A special class of differentiable functions on an infinite integral domain which is not a field is introduced. Some facts about these functions are established and the special case of z is studied in more detail

In this paper we study optimization problems with infinite many inequality constraints on a Banach space where the objective function and the binding constraints are locally Lipschitz‎. ‎Necessary optimality conditions and regularity conditions are given‎. ‎Our approach are based on the Michel-Penot subdifferential.

Simulating frictional contacts remains a challenging research topic in robotics. Recently, differentiable physics emerged and has proven to be key element model-based Reinforcement Learning (RL) optimal control fields. However, most of the current formulations deploy coarse approximations underlying physical principles. Indeed, classic simulators loose precision by casting Nonlinear Complementa...

In this article, the local fractional Homotopy perturbation method is utilized to solve the non-homogeneous heat conduction equations. The operator is considered in the sense of the local fractional differential operator. Comparative results between non-homogeneous and homogeneous heat conduction equations are presented. The obtained result shows the non-differentiable behavior of heat conducti...

on utilizing the spectral representation of selfadjoint operators in hilbert spaces, some error bounds in approximating $n$-time differentiable functions of selfadjoint operators in hilbert spaces via a taylor's type expansion are given.

In early 1999, Professor Frieden of the University of Arizona published a book through Cambridge University Press titled ”Physics from Fisher Information”. It is the purpose of this dissertation to further develop some of his ideas, as well as explore various exotic differentiable structures and their relationship to physics. In addition to the original component of this work, a series of surve...

∆u = ∂2u ∂x1 + ∂2u ∂x2 where x = (x1, x2) ∈ R2 are Cartesian coordinates. Even though the Poisson equation looks very special it is an important model case representing several problems from physics and engineering, e.g. electrostatics, stationary heat transfer and other diffusion problems. Variations of the techniques we will study apply to a wide class of second order so-called elliptic probl...

We address the problem of consensus control second-order nonholonomic systems via distributed under assumption that each vehicle receives measured states from a set neighbors, with bounded, time-varying, but non-differentiable delay. The controller we propose guarantees full consensus, in sense common point may be reached both Cartesian positions on plane and orientations all robots referred to...