Let P1, P2, . . . , Pd+1 be pairwise disjoint n-element point sets in general position in d-space. It is shown that there exist a point O and suitable subsets Qi ⊆ Pi (i = 1, 2, . . . , d + 1) such that |Qi| ≥ cd|Pi|, and every d-dimensional simplex with exactly one vertex in each Qi contains O in its interior. Here cd is a positive constant depending only on d.

This paper presents a hybrid scheme for the control of active and reactive powers using the direct vector control with stator flux orientation (SFO) of the DFIG. The hybrid scheme consists of Fuzzy logic, Reference Signal Tracking (F-RST) controllers. The proposed (F-RST) controller is compared with the classical Proportional-Integral (PI) and the Polynomial (RST) based on the pole placement th...

Finding disjoint paths in graphs is a problem that has attracted considerable attention from at least three perspectives: graph theory, VLSI design and network routing/flow. The corresponding literature is extensive. In this chapter we focus mostly on results on offline approximation algorithms for problems on general graphs as influenced from the network flow perspective. Surveys examining the...

We show that the Min Cut Linear Arrangement Problem (Min Cut) is NP-complete for trees with polynomial size edge weights and derive from this the NP-completeness of Min Cut for planar graphs with maximum vertex degree 3. This is used to show the NP-completeness of Search Number, Vertex Separation, Progressive Black/ White Pebble Demand, and Topological Bandwidth for planar graphs with maximum v...

A commutative associative algebra A over C with a derivation is one of the simplest examples of a vertex algebra. However, the differences between the modules for A as a vertex algebra and the modules for A as an associative algebra are not well understood. In this paper, I give the classification of finite-dimensional indecomposable untwisted or twisted modules for the polynomial ring in one v...

Let P1, . . . , Pk be k vertex disjoint paths in a graph G where the ends of Pi are xi, and yi. Let H be the subgraph induced by the vertex sets of the paths. We find edge bounds E1(n), E2(n) such that, 1. If e(H) ≥ E1(|V (H)|), then there exist disjoint paths P ′ 1, . . . , P ′ k where the ends of P ′ i are xi and yi such that | S

The terminal matrix is the distance matrix between all pairs of valence one vertices of a given graph and the terminal polynomial is the characteristic polynomial of the terminal matrix. Star-like graphs are connected graphs with at most one vertex of degree 3 d  . The recursive formula that calculates the terminal polynomial of a star-like graph is given. Particularly, the formula that calcul...

This paper offers a generalization of the independence polynomial, the co-k-plex polynomial. The resulting family of polynomials carries combinatorial information on a class of independence systems defined over the vertex set of a finite graph. Specifically, we offer a recursion formula and examples of the co-2-plex polynomial on certain graphs. In addition, we characterize the class of graphs ...

Consider a graph G = (V, E) and a vertex subset A ⊆ V . A vertex v is positive-influence dominated by A if either v is in A or at least half the number of neighbors of v belong to A. For a target vertex subset S ⊆ V , a vertex subset A is a positive-influence target-dominating set for target set S if every vertex in S is positive-influence dominated by A. Given a graph G and a target vertex sub...