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.     

New Proof of the Cheeger–Müller Theorem

We present a short analytic proof of the equality between the analytic and combinatorialtorsion. We use the same approach as in the proof given by Burghelea, Friedlander andKappeler, but avoid using the difficult Mayer-Vietoris type formula for the determinantsof elliptic operators. Instead, we provide a direct way of analyzing the behaviour of thedeterminant of the Witten deformation of the Laplacian. In particular, we show that thisdeterminant can be written as a sum of two terms, one of which has an asymptoticexpansion with computable coefficients and the other is very simple (no zeta-functionregularization is involved in its definition).     

Phase diagram of the Kohn-Luttinger superconducting state for bilayer graphene

The effect of Coulomb interaction between Dirac fermions on the formation of the Kohn-Luttinger superconducting state in bilayer doped graphene is studied disregarding of the effect of the van der Waals potential of the substrate and impurities. The phase diagram determining the boundaries of superconductive domains with different types of symmetry of the order parameter is built using the extended Hubbard model in the Born weak-coupling approximation with allowance for the intratomic, interatomic, and interlayer Coulomb interactions between electrons. It is shown that the Kohn-Luttinger polarization contributions up to the second order of perturbation theory in the Coulomb interaction inclusively and an account for the long-range intraplane Coulomb interactions significantly affect the competition between the superconducting phases with the f-, p + ip-, and d + id-wave symmetries of the order parameter. It is demonstrated that the account for the interlayer Coulomb interaction enhances the critical temperature of the transition to the superconducting phase.     

New measurements of Cabibbo-suppressed decays of mesons with the CLEO-c detector

Using of data collected with the CLEO-c detector, we report on first observations and measurements of Cabibbo-suppressed decays of D mesons in the following six decay modes: pi+ pi- pi0 pi0, pi+ pi+ pi- pi- pi0, pi+ pi0 pi0, pi+ pi+ pi- pi0, eta pi0, and omega pi+ pi-. Improved branching fraction measurements in eight other multipion decay modes are also presented. The measured D --> pi pi rates allow us to extract the ratio of isospin amplitudes A(DeltaI = (3/2) / A(DeltaI = (1/2)) = 0.420 +/- 0.014(stat) +/- 0.016(syst) and the strong phase shift of delta1 = (86.4 +/- 2.8 +/- 3.3) degrees, which is quite large and now more precisely determined.     

Observation of B-->K(0)(S)pi(+)pi(-) and Evidence for B-->K(*+/-)pi(-/+)

We report on a search for charmless hadronic B decays to the three-body final states K(0)(S)h(+)pi(-), K(+)h(-)pi(0), K(0)(S)h(+)pi(0) (h(+/-) denotes a charged pion or kaon), and their charge conjugates, using 13.5 fb(-1) of integrated luminosity produced near sqrt[s]=10.6 GeV, and collected with the CLEO detector. We observe the decay B-->K0pi(+)pi(-) with a branching fraction (50(+10)(-9)(stat.)+/-7(syst.))x10(-6) and the decay B-->K(*+)(892)pi(-) with a branching fraction (16(+6)(-5)(stat.)+/-2(syst.))x10(-6).