Approximations in Sobolev spaces by prolate spheroidal wave functions

Recently, there is a growing interest in the spectral approximation by the Prolate Spheroidal Wave Functions (PSWFs) ${\psi }_{n,c},c>0$. This is due to the promising new contributions of these functions in various classical as well as emerging applications from Signal Processing, Geophysics, Numerical Analysis, etc. The PSWFs form a basis with remarkable properties not only for the space of band-limited functions with bandwidth c, but also for the Sobolev space $H^s([?1,1])$. The quality of the spectral approximation and the choice of the parameter c when approximating a function in $H^s([?1,1])$ by its truncated PSWFs series expansion, are the main issues. By considering a function $f\in H^s([?1,1])$ as the restriction to $[?1,1]$ of an almost time-limited and band-limited function, we try to give satisfactory answers to these two issues. Also, we illustrate the different results of this work by some numerical examples.     

EPR Studies of the Binding Properties,Guest Dynamics,and Inner‐Space Dimensions of a Water‐Soluble Resorcinarene Capsule

Nitroxide free radicals have been used to study the inner space of one of Rebek’s water‐soluble capsules. EPR and ¹H NMR spectroscopy, ESI‐MS, and DFT calculations showed a preference for the formation of 1:2 complexes. EPR titrations allowed us to determine binding constants (K_a) in the order of 10⁷ M ^?2. EPR spectral‐shape analysis provided information on the guest rotational dynamics within the capsule. The interplay between optimum hydrogen bonding upon capsule formation and steric strain for guest accommodation highlights some degree of flexibility for guest inclusion, particularly at the center of the capsule where the hydrogen bond seam can be barely distorted or slightly disturbed.     

Finite element method for the stress analysis of isotropic cylindrical helical spring

This paper presents an efficient two nodes finite element with six degrees of freedom per node, capable to model the total behaviour of a helical spring. The formulation, which includes the shear deformation effects, is based on the assumed forces hybrid approach. The resultant forces approximation verifies exactly the resultant equilibrium equations. The developed model proves its accuracy compared with other elements. This element permits to get the distribution of different stresses along the spring and through the wire surface by only one element.     

A family of orthonormal wavelet bases with dilation factor 4

In this paper, we study a method for the construction of orthonormal wavelet bases with dilation factor 4. More precisely, for any integer M>0, we construct an orthonormal scaling filter mM(ξ) that generates a mother scaling function ?M, associated with the dilation factor 4. The computation of the different coefficients of ²|mM(ξ)| is done by the use of a simple iterative method. Also, this work shows how this construction method provides us with a whole family of compactly supported orthonormal wavelet bases with arbitrary high regularity. A first estimate of α(M), the asymptotic regularity of ?M is given by α(M)∼0.25M. Examples are provided to illustrate the results of this work.     

Assignment of the EPR spectrum of 5,5-dimethyl-1-pyrroline N-oxide (DMPO) superoxide spin adduct

[structure: see text] Spin trapping consists of using a nitrone or a nitroso compound to "trap" an unstable free radical as a long-lived nitroxide that can be characterized by electron paramagnetic resonance (EPR) spectroscopy. The formation of DMPO-OOH, the spin adduct resulting from trapping superoxide (O(2)(*)(-)) with 5,5-dimethyl-1-pyrroline N-oxide (DMPO), has been exploited to detect the generation of superoxide in a wide variety of biological and chemical systems. The 12-line EPR spectrum of DMPO-OOH has been either reported or mentioned in more than a thousand papers. It has been interpreted as resulting from the following couplings: A(N) approximately 1.42 mT, A(H)beta approximately 1.134 mT, and A(H)gamma(1H) approximately 0.125 mT. However, the DMPO-OOH EPR spectrum has an asymmetry that cannot be reproduced when the spectrum is calculated considering a single species. Recently, it was proposed that the 0.125 mT splitting was misassigned and actually results from the superimposition of two individual EPR spectra associated with different conformers of DMPO-OOH. We have prepared 5,5-dimethyl-[3,3-(2)H(2)]-1-pyrroline N-oxide (DMPO-d(2)), and we showed that the EPR spectrum of the corresponding superoxide spin adduct is composed of only six lines, in agreement with the assignment of the 0.125 mT splitting to a gamma-splitting from a hydrogen atom bonded to carbon 3 of DMPO. This result was supported by DFT calculations including water solvation, and the asymmetry of the DMPO-OOH EPR spectrum was nicely reproduced assuming a chemical exchange between two conformers.     

Probabilistic aspects of finite-fuel,reflected follower problems

The issue is that of following the path of a Brownian particle by a process of bounded total variation and subject to a reflecting barrier at the origin, in such a way as to minimize expected total cost over a finite horizon. We establish the existence of optimal processes and the dynamic programming equations for this question, and show (by purely probabilistic arguments) its relation to an appropriatefamily of optimal stopping problems with absorption at the origin.Work carried out during a visit by the second author at the University Pierre et Marie Curie (Paris VI), and at INRIA (Institut National de Recherche en Informatique et en Automatique). The hospitality of these institutions is gratefully acknowledged.Research supported in part by the U.S. Air Force Office of Scientific Research, under grant AFOSR-86-0203.     

EPR, NMR, and Thermodynamic Evidences for Forced Nuclear Spin–Electron Spin Interactions in the Case of 1-Phenyl-2-Methylpropyl-1,1-Dimethyl-2-Nitroxide (TIPNO) Attached to Permethylated β-Cyclodextrin

In a recent paper (Bardelang et al. in J Org Chem 71:7657–7667, 2006), the deep inclusion of the TIPNO (1-phenyl-2-methylpropyl-1,1-dimethylethyl-2-nitroxide) free radical attached to a permethylated β-cyclodextrin (TRIMEB) into its cavity was questioned. In the present paper it is shown that the results of X-band and W-band electron paramagnetic resonance (EPR) and ¹H nuclear magnetic resonance (NMR) studies of the TIPNO–TRIMEB in the presence of competitors of complexation (1-adamantanol, methyl orange and 1-adamantylamine) are consistent with a situation where the nitroxide is capping the small cavity entrance. The inclusion of the incoming guest was proven by ¹H NMR, whereas no changes in EPR spectra were noticed whatever the competitors’ concentrations. These observations are rationalized in terms of an equilibrium between a nitroxide-capped cyclodextrin (weak complex) and a non-self included form, both species involving competitors’ inclusion without significant EPR spectral changes. These results not only confirm our preliminary findings, but also point out to the peculiar role of the cyclodextrin methoxy crown of the primary rim stabilizing the appended guest by means of weak interactions.