In this paper we present fixed-parameter algorithms for the problem Dual—given two hypergraphs, decide if one is the transversal hypergraph of the other—and related problems. In the first part, we consider the number of edges of the hypergraphs, the maximum degree of a vertex, and a vertex complementary degree as our parameters. In the second part, we use an Apriori approach to obtain FPT resul...

Let S(n, 0) be the set of monic complex polynomials of degree n ≥ 2 having all their zeros in the closed unit disk and vanishing at 0. For p ∈ S(n, 0) denote by |p|0 the distance from the origin to the zero set of p. We determine all 0-maximal polynomials of degree n, that is, all polynomials p ∈ S(n, 0) such that |p|0 ≥ |q|0 for any q ∈ S(n, 0). Using a second order variational method we then ...

From the degree zero part of the logarithmic vector fields along an algebraic hypersurface singularity we identify the maximal multihomogeneity of a defining equation in form of a maximal algebraic torus in the embedded automorphism group. We show that all such maximal tori are conjugate and in one–to–one correspondence to maximal tori in the linear jet of the embedded automorphism group. These...

0 ∈ Tx + λCx, where T : D(T )⊂ X → 2X is a strongly quasibounded maximal monotone operator and C : D(C)⊂ X → X∗ satisfies the condition (S+)D(C) with L⊂ D(C). The method of approach is to use a topological degree theory for (S+)L-perturbations of strongly quasibounded maximal monotone operators, recently developed by Kartsatos and Quarcoo. Moreover, applying degree theory, a variant of the Fred...

In [6] N. Hamilton and J. A. Thas describe a link between maximal arcs of Mathon type and partial flocks of the quadratic cone. This link is of a rather algebraic nature. In this paper we establish a geometric connection between these two structures. We also define a composition on the flock planes and use this to work out an analogue of the synthetic version of Mathon’s Theorem (see [3]). Fina...

We extend the primal-dual approximation technique of Goemans and Williamson to the Steiner connectivity problem, a kind of Steiner tree problem in hypergraphs. This yields a (k+1)-approximation algorithm for the case that k is the minimum of the maximal number of nodes in a hyperedge minus 1 and the maximal number of terminal nodes in a hyperedge. These results require the proof of a degree pro...

We use the theory of differential forms, orientation, and mapping degree to prove that all maximal tori in a compact connected Lie group are conjugate. We also prove that all Lie groups are orientable, and that if G is a compact connected Lie group and T a maximal torus of G, then dim G/T is even.

0. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1. Seshadri constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2. Very ample line bundles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3. Bounds on global Seshadri constants . . . . . . . . . . . . . . . . . . . . . . . . 9 4. The degree of sub-maximal cu...

We give a recursive formula to count maximal small copies of the Mandelbrot set and its higher degree analogues. This formula is used to compute the asymptotic growth of the number of maximal small copies of period n. Mathematics Subject Classification: 37F20

The effect of perturbations of parameters for uniquely convergent imprecise Markov chains is studied. We provide the maximal distance between the distributions of original and perturbed chain and maximal degree of imprecision, given the imprecision of the initial distribution. The bounds on the errors and degrees of imprecision are found for the distributions at finite time steps, and for the s...