Let G1 and G2 be two given graphs. The Ramsey number R(G1, G2) is the least integer r such that for every graph G on r vertices, either G contains a G1 or G contains a G2. We denote by Pn the path on n vertices and Wm the wheel on m + 1 vertices. Chen et al. and Zhang determined the values of R(Pn,Wm) when m 6 n + 1 and when n + 2 6 m 6 2n, respectively. In this paper we determine all the value...

In front wheels driven vehicles, fuel economy can be obtained by summing torques applied to rear wheels. On the other hand, unequal torques applied to rear wheels provides enhanced safety. In this paper, a model with seven degrees of freedom is considered for the vehicle body. Thereafter, power-train subsystems are modeled. Considering an electrical machine on each rear wheel, a fuzzy controlle...

The research on two-wheels balancing robot has gained momentum due to their functionality and reliability when completing certain tasks. This paper presents investigations into the performance comparison of Linear Quadratic Regulator (LQR) and PID-PID controllers for a highly nonlinear 2–wheels balancing robot. The mathematical model of 2-wheels balancing robot that is highly nonlinear is deriv...

The circadian locomotor rhythm of the terrestrial slug, Limax maximus, was measured with activity wheels during exposure to both humid and drying conditions. Slugs kept in wet wheels (100% RH) remained fully hydrated while those in dry wheels (less than 30% RH) experienced progressive dehydration. Transfer of slugs from a wet wheel to a dry wheel resulted in an increase in the intensity and dur...

This paper proposes a control method for wheels to pass over rough terrain. In our previous work, we have developed a holonomic mobile mechanism capable of running over steps. The mechanism realizes omni-directional motion on a flat floor and passes over uneven ground in forward and backward directions. The vehicle has seven special wheels with cylindrical free rollers and two passive body axes...