Universally coupled massive gravity,III: dRGT–Maheshwari pure spin-2, Ogievetsky–Polubarinov and arbitrary mass terms

Einstein’s equations were derived for a free massless spin-2 field using universal coupling in the 1950–1970s by various authors; total stress–energy including gravity’s served as a source for linear free field equations. A massive variant was likewise derived in the late 1960s by Freund, Maheshwari and Schonberg, and thought to be unique. How broad is universal coupling? In the last decade four 1-parameter families of massive spin-2 theories (contravariant, covariant, tetrad, and cotetrad of almost any density weights) have been derived using universal coupling. The (co)tetrad derivations included 2 of the 3 pure spin-2 theories due to de Rham, Gabadadze, and Tolley; those two theories first appeared in the 2-parameter Ogievetsky–Polubarinov family (1965), which developed the symmetric square root of the metric as a nonlinear group realization. One of the two theories was identified as pure spin-2 by Maheshwari in 1971–1972, thus evading the Boulware–Deser–Tyutin–Fradkin ghost by the time it was announced. Unlike the previous 4 families, this paper permits nonlinear field redefinitions to build the effective metric. By not insisting in advance on knowing the observable significance of the graviton potential to all orders, one finds that an arbitrary graviton mass term can be derived using universal coupling. The arbitrariness of a universally coupled mass/self-interaction term contrasts sharply with the uniqueness of the Einstein kinetic term. One might have hoped to use universal coupling as a tie-breaking criterion for choosing among theories that are equally satisfactory on more crucial grounds (such as lacking ghosts and having a smooth massless limit). But the ubiquity of universal coupling implies that the criterion does not favor any particular theories among those with the Einstein kinetic term.     

Norming algebras and automatic complete boundedness of isomorphisms of operator algebras

We combine the notion of norming algebra introduced by Pop, Sinclair and Smith with a result of Pisier to show that if and are operator algebras, then any bounded epimorphism of onto is completely bounded provided that contains a norming -subalgebra. We use this result to give some insights into Kadison's Similarity Problem: we show that every faithful bounded homomorphism of a -algebra on a Hilbert space has completely bounded inverse, and show that a bounded representation of a -algebra is similar to a -representation precisely when the image operator algebra -norms itself. We give two applications to isometric isomorphisms of certain operator algebras. The first is an extension of a result of Davidson and Power on isometric isomorphisms of CSL algebras. Secondly, we show that an isometric isomorphism between subalgebras of -diagonals () satisfying extends uniquely to a -isomorphism of the -algebras generated by and ; this generalizes results of Muhly-Qiu-Solel and Donsig-Pitts.

     

Rate constants for the reaction of OH radicals with a series of alkanes and alkenes at 299 ± 2 K

Using methyl nitrite photolysis in air as a source of hydroxyl radicals, relative rate constants for the reaction of OH radicals with a series of alkanes and alkenes have been determined at 299 ± 2 K. The rate constant ratios obtained are: relative to n-hexane = 1.00, neopentane 0.135 ± 0.007, n-butane 0.453 ± 0.007, cyclohexane 1.32 ± 0.04; relative to cyclohexane = 1.00, n-butane 0.341 ± 0.002, cyclopentane 0.704 ± 0.007, 2,3-dimethylbutane 0.827 ± 0.004, ethene 1.12 ± 0.05; relative to propene = 1.00, 2-methyl-2-butene 3.43 ± 0.13, isoprene 3.81 ± 0.17, 2,3-dimethyl-2-butene 4.28 ± 0.21. These relative rate constants are placed on an absolute basis using previous absolute rate constant data and are compared and discussed with literature data.     

Infrared absorptivity of the 9.6 μm ozone band as a function of spectral resolution and abundance

The i.r. absorptivity of the R-branch maximum (9.48 μm) of gaseous ozone was determined at 25°C as a function of spectral resolution and absorbance a/a total pressure of 735 torr of dry air. Ozone samples produced by a high voltage discharge in oxygen, and measured accurately by either a pressure or volume change, were spectroscopically measured in a 57741. environmental chamber at paths up to 69.17 m. A linear relation between spectral slit (Δv) and the ratio of the absorbances (R_v/p) of the observed absorption minimum between the R and Q branches to the absorption maximum of the R-branch was found for cm^-1 < Δv < 10cm^-1 and for absorption up to 48%. The i.r. absorptivity varied approx. 20% (from 3.9 to 4.8 cm^-1 STP) over the range of values for R_v/p studied. Absorptivity was weakly dependent on ozone abundance (w) for w?0.03 cm STP.     

Experimental investigation of chamber-dependent radical sources

While environmental chamber data have been widely used to generate and validate computer models of the chemistry occurring in polluted atmospheres, the effects of the chambers on the gas-phase chemistry being studied have been poorly characterized. In order to investigate such chamber effects, a series of NO_x—air irradiations, with trace levels of organics present to monitor OH radical concentrations, have been carried out in four different environmental chambers (ranging in volume from ～100 to 40,000 L) at varying temperatures, humidities, pressures, and reaction conditions. In addition, a number of control experiments have been carried out to validate the technique for measuring OH radical levels in these irradiations. The data show that unknown sources of OH radicals are present in all of the chambers studied. The data are consistent with the presence of two distinct radical sources: (1) the photolysis of initially present HONO, whose importance increases with increasing NO₂/NO concentration ratios, but which is a minor contributor to the overall radical flux after 30–60 min of irradiation, and (2) a constant (for these NO_x—air irradiations) radical source which dominates beyond approximately the first 60 min of irradiation. The radical input rates, after the first ∽30–60 min of irradiation, are independent of the NO concentration, increase with increasing temperature, humidity, and NO₂ concentration, are proportional to light intensity, and are dependent on the chamber employed. Although the exact nature of this radical source is still undetermined, results of experiments reported here allow a number of possible mechanisms to be ruled, out, and these are discussed.     

Pentafluoro(aryl)‐λ6‐tellanes and Tetrafluoro(aryl)(trifluoromethyl)‐λ6‐tellanes: From SF5 to the TeF5 and TeF4CF3 Groups

The TeF₅ group is significantly underexplored as a highly fluorinated substituent on an organic framework, despite it being a larger congener of the acclaimed SF₅ group. In fact, only one aryl‐TeF₅ compound (phenyl‐TeF₅) has been reported to date, synthesized using XeF₂. Our recently developed mild TCICA/KF approach to oxidative fluorination provides an affordable and scalable alternative to XeF₂. Using this method, we report a scope of extensively characterized aryl‐TeF₅ compounds, along with the first SC‐XRD data on this compound class. The methodology was also extended to the synthesis and structural study of heretofore unknown aryl‐TeF₄CF₃ compounds. Additionally, preliminary reactivity studies unveiled some inconsistencies with previous literature regarding phenyl‐TeF₅. Although our studies conclude that the arene‐based TeF₅ (and TeF₄CF₃) group is not quite as robust as the SF₅ group, we find that the TeF₅ group is more stable than previously thought, thus opening a door to explore new applications of this motif.     

Decompounding random sums: a nonparametric approach

A compound distribution is the distribution of a random sum, which consists of a random number N of independent identically distributed summands, independent of N. Buchmann and Grübel (Ann Stat 31:1054–1074, 2003) considered decompounding a compound Poisson distribution, i.e. given observations on a random sum when N has a Poisson distribution, they constructed a nonparametric plug-in estimator of the underlying summand distribution. This approach is extended here to that of general (but known) distributions for N. Asymptotic normality of the proposed estimator is established, and bootstrap methods are used to provide confidence bounds. Finally, practical implementation is discussed, and tested on simulated data. In particular we show how recursion formulae can be inverted for the Panjer class in general, as well as for an example drawn from the Willmot class.     

Universally coupled massive gravity, II: Densitized tetrad and cotetrad theories

Einstein’s equations in a tetrad formulation are derived from a linear theory in flat spacetime with an asymmetric potential using free field gauge invariance, local Lorentz invariance and universal coupling. The gravitational potential can be either covariant or contravariant and of almost any density weight. These results are adapted to produce universally coupled massive variants of Einstein’s equations, yielding two one-parameter families of distinct theories with spin 2 and spin 0. The theories derived, upon fixing the local Lorentz gauge freedom, are seen to be a subset of those found by Ogievetsky and Polubarinov some time ago using a spin limitation principle. In view of the stability question for massive gravities, the proven non-necessity of positive energy for stability in applied mathematics in some contexts is recalled. Massive tetrad gravities permit the mass of the spin 0 to be heavier than that of the spin 2, as well as lighter than or equal to it, and so provide phenomenological flexibility that might be of astrophysical or cosmological use.     

Performance of the constrained minimization of the total energy in density functional approximations: the electron repulsion density and potential

In the constrained minimization method of Gidopoulos and Lathiotakis [N.I. Gidopoulos, N.N. Lathiotakis, J. Chem. Phys. 136, 224109 (2012)], the Hartree exchange and correlation Kohn-Sham potential of a finite N-electron system is replaced by the electrostatic potential of an effective charge density that is everywhere positive and integrates to a charge of N ? 1 electrons. The optimal effective charge density (electron repulsion density, ρ_rep) and the corresponding optimal effective potential (electron repulsion potential v_rep) are obtained by minimizing the electronic total energy in any density functional approximation. The two constraints are sufficient to remove the self-interaction errors from v_rep, correcting its asymptotic behavior at large distances from the system. In the present work, we describe, in complete detail, the constrained minimization method, including recent refinements. We also assess its performance in removing the self-interaction errors for three popular density functional approximations, namely LDA, PBE and B3LYP, by comparing the obtained ionization energies to their experimental values for an extended set of molecules. We show that the results of the constrained minimizations are almost independent of the specific approximation with average percentage errors 15%, 14%, 13% for the above DFAs respectively. These errors are substantially smaller than the corresponding errors of the plain (unconstrained) Kohn-Sham calculations at 38%, 39% and 27% respectively. Finally, we showed that this method correctly predicts negative values for the HOMO energies of several anions.