We establish existence and non-existence results for entire solutions to the fractional Allen-Cahn equation in R, which vanish on helicoids and are invariant under screw-motion. In addition, we prove that helicoids are surfaces with vanishing nonlocal mean curvature.

We study the effect of a higher-order nonlinearity in the standard Kuramoto-Sivashinsky equation: partial differentialxG(Hx). We find that the stability of steady states depends on dv/dq , the derivative of the interface velocity on the wave vector q of the steady state. If the standard nonlinearity vanishes, coarsening is possible, in principle, only if G is an odd function of Hx. In this case...

We show that for any free Araki-Woods factor M = Γ(HR, Ut) ′′ of type III1, the bicentralizer of the free quasi-free state φU is trivial. Using Haagerup’s Theorem, it follows that there always exists a faithful normal state ψ on M such that (M) ∩M = C.

Article history: Received 25 August 2008 Received in revised form 17 October 2008 Accepted 21 October 2008 Available online 17 November 2008

The production task queue has a great significance for manufacturing resource allocation and scheduling decision. Man-made qualitative queue optimization method has a poor effect and makes the application difficult. A production task queue optimization method is proposed based on multi-attribute evaluation. According to the task attributes, the hierarchical multi-attribute model is established ...