This article focuses on the approximation of conventional second order derivative via the combined (diamond-α) dynamic derivative on time scales with necessary smoothness conditions embedded. We will show the constraints under which the second order dynamic derivative provides a consistent approximation to the conventional second derivative; the cases where the dynamic derivative approximates t...

This paper presents a Wasserstein attraction approach for solving dynamic mass transport problems over networks. In the problem networks, we start with distribution set of nodes that needs to be “transported” target accounting network topology. We exploit specific structure problem, characterized by computation implicit gradient steps, and formulate an based on discretized flows. As result, our...

We prove that, in all finite generic extensive-form games of perfect information, a continuous-time best response dynamic always converges to a Nash equilibrium component. We show the robustness of convergence by an approximate best response dynamic: whatever the initial state and an allowed approximate best response dynamic, the state is close to the set of Nash equilibria most of the time. In...

In this paper, modified solutions were compared through utilizing three different approximate methods for bar structures. The modifications considered various changes in the initial design. To authors' best of knowledge, the studies have carried out on this matter so far are not broad enough and have considerred the simeltaneous variations of size, geometry and topology on the bar structures. I...