The classical condition number is a very rough measure of the effect of perturbations on the inverse of a square matrix. First, it assumes the perturbation is infinitesimally small. Second, it does not take into account the perturbation structure (e.g., Vandermonde). Similarly, the classical...

In this paper we propose a new multivariate GARCH model with time-varying correlations. We adopt the vech representation based on the conditional variances and the conditional correlations. While each conditional-variance term is assumed to follow a univariate GARCH formulation, the...

The hyperbolic singular value decomposition (HSVD) of the pair (), where has full column rank and is diagonal matrix of signs, is defined as = Σ, where is orthogonal, Σ is positive definite diagonal, and is -orthogonal matrix, = . We analyze when it is possible to compute the HSVD with high...

We give relative perturbation bounds for singular values and perturbation bounds for singular subspaces of a hyperbolic singular value problem for the pair (), where is a full rank matrix and is a diagonal matrix of signs. We consider two types of relative perturbations: + = ( + ) and ,...

This paper is concerned with the stochastic shortest path problem with recourse when limited forms of spatial and temporal arc cost dependencies are accounted for. Recourse is defined as the opportunity for a decision-maker to re-evaluate his or her remaining path when en route information is...

An algorithm is presented to determine the symmetry type of an explicit o.d.e. of order at least 2. From a Janet basis for the determining system the Lie algebra of point symmetries can be obtained abstractly, as well as the isotropy subalgebra at the origin. This pair is the input of a decision...

We prove that a Tate construction ⟨,…, | ∂() = over a DG algebra , on cycles ,…, in , is acyclic if and only the map of graded-commutative algebras H()[,…] → H(), with , ↦ cls(), is an isomorphism. This is used to establish that if a large homomorphism → has an acyclic closure...

In this article we prove the existence of coercive limits in the theory of inelastic material behaviour of metals with nonelastic constitutive equations of monotone-gradient type ([Al]) without any growth conditions

We consider, within the framework of inductive inference, the concept of refuting learning as introduced by Mukouchi and Arikawa, where the learner is not only required to learn all concepts in a given class but also has to explicitly refute concepts outside the class.In the first part of the...