Reactions between organic derivatives of group III elements and acids

The cyanides Me(_2)MCN(M = Al, Ga, In or Tl) were prepared from the trimethylmetal and hydrogen cyanide. In contrast to the polymeric boron cyanides, RgBCN, the aluminium, gallium, and indium compounds are tetrameric in benzene, and dimethylthallium cyanide is a salt in aqueous solution. Reactions between dimethylberyllium (and its trimethylamine complex) and hydrogen cyanide were also investigated. The phosphinates, thiophosphinates, sulphinates, one arsinate and carboxylates of many of the Group III metals were prepared from reactions between the triraethylmetal and the corresponding acid in an inert solvent (ether or benzene). These were sufficiently volatile to be purified by vacuum sublimation. The compounds were air-sensitive. Molecular weights were determined cryoscopically in benzene and the compounds were found to be dimers. The structures of these dimers were established on the basis of their infrared spectra, as eight-membered ring compounds in which the P = 0 or similar groups participated in co-ordinate bond formation. The dithiophosphinates of aluminium, gallium and indium were prepared from reactions between the trimethylmetal and dimethyldithiophosphinic acid in an inert solvent. These were purified by vacuum sublimation as colourless crystals. Molecular weights were determined cryoscopically in benzene and the compounds were found to be monomers (compare the phosphinates, sulphinates etc. which were found to be dimers). Bimethylaluminium methane-sulphonate and the corresponding gallium compound were prepared by similar reactions. They were purified by vacuum sublimation as white crystalline solids. Molecular weights were determined cryoscopically in benzene and the compounds were found to be trimers. The infrared spectra of all the compounds prepared were investigated and several new assignments for different structural features were made

Duality for Multiobjective Fractional Variational Problems

AbstractA class of multiobjective fractional variational problems is considered and duals are formulated. Under concavity assumptions on the functions involved, duality theorems are proved through a parametric approach to relate efficient solutions of the primal and dual problems. We generalize those results for control problems also

Sensitivity analysis of generalized variational inequalities

AbstractDafermos studied the sensitivity properties of the solutions of a variational inequality with regard to continuity and differentiability of such solutions with respect to a parameter λ. In the present paper we extend this analysis for a generalized variational inequality of the type introduced by Noor of which the variational inequality of Dafermos is a particular case. Our results are such that they automatically extend the regularity properties of solutions with respect to a parameter λ when the variational inequality is treated on a Hilbert space

Analysis of Hamiltonian formulations of linearized General Relativity

The different forms of the Hamiltonian formulations of linearized General Relativity/spin-two theories are discussed in order to show their similarities and differences. It is demonstrated that in the linear model, non-covariant modifications to the initial covariant Lagrangian (similar to those modifications used in full gravity) are in fact unnecessary. The Hamiltonians and the constraints are different in these two formulations but the structure of the constraint algebra and the gauge invariance derived from it are the same. It is shown that these equivalent Hamiltonian formulations are related to each other by a canonical transformation which is explicitly given. The relevance of these results to the full theory of General Relativity is briefly discussed.Comment: Section Discussion is modified and references are added; 19 page

Magnetic enhancement of Co0.2_{0.2}Zn0.8_{0.8}Fe2_2O4_4 spinel oxide by mechanical milling

We report the magnetic properties of mechanically milled Co$_{0.2}$Zn$_{0.8}$Fe$_2$O$_4$ spinel oxide. After 24 hours milling of the bulk sample, the XRD spectra show nanostructure with average particle size $\approx$ 20 nm. The as milled sample shows an enhancement in magnetization and ordering temperature compared to the bulk sample. If the as milled sample is annealed at different temperatures for the same duration, recrystallization process occurs and approaches to the bulk structure on increasing the annealing temperatures. The magnetization of the annealed samples first increases and then decreases. At higher annealing temperature ($\sim$ 1000$^{0}$C) the system shows two coexisting magnetic phases {\it i.e.}, spin glass state and ferrimagnetic state, similar to the as prepared bulk sample. The room temperature M\"{o}ssbauer spectra of the as milled sample, annealed at 300$^{0}$C for different durations (upto 575 hours), suggest that the observed change in magnetic behaviour is strongly related with cations redistribution between tetrahedral (A) and octahedral (O) sites in the spinel structure. Apart from the cation redistribution, we suggest that the enhancement of magnetization and ordering temperature is related with the reduction of B site spin canting and increase of strain induced anisotropic energy during mechanical milling.Comment: 14 pages LaTeX, 10 ps figure

Erratum: "A Gravitational-wave Measurement of the Hubble Constant Following the Second Observing Run of Advanced LIGO and Virgo" (2021, ApJ, 909, 218)

[no abstract available

Search for Tensor, Vector, and Scalar Polarizations in the Stochastic Gravitational-Wave Background

The detection of gravitational waves with Advanced LIGO and Advanced Virgo has enabled novel tests of general relativity, including direct study of the polarization of gravitational waves. While general relativity allows for only two tensor gravitational-wave polarizations, general metric theories can additionally predict two vector and two scalar polarizations. The polarization of gravitational waves is encoded in the spectral shape of the stochastic gravitational-wave background, formed by the superposition of cosmological and individually unresolved astrophysical sources. Using data recorded by Advanced LIGO during its first observing run, we search for a stochastic background of generically polarized gravitational waves. We find no evidence for a background of any polarization, and place the first direct bounds on the contributions of vector and scalar polarizations to the stochastic background. Under log-uniform priors for the energy in each polarization, we limit the energy densities of tensor, vector, and scalar modes at 95% credibility to Ω0T<5.58×10-8, Ω0V<6.35×10-8, and Ω0S<1.08×10-7 at a reference frequency f0=25 Hz. © 2018 American Physical Society