The object of the investigation is to study reducible $M$-ideals in Banach spaces. It is shown that if the number of $M$-ideals in a Banach space $X$ is $n(<infty)$, then the number of reducible $M$-ideals does not exceed of $frac{(n-2)(n-3)}{2}$. Moreover, given a compact metric space $X$, we obtain a general form of a reducible $M$-ideal in the space $C(X)$ of continuous functions on $X$. The...

In this paper, I analyze the constant factors for implementations of line segment intersection algorithms. I explore how these algorithms could be applied to stochastic local search algorithms to determine the rectilinear crossing number of complete graphs.

Projective Hjelmslev planes (PH-planes) are a generalization of projective planes in which each point-pair is joined by at least one line and, dually, each line-pair has a nontrivial intersection. Multiply joined points (and multiply intersecting lines) are called neighbor points (and neighbor lines). By hypothesis, the neighbor relations of a PH-plane A are equivalence relations which induce a...

Given a combinatorial designD with block set B, its traditional block-intersection graph GD is the graph having vertex set B such that two vertices b1 and b2 are adjacent if and only if b1 and b2 have non-empty intersection. In this paper we consider the S-block-intersection graph, in which two vertices b1 and b2 are adjacent if and only if |b1 ∩ b2| ∈ S. As our main result we prove that {1, 2,...

We show that the edge-clique graphs of cocktail party graphs have unbounded rankwidth. This, and other observations lead us to conjecture that the edge-clique cover problem is NP-complete for cographs. We show that the independent set problem on edge-clique graphs of cographs and of distance-hereditary graphs can be solved in O(n4) time. We show that the independent set problem on edge-clique g...

We exploit the properties of the hyperbolic space H to discuss a simplicial setting for open/closed string duality based on (random) Regge triangulations decorated with null twistorial fields. We explicitly show that the twistorial N-points function, describing Dirichlet correlations over the moduli space of open N-bordered genus g surfaces, is naturally mapped into the Witten-Kontsevich inters...

Let ⊢ be a rank-2 intersection type system. We say that a term is ⊢-simple (or just simple when the system ⊢ is clear from the context) if system ⊢ can prove that it has a simple type. In this paper we propose new typing rules and algorithms that are able to type recursive definitions that are not simple. At the best of our knowledge, previous algorithms for typing recursive definitions in the ...

We discuss a unified approach to a class of geometric combinatorics incidence problems in two dimensions, of the Erdős distance type. The goal is obtaining the second moment estimate. That is, given a finite point set S in 2D, and a function f on S × S, find the upper bound for the number of solutions of the equation (1) f(p, p′) = f(q, q′) 6= 0, (p, p′, q, q′) ∈ S × S × S × S. E.g., f is the E...

For undirected graphs G (V, E) and G0 (V0 , E0), say that G is a region intersection graph over G0 if there is a family of connected subsets {Ru ⊆ V0 : u ∈ V} of G0 such that {u , v} ∈ E ⇐⇒ Ru ∩ Rv , ∅. We show if G0 excludes the complete graph Kh as a minor for some h > 1, then every region intersection graph G over G0 with m edges has a balanced separator with at most ch √ m nodes, where ch i...

Upscaling based on the bandwidth of the kernel function is a flexible approach to upscale the data because the cells will be coarse-based on variability. The intensity of the coarsening of cells in this method can be controlled with bandwidth. In a smooth variability region, a large number of cells will be merged, and vice versa, they will remain fine with severe variability. Bandwidth variatio...