F and C spectra of fluorinated and partially fluorinated vinyl alkyl ethers

Fluorine, hydrogen, and ¹³C NMR spectral data have been obtained for vinyl alkyl ethers containing fluorines. Some of the molecules are perfluorinated and others include hydrogen, bromine, and chlorine substituents. New generalizations regarding FF spin-spin coupling are developed and used, along with previously recognized correlations, in the confirmation of structures and the assignments of resonances. ¹³C spectroscopy, especially the analysis of ¹³C¹⁹F coupling, is critical in several of the structure determinations. Chlorine isotope effects on fluorine chemical shifts are observed when the chlorine and fluorine are attached to the same carbon, and are also used in the structure analyses. Long-range couplings between fluorines in the vinyl group and fluorines in the alkyl group are interpreted in terms of molecular geometry which allows certain of the alkyl fluorines to “touch” the fluorines cis and gem to the ether oxygen but not the fluorine trans to the oxygen. Two bond ¹³C¹⁹F coupling across the vinyl double bond is found to vary dramatically with the electronegativity of the vinyl substituents in the ethers, in accordance with previous observations for olefins.     

AC susceptibility measurements in some RTiFe11-xCox (R = Dy, Ho, Er) compounds: Spin-reorientation behavior

The DyTiFe_{11 - x}Co_x (x = 0, 1, 3), HoTiFe_{11 - x}Co_x (x = 0, 3) and ErTiFe₁₁ compounds, all exhibiting the T hMn₁₂-type structure, were studied for their ac susceptibility in the temperature range 20–300 K. The Dy- and Ho-containing compounds exhibited spin reorientation from axial to cone to planar, or from axial to cone in the temperature range 250-50 K, as expected. In this structure Dy and Ho with negative second-order Stevens' coefficients (_J < 0) favor planar rare earth sublattice anisotropy, while Fe and Co sublattices favor uniaxial and planar anisotropies, respectively and would be in competition as a function of temperature. A spin-reorientation type of behavior was also observed in the ErTiFe₁₁ compound near 50 K. This observation appears to imply that, in this compound, the higher-order crystal-field terms are important. The magnetization data revealed that in these systems the rare earth and transition metal sublattices coupled antiparallel, as is normally the case in the heavy rare-earth-transition-metal compounds.     

Uncertainty of measurement for summed masses: application to controlled substances

Because sentences for drug possession depend on the mass of the seized drug, testing laboratories must often determine the summed mass of numerous items submitted under a single case. One common practice for this purpose is to continue analyzing and weighing samples until a legal threshold is passed, at which point it is important to inform the court whether the summed mass is significantly above the threshold, or only marginally so. This paper develops a means for estimating the uncertainty of the summed mass for the common situation where the readability, d, of the balance dominates the uncertainty. It is seen that for all sample sizes the uncertainty, UM, is given by the remarkable simple expression UM = (d/2) × [N + SQRT(3N)] + N × CCE, where N is the number of items and CCE is the absolute value of the calibration check error. In most instances, this can be further simplified to UM = N × d.     

Stochastic programming and the option of doing it differently

Option theory and stochastic programming are tightly linked. Most options can be analyzed in both frameworks, and the two approaches support each other in many slightly more complex situations. But this similarity hides some central differences in perspective. This short note tries to focus on one of these, namely the fact that option theory can be applied only to options already identified, while stochastic programming is able to help us find options in contexts where it is not at all clear what they are, and where finding might be more important than valuing.