Straightforward conversion of alcohols into dibenzenesulfonimides

The reaction of various alcohols with N-fluorodibenzenesulfonimide and triphenylphosphine leads to the corresponding dibenzenesulfonylated amines in high yields.     

Systematic Errors Associated with the CPMG Pulse Sequence and Their Effect on Motional Analysis of Biomolecules

A theoretical approach to calculate the time evolution of magnetization during a CPMG pulse sequence of arbitrary parameter settings is developed and verified by experiment. The analysis reveals that off-resonance effects can cause systematic reductions in measured peak amplitudes that commonly lie in the range 5–25%, reaching 50% in unfavorable circumstances. These errors, which are finely dependent upon frequency offset and CPMG parameter settings, are subsequently transferred into erroneousT₂values obtained by curve fitting, where they are reduced or amplified depending upon the magnitude of the relaxation time. Subsequent transfer to Lipari–Szabo model analysis can produce significant errors in derived motional parameters, with τ_einternal correlation times being affected somewhat more thanS²order parameters. A hazard of this off-resonance phenomenon is its oscillatory nature, so that strongly affected and unaffected signals can be found at various frequencies within a CPMG spectrum. Methods for the reduction of the systematic error are discussed. Relaxation studies on biomolecules, especially at high field strengths, should take account of potential off-resonance contributions.     

Multiple recurrence and nilsequences

Aiming at a simultaneous extension of Khintchine(X,X,m,T)(X,\mathcal{X},\mu,T) and a set A ? XA\in\mathcal{X} of positive measure, the set of integers n such that A T^2nA T^knA)(A)^k+1-\mu(A{\cap} T^{n}A{\cap} T^{2n}A{\cap} \ldots{\cap} T^{kn}A)>\mu(A)^{k+1}-\epsilon is syndetic. The size of this set, surprisingly enough, depends on the length (k+1) of the arithmetic progression under consideration. In an ergodic system, for k=2 and k=3, this set is syndetic, while for kòf(x)f(Tⁿx)f(T²ⁿx)? f(T^knx)  dm(x)\int{f(x)f(T^{n}x)f(T^{2n}x){\ldots} f(T^{kn}x) \,d\mu(x)} , where k and n are positive integers and f is a bounded measurable function. We also derive combinatorial consequences of these results, for example showing that for a set of integers E with upper Banach density d^*(E)>0 and for all {n ? \mathbbZ\colon d^*(E?(E+n)?(E+2n)?(E+3n)) > d^*(E)⁴-e}\big\{n\in\mathbb{Z}{\colon} d^*\big(E\cap(E+n)\cap(E+2n)\cap(E+3n)\big) > d^*(E)^4-\epsilon\big\}     

Inverse gas chromatography of lignocellulosic fibers coated with a thermosetting polymer: Use of peak maximum and conder and young methods

The Conder and Young (CY) and the peak maximum (PM) methods were used to estimate the retention time of n-alkane probes on chemithermomechanical pulp (CTMP) wood fibers treated with a low molecular weight grade phenol-formaldehyde resin (PFR). Thermodynamic functions (ΔH_a^o, ΔG_a^o, and ΔS_a^o) and the London dispersive component of the surface energy were derived from these retention times. Treated wood fibers show a high energy surface due to the presence of the thermoset resin on their surface. Values of ΔH_a^o obtained from the CY method were higher than those obtained with the PM method at relatively high temperatures and with relatively low molecular weight alkanes. The results from the two methods were identical at low temperature (293 K) and with the relatively high molecular weight alkane n-undecane.     

Photothermal microanalysis of thermal discontinuities in metallic samples

Modeling the behavior of a protective coating during a thermal shock not only requires the knowledge of its own thermophysical characteristics, but also those of the coating–substrate discontinuity. According to its nature, this discontinuity can be modeled as a zero-thickness interface (thermal contact resistance) or a finite thickness layer (thermal third body). This paper presents an experimental device and two associated thermal transfer models developed in view of the microscale characterization of such discontinuities.     

Robinson-Trautman equations and Chandrasekhar's special perturbation of the Schwarzschild metric

A perturbation wave solution of the Robinson-Trautman equations is proved to be a perturbation of the Schwarzschild black hole which describes an outgoing axial gravitational wave and corresponds to a special case of Chandrasekhar's algebraically special perturbation of the Schwarzschild metric.     

Output dynamics and stabilisation of a multi-mode double-clad Yb-doped silica fibre laser

The intensity dynamics of the double-clad Yb fibre laser have been characterised. Stabilisation of the fibre laser intensity by using uniform bi-directional pumping is demonstrated. For the single-end-pumped Yb fibre laser, the output becomes more stable for the shorter fibre length due to the higher threshold of stimulated Brillouin scattering, SBS, and Kerr effects and the reduction of saturated absorber effects caused by any unpumped fibre section. By additional pumping in a double-end-pumped configuration, the output power can be scaled higher before detecting high intensity pulses initiated by SBS in the Yb fibre laser due to the reduction of saturable absorption effect. It is confirmed that uniform pumping enhances the stability of the laser output.