A new Darboux transformation is presented for the Hirota-Satsuma coupled KdV system. It is shown that this Darboux transformation can be constructed by means of two methods: Painlevé analysis and reduction of a binary Darboux transformation. By iteration of the Darboux transformation, the Grammian type solutions are found for the coupled KdV system.

We consider the problem of completely characterizing when a system of integer translates in a finitely generated shift-invariant subspace of L2(R) is stable in the sense that rectangular partial sums for the system are norm convergent. We prove that a system of integer translates is stable in L2(R) precisely when its associated Gram matrix satisfies a suitable Muckenhoupt A2 condition.

We give an algorithmic approach to the approximative solution of operator Lyapunov equations for controllability. Motivated by the successfully applied alternating direction implicit (ADI) iteration for matrix Lyapunov equations, we consider this method for the determination of Gramian operators of infinite-dimensional control systems. In the case where the input space is finitedimensional, thi...

In this paper, a quantitative measure of partial observability is defined for PDEs. The quantity is proved to be consistent in well-posed approximation schemes. A first order approximation of an unobservability index using empirical gramian is introduced. For linear systems with full state observability, the empirical gramian is equivalent to the observability gramian in control theory. The con...

An efficient method for evaluating inner products of repeated integrals and derivatives of a function described by a Laguerre model is presented. An immediate and promising application is model reduction of infinite-dimensional transfer functions. r 2004 Elsevier B.V. All rights reserved.

We consider a set of probability measures on a finite event space Ω. The mutual affinity is introduced in terms of the spectrum of the associated Gram matrix. We show that, for randomly chosen measures, the empirical eigenvalue distribution of the Gram matrix converges to a fixed distribution in the limit where the number of measures, together with the cardinality of Ω, goes to infinity.

The elementary divisors of the Gram matrices of Specht modules S λ over the symmetric group are determined for two-row partitions and for two-column partitions λ. More precisely, the subquotients of the Jantzen filtration are calculated using Schaper's formula. Moreover, considering a general partition λ of n at a prime p > n − λ 1 , the only possible non trivial composition factor of S λ Fp is...

This work presents a parametrized family of divergences, namely Alpha-Beta LogDeterminant (Log-Det) divergences, between positive definite unitized trace class operators on a Hilbert space. This is a generalization of the Alpha-Beta Log-Determinant divergences between symmetric, positive definite matrices to the infinite-dimensional setting. The family of Alpha-Beta Log-Det divergences is highl...

We investigate the factored ADI iteration for large and sparse Sylvester equations. A novel low-rank expression for the associated Sylvester residual is established which enables cheap computations of the residual norm along the iteration, and which yields a reformulated factored ADI iteration. The application to generalized Sylvester equations is considered as well. We also discuss the efficie...

For two integral histograms r = (r1, . . . , rd) and c = (c1, . . . , cd) of equal sum N , the MongeKantorovich distance dMK(r, c) between r and c parameterized by a d × d distance matrix T is the minimum of all costs < F, T > taken over matrices F of the transportation polytopeU(r, c). Recent results suggest that this distance is not negative definite, and hence, through Schoenberg’s well-know...