This paper is concerned with the cubic Szego{double acute} equationi ∂t u = Π (| u |2 u), defined on the L2 Hardy space on the one-dimensional torus T, where Π : L2 (T) → L+2 (T) is the Szego{double acute} projector onto the non-negative frequencies. For analytic initial data, it is shown that the solution remains spatial analytic for all time t ∈ (- ∞, ∞). In addition, we find a lower bound for the radius of analyticity of the solution. Our method involves energy-like estimates of the special Gevrey class of analytic functions based on the ℓ1 norm of Fourier transforms (the Wiener algebra). © 2013 Elsevier Masson SAS. All rights reserved.

The endoplasmic reticulum (ER) consists of a polygonal network of sheets and tubules interconnected by three-way junctions. This network undergoes continual remodeling through competing processes: the branching and fusion of tubules forms new three-way junctions and new polygons, and junction sliding and ring closure leads to polygon loss. However, little is known about the machinery required to generate and maintain junctions. We previously reported that yeast Lnp1 localizes to ER junctions, and that loss of Lnp1 leads to a collapsed, densely reticulated ER network. In mammalian cells, only approximately half the junctions contain Lnp1. Here we use live cell imaging to show that mammalian Lnp1 (mLnp1) affects ER junction mobility and hence network dynamics. Three-way junctions with mLnp1 are less mobile than junctions without mLnp1. Newly formed junctions that acquire mLnp1 remain stable within the ER network, whereas nascent junctions that fail to acquire mLnp1 undergo rapid ring closure. These findings imply that mLnp1 plays a key role in stabilizing nascent three-way ER junctions.