On a Watson-like Uniqueness Theorem and Gevrey Expansions

We present a maximal class of analytic functions, elements of which are in one-to-one correspondence with their asymptotic expansions. In recent decades it has been realized (B. Malgrange, J. Ecalle, J.-P. Ramis, Y. Sibuya et al.), that the formal power series solutions of a wide range of systems of ordinary (even non-linear) analytic differential equations are in fact the Gevrey expansions for the regular solutions. Watson's uniqueness theorem belongs to the foundations of this new theory. This paper contains a discussion of an extension of Watson's uniqueness theorem for classes of functions which admit a Gevrey expansion in angular regions of the complex plane with opening less than or equal to (\frac \pi k,) where (k) is the order of the Gevrey expansion. We present conditions which ensure uniqueness and which suggest an extension of Watson's representation theorem. These results may be applied for solutions of certain classes of differential equations to obtain the best accuracy estimate for the deviation of a solution from a finite sum of the corresponding Gevrey expansion.Comment: 18 pages, 4 figure

On theorems of Jackson and Bernstein type in the complex plane

We consider best polynomial approximation to functions analytic in a Jordan domain D and continuous on . We relate theorems of Jackson and Bernstein type to the Hölder continuity of the exterior conformal mapping functions for D .Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/41343/1/365_2005_Article_BF02075464.pd

Confinement, phase transitions and non-locality in the entanglement entropy

In this paper we study the conjectural relation between confinement in a quantum field theory and the presence of a phase transition in its corresponding entanglement entropy. We determine the sufficient conditions for the latter and compare to the conditions for having a confining Wilson line. We demonstrate the relation in several examples. Superficially, it may seem that certain confining field theories with a non-local high energy behaviour, like the dual of D5 branes wrapping a two-cycle, do not admit the corresponding phase transition. However, upon closer inspection we find that, through the introduction of a regulating UV-cutoff, new eight-surface configurations appear, that satisfy the correct concavity condition and recover the phase transition in the entanglement entropy. We show that a local-UV-completion to the confining non-local theories has a similar effect to that of the aforementioned cutoff.Comment: 64 pages. Lots of figure

Effects of membrane peptide dynamics on high-resolution magic-angle spinning NMR

In the past fifteen years, interference between molecular dynamics and coherent manipulation of nuclear magnetization in nuclear magnetic resonance (NMR) experiments such as spin decoupling, cross-polarization or magic-angle spinning (MAS) have been identified and studied carefully. Recent experiments performed in our laboratory on model compounds have provided insight into the nature of a perturbation responsible for the broadening of 13C and 15N signals, namely the interference of some molecular motion with 1H-decoupling. The same effect is demonstrated here for the first time in the case of a membrane peptide, gramicidin A (gA), in an hydrated lipid bilayer. The present experiment provides the first successful attempt to observe high-resolution solid-state 13C NMR spectra of a Cα moiety in membrane peptide contained in a lipid bilayer. Furthermore, the development of stategies to circumvent the broadening effect allows the extraction of relevant data concerning the dynamics of gA under physiological conditions

Solid-state NMR for the study of membrane systems: the use of anisotropic interactions

A review with 91 refs. The use of solid-state NMR as a tool to det. the structure of membrane mols. is reviewed with a particular emphasis on techniques that provide information on orientation or order. Expts. reported here have been performed in membranes, rather than in micelles or org. solvents. Several ways to prep. and handle the samples are discussed, like sample orientation and magic-angle spinning (MAS). Results concerning lipids, membrane peptides and proteins are included, as well as a discussion regarding the potential of such methods and their pitfalls. [on SciFinder (R)