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.     

Sums of Two Exact Powers

An asymptotic formula is obtained for the number of representations of an element of a finite field as a weighted sum of two prescribed powers of primitive elements. This generalises previous work on sums of primitive elements, including that relating to some conjectures of Golomb.     

Triple quadrupole mass spectrometry as applied to flame diagnostics: study of the C2H4/N2O/Ar flame

A recently developed research apparatus for characterization of low-pressure premixed flames has been developed and was used to characterize the C₂H₄/N₂O/Ar flame at 20 torr. This instrument incorporates several diagnostic techniques in one apparatus so that individual techniques can be quantitatively compared and the usable detection range (both in terms of resolution and species detection) expanded. Results discussed in this report include mass analysis by triple quadrupole mass spectrometer and temperature measurement by thermocouple. Concentration profiles in the one-dimensional flame include CO, N₂, and C₂H₄, at nominal m/z 28 as well as CO₂ and N₂O at m/z 44.     

Finite Hurwitz braid group actions for Artin groups

We prove that (with two possible exceptions) the Hurwitz braid group action on the sequence of standard generators of an irreducible Artin group has a finite orbit if and only if the Artin group is of finite type (i.e., the corresponding Coxeter group is finite).