The chapter represents a comparison of ultrapower fields (loosely surreals, hyper-reals, long line) and number fields generated by infinite primes having a physical interpretation in Topological Geometrodynamics. Ultrapower fields are discussed in very physicist friendly manner in the articles of Elemer Rosinger and these articles are taken as a convenient starting point. The physical interpret...

The paper mostly concerns the study of generalized differential properties of the so-called minimal time functions associated, in particular, with constant dynamics and arbitrary closed target sets in control theory. Functions of this type play a significant role in many aspects of optimization, control theory: and Hamilton-Jacobi partial differential equations. We pay the main attention to com...

We propose a method for learning skills by learning kinesthetic skills via trajectory optimization. We recreate demonstrations by optimizing the trajectory to be near the demonstration. We use the trajectory optimizer, TrajOpt to turn distance metrics, the Frechet and Hausdorff distances, into cost functions that penalize a trajectory from deviating from the demonstration. Using a few technique...

the present study aims at indicating the existence and uniqueness result of system in extended colombeaualgebra. the caputo fractional derivative is used for solving the system of odes. in addition, rieszfractional derivative of colombeau generalized algebra is considered. the purpose of introducing rieszfractional derivative is regularizing it in colombeau sense. we also give a solution to a n...

In this paper, the norm attaining operators in Frechet spaces are considered. These characterized based on their density, normality, linearity and compactness. It is shown that image dense for a normal injective operator space, as well its inverse given self-adjoint. A space also to be if adjoint attains condition under which attainability normality of an coincides given. Furthermore, between l...