We consider methods based on the topological degree theory to compute periodic orbits of area preserving maps. Numerical approximations to the Kronecker integral give the number of fixed points of the map provided that the integration step is small ''enough''. Since in any neighborhood of a fixed point the map gets four different combination of its algebraic signs we use points on a lattice to ...

In mathematical chemistry, a particular attention is given to degree-based graph invariant. The Zagrebpolynomial is one of the degree based polynomials considered in chemical graph theory. A dendrimer isan artificially manufactured or synthesized molecule built up from branched units called monomers. Inthis note, the first, second and third Zagreb poly...

A graph G is called (H; k)-vertex stable if G contains a subgraph isomorphic to H ever after removing any k of its vertices. By stab(H; k) we denote the minimum size among the sizes of all (H; k)-vertex stable graphs. In this paper we present a first (non-trivial) general lower bound for stab(H; k) with regard to the order, connectivity and minimum degree of H. This bound is nearly sharp for k ...

argumentation offers an appealing way of representing and evaluating arguments and counterarguments. This approach can be enhanced by a probability assignment to each argument. There are various interpretations that can be ascribed to this assignment. In this paper, we regard the assignment as denoting the belief that an agent has that an argument is justifiable, i. e., that both the premises o...

In this paper we show that the relative canonical sheaf of a relatively minimal fibration of curves over a curve is semi-ample ; in fact, its m-tensored product is base point free for any m ≥ 2. We use Koszul cohomology with it to prove that the relative canonical ring of the fibration is generated in degree up to five.

The canonical structure of higher dimensional pure Chern-Simons theories is analysed. It is shown that these theories have generically a non-vanishing number of local degrees of freedom, even though they are obtained by means of a topological construction. This number of local degrees of freedom is computed as a function of the spacetime dimension and the dimension of the gauge group.

We review the status of a certain (infinite) class of four-dimensional generally covariant theories propagating two degrees of freedom that are formulated without any direct mention of the metric. General relativity itself (in its Plebański formulation) belongs to the class, so these theories are examples of modified gravity. We summarize the current understanding of the nature of the modificat...

We prove that, for all d ≥ 4, there are Salem numbers of degree 2d and trace −1, and that the number of such Salem numbers is d/ (log log d). As a consequence, it follows that the number of totally positive algebraic integers of degree d and trace 2d − 1 is also d/ (log log d).

Let X be a smooth complex projective variety of dimension d. We show that its primitive cohomology in degree d is generated by certain “tube classes,” constructed from the monodromy in the family of all hyperplane sections of X. The proof makes use of a result about the group cohomology of certain representations that may be of independent interest.