Motivated by problems in the spectral theory of linear operators the authors previously introduced a new concept of variation for functions defined on a nonempty compact subset of the plane. In this paper we examine the algebras of functions of bounded variation one obtains from these new definitions for the case where the underlying compact set is either a rectangle or the unit circle, and com...

We show that flag manifold $$\sigma $$ -models (including $$\mathbb{C}\mathbb{P}^{n-1}$$ , Grassmannian models as special cases) and their deformed versions may be cast in the form of gauged bosonic Thirring/Gross-Neveu-type systems. Quantum mechanically gauging is violated by chiral anomalies, which cancelled adding fermions. conjecture such are integrable check on some examples trigonometrica...

Langmuir waves propagate in fractal complex plasma with characteristics, which may cause some particles to be trapped or causes wave turbulences. This phenomenon appears the form of fractional order equations. Using an effective unified solver, new solitary profiles such as rational, trigonometrically and hyperbolical functions forms are discussed, using derivatives conformable sense. The modul...

We describe the reinforcement learning problem, motivate algorithms which seek an approximation to the Q function, and present new convergence results for two such algorithms.

In this paper, we address the problem of how to seamlessly and without repetition artifacts or visible projective distortion cover the surface of a polygonally-defined model with a texture pattern derived from an acquired 2D image such that the dominant orientation of the pattern will everywhere follow the surface shape in an aesthetically pleasing way. Specifically, we propose an efficient, au...