We show that graphs generated by collapsible pushdown systems of level 2 are tree-automatic. Even if we allow ε-contractions and reachability predicates (with regular constraints) for pairs of configurations, the structures remain tree-automatic whence their first-order logic theories are decidable. As a corollary we obtain the tree-automaticity of the second level of the Caucal-hierarchy.

We study the partition of the set of pairs of matrices according to the Brunovsky Kronecker type We show that it is a constructible strati cation and that it is Whitney regular when the second matrix is a column matrix We give an application to the obtention of bifurcation diagrams for few parameter generic families of linear systems

Let G be a 3-connected graph on more than 4 vertices. We show that every depth-first-search tree of G contains a contractible edge. Moreover, we show that if G is 3-regular or does not have two disjoint pairs of adjacent degree-3 vertices, every spanning tree of G contains a contractible edge.

We report that the hydrogen-bonding pattern in a molecular beacon can be replaced by metal-dependent pairs of Hg(2+) and DNA thymine (T) bases. A molecular beacon based on T-Hg(2+)-T exhibits a lower background signal and higher thermostability than regular molecular beacons.

Solving a decades-old problem we show that Keisler's 1967 order on theories has the maximum number of classes. In fact, it embeds P(?)/fin. The build are simple unstable with no nontrivial forking, and reflect growth rates sequences which may be thought as densities certain regular pairs, in sense Szemerédi's regularity lemma. proof involves ideas from model theory, set finite combinatorics.

This research paper emphasizes that the Stable Matching problems are the same as the problems of stable configurations of Multi–stage Interconnection Networks (MIN). The authors have solved the Stability Problem of Existing Regular Gamma Multistage Interconnection Network (GMIN), 3-Disjoint Gamma Multi-stage Interconnection Network (3DGMIN) and 3-Disjoint Path Cyclic Gamma Multi-stage Interconn...

We introduce a new method to approximate algebraic space curves. The algorithm combines a subdivision technique with local approximation of piecewise regular algebraic curve segments. The local technique computes pairs of polynomials with modified Taylor expansions and generates approximating circular arcs. We analyze the connection between the generated approximating arcs and the osculating ci...

We present a new extension of the well-known Perron-Frobenius theorem to regular matrix pairs (E, A). The new extension is based on projector chains and is motivated from the solution of positive differential-algebraic systems or descriptor systems. We present several examples where the new condition holds, whereas conditions in previous literature are not satisfied.

We show, for any positive integer k, that there exists a graph in which any equitable partition of its vertices into k parts has at least ck/ log∗ k pairs of parts which are not -regular, where c, > 0 are absolute constants. This bound is tight up to the constant c and addresses a question of Gowers on the number of irregular pairs in Szemerédi’s regularity lemma. In order to gain some control ...

It has been argued by Dyson in the context of QED in flat spacetime that perturbative expansions in powers of the electric charge e cannot be convergent because if e is purely imaginary then the vacuum should be unstable to the production of charged pairs. We investigate the spontaneous production of such Dyson pairs in electrodynamics coupled to gravity. They are found to consist of pairs of z...