The deliberately prepared one ssDNA/one micelle complex has an unstable toroidal DNA-bound region and stable upper and lower hemispheres, and thus can self-assemble along the plane of the unstable toroidal region into free-suspending films.

Existence and uniqueness theorems for unstable manifolds are well-known. Here we prove certain refinements. Let f : (C, 0) → C be a germ of an analytic diffeomorphism, whose derivative Df(0) has eigenvalues λ1, . . . , λn such that |λ1| ≥ · · · ≥ |λk| > |λk+1| ≥ · · · ≥ |λn|, with |λk| > 1. Then there is a unique k-dimensional invariant submanifold whose tangent space is spanned by the generali...

in this paper we investigate the behavior of solutions, stable and unstable of the solutions a second-order rational difference equation. also we will discuss about the behavior of solutions a the rational system, we show these solutions may be stable or unstable.

this paper addresses the validity of two hypotheses concerning changes of vowel quality in persian. the theory of centralization claims that there is a strong correlation between vowel duration and vowel quality. as vowel duration is shortened in unstressed contexts, the size of the vowel inventory reduces toward the center, leading to considerable overlap between different categories and a red...