We derive transport equations for the propagation of water wave action in the presence of a static, spatially random surface drift. Using the Wigner distribution W(x,k, t) to represent the envelope of the wave amplitude at position x contained in waves with wavevector k, we describe surface wave transport over static flows consisting of two length scales; one varying smoothly on the wavelength ...

We develop a new envelope-function formalism to describe electrons in slowly-varying inhomogeneously strained semiconductor crystals. A coordinate transformation is used to map a deformed crystal back to a geometrically undeformed structure with deformed crystal potential. The single-particle Schrödinger equation is solved in the undeformed coordinates using envelope function expansion, wherein...

In this paper, we introduce the  probabilistic normed groups. Among other results, we investigate the continuityof inner automorphisms of a group and the continuity of left and right shifts in probabilistic group-norm. We also study midconvex functions defined  on probabilistic normed groups and  give  some results about locally boundedness of such  functions.