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).     

Working group report: Collider Physics

This is summary of the activities of the working group on collider physics in the IXth Workshop on High Energy Physics Phenomenology (WHEPP-9) held at the Institute of Physics, Bhubaneswar, India in January 2006. Some of the work subsequently done on these problems by the subgroups formed during the workshop is included in this report.     

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.     

Associated φΛ0 production in the EXCHARM experiment

The features of the associated production of φ mesons with Λ⁰ hyperons in neutron-carbon interactions were investigated. The experiment was performed with the aid of the EXCHARM spectrometer at the Serpukhov accelerator in a neutron beam of energy in the interval 20–70 GeV. The differential cross section for inclusive associated φΛ⁰ production was measured.     

Separating the solution sets of analytical and polynomial systems

A linear inequality system with infinitely many constraints is polynomial (analytical) if its index set is a compact interval of the real line and all its coefficients are polynomial (analytical, respectively) functions of the index on this interval. This paper provides an example of analytical system whose solution set cannot be the solution set of any polynomial system. Research supported by DGES of Spain and FEDER of UE, Grant BFM2002-04114-C02-01. Research supported by CONACyT of Mexico, Grant 130036. Research partially supported by CONACyT of Mexico, Grant 44003.     

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.