A partial difference set having parameters (n2, r(n − 1), n + r2 − 3r, r2 − r) is called a Latin square type partial difference set, while a partial difference set having parameters (n2, r(n + 1),−n + r2 + 3r, r2 + r) is called a negative Latin square type partial difference set. In this paper, we generalize well-known negative Latin square type partial difference sets derived from the theory o...

This paper considers the problem of achieving attitude consensus in spacecraft formations with bounded, time-varying communication delays between spacecraft connected as specified by a strongly connected topology. A state feedback controller is proposed and investigated using a time domain approach (via LMIs) and a frequency domain approach (via the small-gain theorem) to obtain delay dependent...

1 Stationary Points of the Log-Likelihood In this section, we briefly explain why the log-likelihood in Luce's model has a unique stationary point, that at the ML estimate. Recall that we assume that the comparison graph G D is strongly connected. The log-likelihood is given by

In this paper we propose a multipartite version of the classical Turán problem of determining the minimum number of edges needed for an arbitrary graph to contain a given subgraph. As it turns out, here the non-trivial problem is the determination of the minimal edge density between two classes that implies the existence of a given subgraph. We determine the critical edge density for trees and ...

Let Γ be a triangle-free distance-regular graph with diameter d ≥ 3, valency k ≥ 3 and intersection number a2 6= 0. Assume Γ has an eigenvalue with multiplicity k. We show that Γ is 1-homogeneous in the sense of Nomura when d = 3 or when d ≥ 4 and a4 = 0. In the latter case we prove that Γ is an antipodal cover of a strongly regular graph, which means that it has diameter 4 or 5. For d = 5 the ...

In this paper we investigate new sufficient conditions for a digraph to be kernel-perfect (KP) and some structural properties of kernel-perfect critical (KPC) digraphs. In particular, it is proved that the asymmetrical part of any KPC digraph is strongly connected. A new method to construct KPC digraphs is developed. The existence of KP and KPC digraphs with arbitrarily large dichromatic number...

The notion of strongly Lie zero-product preserving maps on normed algebras as a generalization of Lie zero-product preserving maps are dened. We give a necessary and sufficient condition from which a linear map between normed algebras to be strongly Lie zero-product preserving. Also some hereditary properties of strongly Lie zero-product preserving maps are presented. Finally the second dual of...

In this paper, we propose a metric for measuring the complexity of a DTD. For the same purpose, different designers may create different DTDs. A complexity metric can assist us to evaluate and compare their different merits. Through the recognition of strongly connected components, the metric accommodates the recursive relationship of elements in a DTD. The metric presented here can be expresse...

Article history: Received 15 April 2014 Accepted 5 May 2014 Available online 29 May 2014 Submitted by R. Brualdi MSC: 05C20 05C50 15A18

Understanding multi-dimensional data and in particular multi-dimensional dependencies is hard. Information visualization can help to understand this type of data. Still, the problem of how users gain insights from such visualizations is not well understood. Both the visualizations and the users play a role in understanding the data. In a case study, using both, a scatterplot matrix and a HyperS...