An independent transversal of a graph G $G$ with vertex partition P ${\mathscr{P}}$ is an set intersecting each block in single vertex. Wanless and Wood proved that if has size at least t $t$ the average degree vertices most ∕ 4 $t\unicode{x02215}4$ , then exists. We present construction showing this result optimal: for any ε > 0 $\varepsilon \gt 0$ sufficiently large there forest into parts su...

Induction motors (IMs) are commonly used in various industrial applications. To improve energy consumption efficiency, a reliable IM health condition monitoring system is very useful to detect IM fault at its earliest stage to prevent operation degradation, and malfunction of IMs. An intelligent harmonic synthesis technique is proposed in this work to conduct incipient air-gap eccentricity faul...

If the Moon’s spin evolved from faster prograde rates, it could have been captured into a higher spin–orbit resonance than the current 1:1 resonance. At the current value of orbital eccentricity, the probability of capture into the 3:2 resonance is as high as 0.6, but it strongly depends on the temperature and average viscosity of the Moon’s interior. A warmer, less viscous Moon on a higher ecc...

Using the characteristic property of chordal graphs that they are the intersection graphs of subtrees of a tree, Erich Prisner showed that every chordal graph admits an eccentricity 2approximating spanning tree. That is, every chordal graph G has a spanning tree T such that eccT (v) − eccG(v) ≤ 2 for every vertex v, where eccG(v) (eccT (v)) is the eccentricity of a vertex v in G (in T , respect...