Acta Applicandae Mathematicae

De la Sen, M.

doi: 10.1023/A:1016267220817pmid: N/A

This paper addresses the investigation of the reachability, observability and stabilizability properties of hybrid linear systems under multirate sampling. Technical results guaranteeing such properties at sampling instants and in between samples are formulated and proved. It is shown that the above properties can be investigated in terms of ranks of real or complex matrices if the system parameters are periodic or constant. The freedom in the choice of the sampling rates is finally used, under observability and exponential stability conditions, in the context of a optimal worst-case design. Two numerical examples are given. The first one is related to the design of such sampling rates for all possible choices of the inputs in a worst-case design context by using loss functions involving linear combinations of the L 2 and induced l 2 norms. The second one considers the choice of the sampling rates for an optimal transmission of possible rounding or measurement errors in the reachability problem.

Dobrynin, Andrey; Gutman, Ivan; Klavžar, Sandi; Žigert, Petra

doi: 10.1023/A:1016290123303pmid: N/A

The Wiener index W is the sum of distances between all pairs of vertices of a (connected) graph. Hexagonal systems (HS's) are a special type of plane graphs in which all faces are bounded by hexagons. These provide a graph representation of benzenoid hydrocarbons and thus find applications in chemistry. The paper outlines the results known for W of the HS: method for computation of W, expressions relating W with the structure of the respective HS, results on HS's extremal w.r.t. W, and on integers that cannot be the W-values of HS's. A few open problems are mentioned. The chemical applications of the results presented are explained in detail.

Manturov, V.

doi: 10.1023/A:1016258728022pmid: N/A

We propose a new method of generalizing classical link invariants for the case of virtual links. In particular, we have generalized the knot quandle, the knot fundamental group, the Alexander module, and the coloring invariants. The virtual Alexander module leads to a definition of VA-polynomial that has no analogue in the classical case (i.e. vanishes on classical links).

doi: 10.1023/A:1016292417802pmid: N/A