On regular set systems containing regular subsystems

Set Constraints on Regular Terms

Set constraints are a useful formalism for verifying properties of programs. Usually, they are interpreted over the universe of finite terms. However, some logic languages allow infinite regular terms, so it seems natural to consider set constraints over this domain. In the paper we show that the satisfiability problem of set constraints over regular terms is undecidable. We also show that, if ...

The core of games on k-regular set systems

Regular Unbounded Set Functions

Set functions which are unbounded on an algebra of sets arise naturally by taking the products of bounded operators and spectral measures acting on a space of square integrable functions. The purpose of this note is to show that, provided a certain regularity condition is satissed, there is a natural integration structure associated with such a set function and an auxiliary measure, so providin...

Signed Domination in Regular Graphs and Set-Systems

Suppose G is a graph on n vertices with minimum degree r. Using standard random methods it is shown that there exists a two-coloring of the vertices of G with colors, +1 and −1, such that all closed neighborhoods contain more 1’s than −1’s, and altogether the number of 1’s does not exceed the number of −1’s by more than (4 p log r/r + 1/r)n. For large r this greatly improves earlier results and...

Vibration Analysis of Global Near-regular Mechanical Systems

Some near-regular mechanical systems involve global deviations from their corresponding regular system. Despite extensive research on vibration analysis (eigensolution) of regular and local near-regular mechanical systems, the literature on vibration analysis of global near-regular mechanical systems is scant. In this paper, a method for vibration analysis of such systems was developed using Kr...