Ray-Singer type theorem for the refined analytic torsion

We show that the refined analytic torsion is a holomorphic section of the determinant line bundle over the space of complex representations of the fundamental group of a closed oriented odd-dimensional manifold. Further, we calculate the ratio of the refined analytic torsion and the Farber-Turaev combinatorial torsion. As an application, we establish a formula relating the eta-invariant and the phase of the Farber-Turaev torsion, which extends a theorem of Farber and earlier results of ours. This formula allows to study the spectral flow using methods of combinatorial topology.     

Algebro-Geometric Approach in the Theory of Integrable Hydrodynamic Type Systems

The algebro-geometric approach for integrability of semi-Hamiltonian hydrodynamic type systems is presented. The class of symmetric hydrodynamic type systems is defined and the calculation of the associated Riemann surfaces is greatly simplified for this class. Many interesting and physically motivated examples are investigated.     

Little higgs models and T parity

Little Higgs models are an interesting extension of the Standard Model at the TeV scale. They provide a simple and attractive mechanism of electroweak symmetry breaking. We review one of the simplest models of this class, the Littlest Higgs model, and its extension with T parity. The model with T parity satisfies precision electroweak constraints without fine-tuning, contains an attractive dark matter candidate, and leads to interesting phenomenology at the Large Hadron Collider (LHC).     

Analysis of the structure of an amorphous sediment obtained upon decomposition of potassium oxofluroniobate in water

An amorphous sediment was prepared by the decomposition of potassium oxofluoroniobate K_{2 ? x} Nb₄O₃(O, F)₃F in water. For this sediment, the atomic radial distribution function was analyzed with the use of a fragment model, which allows one to interpret expanded coordination spheres as being formed by first several strongest diffusion maxima. These spheres carry the most reliable information on the structure. It is shown that the amorphous sediment consists of the randomly packed Nb(O,F)₆-octahedra with interatomic distances close to those observed in the ordered region in the N-Nb₂O₅ structure. During decomposition in water, the initial K_{2 ? x} Nb₄O₃(O, F)₃F phase loses KF-layers, whereas Nb₆ clusters with metal bonds are destroyed.     

Identification and quantitative determination of some inorganic lanthanide compounds by diffuse reflectance spectroscopy

Diffuse reflectance spectroscopy in the UV, visible, and near-IR regions is found to allow the detection and identification of lanthanide oxides, fluorides, sulfides, and sulfofluorides without decomposing and dissolving samples. A nondestructive method for the detection and quantitative determination of more than 1 wt % of Eu(II) in the corresponding fluorides is proposed.     

Notes on relativistic equations of spin motion

Grounds and applications of Bargmann-Michel-Telegdi equations for the precession of the polarization vector of relativistic particles are considered. A critical question in the discussion is the orientation of the rest frame reference vectors. Møller reference frames which keep constant the mutual orientation of the two infinitely close in time rest frames are shown to have a special role. The generally covariant form of the equations is discussed. The assertion that the principle of relativity is violated in the phenomenon of spin precession is proved to be untrue.     

Bonding Properties of a Novel Inorganometallic Complex, Ru(SnPh(3))(2)(CO)(2)(iPr-DAB) (iPr-DAB = N,N'-Diisopropyl-1,4-diaza-1,3-butadiene), and its Stable Radical-Anion, Studied by UV-Vis, IR, and EPR Spectroscopy, (Spectro-) Electrochemistry, and Density Functional Calculations

Ru(SnPh(3))(2)(CO)(2)(iPr-DAB) was synthesized and characterized by UV-vis, IR, (1)H NMR, (13)C NMR, (119)Sn NMR, and mass (FAB(+)) spectroscopies and by single-crystal X-ray diffraction, which proved the presence of a nearly linear Sn-Ru-Sn unit. Crystals of Ru(SnPh(3))(2)(CO)(2)(iPr-DAB).3.5C(6)H(6) form in the triclinic space group P&onemacr; in a unit cell of dimensions a = 11.662(6) ?, b = 13.902(3) ?, c = 19.643(2) ?, alpha = 71.24(2) degrees, beta = 86.91(4) degrees, gamma = 77.89(3) degrees, and V = 2946(3) ?(3). One-electron reduction of Ru(SnPh(3))(2)(CO)(2)(iPr-DAB) produces the stable radical-anion [Ru(SnPh(3))(2)(CO)(2)(iPr-DAB)](*-) that was characterized by IR, and UV-vis spectroelectrochemistry. Its EPR spectrum shows a signal at g = 1.9960 with well resolved Sn, Ru, and iPr-DAB (H, N) hyperfine couplings. DFT-MO calculations on the model compound Ru(SnH(3))(2)(CO)(2)(H-DAB) reveal that the HOMO is mainly of sigma(Sn-Ru-Sn) character mixed strongly with the lowest pi orbital of the H-DAB ligand. The LUMO (SOMO in the reduced complex) should be viewed as predominantly pi(H-DAB) with an admixture of the sigma(Sn-Ru-Sn) orbital. Accordingly, the lowest-energy absorption band of the neutral species will mainly belong to the sigma(Sn-Ru-Sn)-->pi(iPr-DAB) charge transfer transition. The intrinsic strength of the Ru-Sn bond and the delocalized character of the three-center four-electron Sn-Ru-Sn sigma-bond account for the inherent stability of the radical anion.