let r be a g-graded ring and m be a g-graded r-module. in this article, we introduce the concept of graded weakly classical prime submodules and give some properties of such submodules.

The formation of new aerosol from the gas phase is commonly represented in atmospheric modeling with parameterizations of the steady state nucleation rate. Present parameterizations are based on classical nucleation theory or on nucleation rates calculated with a numerical aerosol model. These parameterizations reproduce aerosol nucleation rates calculated with a numerical aerosol model only im...

We consider the classical limit of the quantum evolution, with some rough potential, of wave packets concentrated near singular trajectories of the underlying dynamics. We prove that under appropriate conditions, even in the case of BV vector fields, the correct classical limit can be selected.

Arrays of aligned carbon nanotubes (CNTs) under compression are known to exhibit a dissipative hysteretic response similar to classical foams. Here, we control the microstructure of the arrays during synthesis using a variable supply of carbon source and catalyst. We control CNT alignment and density along the array height, creating bands of highand low-density regions. We study the dynamic res...

We review some results concerning the semi-classical limit for the nonlinear Schrödinger equation, with or without an external potential. We consider initial data which are either of the WKB type, or very concentrated as the semi-classical parameter goes to zero. We sketch the techniques used according to various frameworks, and point out some open problems.