2,135 research outputs found
Lax pair and super-Yangian symmetry of the non-linear super-Schr\"odinger equation
We consider a version of the non-linear Schr\"odinger equation with M bosons
and N fermions. We first solve the classical and quantum versions of this
equation, using a super-Zamolodchikov-Faddeev (ZF) algebra. Then we prove that
the hierarchy associated to this model admits a super-Yangian Y(gl(M|N))
symmetry. We exhibit the corresponding (classical and quantum) Lax pairs.
Finally, we construct explicitly the super-Yangian generators, in terms of the
canonical fields on the one hand, and in terms of the ZF algebra generators on
the other hand. The latter construction uses the well-bred operators introduced
recently.Comment: 32 pages, no figur
Multilinear functional inequalities involving permanents, determinants, and other multilinear functions of nonnegative matrices and M-matrices
AbstractMotivated by a proof due to Fiedler of an inequality on the determinants of M-matrices and a recent paper by the authors, we now obtain various inequalities on permanents and determinants of nonsingular M-matrices. This is done by extending the multilinear considerations of Fiedler and, subsequently, of the authors, to fractional multilinear functionals on pairs of nonnegative matrices. Two examples of our results: For an n×n nonsingular M-matrix M (i) we give a sharp upper bound for det(M)+per(M), when M is a nonsingular M-matrix, (ii) we determine an upper bound on the relative error |per(M+E)−per(M)|/|per(M)|, when M+E is a certain componentwise perturbation of M
Direct and Inverse Computation of Jacobi Matrices of Infinite Homogeneous Affine I.F.S
We introduce a new set of algorithms to compute Jacobi matrices associated
with measures generated by infinite systems of iterated functions. We
demonstrate their relevance in the study of theoretical problems, such as the
continuity of these measures and the logarithmic capacity of their support.
Since our approach is based on a reversible transformation between pairs of
Jacobi matrices, we also discuss its application to an inverse / approximation
problem. Numerical experiments show that the proposed algorithms are stable and
can reliably compute Jacobi matrices of large order.Comment: 20 pages 6 figure
Semigroups of distributions with linear Jacobi parameters
We show that a convolution semigroup of measures has Jacobi parameters
polynomial in the convolution parameter if and only if the measures come
from the Meixner class. Moreover, we prove the parallel result, in a more
explicit way, for the free convolution and the free Meixner class. We then
construct the class of measures satisfying the same property for the two-state
free convolution. This class of two-state free convolution semigroups has not
been considered explicitly before. We show that it also has Meixner-type
properties. Specifically, it contains the analogs of the normal, Poisson, and
binomial distributions, has a Laha-Lukacs-type characterization, and is related
to the case of quadratic harnesses.Comment: v3: the article is merged back together with arXiv:1003.4025. A
significant revision following suggestions by the referee. 2 pdf figure
Laguerre-Hahn orthogonal polynomials on the real line
A survey is given on sequences of orthogonal polynomials related to
Stieltjes functions satisfying a Riccati type differential equation with polynomial
coeffcients - the so-called Laguerre-Hahn class. The main goal is to describe analytical
aspects, focusing on differential equations for those orthogonal polynomials,
difference and differential equations for the recurrence coeffcients, and distributional
equations for the corresponding linear functionals.info:eu-repo/semantics/publishedVersio
Relative trace formulae toward Bessel and Fourier-Jacobi periods of unitary groups
We propose a relative trace formula approach and state the corresponding
fundamental lemma toward the global restriction problem involving Bessel or
Fourier-Jacobi periods of unitary groups ,
extending the work of Jacquet-Rallis for (which is a Bessel period). In
particular, when , we recover a relative trace formula proposed by Flicker
concerning Kloosterman/Fourier integrals on quasi-split unitary groups. As
evidence for our approach, we prove the fundamental lemma for
in positive characteristics.Comment: 55 page
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