Recently, a number of authors [KS, Oh2, Ro] have independently shown that the universal finite type invariant of rational homology 3-spheres on the level of sl2 can be recovered from the Reshetikhin-Turaev sl2 invariant. An important role in Ohtsuki’s proof [Oh3] plays a map j1 (which joins the legs of 2-legged chinese characters) and its relation to a map α in terms of a power series (on the l...

Let the vertices of a graph such that every two adjacent vertices have different color is a very common problem in the graph theory. This is known as proper coloring of graphs. The possible number of different proper colorings on a graph with a given number of colors can be represented by a function called the chromatic polynomial. Two graphs G and H are said to be chromatically equivalent, if ...

In this paper, the concept of incidence domination number of graphs  is introduced and the incidence dominating set and  the incidence domination number  of some particular graphs such as  paths, cycles, wheels, complete graphs and stars are studied.

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...