Coulomb potential (1 ) exhibits infinitely fast and complete oscillation at the zero energy boundary and a suppression to zero in the highenergy limit. In the more singular region with 1 , the tunneling becomes forbidden, thereby repeating the well-known result of the regularized counterparts.
Key information extraction from unstructured documents is a practical problem in many industries. Machine learning models aimed at solving this problem should efficiently utilize textual, visual, and 2D spatial layout information of the document. Grid based approaches achieve this by representing the document as a 2D grid and feeding it to a fully convolutional encoder-decoder network that solves a semantic instance segmentation problem. We propose a new method for the instance detection branch of that network for the task of automatic information extraction from invoices. Our approach reduces this problem to 1D region detection. The proposed network has fewer parameters and a shorter inference times. Additionally, we suggest a new metric for evaluating the results.
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