Let r(G,H) be the smallest integer N such that for any 2-coloring (say, red and blue) of the edges of Kn, n > N there is either a red copy of G or a blue copy of H . Let Kn − K1,s be the complete graph on n vertices from which the edges of K1,s are dropped. In this note we present exact values for r(Km −K1,1,Kn −K1,s) and new upper bounds for r(Km,Kn−K1,s) in numerous cases. We also present som...

Traditional two wheels differential drive normally used on mobile robots have manoeuvrability limitations and take time to sort out. Most teams use two driving wheels (with one or two cast wheels), four driving wheels and even three driving wheels. A three wheel drive with omni-directional wheel has been tried with success, and was implemented on fast moving autonomous mobile robots. This paper...

Using an Electric Differential (ED) in electric vehicle has many advantages such as flexibility and direct torque control of the wheels during cornering and risky maneuvers. Despite its reported successes and advantages, the ED has several problems limits its applicability, for instance, an increment of control loops and an increase of computational effort. In this paper, an electric differenti...

Physical inactivity is associated with the increased risk of developing chronic metabolic diseases. To understand early alterations caused by physical inactivity, we utilize an animal model in which rats are transitioned from daily voluntary wheel running to a sedentary condition. In the hours and days following this transition, adipose tissue mass rapidly increases, due in part to increased li...

INTRODUCTION The Attitude and Orbit Control System (AOCS) plays an essential role in the flight control of a spacecraft. This system usually contains a minimum of three reaction wheels (often 4-5 wheels are used for optimization and redundancy [1]). By accelerating the appropriate wheels, the system can produce a zero-mean reaction torque about any axis to the spacecraft, which enables the spac...

The development of an assistive robotic platform poses exciting engineering and design challenges due to the diversity of possible applications. This article introduces Vizzy, a wheeled humanoid robot with an anthropomorphic upper torso, that combines easy mobility, grasping ability, human-like visual perception, eye-head movements and arm gestures. The humanoid appearance improves user accepta...

The Turán number ex(n,G) is the maximum number of edges in any n-vertex graph that does not contain a subgraph isomorphic to G. We consider a very special case of the Simonovits’s theorem (Simonovits in: Theory of graphs, Academic Press, New York, 1968) which determine an asymptotic result for Turán numbers for graphs with some properties. In the paper we present a more precise result for even ...

An element e of a 3–connected matroid M is essential if neither the deletion nor the contraction of e from M is 3–connected. Tutte’s 1966 Wheels and Whirls Theorem proves that the only 3–connected matroids in which every element is essential are the wheels and whirls. It was proved by Oxley and Wu that if a 3–connected matroid M has a non-essential element, then it has at least two such element...

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...