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 ...

Biodiversity underlies many of the ecosystem services demanded by humans. For cities, the design of ‘green infrastructures’ or ‘nature-based solutions’ has been proposed to maintain the provisioning of these services and the preservation of biodiversity. It is unclear, however, how such green infrastructure can be implemented, given existing planning practices that generally ignore biodiversity...

In this work, we proposed an effective method based on cubic and pantic B-spline scaling functions to solve partial differential equations of fractional order. Our method is based on dual functions of B-spline scaling functions. We derived the operational matrix of fractional integration of cubic and pantic B-spline scaling functions and used them to transform the mentioned equations to a syste...

In this paper the Feynman path-integral technique is applied for superintegrable potentials on two-dimensional spaces of nonconstant curvature: these spaces are Darboux spaces DI and DII, respectively. On DI there are three and on DII four such potentials, respectively. We are able to evaluate the path integral in the most of the separating coordinate systems, leading to expressions for the Gre...