Conformal Operators on Forms and Detour Complexes on Einstein Manifolds

For even dimensional conformal manifolds several new conformally invariant objects were found recently: invariant differential complexes related to, but distinct from, the de Rham complex (these are elliptic in the case of Riemannian signature); the cohomology spaces of these; conformally stable form spaces that we may view as spaces of conformal harmonics; operators that generalise Branson’s Q-curvature; global pairings between differential form bundles that descend to cohomology pairings. Here we show that these operators, spaces, and the theory underlying them, simplify significantly on conformally Einstein manifolds. We give explicit formulae for all the operators concerned. The null spaces for these, the conformal harmonics, and the cohomology spaces are expressed explicitly in terms of direct sums of subspaces of eigenspaces of the form Laplacian. For the case of non-Ricci flat spaces this applies in all signatures and without topological restrictions. In the case of Riemannian signature and compact manifolds, this leads to new results on the global invariant pairings, including for the integral of Q-curvature against the null space of the dimensional order conformal Laplacian of Graham et al.     

Hypernuclear physics at overline{mbox{P}} anda

Samples obtained as a result of the valleriite synthesis process under different conditions (temperature and proportion Cu:Fe:Mg in the initial mixture) were investigated by ⁵⁷Fe M?ssbauer spectroscopy with attraction data of X-ray diffraction. Parameters of hyperfine interactions for valleriite were determined and crystal chemical identification of ⁵⁷Fe subspectra was carried out. It was found that valleriite was formed in samples synthesized at 150°C and 180°C and not formed in samples synthesized at 250°C.     

The effect of composite resonances on Higgs decay into two photons

In scenarios of strongly coupled electroweak symmetry breaking, heavy composite particles of different spin and parity may arise and cause observable effects on signals that appear at loop levels. The recently observed process of Higgs to $\gamma \gamma $ at the LHC is one of such signals. We study the new constraints that are imposed on composite models from $H\rightarrow \gamma \gamma $ , together with the existing constraints from the high precision electroweak tests. We use an effective chiral Lagrangian to describe the effective theory that contains the Standard Model spectrum and the extra composites below the electroweak scale. Considering the effective theory cutoff at $\Lambda = 4\pi v \sim 3\text { TeV}$ , consistency with the $T$ and $S$ parameters and the newly observed $H\rightarrow \gamma \gamma $ can be found for a rather restricted range of masses of vector and axial-vector composites from 1.5 to 1.7 and 1.8 to 1.9 TeV, respectively, and only provided a non-standard kinetic mixing between the $W^{3}$ and $B^{0}$ fields is included.     

Internal magnetic fields in submicron particles of barium hexaferrite detected by 57Fe NMR

⁵⁷Fe nuclear magnetic resonance (NMR) spectra of hexaferrite BaFe₁₂O₁₉ powder samples prepared by glass crystallization method were measured at 4.2 K and analyzed in comparison to spectra of single crystals. Samples with various mean particle dimensions were tested. NMR spectral lines corresponding to individual iron sublattices showed pronounced frequency shifts of their positions and a significant line broadening compared to single crystals. The significant contribution to the line shifts and line shape had a uniform macroscopic origin giving identical absolute value of shifts and the same line shapes for all measured lines of a particular sample. Estimations of demagnetization fields based on mean particle dimensions reasonably corresponded to the observed frequency shifts for particle mean diameter 67 nm, or had a higher value for a sample with mean diameter of 340 nm, for which a presence of domain walls was detected by NMR. In the spectrum of a sample with the smallest particles (～16 nm), an additional contribution having broader lines and faster spin-spin relaxations was found. It could be assigned to weaker exchange interactions or deviations of magnetic moment directions from the hexagonal axis in a surface layer.     

Excited states of dinaphth[de-1, 2, 3; d′e′-5, 6, 7]azulene: Polarized absorption in stretched polymers and magnetic circular dichroism

UV-visible polarized absorption spectra of dinaphth[de-1,2,3; d′e′-5,6,7]azulene I have been determined from measurements of linear dichroism in stretched polymer sheets. Magnetic circular dichroic (MCD) spectra have been measured in solution and help to distinguish individual electronic transitions. π-Electron calculations of transition energies, oscillator strengths, and polarization directions are in good agreement with the experimental data and permit a straightforward correlation of the low-energy part of the spectrum of I with that of the parent pleiadiene II.     

Rare-earth Metal Borosilicides R9Si15–xB3 (R = Tb,Yb): New Ordered Structures Derived from the AlB2 Structure Type

Two novel ternary borosilicides R₉Si_15–xB₃ (R = Tb, x = 1.80, R = Yb, x = 1.17) were synthesized from the initial elements using tin flux method. Their crystal structures were determined by means of X-ray single crystal diffraction. Both refer to space group R32, Z = 1: a = 6.668(2) Å, c = 12.405(4) Å [R₁ = 0.027, wR₂ = 0.031 for 1832 reflections with I_o > 2σ (I_o)] for Tb₉Si_15–xB₃, and a = 6.5796(3) Å, c = 12.2599(5) Å [R_F = 0.052, wR = 0.090 for 1369 reflections with I_o > 2σ (I_o)] for Yb₉Si_15–xB₃. The structures represent a new structure type, derived from that of AlB₂, with ordering in the metalloid sublattice resulting in distorted [Si₅B] hexagons. The presence or absence of boron in this ordered structure is discussed on the basis of difference Fourier syntheses, interatomic distances, structural analysis, and theoretical calculations in relation with the parent structures of the binaries AlB₂ and Yb₃Si₅ (Th₃Pd₅ type of structure). Theoretical calculations show substantial covalent interactions between the metal and nonmetal elements. The small percentage of silicon atoms, which are missing in these nonstoichiometric compounds, probably allows strengthening boron-metal and boron-silicon bonding.