In this paper we will give three infinite families of examples of nonhyperbolic Dehn fillings on hyperbolic manifolds. A manifold in the first family admits two Dehn fillings of distance two apart, one of which is toroidal and annular, and the other is reducible and ∂-reducible. A manifold in the second family has boundary consisting of two tori, and admits two reducible Dehn fillings. A manifo...

In this talk, we give a criterion for a companion matrix to be reducible and give a complete characterization of reducible companion matrices. We also consider properties of the numerical ranges of reducible companion matrices. To be more precise, if C is an n-by-n reducible companion matrix which is unitarily equivalent to the direct sum of A and B, we study properties of the numerical ranges ...

Let G be a connected and reductive group over the algebraically closed field K. J-P. Serre has introduced the notion of a G-completely reducible subgroup H ≤ G. In this note, we give a notion of G-complete reducibility – G-cr for short – for Lie subalgebras of Lie(G), and we show that if the smooth subgroup H < G is G-cr, then Lie(H) is G-cr as well.

The concept of a canonical number system can be regarded as a natural generalization of decimal representations of rational integers to elements of residue class rings of polynomial rings. Generators of canonical number systems are CNS polynomials which are known in the linear and quadratic cases, but whose complete description is still open. In the present note reducible CNS polynomials are tr...

We consider the reducibility problem of cocycles by isometries Gromov hyperbolic metric spaces in Livsic setting. show that provided boundary cocycle (that acts on a compact space) is reducible suitable H\"older class, then original an unbounded also reducible.

In this paper, we generalize the previous formal de nitions of random-self-reducibility. We show that, even under our very general de nition, sets that are complete for any level of the polynomial hierarchy are not nonadaptively random-self-reducible, unless the hierarchy collapses. In particular, NP-complete sets are not nonadaptively random-self-reducible, unless the hierarchy collapses at th...

We study the parity of the number of irreducible factors of trinomials over Galois elds of characteristic 2. As a consequence , some suucient conditions for a trinomial being reducible are obtained. For example, x n + ax k + b 2 GF (2 t))x] is reducible if both n; t are even, except possibly when n = 2k, k odd. The case t = 1 was treated by R.G.Swan 10], who showed that x n + x k + 1 is reducib...