2,846 research outputs found
Relations between the correlators of the topological sigma-model coupled to gravity
We prove a new recursive relation between the correlators , which together with known
relations allows one to express all of them through the full system of
Gromov-Witten invariants in the sense of Kontsevich-Manin and the intersection
indices of tautological classes on , effectively calculable in
view of earlier results due to Mumford, Kontsevich, Getzler, and Faber. This
relation shows that a linear change of coordinates of the big phase space
transforms the potential with gravitational descendants to another function
defined completely in terms of the Gromov-Witten correspondence and the
intersection theory on . We then extend the formalism
of gravitational descendants from quantum cohomology to more general Frobenius
manifolds and Cohomological Field Theories.Comment: AMS-Tex, 13 pages, no figure
Exact Solutions of the Equations of Relativistic Hydrodynamics Representing Potential Flows
We use a connection between relativistic hydrodynamics and scalar field
theory to generate exact analytic solutions describing non-stationary
inhomogeneous flows of the perfect fluid with one-parametric equation of state
(EOS) . For linear EOS we obtain
self-similar solutions in the case of plane, cylindrical and spherical
symmetries. In the case of extremely stiff EOS () we obtain
''monopole + dipole'' and ''monopole + quadrupole'' axially symmetric
solutions. We also found some nonlinear EOSs that admit analytic solutions.Comment: This is a contribution to the Proc. of the Seventh International
Conference ''Symmetry in Nonlinear Mathematical Physics'' (June 24-30, 2007,
Kyiv, Ukraine), published in SIGMA (Symmetry, Integrability and Geometry:
Methods and Applications) at http://www.emis.de/journals/SIGMA
Szeg\H{o}-type asymptotics for ray sequences of Frobenius-Pad\'e approximants
Let be a Cauchy transform of a possibly complex-valued Borel
measure and be a system of orthonormal polynomials with
respect to a measure ,
. An -th
Frobenius-Pad\'e approximant to is a rational function ,
, , such that the first
Fourier coefficients of the linear form vanish when the
form is developed into a series with respect to the polynomials . We
investigate the convergence of the Frobenius-Pad\'e approximants to
along ray sequences , , when
and are supported on intervals on the real line and their
Radon-Nikodym derivatives with respect to the arcsine distribution of the
respective interval are holomorphic functions
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