Various Green functions of the Dirac equation with a magnetic-solenoid field (the superposition of the Aharonov-Bohm field and a collinear uniform magnetic field) are constructed and studied. The problem is considered in 2 + 1 and 3 + 1 dimensions for the natural extension of the Dirac operator (the extension obtained from the solenoid regularization). Representations of the Green functions as ...

A macrostate consisting of N approximately 3.5x10{4} photons in a quantum superposition and entangled with a far apart single-photon state (microstate) is generated. Precisely, an entangled photon pair is created by a nonlinear optical process; then one photon of the pair is injected into an optical parametric amplifier operating for any input polarization state, i.e., into a phase-covariant cl...

In this paper we address the problem of determining and efficiently computing an approximation to the eigenvalues of the negative Laplacian −" on general domain Ω ⊂ R2 subject to homogeneous Dirichlet or Neumann boundary conditions. The basic idea is to look for eigenfunctions as the superposition of generalized eigenfunctions of the corresponding free space operator in the spirit of the classi...

An algorithm is described for transforming a quad tree encoding for a picture into a quad tree for the same picture after application of a general linear operator. The technique relies on algorithms and data structures described previously for the construction and superposition of quad trees. The transformation algorithm is shown to take time O(n + sp + mp), where n is the number of nodes in th...

Training artificial neural networks requires a tedious empirical evaluation to determine a suitable neural network architecture. To avoid this empirical process several techniques have been proposed to automatise the architecture selection process. In this paper, we propose a method to perform parameter and architecture selection for a quantum weightless neural network (qWNN). The architecture ...

An approach is proposed which, given a family of linearly independent functions, constructs the appropriate bi-orthogonal set so as to represent the orthogonal projector operator onto the corresponding subspace. The procedure evolves iteratively and it is endowed with the following properties: i) it yields the desired bi-orthogonal functions avoiding the need of inverse operations ii) it allows...

A linear superposition method was used for modeling the time history of the production blast vibrations and optimizing the blast sequence to reduce vibration levels in Sar-Cheshmeh copper mine, Kerman, Iran. A single-hole blast for modeling and two double-hole blasts with time delays of 25 and 65 ms between two holes for modeling validation were carried out. The generated vibrations were measur...

As we know, observables are associated to Hermitian operators. Given one such operator A we can use it to measure some property of the physical system, as represented by a state Ψ. If the state is in an eigenstate of the operator A, we have no uncertainty in the value of the observable, which coincides with the eigenvalue corresponding to the eigenstate. We only have uncertainty in the value of...