Massive Nordström scalar (density) gravities from universal coupling

Both particle physics and the 1890s Seeliger–Neumann modification of Newtonian gravity suggest considering a “mass term” for gravity, yielding a finite range due to an exponentially decaying Yukawa potential. Unlike Nordström’s “massless” theory, massive scalar gravities are strictly Special Relativistic, being invariant under the Poincaré group but not the conformal group. Geometry is a poor guide to understanding massive scalar gravities: matter sees a conformally flat metric, but gravity also sees the rest of the flat metric, barely, in the mass term. Infinitely many theories exhibit this bimetric ‘geometry,’ all with the total stress–energy’s trace as source. All are new except the Freund–Nambu theory. The smooth massless limit indicates underdetermination of theories by data between massless and massive scalar gravities. The ease of accommodating electrons, protons and other fermions using density-weighted Ogievetsky–Polubarinov spinors in scalar gravity is noted.     

Fuzzy sets do not form a topos

The relationship between fuzzy sets and H-valued sets is briefly examined and a claim of Eytan's that the former comprise the objects of a topos is corrected.     

Approximations for the moments of ruin time in the compound Poisson model

In the classical risk model with Poisson arrivals, we study a functional approach which can be used to obtain new approximation formulae for the moments of the time to ruin. We explain how establishing differentiability of a functional, in appropriate function spaces, may lead to approximations for these moments. We consider various choices for the function spaces, which are suitable both for heavy-tailed and light-tailed claim-size distributions. The results are illustrated by some particular examples.     

Formation of alkyl nitrates from the reaction of branched and cyclic alkyl peroxy radicals with NO

The yields of C₅ and C₆ alkyl nitrates from neopentane, 2-methylbutane, 2-methylpentane, 3-methylpentane, and cyclohexane have been measured in irradiated CH₃ONONO-alkane-air mixtures at 298 ± 2 K and 735-torr total pressure. Additionally, OH radical rate constants for neopentyl nitrate, 3-nitro-2-methylbutane, 2-nitro-2-methylpentane, 2-nitro-3-methylpentane, and cyclohexyl nitrate, relative to that for n-butane, have been determined at 298 ± 2 K. Using a rate constant for the reaction of OH radicals with n-butane of 2.58 × 10^?12 cm³ molecule^?1 s^?1, these OH radical rate constants are (in units of 10^?12 cm³ molecule^?1 s^?1): neopentyl nitrate, 0.87 ± 0.21; cyclohexyl nitrate, 3.35 ± 0.36; 3-nitro-2-methylbutane, 1.75 ± 0.06; 2-nitro-2-methylpentane, 1.75 ± 0.22; and 2-nitro-3-methylpentane, 3.07 ± 0.08. After accounting for consumption of the alkyl nitrates by OH radical reaction and for the yields of the individual alkyl peroxy radicals formed in the reaction of OH radicals with the alkanes studied, the alkyl nitrate yields (which reflect the fraction of the individual RO₂ radicals reacting with NO to form RONO₂) determined were: neopentyl nitrate, 0.0513 ± 0.0053; cyclohexyl nitrate, 0.160 ± 0.015; 3-nitro-2-methylbutane, 0.109 ± 0.003; 2-nitro-2methylbutane, 0.0533 ± 0.0022; 2-nitro-2-methylpentane, 0.0350 ± 0.0096; 3- + 4-nitro-2-methylpentane, 0.165 ± 0.016; and 2-nitro-3-methylpentane, 0.140 ± 0.014. These results are discussed and compared with previous literature values for the alkyl nitrates formed from primary and secondary alkyl peroxy radicals generated from a series of n-alkanes.     

A study of the reaction NO3 + NO2 + M → N2O5 + M(M = N2, O2)

The gas-phase reaction of the NO₃ radical with NO₂ was investigated, using a flash photolysis-visible absorption technique, over the total pressure range 25–400 Torr of nitrogen or oxygen diluent at 298 ± 2 K. The absolute rate constants determined (in units of 10^?13 cm³ molecule^?1 s^?1) at 25, 100, and 400 Torr total pressure were, respectively, (4.0 ± 0.5), (7.0 ± 0.7), and (10 ± 2) for M = N₂ and (4.5 ± 0.5), (8.0 ± 0.4), and (8.8 ± 2.0) for M = O₂. These data show that the third-body efficiencies of N₂ and O₂ are identical, within the error limits, and that previous evaluations for M = N₂ are applicable to the atmosphere. In addition, upper limits were determined for the rate constants of the reactions of the NO₃ radical with methanol, ethanol, and propan-2-ol of ?6 × 10^?16, ?9 × 10^?16, and ?2.3 × 10^?15 cm³ molecule^?1 s^?1, respectively, at 298 ± 2 K.     

The Supramolecular Structural Chemistry of Pentafluorosulfanyl and Tetrafluorosulfanylene Compounds

The analysis of crystal structures of SF₅- or SF₄-containing molecules revealed that these groups are often surrounded by hydrogen or other fluorine atoms. Even though fluorine prefers F⋅⋅⋅H over F⋅⋅⋅F contacts, the latter appeared to be important in many compounds. In a significant number of datasets, the closest F⋅⋅⋅F contacts are below 95 % of the van der Waals distance of two F atoms. Moreover, a number of repeating structural motifs formed by contacts between SF₅ groups was identified, including different supramolecular dimers and infinite chains. Among SF₄-containing molecules, the study focused on SF₄Cl compounds, including the first solid-state structure analyses of these reactive species. Additionally, electrostatic potential surfaces of a series of Ph-SF₅ derivatives were calculated, pointing out the substituent influence on the ability of F⋅⋅⋅X contact formation (X=F or other electronegative atom). Interaction energies were calculated for different dimeric arrangements of Ph-SF₅, which were extracted from experimental crystal structure determinations.     

In vivo sodium-23 magnetic resonance surface coil imaging: Observing experimental cerebral ischemia in the rat

Sodium-23 magnetic resonance imaging can be used to detect and assess experimental cerebral ischemia in the rat. An imaging technique utilizing a surface coil is described to produce sodium magnetic resonance images of good quality and resolution within 10 min. A novel method of hemispheric occlusion showed edema in the right brain of the rat head within 3 hr after injury. The edema was especially pronounced by 12 hr with effects in the right brain, eye and surrounding muscle evident.     

Rate constants for the reaction of (sP) atoms with SO2 (M = N2O) over the temperature range 299–392 K

Third order rate constants have been determined for the reaction O + SO₂ + N₂O → SO₃ + N₂O over the temperature range 299–392 K using a modulation technique. The Arrhenius expression obtained is k₂^N₂O = 3.32 × 10¹⁰ exp[?(2000±400)/RT] liter² mole^?2 s^?1. This temperature dependence is in good agreement with recent flash photolysis-resonance fluorescence measurements using N₂ as a third body.