288 research outputs found
On the algebraic structures connected with the linear Poisson brackets of hydrodynamics type
The generalized form of the Kac formula for Verma modules associated with
linear brackets of hydrodynamics type is proposed. Second cohomology groups of
the generalized Virasoro algebras are calculated. Connection of the central
extensions with the problem of quntization of hydrodynamics brackets is
demonstrated
Quadratic Poisson brackets and Drinfeld theory for associative algebras
The paper is devoted to the Poisson brackets compatible with multiplication
in associative algebras. These brackets are shown to be quadratic and their
relations with the classical Yang--Baxter equation are revealed. The paper also
contains a description of Poisson Lie structures on Lie groups whose Lie
algebras are adjacent to an associative structure.Comment: 16 pages, latex, no figure
Quadratic Poisson brackets and Drinfel'd theory for associative algebras
Quadratic Poisson brackets on associative algebras are studied. Such a
bracket compatible with the multiplication is related to a differentiation in
tensor square of the underlying algebra. Jacobi identity means that this
differentiation satisfies a classical Yang--Baxter equation. Corresponding Lie
groups are canonically equipped with a Poisson Lie structure. A way to quantize
such structures is suggested.Comment: latex, no figures
Hydrodynamic chains and a classification of their Poisson brackets
Necessary and sufficient conditions for an existence of the Poisson brackets
significantly simplify in the Liouville coordinates. The corresponding
equations can be integrated. Thus, a description of local Hamiltonian
structures is a first step in a description of integrable hydrodynamic chains.
The concept of Poisson bracket is introduced. Several new Poisson brackets
are presented
Stability of the magnetic Schr\"odinger operator in a waveguide
The spectrum of the Schr\"odinger operator in a quantum waveguide is known to
be unstable in two and three dimensions. Any enlargement of the waveguide
produces eigenvalues beneath the continuous spectrum. Also if the waveguide is
bent eigenvalues will arise below the continuous spectrum. In this paper a
magnetic field is added into the system. The spectrum of the magnetic
Schr\"odinger operator is proved to be stable under small local deformations
and also under small bending of the waveguide. The proof includes a magnetic
Hardy-type inequality in the waveguide, which is interesting in its own
Quadratic Poisson brackets compatible with an algebra structure
Quadratic Poisson brackets on a vector space equipped with a bilinear
multiplication are studied. A notion of a bracket compatible with the
multiplication is introduced and an effective criterion of such compatibility
is given. Among compatible brackets, a subclass of coboundary brackets is
described, and such brackets are enumerated in a number of examples.Comment: 6 page
Chern-Simons action for zero-mode supporting gauge fields in three dimensions
Recent results on zero modes of the Abelian Dirac operator in three
dimensions support to some degree the conjecture that the Chern-Simons action
admits only certain quantized values for gauge fields that lead to zero modes
of the corresponding Dirac operator. Here we show that this conjecture is wrong
by constructing an explicit counter-example.Comment: version as published in PRD, minor change
A simple proof of Hardy-Lieb-Thirring inequalities
We give a short and unified proof of Hardy-Lieb-Thirring inequalities for
moments of eigenvalues of fractional Schroedinger operators. The proof covers
the optimal parameter range. It is based on a recent inequality by Solovej,
Soerensen, and Spitzer. Moreover, we prove that any non-magnetic Lieb-Thirring
inequality implies a magnetic Lieb-Thirring inequality (with possibly a larger
constant).Comment: 12 page
Assay, purification, properties and mechanism of action of Îł-glutamylcysteine synthetase from the liver of the rat and Xenopus laevis
Eigenfunctions at the threshold energies of magnetic Dirac operators
Discussed are modes and resonances of Dirac operators with
vector potentials . Asymptotic
limits of modes at infinity are derived when ,
, provided that has modes. In wider classes of vector
potentials, sparseness of the vector potentials which give rise to the
modes of are established. It is proved that no has
resonances if , .Comment: 25 pages, New results are adde
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