This paper o ers a way to construct a locally optimal stationary approximation for a nonstationary Gaussian process. In cases where this construction leads to a unique stationary approximation we call it a stationary tangent. This is the case with Gaussian processes governed by smooth n-dimensional correlations. We associate these correlations with equivalence classes of curves in R. These are ...

Let f be an orientation preserving homeomorphism on the circle with several break points, that is, its derivative Df has jump discontinuities at these points. We study Rauzy-Veech renormalizations of piecewise smooth homeomorphisms by considering such maps as generalized interval exchange genus one. Suppose is absolutely continuous each continuity and \(D\ln {Df}\in {\mathbb {L}}_{p}\) for some...

the sugar beet plant has a conical-shaped root and at harvest the tap-root breaks which remains in the soil. as a result, a significant amount of root yield and consequently sugar content is lost. furthermore, the field soil remains in the root fissures and is carried with the root to sugar factory. in rhizomania and nematode-infested areas, the soil movement causes the disease wide spread. in ...