Decomposability for stable processes

We characterize all possible independent symmetric α-stable (SαS) components of an SαS process, 0<α<2. In particular, we focus on stationary SαS processes and their independent stationary SαS components. We also develop a parallel characterization theory for max-stable processes.     

A new stability criterion for linear discrete systems

This paper is concerned with the stability of difference equations. A criterion to decide whether a certain polynomial has all its zeros inside the unit circle is applied to multistep linear methods in order to obtain the absolute stability region, and it is shown how this region can be extended. Systems of linear difference equations are also considered and an extension to partial difference equations is discussed.     

A new stopping criterion for linear perturbed asynchronous iterations

A new stopping criterion is proposed for asynchronous linear fixed point methods in finite precision. The case of absolute error is considered. The originality of this stopping criterion relies on the fact that all tests are made within the same macroiteration.     

Nonintegral criterion for oscillations of linear Hamiltonian matrix systems

In this paper we present nonintegral criteria for oscillation of linear Hamiltonian matrix system U^′=A(x)U+B(x)V, V^′=C(x)U−A^*(x)V under the hypothesis (H): A(x), B(x)=B^*(x)>0, and C(x)=C^*(x) are 2×2 matrices of real valued continuous functions on the interval I=[a,∞),(−∞<a). These criteria are conditions of algebraic type only. Our results are also useful for the detection of the oscillation of particular matrix differential systems.     

A uniqueness criterion for linear problems of wave-body interaction

The question of uniqueness for linearized problems describinginteraction of submerged bodies with an ideal unbounded fluidis far from its final resolution. In this work a new criterionof uniqueness is suggested based on Green's integral identityand maximum principles for elliptic differential equations.The criterion is formulated as an inequality involving integralsof the Green function over the bodies' wetted surfaces. Thiscriterion is quite general and applicable for any number ofsubmerged bodies of arbitrary shape (provided the boundary issufficiently regular) and in any dimension; it can also be generalizedto more complicated elliptic problems. Very simple bounds arealso derived from the criterion, which deliver uniqueness setsin the space of parameters defined by submergence of the systemof bodies and the frequency of oscillation. Results of numericalinvestigation and comparison with known uniqueness criteriaare presented.     

f-Vectors Implying Vertex Decomposability

We prove that if a pure simplicial complex $\Delta $ of dimension $d$ with $n$ facets has the least possible number of $(d-1)$ -dimensional faces among all complexes with $n$ faces of dimension $d$ , then it is vertex decomposable. This answers a question of J. Herzog and T. Hibi. In fact, we prove a generalization of their theorem using combinatorial methods.     

Decomposability of Polytopes

A known characterization of the decomposability of polytopes is reformulated in a way which may be more computationally convenient, and a more transparent proof is given. New sufficient conditions for indecomposability are then deduced, and illustrated with some examples.     

Decomposability of matrix polynomials with commuting coefficients into a product of linear factors

The list of known sets of factorizable matrix polynomials is supplemented by new sets of polynomials of this sort. The known set of nonfactorizable matrix polynomials is extended. These results can be applied to the study of polynomial equations and systems of differential equations with constant coefficients.     

A linear matrix equation: a criterion for block similarity

In this paper we study a homogeneous linear matrix equation related to the block similarity of rectangular matrices. We obtain the dimension of the vector space of its solutions and we describe these solutions. We give a characterization of the block similarity by rank tests. We extend Roth's criterion to the corresponding non homogeneous equation.