The Brownian motion in equation (1) is defined on a complete probability space and generates a filtration F . Throughout this appendix, “adapted process” means F (t) adapted. Lemma 1. Let me scale all variables by output. Then, given the conjecture that the saver’s value function only depends on scaled deposits and scaled net transfers, U(D̃,Π̃), the optimization problem is solved by the followin...

The unsmooth boundary will greatly affect motion morphology of a shallow water wave, and a fractal space is introduced to establish a generalized KdV-Burgers equation with fractal derivatives. The semi-inverse method is used to establish a fractal variational formulation of the problem, which provides conservation laws in an energy form in the fractal space and possible solution structures of t...

A 3D system of springs and dashpots is presented to model the motion of a lung tumour during respiration. The main guiding factor in configuring the system is the spatial relationship between abdominal and lung tumour motion. A coupled, non-dimensional triple of ordinary differential equations models the tumour motion when driven by a 3D breathing signal. Asymptotic analysis is used to reduce t...

in the present article, a numerical method is proposed for the numerical solution of thekdv equation by using a new approach by combining cubic b-spline functions. in this paper we convert the kdv equation to system of two equations. the method is shown to be unconditionally stable using von-neumann technique. to test accuracy the error norms2l, ∞l are computed. three invariants of motion are p...

In this research we design a passive controller for an above knee prosthesis. The controller is a linear spring and damper for swing phase motion, parameters of which determined via optimization of adjustment of the prosthesis shank motion with a desired shank angle trajectory comes from experimental data. In this way, we exerted a certain thigh motion, hip movement included, into the system as...

Manual derivation of the dynamic model of a modular robot is almost impossible because it may have very different geometries and DOFS through module reconfiguration. This paper presents an algorithm to automatically generate the closed-form equation of motion of a modular robot from a kinematic graph based representation of the assembly configuration. We consider modular robots with the more ge...

Due to considerable stored energy in surfaces of nano-scales in comparison with the stored energy in their bulk, considering the surface energy is necessary for the analysis of various behaviors of nano-scales for more precise design and manufacturing. In this article, the longitudinal dynamic behavior of nanobars in the presence of the surface energy parameters is studied. To this end, the lon...