This paper gives an overview of recent achievements of the multiwavelet theory. The construction of multiwavelets is based on a multiresolution analysis with higher multiplicity generated by a scaling vector. The basic properties of scaling vectors such as L-stability, approximation order and regularity are studied. Most of the proofs are sketched.

Many discrete event systems (DESs) such as manufacturing systems, database management systems, communication networks, tra c systems, etc., can be modeled as input-output discrete event systems (I/O DESs). In this paper we formulate and study the problem of stable realization of such systems in the logical setting. Given an input and an output language describing the sequences of events that oc...

In this paper, we study the qualitative behaviour of approximation schemes for Backward Stochastic Differential Equations (BSDEs) by introducing a new notion of numerical stability. For the Euler scheme, we provide sufficient conditions in the one-dimensional and multidimensional case to guarantee the numerical stability. We then perform a classical Von Neumann stability analysis in the case of...

Three squaraine [2]catenanes are synthesized and found to have bright, deep-red fluorescence and high chemical stability. The interlocked molecules undergo two large-amplitude dynamic processes, twisting of the squaraine macrocycle and skipping over the partner tetralactam.

For the two sixth-order polynomials a(s) and b(s), Hurwitz stability of their convex combination is necessary and sufficient for the existence of a polynomial c(s) such that c(s)/a(s) and c(s)/b(s) are both strictly positive real. Our reasoning method is constructive, and is insightful and helpful in solving the general robust strictly positive real synthesis problem.

In this paper, we investigate in a unified way the structural properties of solutions to inverse problems. These solutions are regularized by the generic class of semi-norms defined as a decomposable norm composed with a linear operator, the so-called analysis type decomposable prior. This encompasses several well-known analysis-type regularizations such as the discrete total variation (in any ...

This note introduces practical set invariance notions for physically interconnected, discrete–time systems, subject to additive but bounded disturbances. We offer a concept which allows us to investigate invariance properties for each of the subsystems separately and, hence, to study invariance properties of the overall system in a sensible and decentralized way. The analysis part makes use of ...

We describe the pairs (p, n) such that n-dimensional affine space is fibered by pairwise skew p-dimensional affine subspaces. The problem is closely related with the theorem of Adams on vector fields on spheres and the Hurwitz-Radon theory of composition of quadratic forms.

Boron, discovered as an element in 1808 and produced in pure form in 1909, has still remained the last elemental material, having stable natural isotopes, with the ground state crystal phase to be unknown. It has been a subject of long-standing controversy, if α-B or β-B is the thermodynamically stable phase at ambient pressure and temperature. In the present work this enigma has been resolved ...