Cauchy-type determinants and integrable systems
نویسندگان
چکیده
منابع مشابه
Generalized Cauchy Determinants
This paper classifies the sequences that satisfy a generalization of the Cauchy determinant formula. They are the generalized Fibonacci numbers, up to a scalar multiple. Following this, it is determined which of these sequences generate Hankel matrices of unit fractions with integer inverses. As a corollary we obtain another proof that the Filbert Matrix has an inverse with integer entries, com...
متن کاملRandom Words, Toeplitz Determinants, and Integrable Systems I
It is proved that the limiting distribution of the length of the longest weakly increasing subsequence in an inhomogeneous random word is related to the distribution function for the eigenvalues of a certain direct sum of Gaussian unitary ensembles subject to an overall constraint that the eigenvalues lie in a hyperplane.
متن کاملRandom words, Toeplitz determinants and integrable systems: II
This paper connects the analysis of the length of the longest weakly increasing subsequence of inhomogeneous random words to a Riemnn-Hilbert problem and an associated system of integrable partial differential equations. In particular, we show that the Poissonization of the distribution function of this length can be identified as the Jimbo-Miwa-Ueno tau function. © 2001 Elsevier Science B.V. A...
متن کاملCauchy Problem for a Darboux Integrable Wave Map System and Equations of Lie Type
The Cauchy problem for harmonic maps from Minkowski space with its standard flat metric to a certain non-constant curvature Lorentzian 2-metric is studied. The target manifold is distinguished by the fact that the Euler–Lagrange equation for the energy functional is Darboux integrable. The time evolution of the Cauchy data is reduced to an ordinary differential equation of Lie type associated t...
متن کاملConstructing integrable systems of semitoric type
Let (M, ω) be a connected, symplectic 4-manifold. A semitoric integrable system on (M, ω) essentially consists of a pair of independent, real-valued, smooth functions J and H on M , for which J generates a Hamiltonian circle action under which H is invariant. In this paper we give a general method to construct, starting from a collection of five ingredients, a symplectic 4-manifold equipped a s...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2010
ISSN: 0024-3795
DOI: 10.1016/j.laa.2010.03.011